Finite Group Databasebeta

← #35566548

Subgroups — #35566548

Order 21248.

2396 conjugacy classes of subgroups.

The subgroup lattice has 1522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128378C211yesmaximal, characteristic
2#24910592C211yesmaximal, characteristic, complemented
3#24910592C211yesmaximal, characteristic, complemented
4#24910577C211yesmaximal, characteristic, complemented
5#24910577C211yesmaximal, characteristic, complemented
6#24910548C211yesmaximal, characteristic, complemented
7#24910530C211yesmaximal, characteristic, complemented
8#24910486C211yesmaximal, characteristic, complemented
9#24910453C211yesmaximal, characteristic, complemented
10#24910439C211yesmaximal, characteristic
11#24910432C211yesmaximal, characteristic, complemented
12#24910405C211yesmaximal, characteristic, complemented
13#24910352C211yesmaximal, characteristic, complemented
14#24910321C211yesmaximal, characteristic, complemented
15#24910310C211yesmaximal, characteristic, complemented
16#24910309C211yesmaximal, characteristic, complemented
17#24910275C211yesmaximal, characteristic, complemented
18#24910256C211yesmaximal, characteristic, complemented
19#24910237C211yesmaximal, characteristic, complemented
20#24910218C211yesmaximal, characteristic, complemented
21#24910134C211yesmaximal, characteristic, complemented
22#24910123C211yesmaximal, characteristic
23#24910013C211yesmaximal, characteristic, complemented
24#24909984C211yesmaximal, characteristic, complemented
25#24909955C211yesmaximal, characteristic, complemented
26#24909901C211yesmaximal, characteristic, complemented
27C2×#19127592C211yesmaximal, characteristic, complemented
28#24909818C211yesmaximal, characteristic, complemented
29#24909815C211yesmaximal, characteristic, complemented
30C42×C22⋊D83C211yesmaximal, characteristic, complemented
31C4×C22⋊Q8×C83C211yesmaximal, characteristic, complemented
32#19128378C4116yescomplemented
33C2×#14581787C2211yescharacteristic
34C2×#14581787C2211yescharacteristic
35C2×#14581781C2211yescharacteristic
36C2×#14581777C2211yescharacteristic
37C2×#14581777C2211yescharacteristic
38C2×#14581776C2211yescharacteristic
39C2×#14581768C2211yescharacteristic
40C2×#14581762C2211yescharacteristic
41C2×#14581754C2211yescharacteristic
42C2×#14581754C2211yescharacteristic
43C2×C4×C22⋊D83C2211yescharacteristic
44C2×C4×C22⋊D83C2211yescharacteristic
45C2×C4×C22⋊D83C2211yescharacteristic
46C2×#14581750C2211yescharacteristic
47C2×#14581750C2211yescharacteristic
48C2×#14581748C2211yescharacteristic
49C2×#14581748C2211yescharacteristic
50C22×Dic83⋊C4C2211yescharacteristic
51C22×(C2×D83)⋊C4C2211yescharacteristic
52C22×(C2×D83)⋊C4C2211yescharacteristic
53C22×(C2×D83)⋊C4C2211yescharacteristic
54C2×C22⋊C4×D83C2211yescharacteristic
55C2×C22⋊C4×D83C2211yescharacteristic
56C2×C42×D83C2211yescharacteristic, complemented
57#19127608C2211yescharacteristic, complemented
58#19127608C2211yescharacteristic, complemented
59#19127603C2211yescharacteristic
60#19127603C2211yescharacteristic
61#19127602C2211yescharacteristic
62#19127599C2211yescharacteristic, complemented
63#19127599C2211yescharacteristic, complemented
64#19127597C2211yescharacteristic, complemented
65#19127593C2211yescharacteristic
66#19127593C2211yescharacteristic
67#19127593C2211yescharacteristic
68#19127593C2211yescharacteristic
69#19127592C2211yescharacteristic
70#19127592C2211yescharacteristic
71#19127592C2211yescharacteristic
72#19127592C2211yescharacteristic
73#19127592C2211yescharacteristic
74#19127592C2211yescharacteristic
75#19127592C2211yescharacteristic
76#19127592C2211yescharacteristic
77#19127592C2211yescharacteristic
78#19127592C2211yescharacteristic
79#19127592C2211yescharacteristic, complemented
80#19127592C2211yescharacteristic, complemented
81#19127591C2211yescharacteristic
82#19127591C2211yescharacteristic
83#19127591C2211yescharacteristic
84#19127591C2211yescharacteristic
85#19127591C2211yescharacteristic
86#19127591C2211yescharacteristic, complemented
87#19127591C2211yescharacteristic, complemented
88#19127591C2211yescharacteristic, complemented
89#19127590C2211yescharacteristic
90#19127590C2211yescharacteristic
91#19127590C2211yescharacteristic
92#19127590C2211yescharacteristic, complemented
93#19127588C2211yescharacteristic, complemented
94#19127588C2211yescharacteristic, complemented
95#19127587C2211yescharacteristic, complemented
96#19127587C2211yescharacteristic, complemented
97#19127587C2211yescharacteristic, complemented
98#19127587C2211yescharacteristic, complemented
99#19127586C2211yescharacteristic, complemented
100#19127586C2211yescharacteristic, complemented
101#19127584C2211yescharacteristic, complemented
102#19127584C2211yescharacteristic, complemented
103#19127582C2211yescharacteristic, complemented
104#19127582C2211yescharacteristic, complemented
105#19127582C2211yescharacteristic, complemented
106#19127582C2211yescharacteristic, complemented
107#19127579C2211yescharacteristic
108#19127579C2211yescharacteristic
109#19127579C2211yescharacteristic
110#19127579C2211yescharacteristic
111#19127578C2211yescharacteristic
112#19127578C2211yescharacteristic
113#19127576C2211yescharacteristic
114#19127576C2211yescharacteristic
115#19127575C2211yescharacteristic, complemented
116#19127575C2211yescharacteristic, complemented
117#19127572C2211yescharacteristic
118#19127572C2211yescharacteristic
119#19127572C2211yescharacteristic
120#19127572C2211yescharacteristic, complemented
121#19127568C2211yescharacteristic, complemented
122#19127568C2211yescharacteristic, complemented
123#19127566C2211yescharacteristic, complemented
124#19127563C2211yescharacteristic
125#19127563C2211yescharacteristic, complemented
126#19127562C2211yescharacteristic
127#19127558C2211yescharacteristic
128#19127556C2211yescharacteristic
129C4⋊C4×Dic83C2211yescharacteristic, complemented
130C4⋊C4×Dic83C2211yescharacteristic, complemented
131C4⋊C4×Dic83C2211yescharacteristic, complemented
132C4⋊C4×Dic83C2211yescharacteristic, complemented
133C4×Dic83⋊C4C2211yescharacteristic, complemented
134C4×Dic83⋊C4C2211yescharacteristic, complemented
135C4×Dic83⋊C4C2211yescharacteristic, complemented
136C4×Dic83⋊C4C2211yescharacteristic, complemented
137C4×Dic83⋊C4C2211yescharacteristic, complemented
138C4×Dic83⋊C4C2211yescharacteristic, complemented
139C4×Dic83⋊C4C2211yescharacteristic, complemented
140#19127552C2211yescharacteristic, complemented
141#19127552C2211yescharacteristic, complemented
142#19127552C2211yescharacteristic, complemented
143#19127552C2211yescharacteristic, complemented
144C22⋊C4×Dic83C2211yescharacteristic
145C22⋊C4×Dic83C2211yescharacteristic
146C22⋊C4×Dic83C2211yescharacteristic
147C22⋊C4×Dic83C2211yescharacteristic
148C4×(C2×D83)⋊C4C2211yescharacteristic
149C4×(C2×D83)⋊C4C2211yescharacteristic
150C4×(C2×D83)⋊C4C2211yescharacteristic
151C4×(C2×D83)⋊C4C2211yescharacteristic
152C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
153C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
154C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
155C4×C22⋊Dic83C2211yescharacteristic
156C4×C22⋊Dic83C2211yescharacteristic
157C4×C22⋊Dic83C2211yescharacteristic
158#19127548C2211yescharacteristic
159#19127548C2211yescharacteristic
160#19127548C2211yescharacteristic
161#19127548C2211yescharacteristic
162#19127548C2211yescharacteristic
163#19127548C2211yescharacteristic
164#19127548C2211yescharacteristic
165#19127548C2211yescharacteristic
166#19127548C2211yescharacteristic, complemented
167#19127548C2211yescharacteristic, complemented
168#19127546C2211yescharacteristic, complemented
169#19127546C2211yescharacteristic, complemented
170C2×C83⋊#95C2211yescharacteristic
171C2×C83⋊#95C2211yescharacteristic
172C42×Dic83C2211yescharacteristic, complemented
173C2×C22⋊Q8×C83C2211yescharacteristic
174C2×C4×Q8×C83C2211yescharacteristic, complemented
175C22×C42×C83C2211yescharacteristic
176#391×C83C2211yescharacteristic, complemented
177#389×C83C2211yescharacteristic, complemented
178#387×C83C2211yescharacteristic, complemented
179#387×C83C2211yescharacteristic, complemented
180#385×C83C2211yescharacteristic
181#385×C83C2211yescharacteristic
182#380×C83C2211yescharacteristic
183C4×C4⋊C4×C83C2211yescharacteristic, complemented
184C4×C4⋊C4×C83C2211yescharacteristic, complemented
185C4×C4⋊C4×C83C2211yescharacteristic, complemented
186C4×C22⋊C4×C83C2211yescharacteristic
187C4×C22⋊C4×C83C2211yescharacteristic
188C24×D83C2311yescharacteristic
189C22×D332C2311yescharacteristic
190C22×D332C2311yescharacteristic
191C22×C22⋊D83C2311yescharacteristic
192C23×Dic83C2311yescharacteristic
193C23×Dic83C2311yescharacteristic
194C23×Dic83C2311yescharacteristic
195C22×C4×D83C2311yescharacteristic
196C22×C4×D83C2311yescharacteristic
197C22×C4×D83C2311yescharacteristic
198C22×C4×D83C2311yescharacteristic
199C22×C4×D83C2311yescharacteristic
200C22×C4×D83C2311yescharacteristic
201C22×C4×D83C2311yescharacteristic
202#14581787C2×C418yescomplemented
203#14581787C2×C418yescomplemented
204#14581781C2×C418yescomplemented
205#14581777C2×C418yescomplemented
206#14581777C2×C418yescomplemented
207#14581776C2×C418yescomplemented
208#14581768C2×C418yescomplemented
209#14581762C2×C418yes—
210#14581754—42no—
211#14581754C2×C418yescomplemented
212C4×C22⋊D83—24no—
213C4×C22⋊D83—24no—
214C4×C22⋊D83C2×C418yescomplemented
215#14581750—42no—
216#14581750C2×C418yescomplemented
217#14581748—24no—
218#14581748C2×C418yescomplemented
219C2×C4⋊Dic83C2311yescharacteristic
220C2×C4⋊Dic83C2311yescharacteristic
221C2×C4⋊Dic83C2311yescharacteristic
222C2×C4⋊Dic83C2311yescharacteristic
223C2×C4⋊Dic83C2311yescharacteristic
224C2×C4⋊Dic83C2311yescharacteristic
225C2×Dic83⋊C4—24no—
226C2×Dic83⋊C4C2311yescharacteristic
227C2×Dic83⋊C4C2311yescharacteristic
228C2×Dic83⋊C4C2311yescharacteristic
229C2×Dic83⋊C4C2311yescharacteristic
230C2×Dic83⋊C4C2311yescharacteristic
231C2×Dic83⋊C4C2311yescharacteristic
232C2×Dic83⋊C4C2311yescharacteristic
233C2×Dic83⋊C4C2311yescharacteristic
234C2×Dic83⋊C4C2311yescharacteristic
235C2×Dic83⋊C4C2311yescharacteristic
236C2×Dic83⋊C4C2311yescharacteristic
237C2×C22⋊Dic83C2311yescharacteristic
238C2×C22⋊Dic83C2311yescharacteristic
239C2×C22⋊Dic83C2311yescharacteristic
240C2×(C2×D83)⋊C4—24no—
241C2×(C2×D83)⋊C4—42no—
242C2×(C2×D83)⋊C4C2×C418yescomplemented
243C2×(C2×D83)⋊C4C2311yescharacteristic
244C2×(C2×D83)⋊C4C2311yescharacteristic
245C2×(C2×D83)⋊C4C2311yescharacteristic
246C2×(C2×D83)⋊C4C2311yescharacteristic
247C2×(C2×D83)⋊C4C2311yescharacteristic
248C2×(C2×D83)⋊C4C2311yescharacteristic
249C2×(C2×D83)⋊C4C2311yescharacteristic
250C2×(C2×D83)⋊C4C2311yescharacteristic
251C2×(C2×D83)⋊C4C2311yescharacteristic
252C2×(C2×D83)⋊C4C2311yescharacteristic
253C2×(C2×D83)⋊C4C2311yescharacteristic
254C2×(C2×D83)⋊C4C2311yescharacteristic
255C2×(C2×D83)⋊C4C2311yescharacteristic
256C2×(C2×D83)⋊C4C2311yescharacteristic
257C2×(C2×D83)⋊C4C2311yescharacteristic
258C2×(C2×D83)⋊C4C2311yescharacteristic
259C2×(C2×D83)⋊C4C2311yescharacteristic
260C2×(C2×D83)⋊C4C2311yescharacteristic
261C2×(C2×D83)⋊C4C2311yescharacteristic
262C2×(C2×D83)⋊C4C2311yescharacteristic
263C2×(C2×D83)⋊C4C2311yescharacteristic
264C2×(C2×D83)⋊C4C2311yescharacteristic
265C2×(C2×D83)⋊C4C2311yescharacteristic
266C2×(C2×D83)⋊C4C2311yescharacteristic
267C2×(C2×D83)⋊C4C2311yescharacteristic
268C2×(C2×D83)⋊C4C2311yescharacteristic
269C2×(C2×D83)⋊C4C2311yescharacteristic
270C2×(C2×D83)⋊C4C2311yescharacteristic
271C2×(C2×D83)⋊C4C2311yescharacteristic
272C2×(C2×D83)⋊C4C2311yescharacteristic
273C2×(C2×D83)⋊C4C2311yescharacteristic
274C22⋊C4×D83—24no—
275C22⋊C4×D83C2×C418yescomplemented
276C2×C4×Dic83C2311yescharacteristic
277C2×C4×Dic83C2311yescharacteristic
278C2×C4×Dic83C2311yescharacteristic
279C2×C4×Dic83C2311yescharacteristic
280C2×C4×Dic83C2311yescharacteristic
281C2×C4×Dic83C2311yescharacteristic
282C2×C4×Dic83C2311yescharacteristic
283C2×C4×Dic83C2311yescharacteristic
284C2×C4×Dic83C2311yescharacteristic
285C2×C4×Dic83C2311yescharacteristic
286C2×C4×Dic83C2311yescharacteristic
287C2×C4×Dic83C2311yescharacteristic
288C2×C4×Dic83C2311yescharacteristic
289C2×C4×Dic83C2311yescharacteristic
290C2×C4×Dic83C2311yescharacteristic
291C2×C4×Dic83C2311yescharacteristic
292C2×C4×Dic83C2311yescharacteristic
293C2×C4×Dic83C2311yescharacteristic
294C2×C4×Dic83C2311yescharacteristic
295C2×C4×Dic83C2311yescharacteristic
296C2×C4×Dic83C2311yescharacteristic
297C42×D83—42no—
298C83⋊#95C2311yescharacteristic
299C83⋊#95C2311yescharacteristic
300C83⋊#95C2311yescharacteristic
301C83⋊#95C2311yescharacteristic
302C83⋊#95C2311yescharacteristic
303C83⋊#95C2311yescharacteristic
304C83⋊#95C2311yescharacteristic
305C83⋊#95C2311yescharacteristic
306C83⋊#95C2311yescharacteristic
307C83⋊#95C2311yescharacteristic
308C83⋊#95C2311yescharacteristic
309C83⋊#95C2311yescharacteristic
310C83⋊#95C2311yescharacteristic
311C83⋊#95C2311yescharacteristic
312C83⋊#95C2311yescharacteristic
313C83⋊#95C2311yescharacteristic
314C83⋊#95C2311yescharacteristic
315C83⋊#95C2311yescharacteristic
316C83⋊#95C2311yescharacteristic
317C83⋊#95C2311yescharacteristic
318C83⋊#95C2311yescharacteristic
319C83⋊#95C2311yescharacteristic
320C83⋊#95C2311yescharacteristic
321C83⋊#95C2311yescharacteristic
322C83⋊#95C2311yescharacteristic
323C83⋊#95C2311yescharacteristic
324C83⋊#95C2311yescharacteristic
325C83⋊#95C2311yescharacteristic
326C83⋊#95C2311yescharacteristic
327C83⋊#95C2311yescharacteristic
328C83⋊#95C2311yescharacteristic
329C83⋊#95C2311yescharacteristic
330C83⋊#95C2311yescharacteristic
331C83⋊#95C2311yescharacteristic
332C22×Q8×C83C2311yescharacteristic
333C23×C4×C83C2311yescharacteristic
334C23×C4×C83C2311yescharacteristic
335C23×C4×C83C2311yescharacteristic
336C22⋊Q8×C83C2×C418yescomplemented
337C4×Q8×C83—42no—
338C2×C4⋊C4×C83C2311yescharacteristic
339C2×C4⋊C4×C83C2311yescharacteristic
340C2×C4⋊C4×C83C2311yescharacteristic
341C2×C4⋊C4×C83C2311yescharacteristic
342C2×C4⋊C4×C83C2311yescharacteristic
343C2×C4⋊C4×C83C2311yescharacteristic
344C2×C4⋊C4×C83C2311yescharacteristic
345C2×C4⋊C4×C83C2311yescharacteristic
346C2×C4⋊C4×C83C2311yescharacteristic
347C2×C22⋊C4×C83C2311yescharacteristic
348C2×C22⋊C4×C83C2311yescharacteristic
349C2×C22⋊C4×C83C2311yescharacteristic
350C2×C22⋊C4×C83C2311yescharacteristic
351C2×C42×C83—42no—
352C2×C42×C83C2311yescharacteristic
353C2×C42×C83C2311yescharacteristic
354C2×C42×C83C2311yescharacteristic
355C2×C42×C83C2311yescharacteristic
356C2×C42×C83C2311yescharacteristic
357C2×C42×C83C2311yescharacteristic
358C2×C42×C83C2311yescharacteristic
359C2×C42×C83C2311yescharacteristic
360#95×C83C2311yescharacteristic
361#95×C83C2311yescharacteristic
362#95×C83C2311yescharacteristic
363#95×C83C2311yescharacteristic
364#95×C83C2311yescharacteristic
365#95×C83C2311yescharacteristic
366#95×C83C2311yescharacteristic
367#95×C83C2311yescharacteristic
368#95×C83C2311yescharacteristic
369#95×C83C2311yescharacteristic
370C23×D83—22no—
371C23×D83—22no—
372C23×D83—41no—
373C23×D83—41no—
374C23×D83—41no—
375C23×D83—41no—
376C23×D83C22×C414yes—
377C23×D83C2411yescharacteristic
378C23×D83C2411yescharacteristic
379C23×D83C2411yescharacteristic
380C2×D332—41no—
381C2×D332—41no—
382C2×D332—41no—
383C2×D332—41no—
384C2×D332C22×C414yes—
385C2×D332C22×C414yes—
386C2×C22⋊D83—22no—
387C2×C22⋊D83—22no—
388C2×C22⋊D83C22×C414yes—
389C22×Dic83—22no—
390C22×Dic83—22no—
391C22×Dic83—22no—
392C22×Dic83—22no—
393C22×Dic83—41no—
394C22×Dic83—41no—
395C22×Dic83—41no—
396C22×Dic83—41no—
397C22×Dic83C22×C414yes—
398C22×Dic83C2411yescharacteristic
399C22×Dic83C2411yescharacteristic
400C22×Dic83C2411yescharacteristic
401C22×Dic83C2411yescharacteristic
402C22×Dic83C2411yescharacteristic
403C22×Dic83C2411yescharacteristic
404C22×Dic83C2411yescharacteristic
405C22×Dic83C2411yescharacteristic
406C22×Dic83C2411yescharacteristic
407C22×Dic83C2411yescharacteristic
408C22×Dic83C2411yescharacteristic
409C22×Dic83C2411yescharacteristic
410C22×Dic83C2411yescharacteristic
411C2×C4×D83—22no—
412C2×C4×D83—22no—
413C2×C4×D83—22no—
414C2×C4×D83—22no—
415C2×C4×D83—22no—
416C2×C4×D83—41no—
417C2×C4×D83—41no—
418C2×C4×D83—41no—
419C2×C4×D83—41no—
420C2×C4×D83—41no—
421C2×C4×D83—41no—
422C2×C4×D83—41no—
423C2×C4×D83—41no—
424C2×C4×D83—41no—
425C2×C4×D83—41no—
426C2×C4×D83—41no—
427C2×C4×D83—41no—
428C2×C4×D83—41no—
429C2×C4×D83C22×C414yes—
430C2×C4×D83C22×C414yes—
431C2×C4×D83C22×C414yes—
432C4⋊Dic83—41no—
433C4⋊Dic83—41no—
434C4⋊Dic83—41no—
435C4⋊Dic83—41no—
436C4⋊Dic83C22×C414yes—
437C4⋊Dic83C22×C414yes—
438Dic83⋊C4—22no—
439Dic83⋊C4—22no—
440Dic83⋊C4—22no—
441Dic83⋊C4—22no—
442Dic83⋊C4—22no—
443Dic83⋊C4—22no—
444Dic83⋊C4—22no—
445Dic83⋊C4—22no—
446Dic83⋊C4C22×C414yes—
447Dic83⋊C4C22×C414yes—
448Dic83⋊C4C22×C414yes—
449C22⋊Dic83—22no—
450C22⋊Dic83C22×C414yes—
451C22⋊Dic83#4114yes—
452(C2×D83)⋊C4—22no—
453(C2×D83)⋊C4—22no—
454(C2×D83)⋊C4—22no—
455(C2×D83)⋊C4—22no—
456(C2×D83)⋊C4—22no—
457(C2×D83)⋊C4—22no—
458(C2×D83)⋊C4—22no—
459(C2×D83)⋊C4—22no—
460(C2×D83)⋊C4—22no—
461(C2×D83)⋊C4—22no—
462(C2×D83)⋊C4—41no—
463(C2×D83)⋊C4—41no—
464(C2×D83)⋊C4—41no—
465(C2×D83)⋊C4—41no—
466(C2×D83)⋊C4—41no—
467(C2×D83)⋊C4—41no—
468(C2×D83)⋊C4—41no—
469(C2×D83)⋊C4—41no—
470(C2×D83)⋊C4—41no—
471(C2×D83)⋊C4—41no—
472(C2×D83)⋊C4C22×C414yes—
473(C2×D83)⋊C4C22×C414yes—
474(C2×D83)⋊C4C22×C414yes—
475(C2×D83)⋊C4C22×C414yes—
476(C2×D83)⋊C4C22×C414yes—
477(C2×D83)⋊C4C22×C414yes—
478(C2×D83)⋊C4C22×C414yes—
479(C2×D83)⋊C4C22×C414yes—
480(C2×D83)⋊C4C22×C414yes—
481(C2×D83)⋊C4C22×C414yes—
482(C2×D83)⋊C4C22×C414yes—
483C4×Dic83—22no—
484C4×Dic83—22no—
485C4×Dic83—22no—
486C4×Dic83—22no—
487C4×Dic83—22no—
488C4×Dic83—41no—
489C4×Dic83—41no—
490C4×Dic83—41no—
491C4×Dic83—41no—
492C4×Dic83—41no—
493C4×Dic83—41no—
494C4×Dic83—41no—
495C4×Dic83—41no—
496C4×Dic83—41no—
497C4×Dic83—41no—
498C4×Dic83—41no—
499C4×Dic83—41no—
500C4×Dic83—41no—
501C4×Dic83C22×C414yes—
502C4×Dic83C22×C414yes—
503C4×Dic83C22×C414yes—
504C24×C83C2411yescharacteristic
505C2×Q8×C83—41no—
506C2×Q8×C83—41no—
507C2×Q8×C83C22×C414yes—
508C22×C4×C83—22no—
509C22×C4×C83—22no—
510C22×C4×C83—41no—
511C22×C4×C83—41no—
512C22×C4×C83—41no—
513C22×C4×C83—41no—
514C22×C4×C83—41no—
515C22×C4×C83C22×C414yes—
516C22×C4×C83#4114yes—
517C22×C4×C83C2411yescharacteristic
518C22×C4×C83C2411yescharacteristic
519C22×C4×C83C2411yescharacteristic
520C22×C4×C83C2411yescharacteristic
521C22×C4×C83C2411yescharacteristic
522C22×C4×C83C2411yescharacteristic
523C22×C4×C83C2411yescharacteristic
524C22×C4×C83C2411yescharacteristic
525C22×C4×C83C2411yescharacteristic
526C22×C4×C83C2411yescharacteristic
527C22×C4×C83C2411yescharacteristic
528C22×C4×C83C2411yescharacteristic
529C22×C4×C83C2411yescharacteristic
530C22×C4×C83C2411yescharacteristic
531C4⋊C4×C83—22no—
532C4⋊C4×C83—22no—
533C4⋊C4×C83—41no—
534C4⋊C4×C83—41no—
535C4⋊C4×C83—41no—
536C4⋊C4×C83—41no—
537C4⋊C4×C83C22×C414yes—
538C4⋊C4×C83C22×C414yes—
539C4⋊C4×C83C22×C414yes—
540C22⋊C4×C83—22no—
541C22⋊C4×C83—22no—
542C22⋊C4×C83C22×C414yes—
543C22⋊C4×C83C22×C414yes—
544C42×C83—22no—
545C42×C83—22no—
546C42×C83—41no—
547C42×C83—41no—
548C42×C83—41no—
549C42×C83—41no—
550C42×C83—41no—
551C42×C83—41no—
552C23×C83—21no—
553C23×C83—21no—
554C23×C83—21no—
555C23×C83—21no—
556C23×C83C23×C412yes—
557C23×C83C2×#4112yes—
558C23×C83C2×#4112yes—
559C23×C83C2511yescharacteristic
560C22×D83—21no—
561C22×D83—21no—
562C22×D83—21no—
563C22×D83—21no—
564C22×D83—21no—
565C22×D83—21no—
566C22×D83—21no—
567C22×D83—21no—
568C22×D83—21no—
569C22×D83—21no—
570C22×D83—21no—
571C22×D83—21no—
572C22×D83—21no—
573C22×D83—21no—
574C22×D83—21no—
575C22×D83—21no—
576C22×D83—21no—
577C22×D83—21no—
578C22×D83—28no—
579C22×D83—44no—
580C22×D83—44no—
581C22×D83—82no—
582C22×D83—82no—
583C22×D83—82no—
584C22×D83—82no—
585C22×D83C23×C412yes—
586C22×D83C23×C412yes—
587C22×D83C23×C412yes—
588Q8×C83—44no—
589C2×C4×C83—21no—
590C2×C4×C83—21no—
591C2×C4×C83—21no—
592C2×C4×C83—21no—
593C2×C4×C83—21no—
594C2×C4×C83—21no—
595C2×C4×C83—21no—
596C2×C4×C83—21no—
597C2×C4×C83—21no—
598C2×C4×C83—21no—
599C2×C4×C83—21no—
600C2×C4×C83—21no—
601C2×C4×C83—21no—
602C2×C4×C83—21no—
603C2×C4×C83—21no—
604C2×C4×C83—21no—
605C2×C4×C83—21no—
606C2×C4×C83—21no—
607C2×C4×C83—21no—
608C2×C4×C83—21no—
609C2×C4×C83—21no—
610C2×C4×C83—21no—
611C2×C4×C83—21no—
612C2×C4×C83—21no—
613C2×C4×C83—21no—
614C2×C4×C83—21no—
615C2×C4×C83—21no—
616C2×C4×C83—21no—
617C2×C4×C83—21no—
618C2×C4×C83—21no—
619C2×C4×C83—21no—
620C2×C4×C83—21no—
621C2×C4×C83—21no—
622C2×C4×C83—44no—
623C2×C4×C83—44no—
624C2×C4×C83—44no—
625C2×C4×C83C23×C412yes—
626C2×C4×C83C23×C412yes—
627C2×C4×C83C23×C412yes—
628C2×C4×C83C23×C412yes—
629C2×C4×C83C23×C412yes—
630C2×C4×C83C23×C412yes—
631C2×C4×C83C2×#4112yes—
632C2×C4×C83C2×#4112yes—
633C2×C4×C83H(5,𝔽2)12yes—
634C22⋊D83—28no—
635C2×Dic83—28no—
636C2×Dic83—21no—
637C2×Dic83—21no—
638C2×Dic83—21no—
639C2×Dic83—21no—
640C2×Dic83—21no—
641C2×Dic83—21no—
642C2×Dic83—21no—
643C2×Dic83—21no—
644C2×Dic83—21no—
645C2×Dic83—21no—
646C2×Dic83—21no—
647C2×Dic83—21no—
648C2×Dic83—21no—
649C2×Dic83—21no—
650C2×Dic83—21no—
651C2×Dic83—21no—
652C2×Dic83—21no—
653C2×Dic83—21no—
654C2×Dic83—21no—
655C2×Dic83—21no—
656C2×Dic83—21no—
657C2×Dic83—21no—
658C2×Dic83—21no—
659C2×Dic83—21no—
660C2×Dic83—21no—
661C2×Dic83—21no—
662C2×Dic83—21no—
663C2×Dic83—21no—
664C2×Dic83—21no—
665C2×Dic83—21no—
666C2×Dic83—21no—
667C2×Dic83—21no—
668C2×Dic83—82no—
669C2×Dic83—82no—
670C2×Dic83C23×C412yes—
671C2×Dic83C23×C412yes—
672C2×Dic83C23×C412yes—
673C2×Dic83C23×C412yes—
674C2×Dic83C23×C412yes—
675C2×Dic83C2×#4112yes—
676C2×Dic83C2×#4112yes—
677D332—44no—
678D332—44no—
679C4×D83—44no—
680C4×D83—44no—
681C4×D83—44no—
682C4×D83—44no—
683C4×D83—44no—
684C4×D83—82no—
685C4×D83—82no—
686C22×C83—22no—
687C22×C83—22no—
688C22×C83—22no—
689C22×C83—22no—
690C22×C83—22no—
691C22×C83—22no—
692C22×C83C4×#4114yes—
693C22×C83C24×C411yescharacteristic
694C22×C83C22×#4111yescharacteristic
695C22×C83C22×#4111yescharacteristic
696C22×C83C2×H(5,𝔽2)11yescharacteristic
697C22×C83#58511yescharacteristic
698C22×C83#58511yescharacteristic
699C22×C83#58511yescharacteristic
700C2×D83—22no—
701C2×D83—22no—
702C2×D83—22no—
703C2×D83—22no—
704C2×D83—22no—
705C2×D83—22no—
706C2×D83—22no—
707C2×D83—22no—
708C2×D83—22no—
709C2×D83—41no—
710C2×D83—41no—
711C2×D83—41no—
712C2×D83—41no—
713C2×D83—41no—
714C2×D83—41no—
715C2×D83—41no—
716C2×D83—41no—
717C2×D83—41no—
718C2×D83—41no—
719C2×D83—41no—
720C2×D83—41no—
721C2×D83—88no—
722C4×C83—22no—
723C4×C83—22no—
724C4×C83—22no—
725C4×C83—22no—
726C4×C83—22no—
727C4×C83—22no—
728C4×C83—22no—
729C4×C83—22no—
730C4×C83—22no—
731C4×C83—41no—
732C4×C83—41no—
733C4×C83—41no—
734C4×C83—41no—
735C4×C83—41no—
736Dic83—22no—
737Dic83—22no—
738Dic83—22no—
739Dic83—22no—
740Dic83—22no—
741Dic83—22no—
742Dic83—22no—
743Dic83—41no—
744Dic83—41no—
745Dic83—41no—
746Dic83—41no—
747Dic83—41no—
748Dic83—41no—
749#34315—831nomaximal, Sylow
750C2×C83—24no—
751C2×C83C2×C4×#4111yescharacteristic
752C2×C83#342811yescharacteristic
753C2×C83C4×H(5,𝔽2)11yescharacteristic
754C2×C83#350511yescharacteristic
755C2×C83#351011yescharacteristic
756C2×C83#351311yescharacteristic
757C2×C83#352111yescharacteristic
758D83—42no—
759D83—42no—
760D83—42no—
761C2×#551—831no—
762#2374—831no—
763#2374—831no—
764#2373—831no—
765#2373—831no—
766#2368—831no—
767#2367—831no—
768#2362—831no—
769#2359—831no—
770#2358—831no—
771#2357—831no—
772#2353—831no—
773#2347—831no—
774#2343—831no—
775#2342—831no—
776#2342—831no—
777#2337—831no—
778#2335—831no—
779#2334—831no—
780#2332—831no—
781#2322—831no—
782#2321—831no—
783C4×#126—831no—
784C4×C22⋊Q8D8311yescharacteristic, complemented
785C4×#123—831no—
786#2298—831no—
787#2290—831no—
788C2×#388—831no—
789#2274—831no—
790#2273—831no—
791C42×D4—831no—
792C83#3431511yescharacteristic, complemented, Sylow
793#551—8316no—
794C2×#126—831no—
795C2×#126—831no—
796C2×#124—831no—
797C2×#123—831no—
798C2×#123—831no—
799C2×#123—831no—
800C2×C22⋊Q8—831no—
801C2×C22⋊Q8C2×D8311yescharacteristic
802C2×#120—831no—
803C2×C4×Q8C2×D8311yescharacteristic, complemented
804C2×C4×D4—831no—
805C2×C4×D4—831no—
806C2×C4×D4—831no—
807C2×C4×D4—831no—
808C2×C4×D4—831no—
809C2×#117—831no—
810C2×#117—831no—
811C2×#117—831no—
812C2×#117—831no—
813C22×C4⋊C4—831no—
814C22×C22⋊C4—831no—
815C22×C22⋊C4—831no—
816C22×C22⋊C4—831no—
817C22×C22⋊C4—831no—
818C22×C22⋊C4—831no—
819C22×C42—831no—
820C22×C42C2×D8311yescharacteristic
821#391—831no—
822#391—831no—
823#391C2×D8311yescharacteristic, complemented
824#390—831no—
825#390—831no—
826#390—831no—
827#389—831no—
828#389—831no—
829#389—831no—
830#389C2×D8311yescharacteristic, complemented
831#388—831no—
832#388—831no—
833#388—831no—
834#388—831no—
835#388—831no—
836#388—831no—
837#388—831no—
838#388—831no—
839#388—831no—
840#388—831no—
841#388—831no—
842#388—831no—
843#388—831no—
844#388—831no—
845#388—831no—
846#388—831no—
847#388—831no—
848#388—831no—
849#388—831no—
850#388—831no—
851#388—831no—
852#388—831no—
853#388—831no—
854#388—831no—
855#388—831no—
856#388—831no—
857#388—831no—
858#388—831no—
859#387—831no—
860#387—831no—
861#387—831no—
862#387—831no—
863#387—831no—
864#387—831no—
865#387—831no—
866#387—831no—
867#387—831no—
868#387—831no—
869#387—831no—
870#387—831no—
871#387—831no—
872#387—831no—
873#387C2×D8311yescharacteristic, complemented
874#387C2×D8311yescharacteristic, complemented
875#386—831no—
876#386—831no—
877#386—831no—
878#386—831no—
879#386—831no—
880#386—831no—
881#385—831no—
882#385—831no—
883#385—831no—
884#385—831no—
885#385—831no—
886#385—831no—
887#385—831no—
888#385—831no—
889#385C2×D8311yescharacteristic
890#385C2×D8311yescharacteristic
891#383—831no—
892#383—831no—
893#382—831no—
894#381—831no—
895#381—831no—
896#381—831no—
897#380—831no—
898#380C2×D8311yescharacteristic
899#379—831no—
900C4×C4⋊C4—831no—
901C4×C4⋊C4—831no—
902C4×C4⋊C4—831no—
903C4×C4⋊C4—831no—
904C4×C4⋊C4—831no—
905C4×C4⋊C4—831no—
906C4×C4⋊C4—831no—
907C4×C4⋊C4—831no—
908C4×C4⋊C4—831no—
909C4×C4⋊C4—831no—
910C4×C4⋊C4—831no—
911C4×C4⋊C4—831no—
912C4×C4⋊C4—831no—
913C4×C4⋊C4—831no—
914C4×C4⋊C4—831no—
915C4×C4⋊C4C2×D8311yescharacteristic, complemented
916C4×C4⋊C4C2×D8311yescharacteristic, complemented
917C4×C4⋊C4C2×D8311yescharacteristic, complemented
918C4×C22⋊C4—831no—
919C4×C22⋊C4—831no—
920C4×C22⋊C4—831no—
921C4×C22⋊C4—831no—
922C4×C22⋊C4—831no—
923C4×C22⋊C4—831no—
924C4×C22⋊C4—831no—
925C4×C22⋊C4—831no—
926C4×C22⋊C4—831no—
927C4×C22⋊C4—831no—
928C4×C22⋊C4—831no—
929C4×C22⋊C4—831no—
930C4×C22⋊C4—831no—
931C4×C22⋊C4—831no—
932C4×C22⋊C4—831no—
933C4×C22⋊C4—831no—
934C4×C22⋊C4—831no—
935C4×C22⋊C4—831no—
936C4×C22⋊C4—831no—
937C4×C22⋊C4—831no—
938C4×C22⋊C4—831no—
939C4×C22⋊C4—831no—
940C4×C22⋊C4—831no—
941C4×C22⋊C4—831no—
942C4×C22⋊C4C2×D8311yescharacteristic
943C4×C22⋊C4C2×D8311yescharacteristic
944#376—831no—
945#376—831no—
946C2×#95—831no—
947C2×#95—831no—
948C43—831no—
949C25—831no—
950C22×Q8C22×D8311yescharacteristic
951C22×D4—831no—
952C22×D4—831no—
953C22×D4—831no—
954C23×C4—831no—
955C23×C4—831no—
956C23×C4—831no—
957C23×C4—831no—
958C23×C4—831no—
959C23×C4—831no—
960C23×C4—831no—
961C23×C4—831no—
962C23×C4—831no—
963C23×C4—831no—
964C23×C4C22×D8311yescharacteristic
965C23×C4C22×D8311yescharacteristic
966C23×C4C22×D8311yescharacteristic
967#126—838no—
968#126—838no—
969#124—838no—
970#123—838no—
971#123—838no—
972#123—838no—
973C22⋊Q8—838no—
974C22⋊Q8C4×D8318yescomplemented
975#120—838no—
976C4×Q8—42no—
977C4×D4—3322no—
978C4×D4—838no—
979C4×D4—838no—
980C4×D4—1664no—
981C4×D4—1664no—
982#117—3322no—
983#117—838no—
984#117—838no—
985#117—1664no—
986C2×C4⋊C4—831no—
987C2×C4⋊C4—831no—
988C2×C4⋊C4—831no—
989C2×C4⋊C4—831no—
990C2×C4⋊C4—831no—
991C2×C4⋊C4—831no—
992C2×C4⋊C4—831no—
993C2×C4⋊C4—831no—
994C2×C4⋊C4—831no—
995C2×C4⋊C4—831no—
996C2×C4⋊C4—831no—
997C2×C4⋊C4—831no—
998C2×C4⋊C4—831no—
999C2×C4⋊C4—831no—
1000C2×C4⋊C4—831no—
1001C2×C4⋊C4—831no—
1002C2×C4⋊C4—831no—
1003C2×C4⋊C4—1664no—
1004C2×C4⋊C4C22×D8311yescharacteristic
1005C2×C4⋊C4C22×D8311yescharacteristic
1006C2×C4⋊C4C22×D8311yescharacteristic
1007C2×C4⋊C4C22×D8311yescharacteristic
1008C2×C4⋊C4C22×D8311yescharacteristic
1009C2×C4⋊C4C22×D8311yescharacteristic
1010C2×C4⋊C4C22×D8311yescharacteristic
1011C2×C4⋊C4C22×D8311yescharacteristic
1012C2×C4⋊C4C22×D8311yescharacteristic
1013C2×C22⋊C4—3322no—
1014C2×C22⋊C4—831no—
1015C2×C22⋊C4—831no—
1016C2×C22⋊C4—831no—
1017C2×C22⋊C4—831no—
1018C2×C22⋊C4—831no—
1019C2×C22⋊C4—831no—
1020C2×C22⋊C4—831no—
1021C2×C22⋊C4—831no—
1022C2×C22⋊C4—831no—
1023C2×C22⋊C4—831no—
1024C2×C22⋊C4—831no—
1025C2×C22⋊C4—831no—
1026C2×C22⋊C4—838no—
1027C2×C22⋊C4—831no—
1028C2×C22⋊C4—831no—
1029C2×C22⋊C4—831no—
1030C2×C22⋊C4—831no—
1031C2×C22⋊C4—831no—
1032C2×C22⋊C4—831no—
1033C2×C22⋊C4—831no—
1034C2×C22⋊C4—831no—
1035C2×C22⋊C4—831no—
1036C2×C22⋊C4—831no—
1037C2×C22⋊C4—831no—
1038C2×C22⋊C4—838no—
1039C2×C22⋊C4—831no—
1040C2×C22⋊C4—831no—
1041C2×C22⋊C4—831no—
1042C2×C22⋊C4—831no—
1043C2×C22⋊C4—831no—
1044C2×C22⋊C4—831no—
1045C2×C22⋊C4—831no—
1046C2×C22⋊C4—831no—
1047C2×C22⋊C4—831no—
1048C2×C22⋊C4—831no—
1049C2×C22⋊C4—831no—
1050C2×C22⋊C4—1664no—
1051C2×C22⋊C4—1664no—
1052C2×C22⋊C4C22×D8311yescharacteristic
1053C2×C22⋊C4C22×D8311yescharacteristic
1054C2×C22⋊C4C22×D8311yescharacteristic
1055C2×C22⋊C4C22×D8311yescharacteristic
1056C2×C42—42no—
1057C2×C42—3322no—
1058C2×C42—831no—
1059C2×C42—831no—
1060C2×C42—831no—
1061C2×C42—831no—
1062C2×C42—831no—
1063C2×C42—831no—
1064C2×C42—831no—
1065C2×C42—831no—
1066C2×C42—831no—
1067C2×C42—831no—
1068C2×C42—831no—
1069C2×C42—831no—
1070C2×C42—831no—
1071C2×C42—831no—
1072C2×C42—831no—
1073C2×C42—831no—
1074C2×C42—831no—
1075C2×C42—831no—
1076C2×C42—831no—
1077C2×C42—831no—
1078C2×C42—831no—
1079C2×C42C22×D8311yescharacteristic
1080C2×C42C22×D8311yescharacteristic
1081C2×C42C22×D8311yescharacteristic
1082C2×C42C22×D8311yescharacteristic
1083C2×C42C22×D8311yescharacteristic
1084C2×C42C22×D8311yescharacteristic
1085C2×C42C22×D8311yescharacteristic
1086C2×C42C22×D8311yescharacteristic
1087#95—831no—
1088#95—831no—
1089#95—831no—
1090#95—831no—
1091#95—831no—
1092#95—831no—
1093#95—831no—
1094#95—831no—
1095#95—831no—
1096#95—831no—
1097#95—831no—
1098#95—831no—
1099#95—831no—
1100#95—831no—
1101#95—831no—
1102#95—831no—
1103#95—831no—
1104#95—831no—
1105#95—831no—
1106#95—831no—
1107#95—831no—
1108#95—831no—
1109#95—831no—
1110#95—831no—
1111#95—831no—
1112#95—831no—
1113#95—831no—
1114#95—831no—
1115#95—831no—
1116#95—831no—
1117#95—831no—
1118#95—831no—
1119#95—831no—
1120#95—831no—
1121#95C22×D8311yescharacteristic
1122#95C22×D8311yescharacteristic
1123#95C22×D8311yescharacteristic
1124#95C22×D8311yescharacteristic
1125#95C22×D8311yescharacteristic
1126#95C22×D8311yescharacteristic
1127#95C22×D8311yescharacteristic
1128#95C22×D8311yescharacteristic
1129#95C22×D8311yescharacteristic
1130#95C22×D8311yescharacteristic
1131C24—3321no—
1132C24—3321no—
1133C24—3321no—
1134C24—3321no—
1135C24—834no—
1136C24—831no—
1137C24—831no—
1138C24—831no—
1139C24—1662no—
1140C24—1662no—
1141C24C23×D8311yescharacteristic
1142C2×Q8—41no—
1143C2×Q8—41no—
1144C2×Q8C2×C4×D8314yes—
1145C2×D4—3321no—
1146C2×D4—3321no—
1147C2×D4—3321no—
1148C2×D4—3321no—
1149C2×D4—834no—
1150C2×D4—834no—
1151C2×D4—834no—
1152C2×D4—1662no—
1153C2×D4—1662no—
1154C22×C4—22no—
1155C22×C4—22no—
1156C22×C4—41no—
1157C22×C4—41no—
1158C22×C4—41no—
1159C22×C4—41no—
1160C22×C4—41no—
1161C22×C4—3321no—
1162C22×C4—3321no—
1163C22×C4—3321no—
1164C22×C4—3321no—
1165C22×C4—3321no—
1166C22×C4—3321no—
1167C22×C4—3321no—
1168C22×C4—3321no—
1169C22×C4—3321no—
1170C22×C4—3321no—
1171C22×C4—3321no—
1172C22×C4—3321no—
1173C22×C4—3321no—
1174C22×C4—3321no—
1175C22×C4—3321no—
1176C22×C4—3321no—
1177C22×C4—3321no—
1178C22×C4—834no—
1179C22×C4—834no—
1180C22×C4—834no—
1181C22×C4—834no—
1182C22×C4—831no—
1183C22×C4—831no—
1184C22×C4—831no—
1185C22×C4—831no—
1186C22×C4—831no—
1187C22×C4—831no—
1188C22×C4—831no—
1189C22×C4—831no—
1190C22×C4—831no—
1191C22×C4—831no—
1192C22×C4—831no—
1193C22×C4—831no—
1194C22×C4—831no—
1195C22×C4—1662no—
1196C22×C4—1662no—
1197C22×C4—1662no—
1198C22×C4—1662no—
1199C22×C4—1662no—
1200C22×C4—1662no—
1201C22×C4—1662no—
1202C22×C4—1662no—
1203C22×C4—1662no—
1204C22×C4C2×C4×D8314yes—
1205C22×C4#1305059114yes—
1206C22×C4C23×D8311yescharacteristic
1207C22×C4C23×D8311yescharacteristic
1208C22×C4C23×D8311yescharacteristic
1209C22×C4C23×D8311yescharacteristic
1210C22×C4C23×D8311yescharacteristic
1211C22×C4C23×D8311yescharacteristic
1212C22×C4C23×D8311yescharacteristic
1213C22×C4C23×D8311yescharacteristic
1214C22×C4C23×D8311yescharacteristic
1215C22×C4C23×D8311yescharacteristic
1216C22×C4C23×D8311yescharacteristic
1217C22×C4C23×D8311yescharacteristic
1218C22×C4C23×D8311yescharacteristic
1219C22×C4C23×D8311yescharacteristic
1220C4⋊C4—22no—
1221C4⋊C4—22no—
1222C4⋊C4—41no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
1226C4⋊C4—3321no—
1227C4⋊C4—3321no—
1228C4⋊C4—3321no—
1229C4⋊C4—3321no—
1230C4⋊C4—834no—
1231C4⋊C4—834no—
1232C4⋊C4—834no—
1233C4⋊C4—834no—
1234C4⋊C4—834no—
1235C4⋊C4—1662no—
1236C4⋊C4—1662no—
1237C4⋊C4—1662no—
1238C4⋊C4—1662no—
1239C4⋊C4—1662no—
1240C4⋊C4—1662no—
1241C4⋊C4—1662no—
1242C4⋊C4—1662no—
1243C4⋊C4C2×C4×D8314yes—
1244C4⋊C4C2×C4×D8314yes—
1245C4⋊C4C2×C4×D8314yes—
1246C22⋊C4—22no—
1247C22⋊C4—22no—
1248C22⋊C4—3321no—
1249C22⋊C4—3321no—
1250C22⋊C4—3321no—
1251C22⋊C4—3321no—
1252C22⋊C4—3321no—
1253C22⋊C4—3321no—
1254C22⋊C4—3321no—
1255C22⋊C4—3321no—
1256C22⋊C4—3321no—
1257C22⋊C4—3321no—
1258C22⋊C4—834no—
1259C22⋊C4—834no—
1260C22⋊C4—834no—
1261C22⋊C4—834no—
1262C22⋊C4—834no—
1263C22⋊C4—834no—
1264C22⋊C4—834no—
1265C22⋊C4—834no—
1266C22⋊C4—834no—
1267C22⋊C4—834no—
1268C22⋊C4—834no—
1269C22⋊C4—834no—
1270C22⋊C4—834no—
1271C22⋊C4—1662no—
1272C22⋊C4—1662no—
1273C22⋊C4—1662no—
1274C22⋊C4—1662no—
1275C22⋊C4—1662no—
1276C22⋊C4—1662no—
1277C22⋊C4—1662no—
1278C22⋊C4—1662no—
1279C22⋊C4—1662no—
1280C22⋊C4—1662no—
1281C22⋊C4—1662no—
1282C22⋊C4C2×C4×D8314yes—
1283C22⋊C4C2×C4×D8314yes—
1284C42—22no—
1285C42—22no—
1286C42—41no—
1287C42—41no—
1288C42—41no—
1289C42—41no—
1290C42—41no—
1291C42—41no—
1292C42—3321no—
1293C42—3321no—
1294C42—3321no—
1295C42—3321no—
1296C42—3321no—
1297C42—3321no—
1298C42—3321no—
1299C42—3321no—
1300C42—3321no—
1301C42—3321no—
1302C42—3321no—
1303C42—3321no—
1304C42—3321no—
1305C42—834no—
1306C42—834no—
1307C42—834no—
1308C42—1662no—
1309C42—1662no—
1310C42—1662no—
1311C42—1662no—
1312C42—1662no—
1313C23—21no—
1314C23—21no—
1315C23—21no—
1316C23—21no—
1317C23—3324no—
1318C23—3324no—
1319C23—832no—
1320C23—832no—
1321C23—832no—
1322C23—6642no—
1323C23—6642no—
1324C23—6642no—
1325C23—6642no—
1326C23—1661no—
1327C23—1661no—
1328C23—1661no—
1329C23—1661no—
1330C23—1661no—
1331C23—1661no—
1332C23—1661no—
1333C23—1661no—
1334C23—1661no—
1335C23—1661no—
1336C23—1661no—
1337C23—1661no—
1338C23—1661no—
1339C23—1661no—
1340C23—1661no—
1341C23—1661no—
1342C23—1661no—
1343C23—1661no—
1344C23—1668no—
1345C23C22×C4×D8312yes—
1346C23#41×D8312yes—
1347C23C2×#1305059112yes—
1348C23C24×D8311yescharacteristic
1349Q8—44no—
1350D4—3324no—
1351D4—3324no—
1352D4—1668no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—44no—
1387C2×C4—44no—
1388C2×C4—44no—
1389C2×C4—3324no—
1390C2×C4—3324no—
1391C2×C4—3324no—
1392C2×C4—3324no—
1393C2×C4—3324no—
1394C2×C4—832no—
1395C2×C4—832no—
1396C2×C4—832no—
1397C2×C4—832no—
1398C2×C4—832no—
1399C2×C4—832no—
1400C2×C4—832no—
1401C2×C4—6642no—
1402C2×C4—6642no—
1403C2×C4—6642no—
1404C2×C4—6642no—
1405C2×C4—1661no—
1406C2×C4—1661no—
1407C2×C4—1661no—
1408C2×C4—1661no—
1409C2×C4—1661no—
1410C2×C4—1661no—
1411C2×C4—1661no—
1412C2×C4—1661no—
1413C2×C4—1661no—
1414C2×C4—1661no—
1415C2×C4—1661no—
1416C2×C4—1661no—
1417C2×C4—1661no—
1418C2×C4—1661no—
1419C2×C4—1661no—
1420C2×C4—1661no—
1421C2×C4—1661no—
1422C2×C4—1661no—
1423C2×C4—1668no—
1424C2×C4—1661no—
1425C2×C4—1661no—
1426C2×C4—1661no—
1427C2×C4—1661no—
1428C2×C4—1661no—
1429C2×C4—1661no—
1430C2×C4—1661no—
1431C2×C4—1661no—
1432C2×C4—1661no—
1433C2×C4—1661no—
1434C2×C4—1661no—
1435C2×C4—1661no—
1436C2×C4—1661no—
1437C2×C4—1661no—
1438C2×C4C22×C4×D8312yes—
1439C2×C4C22×C4×D8312yes—
1440C2×C4C22×C4×D8312yes—
1441C2×C4C22×C4×D8312yes—
1442C2×C4C22×C4×D8312yes—
1443C2×C4C22×C4×D8312yes—
1444C2×C4C2×#1305059112yes—
1445C2×C4C2×#1305059112yes—
1446C2×C4#1458183712yes—
1447C22—22no—
1448C22—22no—
1449C22—22no—
1450C22—22no—
1451C22—22no—
1452C22—22no—
1453C22—3321no—
1454C22—3321no—
1455C22—3321no—
1456C22—3321no—
1457C22—3321no—
1458C22—3321no—
1459C22—3321no—
1460C22—3321no—
1461C22—3321no—
1462C22—3321no—
1463C22—3321no—
1464C22—3321no—
1465C22—6648no—
1466C22—1662no—
1467C22—1662no—
1468C22—1662no—
1469C22—1662no—
1470C22—1662no—
1471C22—1662no—
1472C22—1662no—
1473C22—1662no—
1474C22—1662no—
1475C22C4×#1305059114yes—
1476C22C23×C4×D8311yescharacteristic
1477C22C2×#41×D8311yescharacteristic
1478C22C22×#1305059111yescharacteristic
1479C22C2×#1458183711yescharacteristic
1480C22#1912853711yescharacteristic
1481C22#1912853711yescharacteristic
1482C22#1912853711yescharacteristic
1483C4—22no—
1484C4—22no—
1485C4—22no—
1486C4—22no—
1487C4—22no—
1488C4—22no—
1489C4—22no—
1490C4—22no—
1491C4—22no—
1492C4—41no—
1493C4—41no—
1494C4—41no—
1495C4—41no—
1496C4—41no—
1497C4—3321no—
1498C4—3321no—
1499C4—3321no—
1500C4—3321no—
1501C4—3321no—
1502C4—3321no—
1503C4—1662no—
1504C4—1662no—
1505C4—1662no—
1506C4—1662no—
1507C4—1662no—
1508C4—1662no—
1509C4—1662no—
1510C2—24no—
1511C2—3322no—
1512C2—3322no—
1513C2—3322no—
1514C2C2×C4×#1305059111yescharacteristic
1515C2#2492066211yescharacteristic
1516C2C4×#1458183711yescharacteristic
1517C2#2492130411yescharacteristic
1518C2#2492136111yescharacteristic
1519C2#2492138911yescharacteristic
1520C2#2492151711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC4×C22⋊Q8×C83C2
socle, cosocleC23×C83C25
prime radicalC2×#14581762C22
hypercenterC4×C22⋊Q8D83
hypocenterC83#34315
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C22⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #24910592C2semidirect
3. #24910592C2semidirect
4. #24910577C2semidirect
5. #24910577C2semidirect
6. #24910548C2semidirect
7. #24910530C2semidirect
8. #24910486C2semidirect
9. #24910453C2semidirect
11. #24910432C2semidirect
12. #24910405C2semidirect
13. #24910352C2semidirect
14. #24910321C2semidirect
15. #24910310C2semidirect
16. #24910309C2semidirect
17. #24910275C2semidirect
18. #24910256C2semidirect
19. #24910237C2semidirect
20. #24910218C2semidirect
21. #24910134C2semidirect
23. #24910013C2semidirect
24. #24909984C2semidirect
25. #24909955C2semidirect
26. #24909901C2semidirect
27. C2×#19127592C2semidirect
28. #24909818C2semidirect
29. #24909815C2semidirect
30. C42×C22⋊D83C2semidirect
31. C4×C22⋊Q8×C83C2semidirect
32. #19128378C4semidirect
56. C2×C42×D83C22semidirect
57. #19127608C22semidirect
58. #19127608C22semidirect
62. #19127599C22semidirect
63. #19127599C22semidirect
64. #19127597C22semidirect
79. #19127592C22semidirect
80. #19127592C22semidirect
86. #19127591C22semidirect
87. #19127591C22semidirect
88. #19127591C22semidirect
92. #19127590C22semidirect
93. #19127588C22semidirect
94. #19127588C22semidirect
95. #19127587C22semidirect
96. #19127587C22semidirect
97. #19127587C22semidirect
98. #19127587C22semidirect
99. #19127586C22semidirect
100. #19127586C22semidirect
101. #19127584C22semidirect
102. #19127584C22semidirect
103. #19127582C22semidirect
104. #19127582C22semidirect
105. #19127582C22semidirect
106. #19127582C22semidirect
115. #19127575C22semidirect
116. #19127575C22semidirect
120. #19127572C22semidirect
121. #19127568C22semidirect
122. #19127568C22semidirect
123. #19127566C22semidirect
125. #19127563C22semidirect
129. C4⋊C4×Dic83C22semidirect
130. C4⋊C4×Dic83C22semidirect
131. C4⋊C4×Dic83C22semidirect
132. C4⋊C4×Dic83C22semidirect
133. C4×Dic83⋊C4C22semidirect
134. C4×Dic83⋊C4C22semidirect
135. C4×Dic83⋊C4C22semidirect
136. C4×Dic83⋊C4C22semidirect
137. C4×Dic83⋊C4C22semidirect
138. C4×Dic83⋊C4C22semidirect
139. C4×Dic83⋊C4C22semidirect
140. #19127552C22semidirect
141. #19127552C22semidirect
142. #19127552C22semidirect
143. #19127552C22semidirect
152. C4×(C2×D83)⋊C4C22semidirect
153. C4×(C2×D83)⋊C4C22semidirect
154. C4×(C2×D83)⋊C4C22semidirect
166. #19127548C22semidirect
167. #19127548C22semidirect
168. #19127546C22semidirect
169. #19127546C22semidirect
172. C42×Dic83C22semidirect
174. C2×C4×Q8×C83C22semidirect
176. #391×C83C22semidirect
177. #389×C83C22semidirect
178. #387×C83C22semidirect
179. #387×C83C22semidirect
183. C4×C4⋊C4×C83C22semidirect
184. C4×C4⋊C4×C83C22semidirect
185. C4×C4⋊C4×C83C22semidirect
202. #14581787C2×C4semidirect
203. #14581787C2×C4semidirect
204. #14581781C2×C4semidirect
205. #14581777C2×C4semidirect
206. #14581777C2×C4semidirect
207. #14581776C2×C4semidirect
208. #14581768C2×C4semidirect
211. #14581754C2×C4semidirect
214. C4×C22⋊D83C2×C4semidirect
216. #14581750C2×C4semidirect
218. #14581748C2×C4semidirect
242. C2×(C2×D83)⋊C4C2×C4semidirect
275. C22⋊C4×D83C2×C4semidirect
336. C22⋊Q8×C83C2×C4semidirect
784. C4×C22⋊Q8D83semidirect
792. C83#34315semidirect
803. C2×C4×Q8C2×D83semidirect
823. #391C2×D83semidirect
830. #389C2×D83semidirect
873. #387C2×D83semidirect
874. #387C2×D83semidirect
915. C4×C4⋊C4C2×D83semidirect
916. C4×C4⋊C4C2×D83semidirect
917. C4×C4⋊C4C2×D83semidirect
974. C22⋊Q8C4×D83semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#191283782
#249105922
#249105772
#249105482
#249105302
#249104862
#249104532
#249104392
#249104322
#249104052
#249103522
#249103212
#249103102
#249103092
#249102752
#249102562
#249102372
#249102182
#249101342
#249101232
#249100132
#249099842
#249099552
#249099012
C2×#191275922
#249098182
#249098152
C42×C22⋊D832
C4×C22⋊Q8×C832
#3431583