Finite Group Databasebeta

← #35566791

Subgroups — #35566791

Order 21248.

2584 conjugacy classes of subgroups.

The subgroup lattice has 1556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128360C211yesmaximal, characteristic
2#24910573C211yesmaximal, characteristic, complemented
3#24910570C211yesmaximal, characteristic, complemented
4#24910546C211yesmaximal, characteristic, complemented
5#24910540C211yesmaximal, characteristic, complemented
6#24910529C211yesmaximal, characteristic, complemented
7#24910511C211yesmaximal, characteristic, complemented
8#24910510C211yesmaximal, characteristic, complemented
9#24910485C211yesmaximal, characteristic, complemented
10#24910474C211yesmaximal, characteristic, complemented
11#24910423C211yesmaximal, characteristic, complemented
12#24910397C211yesmaximal, characteristic, complemented
13#24910386C211yesmaximal, characteristic, complemented
14#24910295C211yesmaximal, characteristic, complemented
15#24910287C211yesmaximal, characteristic, complemented
16#24910274C211yesmaximal, characteristic, complemented
17#24910273C211yesmaximal, characteristic, complemented
18#24910217C211yesmaximal, characteristic, complemented
19#24910216C211yesmaximal, characteristic, complemented
20#24910164C211yesmaximal, characteristic, complemented
21#24910163C211yesmaximal, characteristic, complemented
22#24910004C211yesmaximal, characteristic, complemented
23#24909997C211yesmaximal, characteristic, complemented
24#24909973C211yesmaximal, characteristic, complemented
25#24909949C211yesmaximal, characteristic, complemented
26#24909935C211yesmaximal, characteristic, complemented
27C2×#19127605C211yesmaximal, characteristic, complemented
28#24909824C211yesmaximal, characteristic, complemented
29#24909822C211yesmaximal, characteristic, complemented
30C4×(C22⋊D83)⋊C4C211yesmaximal, characteristic, complemented
31C83×#2353C211yesmaximal, characteristic, complemented
32C22×#13050590C2211yescharacteristic
33C23×Dic166C2211yescharacteristic
34#19128360C4116yescomplemented
35C2×#14581780C2211yescharacteristic
36C2×#14581778C2211yescharacteristic
37C2×#14581778C2211yescharacteristic
38C2×#14581771C2211yescharacteristic
39C2×#14581770C2211yescharacteristic
40C2×#14581770C2211yescharacteristic
41C2×#14581766C2211yescharacteristic
42C2×#14581764C2211yescharacteristic
43C2×#14581764C2211yescharacteristic
44C2×C4×Dic166C2211yescharacteristic
45C2×#14581757C2211yescharacteristic
46C2×#14581757C2211yescharacteristic
47C2×D4×Dic83C2211yescharacteristic
48C2×D4×Dic83C2211yescharacteristic
49C2×C4×C22⋊D83C2211yescharacteristic
50C2×C4×C22⋊D83C2211yescharacteristic
51C2×(C22⋊D83)⋊C4C2211yescharacteristic
52C2×(C22⋊D83)⋊C4C2211yescharacteristic
53C2×(C22⋊D83)⋊C4C2211yescharacteristic
54C2×(C22⋊D83)⋊C4C2211yescharacteristic
55C2×(C22⋊D83)⋊C4C2211yescharacteristic
56C2×(C22⋊D83)⋊C4C2211yescharacteristic
57C2×#14581749C2211yescharacteristic
58C22×Dic83⋊C4C2211yescharacteristic
59C22×C4×Dic83C2211yescharacteristic
60C2×C42×D83C2211yescharacteristic
61#19127606C2211yescharacteristic
62#19127606C2211yescharacteristic
63#19127605C2211yescharacteristic
64#19127605C2211yescharacteristic
65#19127605C2211yescharacteristic
66#19127605C2211yescharacteristic
67#19127605C2211yescharacteristic
68#19127605C2211yescharacteristic
69#19127605C2211yescharacteristic
70#19127605C2211yescharacteristic
71#19127605C2211yescharacteristic
72#19127605C2211yescharacteristic
73#19127605C2211yescharacteristic
74#19127605C2211yescharacteristic
75#19127601C2211yescharacteristic
76#19127601C2211yescharacteristic
77#19127598C2211yescharacteristic
78#19127598C2211yescharacteristic
79#19127595C2211yescharacteristic
80#19127595C2211yescharacteristic
81#19127593C2211yescharacteristic
82#19127593C2211yescharacteristic
83#19127592C2211yescharacteristic
84#19127592C2211yescharacteristic
85#19127591C2211yescharacteristic
86#19127591C2211yescharacteristic
87#19127590C2211yescharacteristic
88#19127590C2211yescharacteristic
89#19127590C2211yescharacteristic
90#19127590C2211yescharacteristic
91#19127590C2211yescharacteristic
92#19127590C2211yescharacteristic
93#19127589C2211yescharacteristic
94#19127589C2211yescharacteristic
95#19127588C2211yescharacteristic
96#19127588C2211yescharacteristic
97#19127585C2211yescharacteristic
98#19127585C2211yescharacteristic
99#19127584C2211yescharacteristic
100#19127584C2211yescharacteristic
101#19127584C2211yescharacteristic
102#19127584C2211yescharacteristic
103#19127583C2211yescharacteristic
104#19127583C2211yescharacteristic
105#19127583C2211yescharacteristic
106#19127583C2211yescharacteristic
107#19127580C2211yescharacteristic
108#19127580C2211yescharacteristic
109#19127579C2211yescharacteristic
110#19127579C2211yescharacteristic
111#19127579C2211yescharacteristic
112#19127579C2211yescharacteristic
113#19127578C2211yescharacteristic
114#19127578C2211yescharacteristic
115#19127578C2211yescharacteristic
116#19127578C2211yescharacteristic
117#19127577C2211yescharacteristic
118#19127577C2211yescharacteristic
119#19127575C2211yescharacteristic
120#19127575C2211yescharacteristic
121#19127573C2211yescharacteristic
122#19127573C2211yescharacteristic
123#19127572C2211yescharacteristic
124#19127572C2211yescharacteristic
125#19127568C2211yescharacteristic
126#19127565C2211yescharacteristic
127#19127563C2211yescharacteristic
128#19127560C2211yescharacteristic
129#19127559C2211yescharacteristic
130#19127559C2211yescharacteristic
131C4⋊C4×Dic83C2211yescharacteristic
132C4⋊C4×Dic83C2211yescharacteristic
133C4×Dic83⋊C4C2211yescharacteristic
134C4×Dic83⋊C4C2211yescharacteristic
135C4×Dic83⋊C4C2211yescharacteristic
136C4×Dic83⋊C4C2211yescharacteristic
137C4×C4⋊Dic83C2211yescharacteristic
138#19127552C2211yescharacteristic
139#19127552C2211yescharacteristic
140#19127552C2211yescharacteristic
141#19127552C2211yescharacteristic
142#19127552C2211yescharacteristic
143C22⋊C4×Dic83C2211yescharacteristic
144C22⋊C4×Dic83C2211yescharacteristic
145C22⋊C4×Dic83C2211yescharacteristic
146C22⋊C4×Dic83C2211yescharacteristic
147C22⋊C4×Dic83C2211yescharacteristic
148C22⋊C4×Dic83C2211yescharacteristic
149C22⋊C4×Dic83C2211yescharacteristic
150C22⋊C4×Dic83C2211yescharacteristic
151C4×(C2×D83)⋊C4C2211yescharacteristic
152C4×(C2×D83)⋊C4C2211yescharacteristic
153C4×(C2×D83)⋊C4C2211yescharacteristic
154C4×(C2×D83)⋊C4C2211yescharacteristic
155C4×C22⋊Dic83C2211yescharacteristic
156C4×C22⋊Dic83C2211yescharacteristic
157#19127548C2211yescharacteristic
158#19127548C2211yescharacteristic
159#19127548C2211yescharacteristic
160#19127548C2211yescharacteristic
161#19127548C2211yescharacteristic
162#19127548C2211yescharacteristic
163#19127548C2211yescharacteristic
164#19127547C2211yescharacteristic
165#19127547C2211yescharacteristic
166#19127546C2211yescharacteristic
167C2×C83⋊#95C2211yescharacteristic
168C2×C83⋊#95C2211yescharacteristic
169C2×C83⋊#95C2211yescharacteristic
170C2×C83⋊#95C2211yescharacteristic
171#95×D83C2211yescharacteristic
172C42×Dic83C2211yescharacteristic
173C2×C4×D4×C83C2211yescharacteristic
174#388×C83C2211yescharacteristic
175#388×C83C2211yescharacteristic
176#387×C83C2211yescharacteristic
177#387×C83C2211yescharacteristic
178#386×C83C2211yescharacteristic
179#386×C83C2211yescharacteristic
180#383×C83C2211yescharacteristic
181#381×C83C2211yescharacteristic
182#380×C83C2211yescharacteristic
183C4×C22⋊C4×C83C2211yescharacteristic
184C4×C22⋊C4×C83C2211yescharacteristic
185C4×C22⋊C4×C83C2211yescharacteristic
186#376×C83C2211yescharacteristic
187C2×#95×C83C2211yescharacteristic
188C2×#13050590—42no—
189C2×#13050590—42no—
190C2×#13050590C2×C418yescomplemented
191C22×Dic166—42no—
192C22×Dic166—42no—
193C22×Dic166C2×C418yescomplemented
194C22×Dic166C2311yescharacteristic
195C22×Dic166C2311yescharacteristic
196C22×Dic166C2311yescharacteristic
197C22×Dic166C2311yescharacteristic
198C22×D332C2311yescharacteristic
199C22×C22⋊D83C2311yescharacteristic
200C22×C22⋊D83C2311yescharacteristic
201C22×C22⋊D83C2311yescharacteristic
202C22×C22⋊D83C2311yescharacteristic
203C23×Dic83C2311yescharacteristic
204C23×Dic83C2311yescharacteristic
205C23×Dic83C2311yescharacteristic
206C23×Dic83C2311yescharacteristic
207C23×Dic83C2311yescharacteristic
208C23×Dic83C2311yescharacteristic
209C22×C4×D83C2311yescharacteristic
210C22×C4×D83C2311yescharacteristic
211C22×C4×D83C2311yescharacteristic
212C22×C4×D83C2311yescharacteristic
213C22×C4×D83C2311yescharacteristic
214C22×C4×D83C2311yescharacteristic
215#14581780C2×C418yescomplemented
216#14581778C2×C418yescomplemented
217#14581778C2×C418yescomplemented
218#14581771C2×C418yescomplemented
219#14581770C2×C418yescomplemented
220#14581770C2×C418yescomplemented
221#14581766C2×C418yescomplemented
222#14581764C2×C418yescomplemented
223#14581764C2×C418yescomplemented
224C4×Dic166C2×C418yescomplemented
225#14581757—42no—
226#14581757—42no—
227D4×Dic83—24no—
228D4×Dic83—24no—
229C4×C22⋊D83—24no—
230C4×C22⋊D83—24no—
231(C22⋊D83)⋊C4—24no—
232(C22⋊D83)⋊C4—24no—
233(C22⋊D83)⋊C4—42no—
234(C22⋊D83)⋊C4—42no—
235(C22⋊D83)⋊C4C2×C418yescomplemented
236(C22⋊D83)⋊C4C2×C418yescomplemented
237#14581749—42no—
238C2×C4⋊Dic83C2311yescharacteristic
239C2×C4⋊Dic83C2311yescharacteristic
240C2×C4⋊Dic83C2311yescharacteristic
241C2×Dic83⋊C4—42no—
242C2×Dic83⋊C4C2311yescharacteristic
243C2×Dic83⋊C4C2311yescharacteristic
244C2×Dic83⋊C4C2311yescharacteristic
245C2×Dic83⋊C4C2311yescharacteristic
246C2×Dic83⋊C4C2311yescharacteristic
247C2×Dic83⋊C4C2311yescharacteristic
248C2×Dic83⋊C4C2311yescharacteristic
249C2×Dic83⋊C4C2311yescharacteristic
250C2×Dic83⋊C4C2311yescharacteristic
251C2×Dic83⋊C4C2311yescharacteristic
252C2×Dic83⋊C4C2311yescharacteristic
253C2×Dic83⋊C4C2311yescharacteristic
254C2×Dic83⋊C4C2311yescharacteristic
255C2×Dic83⋊C4C2311yescharacteristic
256C2×Dic83⋊C4C2311yescharacteristic
257C2×Dic83⋊C4C2311yescharacteristic
258C2×C22⋊Dic83C2311yescharacteristic
259C2×C22⋊Dic83C2311yescharacteristic
260C2×C22⋊Dic83C2311yescharacteristic
261C2×C22⋊Dic83C2311yescharacteristic
262C2×C22⋊Dic83C2311yescharacteristic
263C2×C22⋊Dic83C2311yescharacteristic
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
274C2×(C2×D83)⋊C4C2311yescharacteristic
275C2×(C2×D83)⋊C4C2311yescharacteristic
276C2×(C2×D83)⋊C4C2311yescharacteristic
277C2×(C2×D83)⋊C4C2311yescharacteristic
278C2×(C2×D83)⋊C4C2311yescharacteristic
279C2×(C2×D83)⋊C4C2311yescharacteristic
280C2×(C2×D83)⋊C4C2311yescharacteristic
281C2×(C2×D83)⋊C4C2311yescharacteristic
282C2×C4×Dic83—42no—
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
297C2×C4×Dic83C2311yescharacteristic
298C2×C4×Dic83C2311yescharacteristic
299C2×C4×Dic83C2311yescharacteristic
300C2×C4×Dic83C2311yescharacteristic
301C2×C4×Dic83C2311yescharacteristic
302C2×C4×Dic83C2311yescharacteristic
303C2×C4×Dic83C2311yescharacteristic
304C2×C4×Dic83C2311yescharacteristic
305C42×D83—42no—
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
332C83⋊#95C2311yescharacteristic
333C83⋊#95C2311yescharacteristic
334C83⋊#95C2311yescharacteristic
335C83⋊#95C2311yescharacteristic
336C83⋊#95C2311yescharacteristic
337C83⋊#95C2311yescharacteristic
338C83⋊#95C2311yescharacteristic
339C83⋊#95C2311yescharacteristic
340C22×D4×C83C2311yescharacteristic
341C23×C4×C83C2311yescharacteristic
342C23×C4×C83C2311yescharacteristic
343C23×C4×C83C2311yescharacteristic
344C23×C4×C83C2311yescharacteristic
345C4×D4×C83C2×C418yescomplemented
346C2×C4⋊C4×C83C2311yescharacteristic
347C2×C4⋊C4×C83C2311yescharacteristic
348C2×C4⋊C4×C83C2311yescharacteristic
349C2×C22⋊C4×C83C2311yescharacteristic
350C2×C22⋊C4×C83C2311yescharacteristic
351C2×C22⋊C4×C83C2311yescharacteristic
352C2×C22⋊C4×C83C2311yescharacteristic
353C2×C22⋊C4×C83C2311yescharacteristic
354C2×C22⋊C4×C83C2311yescharacteristic
355C2×C22⋊C4×C83C2311yescharacteristic
356C2×C22⋊C4×C83C2311yescharacteristic
357C2×C42×C83C2311yescharacteristic
358C2×C42×C83C2311yescharacteristic
359C2×C42×C83C2311yescharacteristic
360C2×C42×C83C2311yescharacteristic
361C2×C42×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
370#95×C83C2311yescharacteristic
371#95×C83C2311yescharacteristic
372#95×C83C2311yescharacteristic
373#95×C83C2311yescharacteristic
374#95×C83C2311yescharacteristic
375#95×C83C2311yescharacteristic
376C23×D83C2411yescharacteristic
377C23×D83C2411yescharacteristic
378#13050590—416no—
379C2×Dic166—22no—
380C2×Dic166—22no—
381C2×Dic166—22no—
382C2×Dic166—22no—
383C2×Dic166—416no—
384C2×Dic166—41no—
385C2×Dic166—41no—
386C2×Dic166—41no—
387C2×Dic166—41no—
388C2×Dic166C22×C414yes—
389C2×Dic166C22×C414yes—
390C2×Dic166C22×C414yes—
391C2×Dic166C22×C414yes—
392C2×D332—41no—
393C2×D332—41no—
394C2×D332C22×C414yes—
395C2×C22⋊D83—22no—
396C2×C22⋊D83—22no—
397C2×C22⋊D83—22no—
398C2×C22⋊D83—22no—
399C2×C22⋊D83—22no—
400C2×C22⋊D83—22no—
401C2×C22⋊D83—41no—
402C2×C22⋊D83—41no—
403C2×C22⋊D83C22×C414yes—
404C2×C22⋊D83C22×C414yes—
405C2×C22⋊D83C22×C414yes—
406C2×C22⋊D83C22×C414yes—
407C22×Dic83—22no—
408C22×Dic83—22no—
409C22×Dic83—22no—
410C22×Dic83—22no—
411C22×Dic83—22no—
412C22×Dic83—41no—
413C22×Dic83—41no—
414C22×Dic83—41no—
415C22×Dic83—41no—
416C22×Dic83—41no—
417C22×Dic83—41no—
418C22×Dic83—41no—
419C22×Dic83—41no—
420C22×Dic83—41no—
421C22×Dic83—41no—
422C22×Dic83C22×C414yes—
423C22×Dic83C22×C414yes—
424C22×Dic83#4114yescomplemented
425C22×Dic83C2411yescharacteristic
426C22×Dic83C2411yescharacteristic
427C22×Dic83C2411yescharacteristic
428C22×Dic83C2411yescharacteristic
429C22×Dic83C2411yescharacteristic
430C22×Dic83C2411yescharacteristic
431C22×Dic83C2411yescharacteristic
432C22×Dic83C2411yescharacteristic
433C22×Dic83C2411yescharacteristic
434C22×Dic83C2411yescharacteristic
435C22×Dic83C2411yescharacteristic
436C22×Dic83C2411yescharacteristic
437C22×Dic83C2411yescharacteristic
438C22×Dic83C2411yescharacteristic
439C2×C4×D83—22no—
440C2×C4×D83—22no—
441C2×C4×D83—22no—
442C2×C4×D83—22no—
443C2×C4×D83—22no—
444C2×C4×D83—22no—
445C2×C4×D83—22no—
446C2×C4×D83—41no—
447C2×C4×D83—41no—
448C2×C4×D83—41no—
449C2×C4×D83—41no—
450C2×C4×D83—41no—
451C2×C4×D83—41no—
452C2×C4×D83—41no—
453C2×C4×D83—41no—
454C2×C4×D83—41no—
455C2×C4×D83C22×C414yes—
456C2×C4×D83C22×C414yes—
457C4⋊Dic83—22no—
458C4⋊Dic83—22no—
459C4⋊Dic83C22×C414yes—
460Dic83⋊C4—22no—
461Dic83⋊C4—22no—
462Dic83⋊C4—22no—
463Dic83⋊C4—22no—
464Dic83⋊C4—22no—
465Dic83⋊C4—22no—
466Dic83⋊C4—22no—
467Dic83⋊C4—22no—
468Dic83⋊C4—41no—
469Dic83⋊C4—41no—
470Dic83⋊C4—41no—
471Dic83⋊C4—41no—
472Dic83⋊C4C22×C414yes—
473Dic83⋊C4C22×C414yes—
474Dic83⋊C4C22×C414yes—
475Dic83⋊C4C22×C414yes—
476C22⋊Dic83—22no—
477C22⋊Dic83—22no—
478C22⋊Dic83—22no—
479C22⋊Dic83C22×C414yes—
480C22⋊Dic83C22×C414yes—
481C22⋊Dic83#4114yescomplemented
482(C2×D83)⋊C4—22no—
483(C2×D83)⋊C4—22no—
484(C2×D83)⋊C4—22no—
485(C2×D83)⋊C4—22no—
486(C2×D83)⋊C4—22no—
487(C2×D83)⋊C4—41no—
488(C2×D83)⋊C4—41no—
489(C2×D83)⋊C4—41no—
490(C2×D83)⋊C4—41no—
491(C2×D83)⋊C4—41no—
492(C2×D83)⋊C4—41no—
493(C2×D83)⋊C4—41no—
494(C2×D83)⋊C4C22×C414yes—
495(C2×D83)⋊C4C22×C414yes—
496(C2×D83)⋊C4C22×C414yes—
497(C2×D83)⋊C4C22×C414yes—
498(C2×D83)⋊C4C22×C414yes—
499(C2×D83)⋊C4C22×C414yes—
500C4×Dic83—22no—
501C4×Dic83—22no—
502C4×Dic83—22no—
503C4×Dic83—22no—
504C4×Dic83—22no—
505C4×Dic83—22no—
506C4×Dic83—22no—
507C4×Dic83—22no—
508C4×Dic83—22no—
509C4×Dic83—22no—
510C4×Dic83—41no—
511C4×Dic83—41no—
512C4×Dic83—41no—
513C4×Dic83—41no—
514C4×Dic83—41no—
515C4×Dic83—41no—
516C4×Dic83—41no—
517C4×Dic83—41no—
518C4×Dic83—41no—
519C4×Dic83—41no—
520C4×Dic83C22×C414yes—
521C4×Dic83C22×C414yes—
522C24×C83C2411yescharacteristic
523C24×C83C2411yescharacteristic
524C2×D4×C83—22no—
525C2×D4×C83—22no—
526C2×D4×C83C22×C414yes—
527C22×C4×C83—22no—
528C22×C4×C83—22no—
529C22×C4×C83—22no—
530C22×C4×C83—41no—
531C22×C4×C83—41no—
532C22×C4×C83—41no—
533C22×C4×C83—41no—
534C22×C4×C83—41no—
535C22×C4×C83—41no—
536C22×C4×C83—41no—
537C22×C4×C83C22×C414yes—
538C22×C4×C83C22×C414yes—
539C22×C4×C83C2411yescharacteristic
540C22×C4×C83C2411yescharacteristic
541C22×C4×C83C2411yescharacteristic
542C22×C4×C83C2411yescharacteristic
543C22×C4×C83C2411yescharacteristic
544C22×C4×C83C2411yescharacteristic
545C22×C4×C83C2411yescharacteristic
546C22×C4×C83C2411yescharacteristic
547C22×C4×C83C2411yescharacteristic
548C22×C4×C83C2411yescharacteristic
549C22×C4×C83C2411yescharacteristic
550C22×C4×C83C2411yescharacteristic
551C22×C4×C83C2411yescharacteristic
552C4⋊C4×C83—41no—
553C4⋊C4×C83—41no—
554C4⋊C4×C83C22×C414yes—
555C22⋊C4×C83—22no—
556C22⋊C4×C83—22no—
557C22⋊C4×C83—22no—
558C22⋊C4×C83—41no—
559C22⋊C4×C83—41no—
560C22⋊C4×C83—41no—
561C22⋊C4×C83C22×C414yes—
562C22⋊C4×C83C22×C414yes—
563C42×C83—22no—
564C42×C83—41no—
565C42×C83—41no—
566C42×C83—41no—
567C42×C83C22×C414yes—
568C23×C83—21no—
569C23×C83—21no—
570C23×C83—21no—
571C23×C83—21no—
572C23×C83—21no—
573C23×C83—21no—
574C23×C83—21no—
575C23×C83—21no—
576C23×C83—21no—
577C23×C83—21no—
578C23×C83C23×C412yes—
579C23×C83C23×C412yes—
580C23×C83C2×#4112yes—
581C23×C83C2×#4112yes—
582C23×C83C2511yescharacteristic
583C22×D83—21no—
584C22×D83—21no—
585C22×D83—21no—
586C22×D83—21no—
587C22×D83—21no—
588C22×D83—21no—
589C22×D83—21no—
590C22×D83—21no—
591C22×D83—21no—
592C22×D83—21no—
593C22×D83—21no—
594C22×D83—21no—
595C22×D83C23×C412yes—
596C22×D83C23×C412yes—
597D4×C83—28no—
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—21no—
623C2×C4×C83—21no—
624C2×C4×C83—21no—
625C2×C4×C83—21no—
626C2×C4×C83—21no—
627C2×C4×C83—21no—
628C2×C4×C83—21no—
629C2×C4×C83—21no—
630C2×C4×C83—21no—
631C2×C4×C83—44no—
632C2×C4×C83—44no—
633C2×C4×C83—44no—
634C2×C4×C83—82no—
635C2×C4×C83C23×C412yes—
636C2×C4×C83C23×C412yes—
637C2×C4×C83C23×C412yes—
638C2×C4×C83C23×C412yes—
639C2×C4×C83C23×C412yes—
640C2×C4×C832−1+412yes—
641C22⋊D83—28no—
642C22⋊D83—28no—
643C22⋊D83—28no—
644C22⋊D83—44no—
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—28no—
664C2×Dic83—21no—
665C2×Dic83—21no—
666C2×Dic83—21no—
667C2×Dic83—21no—
668C2×Dic83—21no—
669C2×Dic83—21no—
670C2×Dic83—21no—
671C2×Dic83—21no—
672C2×Dic83—21no—
673C2×Dic83—21no—
674C2×Dic83—21no—
675C2×Dic83—21no—
676C2×Dic83—44no—
677C2×Dic83—44no—
678C2×Dic83—82no—
679C2×Dic83—82no—
680C2×Dic83—82no—
681C2×Dic83C23×C412yes—
682C2×Dic83C23×C412yes—
683C2×Dic83C23×C412yes—
684C2×Dic83C23×C412yes—
685C2×Dic83C23×C412yes—
686C2×Dic83C23×C412yes—
687C2×Dic83C2×#4112yes—
688C2×Dic83C2×#4112yes—
689C2×Dic83C2×#4112yes—
690C2×Dic83C2×#4112yes—
691C2×Dic83H(5,𝔽2)12yes—
692C2×Dic83H(5,𝔽2)12yes—
693D332—44no—
694C4×D83—28no—
695C4×D83—44no—
696C4×D83—44no—
697C4×D83—44no—
698C4×D83—82no—
699C4×D83—82no—
700Dic166—28no—
701Dic166—28no—
702Dic166—44no—
703Dic166—44no—
704C22×C83—22no—
705C22×C83—22no—
706C22×C83—22no—
707C22×C83—22no—
708C22×C83—22no—
709C22×C83—22no—
710C22×C83—22no—
711C22×C83—22no—
712C22×C83—22no—
713C22×C83—41no—
714C22×C83—41no—
715C22×C83—41no—
716C22×C83—41no—
717C22×C83C4×#4114yes—
718C22×C83C24×C411yescharacteristic
719C22×C83C22×#4111yescharacteristic
720C22×C83C22×#4111yescharacteristic
721C22×C83C2×H(5,𝔽2)11yescharacteristic
722C22×C83C2×H(5,𝔽2)11yescharacteristic
723C22×C83C2×2−1+411yescharacteristic
724C22×C83#58511yescharacteristic
725C2×D83—22no—
726C2×D83—22no—
727C2×D83—22no—
728C2×D83—22no—
729C2×D83—22no—
730C2×D83—22no—
731C2×D83—41no—
732C2×D83—41no—
733C2×D83—41no—
734C2×D83—41no—
735C2×D83—41no—
736C2×D83—41no—
737C2×D83—41no—
738C2×D83—41no—
739C4×C83—22no—
740C4×C83—22no—
741C4×C83—22no—
742C4×C83—22no—
743C4×C83—22no—
744C4×C83—22no—
745C4×C83—41no—
746C4×C83—41no—
747C4×C83—41no—
748C4×C83—41no—
749C4×C83—41no—
750C4×C83—41no—
751C4×C83—41no—
752Dic83—22no—
753Dic83—22no—
754Dic83—22no—
755Dic83—22no—
756Dic83—22no—
757Dic83—22no—
758Dic83—22no—
759Dic83—22no—
760Dic83—22no—
761Dic83—41no—
762Dic83—41no—
763Dic83—41no—
764Dic83—41no—
765Dic83#51814yes—
766#34327—831nomaximal, Sylow
767C2×C83—24no—
768C2×C83—42no—
769C2×C83C2×C4×#4111yescharacteristic
770C2×C83C2×#51811yescharacteristic
771C2×C83C4×2−1+411yescharacteristic
772C2×C83#350511yescharacteristic
773C2×C83#351111yescharacteristic
774C2×C83#351411yescharacteristic
775C2×C83#352011yescharacteristic
776D83—42no—
777D83—42no—
778C2×#548—831no—
779#2372—831no—
780#2372—831no—
781#2368—831no—
782#2368—831no—
783#2367—831no—
784#2364—831no—
785#2364—831no—
786#2362—831no—
787#2361—831no—
788#2356—831no—
789#2353—831no—
790#2353D8311yescharacteristic, complemented
791#2352—831no—
792Q8×C22⋊C4—831no—
793#2339—831no—
794#2337—831no—
795#2337—831no—
796#2332—831no—
797#2332—831no—
798#2325—831no—
799#2325—831no—
800C4×#124—831no—
801C4×C22⋊Q8—831no—
802C4×#121—831no—
803#2297—831no—
804#2295—831no—
805C2×#391—831no—
806#2275—831no—
807#2275—831no—
808C42×D4—831no—
809C83#3432711yescharacteristic, complemented, Sylow
810C22×#41—831no—
811C23×Q8—831no—
812#548—8316no—
813C2×#124—831no—
814C2×#124—831no—
815C2×#124—831no—
816C2×C22⋊Q8—831no—
817C2×C22⋊Q8—831no—
818C2×C22⋊Q8—831no—
819C2×#121—831no—
820C2×#121—831no—
821C2×#121—831no—
822C2×C4×Q8—831no—
823C2×C4×Q8—831no—
824C2×C4×Q8—831no—
825C2×C4×D4—831no—
826C2×C4×D4—831no—
827C2×C4×D4—831no—
828C2×C4×D4—831no—
829C2×C4×D4—831no—
830C2×C4×D4—831no—
831C2×C4×D4—831no—
832C2×C4×D4—831no—
833C2×C4×D4—831no—
834C2×C4×D4—831no—
835C2×C4×D4C2×D8311yescharacteristic
836C2×#117—831no—
837C22×C4⋊C4—831no—
838C22×C42—831no—
839C22×C42—831no—
840#391—831no—
841#391—831no—
842#391—831no—
843#391—831no—
844#391—831no—
845#391—831no—
846#391—831no—
847#391—831no—
848#391—831no—
849#391—831no—
850#391—831no—
851#391—831no—
852#391—831no—
853#391—831no—
854#390—831no—
855#390—831no—
856#389—831no—
857#389—831no—
858#388—831no—
859#388—831no—
860#388—831no—
861#388—831no—
862#388—831no—
863#388—831no—
864#388—831no—
865#388—831no—
866#388—831no—
867#388—831no—
868#388—831no—
869#388—831no—
870#388—831no—
871#388—831no—
872#388—831no—
873#388—831no—
874#388C2×D8311yescharacteristic
875#388C2×D8311yescharacteristic
876#387—831no—
877#387—831no—
878#387—831no—
879#387—831no—
880#387—831no—
881#387—831no—
882#387—831no—
883#387—831no—
884#387—831no—
885#387—831no—
886#387—831no—
887#387—831no—
888#387C2×D8311yescharacteristic
889#387C2×D8311yescharacteristic
890#386—831no—
891#386—831no—
892#386—831no—
893#386—831no—
894#386—831no—
895#386—831no—
896#386—831no—
897#386—831no—
898#386—831no—
899#386—831no—
900#386—831no—
901#386—831no—
902#386C2×D8311yescharacteristic
903#386C2×D8311yescharacteristic
904#385—831no—
905#385—831no—
906#385—831no—
907#385—831no—
908#385—831no—
909#385—831no—
910#383—831no—
911#383C2×D8311yescharacteristic
912#382—831no—
913#381—831no—
914#381C2×D8311yescharacteristic
915#380—831no—
916#380—831no—
917#380—831no—
918#380C2×D8311yescharacteristic
919C4×C4⋊C4—831no—
920C4×C4⋊C4—831no—
921C4×C4⋊C4—831no—
922C4×C4⋊C4—831no—
923C4×C4⋊C4—831no—
924C4×C4⋊C4—831no—
925C4×C4⋊C4—831no—
926C4×C4⋊C4—831no—
927C4×C4⋊C4—831no—
928C4×C4⋊C4—831no—
929C4×C4⋊C4—831no—
930C4×C4⋊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⋊C4—831no—
943C4×C22⋊C4—831no—
944C4×C22⋊C4—831no—
945C4×C22⋊C4—831no—
946C4×C22⋊C4—831no—
947C4×C22⋊C4—831no—
948C4×C22⋊C4—831no—
949C4×C22⋊C4—831no—
950C4×C22⋊C4—831no—
951C4×C22⋊C4—831no—
952C4×C22⋊C4C2×D8311yescharacteristic
953C4×C22⋊C4C2×D8311yescharacteristic
954C4×C22⋊C4C2×D8311yescharacteristic
955#376—831no—
956#376—831no—
957#376—831no—
958#376C2×D8311yescharacteristic
959C2×#95—831no—
960C2×#95—831no—
961C2×#95—831no—
962C2×#95—831no—
963C2×#95—831no—
964C2×#95C2×D8311yescharacteristic
965C43—831no—
966C2×#41—3322no—
967C2×#41—3322no—
968C2×#41—838no—
969C22×Q8—3322no—
970C22×Q8—3322no—
971C22×Q8—838no—
972C22×Q8—831no—
973C22×Q8—831no—
974C22×Q8—831no—
975C22×Q8—831no—
976C22×D4—831no—
977C22×D4—831no—
978C22×D4—831no—
979C22×D4—831no—
980C22×D4—831no—
981C22×D4C22×D8311yescharacteristic
982C23×C4—831no—
983C23×C4—831no—
984C23×C4—831no—
985C23×C4—831no—
986C23×C4—831no—
987C23×C4—831no—
988C23×C4—831no—
989C23×C4—831no—
990C23×C4—831no—
991C23×C4—831no—
992C23×C4—831no—
993C23×C4—831no—
994C23×C4C22×D8311yescharacteristic
995C23×C4C22×D8311yescharacteristic
996C23×C4C22×D8311yescharacteristic
997C23×C4C22×D8311yescharacteristic
998#124—838no—
999#124—838no—
1000#124—838no—
1001C22⋊Q8—838no—
1002C22⋊Q8—838no—
1003C22⋊Q8—838no—
1004#121—838no—
1005#121—838no—
1006#121—838no—
1007C4×Q8—3322no—
1008C4×Q8—3322no—
1009C4×Q8—838no—
1010C4×D4—3322no—
1011C4×D4—3322no—
1012C4×D4—838no—
1013C4×D4—838no—
1014C4×D4—1664no—
1015C4×D4—1664no—
1016C4×D4—1664no—
1017C4×D4—1664no—
1018C4×D4—1664no—
1019C4×D4—1664no—
1020C4×D4C4×D8318yescomplemented
1021#117—3322no—
1022C2×C4⋊C4—3322no—
1023C2×C4⋊C4—831no—
1024C2×C4⋊C4—831no—
1025C2×C4⋊C4—831no—
1026C2×C4⋊C4—831no—
1027C2×C4⋊C4—831no—
1028C2×C4⋊C4—831no—
1029C2×C4⋊C4—831no—
1030C2×C4⋊C4—831no—
1031C2×C4⋊C4—831no—
1032C2×C4⋊C4—831no—
1033C2×C4⋊C4—831no—
1034C2×C4⋊C4—831no—
1035C2×C4⋊C4—831no—
1036C2×C4⋊C4—831no—
1037C2×C4⋊C4—831no—
1038C2×C4⋊C4—831no—
1039C2×C4⋊C4—831no—
1040C2×C4⋊C4—831no—
1041C2×C4⋊C4—831no—
1042C2×C4⋊C4C22×D8311yescharacteristic
1043C2×C4⋊C4C22×D8311yescharacteristic
1044C2×C4⋊C4C22×D8311yescharacteristic
1045C2×C22⋊C4—831no—
1046C2×C22⋊C4—831no—
1047C2×C22⋊C4—831no—
1048C2×C22⋊C4—831no—
1049C2×C22⋊C4—831no—
1050C2×C22⋊C4—831no—
1051C2×C22⋊C4—831no—
1052C2×C22⋊C4—831no—
1053C2×C22⋊C4—831no—
1054C2×C22⋊C4—831no—
1055C2×C22⋊C4—831no—
1056C2×C22⋊C4—831no—
1057C2×C22⋊C4—831no—
1058C2×C22⋊C4—831no—
1059C2×C22⋊C4—831no—
1060C2×C22⋊C4—831no—
1061C2×C22⋊C4—831no—
1062C2×C22⋊C4—831no—
1063C2×C22⋊C4—831no—
1064C2×C22⋊C4—831no—
1065C2×C22⋊C4—831no—
1066C2×C22⋊C4—831no—
1067C2×C22⋊C4—831no—
1068C2×C22⋊C4—831no—
1069C2×C22⋊C4C22×D8311yescharacteristic
1070C2×C22⋊C4C22×D8311yescharacteristic
1071C2×C22⋊C4C22×D8311yescharacteristic
1072C2×C22⋊C4C22×D8311yescharacteristic
1073C2×C22⋊C4C22×D8311yescharacteristic
1074C2×C22⋊C4C22×D8311yescharacteristic
1075C2×C22⋊C4C22×D8311yescharacteristic
1076C2×C22⋊C4C22×D8311yescharacteristic
1077C2×C42—3322no—
1078C2×C42—3322no—
1079C2×C42—831no—
1080C2×C42—831no—
1081C2×C42—831no—
1082C2×C42—831no—
1083C2×C42—831no—
1084C2×C42—831no—
1085C2×C42—831no—
1086C2×C42—831no—
1087C2×C42—831no—
1088C2×C42—831no—
1089C2×C42—831no—
1090C2×C42—831no—
1091C2×C42—831no—
1092C2×C42—831no—
1093C2×C42—831no—
1094C2×C42—831no—
1095C2×C42—831no—
1096C2×C42—831no—
1097C2×C42—831no—
1098C2×C42—831no—
1099C2×C42—831no—
1100C2×C42—831no—
1101C2×C42C22×D8311yescharacteristic
1102C2×C42C22×D8311yescharacteristic
1103C2×C42C22×D8311yescharacteristic
1104C2×C42C22×D8311yescharacteristic
1105C2×C42C22×D8311yescharacteristic
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#95—831no—
1122#95—831no—
1123#95—831no—
1124#95—831no—
1125#95—831no—
1126#95—831no—
1127#95—831no—
1128#95—831no—
1129#95—831no—
1130#95—831no—
1131#95—831no—
1132#95—831no—
1133#95—831no—
1134#95—831no—
1135#95—831no—
1136#95—831no—
1137#95—831no—
1138#95—831no—
1139#95—831no—
1140#95C22×D8311yescharacteristic
1141#95C22×D8311yescharacteristic
1142#95C22×D8311yescharacteristic
1143#95C22×D8311yescharacteristic
1144#95C22×D8311yescharacteristic
1145#95C22×D8311yescharacteristic
1146#95C22×D8311yescharacteristic
1147#95C22×D8311yescharacteristic
1148#95C22×D8311yescharacteristic
1149#95C22×D8311yescharacteristic
1150#95C22×D8311yescharacteristic
1151#95C22×D8311yescharacteristic
1152#95C22×D8311yescharacteristic
1153#95C22×D8311yescharacteristic
1154C24—831no—
1155C24—831no—
1156C24C23×D8311yescharacteristic
1157C24C23×D8311yescharacteristic
1158#41—33216no—
1159C2×Q8—3321no—
1160C2×Q8—3321no—
1161C2×Q8—3321no—
1162C2×Q8—3321no—
1163C2×Q8—33216no—
1164C2×Q8—834no—
1165C2×Q8—834no—
1166C2×Q8—834no—
1167C2×Q8—834no—
1168C2×Q8—1662no—
1169C2×Q8—1662no—
1170C2×Q8—1662no—
1171C2×Q8—1662no—
1172C2×D4—22no—
1173C2×D4—22no—
1174C2×D4—3321no—
1175C2×D4—3321no—
1176C2×D4—3321no—
1177C2×D4—3321no—
1178C2×D4—834no—
1179C2×D4—834no—
1180C2×D4—834no—
1181C2×D4—834no—
1182C2×D4—834no—
1183C2×D4—1662no—
1184C2×D4—1662no—
1185C2×D4—1662no—
1186C2×D4—1662no—
1187C2×D4—1662no—
1188C2×D4—1662no—
1189C2×D4C2×C4×D8314yes—
1190C22×C4—22no—
1191C22×C4—22no—
1192C22×C4—22no—
1193C22×C4—41no—
1194C22×C4—41no—
1195C22×C4—41no—
1196C22×C4—41no—
1197C22×C4—41no—
1198C22×C4—41no—
1199C22×C4—41no—
1200C22×C4—3321no—
1201C22×C4—3321no—
1202C22×C4—3321no—
1203C22×C4—3321no—
1204C22×C4—3321no—
1205C22×C4—3321no—
1206C22×C4—3321no—
1207C22×C4—3321no—
1208C22×C4—3321no—
1209C22×C4—3321no—
1210C22×C4—3321no—
1211C22×C4—3321no—
1212C22×C4—3321no—
1213C22×C4—3321no—
1214C22×C4—3321no—
1215C22×C4—3321no—
1216C22×C4—3321no—
1217C22×C4—3321no—
1218C22×C4—3321no—
1219C22×C4—834no—
1220C22×C4—834no—
1221C22×C4—834no—
1222C22×C4—831no—
1223C22×C4—834no—
1224C22×C4—831no—
1225C22×C4—831no—
1226C22×C4—831no—
1227C22×C4—831no—
1228C22×C4—831no—
1229C22×C4—831no—
1230C22×C4—831no—
1231C22×C4—831no—
1232C22×C4—831no—
1233C22×C4—834no—
1234C22×C4—831no—
1235C22×C4—831no—
1236C22×C4—831no—
1237C22×C4—831no—
1238C22×C4—1662no—
1239C22×C4—1662no—
1240C22×C4—1662no—
1241C22×C4—1662no—
1242C22×C4—1662no—
1243C22×C4—1662no—
1244C22×C4—1662no—
1245C22×C4—1662no—
1246C22×C4—1662no—
1247C22×C4—1662no—
1248C22×C4—1662no—
1249C22×C4—1662no—
1250C22×C4C2×C4×D8314yes—
1251C22×C4C2×C4×D8314yes—
1252C22×C4C23×D8311yescharacteristic
1253C22×C4C23×D8311yescharacteristic
1254C22×C4C23×D8311yescharacteristic
1255C22×C4C23×D8311yescharacteristic
1256C22×C4C23×D8311yescharacteristic
1257C22×C4C23×D8311yescharacteristic
1258C22×C4C23×D8311yescharacteristic
1259C22×C4C23×D8311yescharacteristic
1260C22×C4C23×D8311yescharacteristic
1261C22×C4C23×D8311yescharacteristic
1262C22×C4C23×D8311yescharacteristic
1263C22×C4C23×D8311yescharacteristic
1264C22×C4C23×D8311yescharacteristic
1265C4⋊C4—41no—
1266C4⋊C4—41no—
1267C4⋊C4—3321no—
1268C4⋊C4—3321no—
1269C4⋊C4—3321no—
1270C4⋊C4—3321no—
1271C4⋊C4—834no—
1272C4⋊C4—834no—
1273C4⋊C4—834no—
1274C4⋊C4—834no—
1275C4⋊C4—834no—
1276C4⋊C4—1662no—
1277C4⋊C4—1662no—
1278C4⋊C4—1662no—
1279C4⋊C4—1662no—
1280C4⋊C4—1662no—
1281C4⋊C4—1662no—
1282C4⋊C4—1662no—
1283C4⋊C4—1662no—
1284C4⋊C4—1662no—
1285C4⋊C4—1662no—
1286C4⋊C4C2×C4×D8314yes—
1287C22⋊C4—22no—
1288C22⋊C4—22no—
1289C22⋊C4—22no—
1290C22⋊C4—41no—
1291C22⋊C4—41no—
1292C22⋊C4—41no—
1293C22⋊C4—3321no—
1294C22⋊C4—3321no—
1295C22⋊C4—3321no—
1296C22⋊C4—3321no—
1297C22⋊C4—3321no—
1298C22⋊C4—3321no—
1299C22⋊C4—3321no—
1300C22⋊C4—834no—
1301C22⋊C4—834no—
1302C22⋊C4—834no—
1303C22⋊C4—834no—
1304C22⋊C4—834no—
1305C22⋊C4—834no—
1306C22⋊C4—834no—
1307C22⋊C4—834no—
1308C22⋊C4—834no—
1309C22⋊C4—1662no—
1310C22⋊C4—1662no—
1311C22⋊C4—1662no—
1312C22⋊C4—1662no—
1313C22⋊C4—1662no—
1314C22⋊C4—1662no—
1315C22⋊C4—1662no—
1316C22⋊C4—1662no—
1317C22⋊C4C2×C4×D8314yes—
1318C22⋊C4C2×C4×D8314yes—
1319C42—22no—
1320C42—41no—
1321C42—41no—
1322C42—41no—
1323C42—3321no—
1324C42—3321no—
1325C42—3321no—
1326C42—3321no—
1327C42—3321no—
1328C42—3321no—
1329C42—3321no—
1330C42—3321no—
1331C42—3321no—
1332C42—3321no—
1333C42—834no—
1334C42—834no—
1335C42—1662no—
1336C42—1662no—
1337C42—1662no—
1338C42—1662no—
1339C42—1662no—
1340C42—1662no—
1341C42—1662no—
1342C42—1662no—
1343C42—1662no—
1344C42—1662no—
1345C42C2×C4×D8314yes—
1346C23—21no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—832no—
1357C23—832no—
1358C23—1661no—
1359C23—1661no—
1360C23—1661no—
1361C23—1661no—
1362C23—1661no—
1363C23—1661no—
1364C23—1661no—
1365C23—1661no—
1366C23—1661no—
1367C23—1661no—
1368C23—1661no—
1369C23—1661no—
1370C23C22×C4×D8312yes—
1371C23C22×C4×D8312yes—
1372C23#41×D8312yes—
1373C23#41×D8312yes—
1374C23C24×D8311yescharacteristic
1375Q8—3324no—
1376Q8—3324no—
1377Q8—1668no—
1378Q8—1668no—
1379D4—28no—
1380D4—3324no—
1381D4—3324no—
1382D4—1668no—
1383D4—1668no—
1384D4—1668no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—44no—
1419C2×C4—44no—
1420C2×C4—44no—
1421C2×C4—82no—
1422C2×C4—3324no—
1423C2×C4—3324no—
1424C2×C4—3324no—
1425C2×C4—3324no—
1426C2×C4—3324no—
1427C2×C4—832no—
1428C2×C4—832no—
1429C2×C4—832no—
1430C2×C4—832no—
1431C2×C4—832no—
1432C2×C4—832no—
1433C2×C4—832no—
1434C2×C4—832no—
1435C2×C4—832no—
1436C2×C4—832no—
1437C2×C4—832no—
1438C2×C4—832no—
1439C2×C4—6642no—
1440C2×C4—6642no—
1441C2×C4—6642no—
1442C2×C4—6642no—
1443C2×C4—6642no—
1444C2×C4—1668no—
1445C2×C4—1661no—
1446C2×C4—1661no—
1447C2×C4—1661no—
1448C2×C4—1661no—
1449C2×C4—1661no—
1450C2×C4—1661no—
1451C2×C4—1661no—
1452C2×C4—1661no—
1453C2×C4—1661no—
1454C2×C4—1661no—
1455C2×C4—1661no—
1456C2×C4—1661no—
1457C2×C4—1668no—
1458C2×C4—1661no—
1459C2×C4—1661no—
1460C2×C4—1661no—
1461C2×C4—1661no—
1462C2×C4—1661no—
1463C2×C4—1661no—
1464C2×C4—1661no—
1465C2×C4—1661no—
1466C2×C4—1661no—
1467C2×C4—1661no—
1468C2×C4—1661no—
1469C2×C4—1661no—
1470C2×C4—1661no—
1471C2×C4—1661no—
1472C2×C4—1661no—
1473C2×C4—1661no—
1474C2×C4—1661no—
1475C2×C4—1661no—
1476C2×C4C22×C4×D8312yes—
1477C2×C4C22×C4×D8312yes—
1478C2×C4C22×C4×D8312yes—
1479C2×C4C22×C4×D8312yes—
1480C2×C4C22×C4×D8312yes—
1481C2×C4#1458183912yes—
1482C22—22no—
1483C22—22no—
1484C22—22no—
1485C22—22no—
1486C22—22no—
1487C22—22no—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—41no—
1492C22—41no—
1493C22—41no—
1494C22—41no—
1495C22—3321no—
1496C22—3321no—
1497C22—3321no—
1498C22—3321no—
1499C22—3321no—
1500C22—3321no—
1501C22—3321no—
1502C22—3321no—
1503C22—1662no—
1504C22—1662no—
1505C22—1662no—
1506C22—1662no—
1507C22—1662no—
1508C22—1662no—
1509C22#1912816914yes—
1510C22C23×C4×D8311yescharacteristic
1511C22C2×#41×D8311yescharacteristic
1512C22C2×#41×D8311yescharacteristic
1513C22H(5,𝔽2)×D8311yescharacteristic
1514C22H(5,𝔽2)×D8311yescharacteristic
1515C22C2×#1458183911yescharacteristic
1516C22#1912853711yescharacteristic
1517C4—22no—
1518C4—22no—
1519C4—22no—
1520C4—22no—
1521C4—22no—
1522C4—22no—
1523C4—41no—
1524C4—41no—
1525C4—41no—
1526C4—41no—
1527C4—41no—
1528C4—41no—
1529C4—41no—
1530C4—3321no—
1531C4—3321no—
1532C4—3321no—
1533C4—3321no—
1534C4—834no—
1535C4—1662no—
1536C4—1662no—
1537C4—1662no—
1538C4—1662no—
1539C4—1662no—
1540C4—1662no—
1541C4—1662no—
1542C4—1662no—
1543C4—1662no—
1544C2—24no—
1545C2—42no—
1546C2—3322no—
1547C2—3322no—
1548C2C2×#1912816911yescharacteristic
1549C2#518×D8311yescharacteristic
1550C2C4×#1458183911yescharacteristic
1551C2#2492129611yescharacteristic
1552C2#2492136511yescharacteristic
1553C2#2492141311yescharacteristic
1554C2#2492150111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2353C2
socle, cosocleC23×C83C25
prime radicalC2×#19128360C2
hypercenter#2353D83
hypocenterC83#34327
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2353

Complements

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

NH ≅ G/Ntype
2. #24910573C2semidirect
3. #24910570C2semidirect
4. #24910546C2semidirect
5. #24910540C2semidirect
6. #24910529C2semidirect
7. #24910511C2semidirect
8. #24910510C2semidirect
9. #24910485C2semidirect
10. #24910474C2semidirect
11. #24910423C2semidirect
12. #24910397C2semidirect
13. #24910386C2semidirect
14. #24910295C2semidirect
15. #24910287C2semidirect
16. #24910274C2semidirect
17. #24910273C2semidirect
18. #24910217C2semidirect
19. #24910216C2semidirect
20. #24910164C2semidirect
21. #24910163C2semidirect
22. #24910004C2semidirect
23. #24909997C2semidirect
24. #24909973C2semidirect
25. #24909949C2semidirect
26. #24909935C2semidirect
27. C2×#19127605C2semidirect
28. #24909824C2semidirect
29. #24909822C2semidirect
30. C4×(C22⋊D83)⋊C4C2semidirect
31. C83×#2353C2semidirect
34. #19128360C4semidirect
190. C2×#13050590C2×C4semidirect
193. C22×Dic166C2×C4semidirect
215. #14581780C2×C4semidirect
216. #14581778C2×C4semidirect
217. #14581778C2×C4semidirect
218. #14581771C2×C4semidirect
219. #14581770C2×C4semidirect
220. #14581770C2×C4semidirect
221. #14581766C2×C4semidirect
222. #14581764C2×C4semidirect
223. #14581764C2×C4semidirect
224. C4×Dic166C2×C4semidirect
235. (C22⋊D83)⋊C4C2×C4semidirect
236. (C22⋊D83)⋊C4C2×C4semidirect
345. C4×D4×C83C2×C4semidirect
424. C22×Dic83#41semidirect
481. C22⋊Dic83#41semidirect
790. #2353D83semidirect
809. C83#34327semidirect
1020. C4×D4C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191283602
#249105732
#249105702
#249105462
#249105402
#249105292
#249105112
#249105102
#249104852
#249104742
#249104232
#249103972
#249103862
#249102952
#249102872
#249102742
#249102732
#249102172
#249102162
#249101642
#249101632
#249100042
#249099972
#249099732
#249099492
#249099352
C2×#191276052
#249098242
#249098222
C4×(C22⋊D83)⋊C42
C83×#23532
#3432783