Finite Group Databasebeta

← #35566544

Subgroups — #35566544

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×#19128377C211yesmaximal, characteristic
2#24910597C211yesmaximal, characteristic, complemented
3#24910594C211yesmaximal, characteristic, complemented
4#24910584C211yesmaximal, characteristic, complemented
5#24910584C211yesmaximal, characteristic, complemented
6#24910541C211yesmaximal, characteristic, complemented
7#24910535C211yesmaximal, characteristic, complemented
8#24910488C211yesmaximal, characteristic, complemented
9#24910457C211yesmaximal, characteristic, complemented
10#24910442C211yesmaximal, characteristic
11#24910437C211yesmaximal, characteristic, complemented
12#24910397C211yesmaximal, characteristic, complemented
13#24910354C211yesmaximal, characteristic, complemented
14#24910317C211yesmaximal, characteristic, complemented
15#24910312C211yesmaximal, characteristic, complemented
16#24910308C211yesmaximal, characteristic, complemented
17#24910271C211yesmaximal, characteristic, complemented
18#24910253C211yesmaximal, characteristic, complemented
19#24910240C211yesmaximal, characteristic, complemented
20#24910219C211yesmaximal, characteristic, complemented
21#24910134C211yesmaximal, characteristic, complemented
22#24910121C211yesmaximal, characteristic
23C4×#14581785C211yesmaximal, characteristic, complemented
24C4×#14581769C211yesmaximal, characteristic, complemented
25C4×#14581774C211yesmaximal, characteristic, complemented
26#24909959C211yesmaximal, characteristic, complemented
27#24909909C211yesmaximal, characteristic, complemented
28C2×#19127595C211yesmaximal, characteristic, complemented
29#24909818C211yesmaximal, characteristic, complemented
30C4×(C22⋊D83)⋊C4C211yesmaximal, characteristic, complemented
31C83×#2273C211yesmaximal, characteristic, complemented
32#19128377C4116yescomplemented
33C2×#14581785C2211yescharacteristic
34C2×#14581785C2211yescharacteristic
35C2×#14581778C2211yescharacteristic
36C2×#14581776C2211yescharacteristic
37C2×#14581775C2211yescharacteristic
38C2×#14581774C2211yescharacteristic
39C2×#14581771C2211yescharacteristic
40C2×#14581769C2211yescharacteristic
41C2×#14581761C2211yescharacteristic
42C2×C4×Dic166C2211yescharacteristic, complemented
43C2×C4×C22⋊D83C2211yescharacteristic
44C2×C4×C22⋊D83C2211yescharacteristic
45C2×C4×C22⋊D83C2211yescharacteristic
46C2×(C22⋊D83)⋊C4C2211yescharacteristic
47C2×(C22⋊D83)⋊C4C2211yescharacteristic
48C2×#14581751C2211yescharacteristic
49C2×#14581751C2211yescharacteristic
50C2×#14581748C2211yescharacteristic
51C2×#14581748C2211yescharacteristic
52C22×Dic83⋊C4C2211yescharacteristic
53C22×C22⋊Dic83C2211yescharacteristic
54C22×C22⋊Dic83C2211yescharacteristic
55C22×C4×Dic83C2211yescharacteristic
56C2×C42×D83C2211yescharacteristic, complemented
57#19127607C2211yescharacteristic, complemented
58#19127605C2211yescharacteristic, complemented
59#19127605C2211yescharacteristic, complemented
60#19127601C2211yescharacteristic
61#19127601C2211yescharacteristic
62#19127601C2211yescharacteristic
63#19127599C2211yescharacteristic, complemented
64#19127599C2211yescharacteristic, complemented
65#19127599C2211yescharacteristic, complemented
66#19127598C2211yescharacteristic, complemented
67#19127595C2211yescharacteristic
68#19127595C2211yescharacteristic
69#19127595C2211yescharacteristic
70#19127595C2211yescharacteristic
71#19127595C2211yescharacteristic
72#19127595C2211yescharacteristic
73#19127595C2211yescharacteristic
74#19127595C2211yescharacteristic
75#19127595C2211yescharacteristic
76#19127595C2211yescharacteristic
77#19127595C2211yescharacteristic
78#19127595C2211yescharacteristic
79#19127595C2211yescharacteristic
80#19127594C2211yescharacteristic
81#19127594C2211yescharacteristic
82#19127594C2211yescharacteristic
83#19127594C2211yescharacteristic
84#19127593C2211yescharacteristic, complemented
85#19127592C2211yescharacteristic, complemented
86#19127592C2211yescharacteristic, complemented
87#19127592C2211yescharacteristic, complemented
88#19127592C2211yescharacteristic, complemented
89#19127590C2211yescharacteristic, complemented
90#19127589C2211yescharacteristic
91#19127589C2211yescharacteristic
92#19127589C2211yescharacteristic
93#19127589C2211yescharacteristic
94#19127589C2211yescharacteristic
95#19127588C2211yescharacteristic, complemented
96#19127588C2211yescharacteristic, complemented
97#19127588C2211yescharacteristic, complemented
98#19127586C2211yescharacteristic, complemented
99#19127586C2211yescharacteristic, complemented
100#19127586C2211yescharacteristic, complemented
101#19127586C2211yescharacteristic, complemented
102#19127585C2211yescharacteristic, complemented
103#19127585C2211yescharacteristic, complemented
104#19127585C2211yescharacteristic, complemented
105#19127585C2211yescharacteristic, complemented
106#19127584C2211yescharacteristic, complemented
107#19127584C2211yescharacteristic, complemented
108#19127583C2211yescharacteristic, complemented
109#19127583C2211yescharacteristic, complemented
110#19127583C2211yescharacteristic, complemented
111#19127580C2211yescharacteristic
112#19127580C2211yescharacteristic
113#19127578C2211yescharacteristic
114#19127577C2211yescharacteristic
115#19127577C2211yescharacteristic
116#19127577C2211yescharacteristic
117#19127576C2211yescharacteristic
118#19127576C2211yescharacteristic
119#19127575C2211yescharacteristic, complemented
120#19127575C2211yescharacteristic, complemented
121#19127575C2211yescharacteristic, complemented
122#19127574C2211yescharacteristic
123#19127574C2211yescharacteristic
124#19127574C2211yescharacteristic
125#19127574C2211yescharacteristic
126#19127573C2211yescharacteristic
127#19127568C2211yescharacteristic, complemented
128#19127568C2211yescharacteristic, complemented
129#19127565C2211yescharacteristic, complemented
130#19127564C2211yescharacteristic
131#19127563C2211yescharacteristic, complemented
132#19127562C2211yescharacteristic
133#19127561C2211yescharacteristic
134#19127559C2211yescharacteristic
135#19127557C2211yescharacteristic
136C4×Dic83⋊C4C2211yescharacteristic, complemented
137C4×Dic83⋊C4C2211yescharacteristic, complemented
138C4×Dic83⋊C4C2211yescharacteristic, complemented
139C4×Dic83⋊C4C2211yescharacteristic, complemented
140C4×Dic83⋊C4C2211yescharacteristic, complemented
141C4×Dic83⋊C4C2211yescharacteristic, complemented
142C4×Dic83⋊C4C2211yescharacteristic, complemented
143C4×Dic83⋊C4C2211yescharacteristic, complemented
144C4×Dic83⋊C4C2211yescharacteristic, complemented
145C4×C4⋊Dic83C2211yescharacteristic, complemented
146C4×C4⋊Dic83C2211yescharacteristic, complemented
147C4×C4⋊Dic83C2211yescharacteristic, complemented
148#19127552C2211yescharacteristic, complemented
149#19127552C2211yescharacteristic, complemented
150#19127552C2211yescharacteristic, complemented
151#19127552C2211yescharacteristic, complemented
152#19127552C2211yescharacteristic, complemented
153#19127552C2211yescharacteristic, complemented
154C22⋊C4×Dic83C2211yescharacteristic
155C22⋊C4×Dic83C2211yescharacteristic
156C22⋊C4×Dic83C2211yescharacteristic
157C22⋊C4×Dic83C2211yescharacteristic
158C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
159C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
160C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
161C4×C22⋊Dic83C2211yescharacteristic
162C4×C22⋊Dic83C2211yescharacteristic
163C4×C22⋊Dic83C2211yescharacteristic
164C4×C22⋊Dic83C2211yescharacteristic
165C4×C22⋊Dic83C2211yescharacteristic
166#19127548C2211yescharacteristic, complemented
167#19127548C2211yescharacteristic, complemented
168#19127547C2211yescharacteristic, complemented
169#19127547C2211yescharacteristic, complemented
170C2×C83⋊#95C2211yescharacteristic
171C2×C83⋊#95C2211yescharacteristic
172C42×Dic83C2211yescharacteristic, complemented
173C22×C22⋊C4×C83C2211yescharacteristic
174C22×C22⋊C4×C83C2211yescharacteristic
175C22×C22⋊C4×C83C2211yescharacteristic
176C4×C22⋊C4×C83C2211yescharacteristic
177C4×C22⋊C4×C83C2211yescharacteristic
178C4×C22⋊C4×C83C2211yescharacteristic
179C4×C22⋊C4×C83C2211yescharacteristic
180C4×C22⋊C4×C83C2211yescharacteristic
181C4×C22⋊C4×C83C2211yescharacteristic
182C4×C22⋊C4×C83C2211yescharacteristic
183C4×C22⋊C4×C83C2211yescharacteristic
184C4×C22⋊C4×C83C2211yescharacteristic
185C4×C22⋊C4×C83C2211yescharacteristic
186C4×C22⋊C4×C83C2211yescharacteristic
187C4×C22⋊C4×C83C2211yescharacteristic
188C22×Dic166C2311yescharacteristic
189C22×C22⋊D83C2311yescharacteristic
190C22×C22⋊D83C2311yescharacteristic
191C22×C22⋊D83C2311yescharacteristic
192C23×Dic83C2311yescharacteristic
193C23×Dic83C2311yescharacteristic
194C23×Dic83C2311yescharacteristic
195C23×Dic83C2311yescharacteristic
196C22×C4×D83C2311yescharacteristic
197C22×C4×D83C2311yescharacteristic
198C22×C4×D83C2311yescharacteristic
199#14581785C2×C418yescomplemented
200#14581785C2×C418yescomplemented
201#14581778C2×C418yescomplemented
202#14581776C2×C418yescomplemented
203#14581775C2×C418yescomplemented
204#14581774C2×C418yescomplemented
205#14581771C2×C418yescomplemented
206#14581769C2×C418yescomplemented
207#14581761C2×C418yes—
208C4×Dic166—42no—
209C4×C22⋊D83—24no—
210C4×C22⋊D83—42no—
211C4×C22⋊D83C2×C418yescomplemented
212(C22⋊D83)⋊C4—24no—
213(C22⋊D83)⋊C4C2×C418yescomplemented
214#14581751—42no—
215#14581751C2×C418yescomplemented
216#14581748—24no—
217#14581748C2×C418yescomplemented
218C2×C4⋊Dic83C2311yescharacteristic
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×Dic83⋊C4C2311yescharacteristic
238C2×Dic83⋊C4C2311yescharacteristic
239C2×Dic83⋊C4C2311yescharacteristic
240C2×Dic83⋊C4C2311yescharacteristic
241C2×Dic83⋊C4C2311yescharacteristic
242C2×Dic83⋊C4C2311yescharacteristic
243C2×Dic83⋊C4C2311yescharacteristic
244C2×Dic83⋊C4C2311yescharacteristic
245C2×C22⋊Dic83—42no—
246C2×C22⋊Dic83C2×C418yescomplemented
247C2×C22⋊Dic83C2311yescharacteristic
248C2×C22⋊Dic83C2311yescharacteristic
249C2×C22⋊Dic83C2311yescharacteristic
250C2×C22⋊Dic83C2311yescharacteristic
251C2×C22⋊Dic83C2311yescharacteristic
252C2×C22⋊Dic83C2311yescharacteristic
253C2×C22⋊Dic83C2311yescharacteristic
254C2×C22⋊Dic83C2311yescharacteristic
255C2×C22⋊Dic83C2311yescharacteristic
256C2×C22⋊Dic83C2311yescharacteristic
257C2×C22⋊Dic83C2311yescharacteristic
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×C4×Dic83—42no—
274C2×C4×Dic83C2311yescharacteristic
275C2×C4×Dic83C2311yescharacteristic
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
295C42×D83—42no—
296C83⋊#95C2311yescharacteristic
297C83⋊#95C2311yescharacteristic
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
332C25×C83C2311yescharacteristic
333C23×C4×C83C2311yescharacteristic
334C23×C4×C83C2311yescharacteristic
335C23×C4×C83C2311yescharacteristic
336C23×C4×C83C2311yescharacteristic
337C23×C4×C83C2311yescharacteristic
338C23×C4×C83C2311yescharacteristic
339C2×C22⋊C4×C83—24no—
340C2×C22⋊C4×C83—24no—
341C2×C22⋊C4×C83C2×C418yescomplemented
342C2×C22⋊C4×C83C2311yescharacteristic
343C2×C22⋊C4×C83C2311yescharacteristic
344C2×C22⋊C4×C83C2311yescharacteristic
345C2×C22⋊C4×C83C2311yescharacteristic
346C2×C22⋊C4×C83C2311yescharacteristic
347C2×C22⋊C4×C83C2311yescharacteristic
348C2×C22⋊C4×C83C2311yescharacteristic
349C2×C22⋊C4×C83C2311yescharacteristic
350C2×C22⋊C4×C83C2311yescharacteristic
351C2×C22⋊C4×C83C2311yescharacteristic
352C2×C22⋊C4×C83C2311yescharacteristic
353C2×C22⋊C4×C83C2311yescharacteristic
354C2×C42×C83C2311yescharacteristic
355C2×C42×C83C2311yescharacteristic
356C2×C42×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
370C23×D83C2411yescharacteristic
371C2×Dic166—41no—
372C2×Dic166—41no—
373C2×Dic166C22×C414yes—
374C2×C22⋊D83—22no—
375C2×C22⋊D83—22no—
376C2×C22⋊D83—41no—
377C2×C22⋊D83—41no—
378C2×C22⋊D83—41no—
379C2×C22⋊D83—41no—
380C2×C22⋊D83C22×C414yes—
381C2×C22⋊D83C22×C414yes—
382C2×C22⋊D83C22×C414yes—
383C22×Dic83—22no—
384C22×Dic83—22no—
385C22×Dic83—22no—
386C22×Dic83—22no—
387C22×Dic83—22no—
388C22×Dic83—41no—
389C22×Dic83—41no—
390C22×Dic83—41no—
391C22×Dic83—41no—
392C22×Dic83—41no—
393C22×Dic83C22×C414yes—
394C22×Dic83C22×C414yes—
395C22×Dic83C2411yescharacteristic
396C22×Dic83C2411yescharacteristic
397C22×Dic83C2411yescharacteristic
398C22×Dic83C2411yescharacteristic
399C22×Dic83C2411yescharacteristic
400C22×Dic83C2411yescharacteristic
401C22×Dic83C2411yescharacteristic
402C22×Dic83C2411yescharacteristic
403C22×Dic83C2411yescharacteristic
404C22×Dic83C2411yescharacteristic
405C22×Dic83C2411yescharacteristic
406C22×Dic83C2411yescharacteristic
407C22×Dic83C2411yescharacteristic
408C22×Dic83C2411yescharacteristic
409C22×Dic83C2411yescharacteristic
410C2×C4×D83—22no—
411C2×C4×D83—22no—
412C2×C4×D83—22no—
413C2×C4×D83—41no—
414C2×C4×D83—41no—
415C2×C4×D83—41no—
416C2×C4×D83—41no—
417C2×C4×D83—41no—
418C2×C4×D83C22×C414yes—
419C4⋊Dic83—22no—
420C4⋊Dic83—41no—
421C4⋊Dic83—41no—
422C4⋊Dic83—41no—
423C4⋊Dic83C22×C414yes—
424C4⋊Dic83C22×C414yes—
425C4⋊Dic83C22×C414yes—
426Dic83⋊C4—22no—
427Dic83⋊C4—22no—
428Dic83⋊C4—22no—
429Dic83⋊C4—22no—
430Dic83⋊C4—22no—
431Dic83⋊C4—22no—
432Dic83⋊C4—22no—
433Dic83⋊C4—22no—
434Dic83⋊C4—22no—
435Dic83⋊C4—41no—
436Dic83⋊C4—41no—
437Dic83⋊C4—41no—
438Dic83⋊C4—41no—
439Dic83⋊C4—41no—
440Dic83⋊C4C22×C414yes—
441Dic83⋊C4C22×C414yes—
442Dic83⋊C4C22×C414yes—
443Dic83⋊C4C22×C414yes—
444Dic83⋊C4C22×C414yes—
445C22⋊Dic83—22no—
446C22⋊Dic83—22no—
447C22⋊Dic83—22no—
448C22⋊Dic83—22no—
449C22⋊Dic83—41no—
450C22⋊Dic83—41no—
451C22⋊Dic83—41no—
452C22⋊Dic83—41no—
453C22⋊Dic83—41no—
454C22⋊Dic83—41no—
455C22⋊Dic83C22×C414yes—
456C22⋊Dic83C22×C414yes—
457C22⋊Dic83C22×C414yes—
458C22⋊Dic83C22×C414yes—
459C22⋊Dic83C22×C414yes—
460C22⋊Dic83C22×C414yes—
461C22⋊Dic83C22×C414yes—
462(C2×D83)⋊C4—22no—
463(C2×D83)⋊C4—22no—
464(C2×D83)⋊C4—41no—
465(C2×D83)⋊C4—41no—
466(C2×D83)⋊C4—41no—
467(C2×D83)⋊C4—41no—
468(C2×D83)⋊C4C22×C414yes—
469(C2×D83)⋊C4C22×C414yes—
470(C2×D83)⋊C4C22×C414yes—
471C4×Dic83—22no—
472C4×Dic83—22no—
473C4×Dic83—22no—
474C4×Dic83—22no—
475C4×Dic83—22no—
476C4×Dic83—22no—
477C4×Dic83—22no—
478C4×Dic83—41no—
479C4×Dic83—41no—
480C4×Dic83—41no—
481C4×Dic83—41no—
482C4×Dic83—41no—
483C4×Dic83—41no—
484C4×Dic83—41no—
485C4×Dic83—41no—
486C4×Dic83—41no—
487C4×Dic83—41no—
488C4×Dic83—41no—
489C4×Dic83C22×C414yes—
490C4×Dic83C22×C414yes—
491C4×Dic83C22×C414yes—
492C24×C83—22no—
493C24×C83—22no—
494C24×C83—41no—
495C24×C83—41no—
496C24×C83—41no—
497C24×C83—41no—
498C24×C83C22×C414yes—
499C24×C83C2411yescharacteristic
500C24×C83C2411yescharacteristic
501C24×C83C2411yescharacteristic
502C22×C4×C83—22no—
503C22×C4×C83—22no—
504C22×C4×C83—22no—
505C22×C4×C83—41no—
506C22×C4×C83—41no—
507C22×C4×C83—41no—
508C22×C4×C83—41no—
509C22×C4×C83—41no—
510C22×C4×C83—41no—
511C22×C4×C83—41no—
512C22×C4×C83—41no—
513C22×C4×C83—41no—
514C22×C4×C83—41no—
515C22×C4×C83—41no—
516C22×C4×C83—41no—
517C22×C4×C83C22×C414yes—
518C22×C4×C83C22×C414yes—
519C22×C4×C83#4114yes—
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
531C22×C4×C83C2411yescharacteristic
532C22⋊C4×C83—22no—
533C22⋊C4×C83—22no—
534C22⋊C4×C83—22no—
535C22⋊C4×C83—22no—
536C22⋊C4×C83—22no—
537C22⋊C4×C83—22no—
538C22⋊C4×C83—22no—
539C22⋊C4×C83C22×C414yes—
540C22⋊C4×C83C22×C414yes—
541C22⋊C4×C83C22×C414yes—
542C22⋊C4×C83C22×C414yes—
543C22⋊C4×C83#4114yes—
544C42×C83—41no—
545C42×C83—41no—
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×C83—21no—
557C23×C83—21no—
558C23×C83—21no—
559C23×C83—21no—
560C23×C83—21no—
561C23×C83—21no—
562C23×C83—21no—
563C23×C83—21no—
564C23×C83—21no—
565C23×C83—21no—
566C23×C83—21no—
567C23×C83—21no—
568C23×C83—28no—
569C23×C83—44no—
570C23×C83—44no—
571C23×C83—82no—
572C23×C83—82no—
573C23×C83—82no—
574C23×C83—82no—
575C23×C83C23×C412yes—
576C23×C83C23×C412yes—
577C23×C83C23×C412yes—
578C23×C83C2×#4112yes—
579C23×C83C2×#4112yes—
580C23×C83C2511yescharacteristic
581C22×D83—21no—
582C22×D83—21no—
583C22×D83—21no—
584C22×D83—21no—
585C22×D83—21no—
586C22×D83—21no—
587C22×D83C23×C412yes—
588C2×C4×C83—21no—
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—44no—
617C2×C4×C83—44no—
618C2×C4×C83—44no—
619C2×C4×C83—82no—
620C2×C4×C83—82no—
621C2×C4×C83—82no—
622C2×C4×C83C23×C412yes—
623C2×C4×C83C23×C412yes—
624C2×C4×C83C23×C412yes—
625C2×C4×C83C23×C412yes—
626C2×C4×C83C2×#4112yes—
627C2×C4×C83C2×#4112yes—
628C2×C4×C83C2×#4112yes—
629C2×C4×C83C2×#4112yes—
630C22⋊D83—28no—
631C22⋊D83—44no—
632C22⋊D83—44no—
633C2×Dic83—28no—
634C2×Dic83—21no—
635C2×Dic83—21no—
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—21no—
669C2×Dic83—21no—
670C2×Dic83—21no—
671C2×Dic83—44no—
672C2×Dic83—44no—
673C2×Dic83—82no—
674C2×Dic83C23×C412yes—
675C2×Dic83C23×C412yes—
676C2×Dic83C23×C412yes—
677C2×Dic83C23×C412yes—
678C2×Dic83C23×C412yes—
679C2×Dic83C23×C412yes—
680C2×Dic83C23×C412yes—
681C2×Dic83H(5,𝔽2)12yes—
682C4×D83—44no—
683C4×D83—44no—
684C4×D83—44no—
685Dic166—44no—
686C22×C83—22no—
687C22×C83—22no—
688C22×C83—22no—
689C22×C83—22no—
690C22×C83—22no—
691C22×C83—22no—
692C22×C83—22no—
693C22×C83—22no—
694C22×C83—22no—
695C22×C83—22no—
696C22×C83—22no—
697C22×C83—22no—
698C22×C83—41no—
699C22×C83—41no—
700C22×C83—41no—
701C22×C83—41no—
702C22×C83—41no—
703C22×C83—41no—
704C22×C83—41no—
705C22×C83—41no—
706C22×C83—88no—
707C22×C83C4×#4114yes—
708C22×C83C24×C411yescharacteristic
709C22×C83C22×#4111yescharacteristic
710C22×C83C22×#4111yescharacteristic
711C22×C83C2×H(5,𝔽2)11yescharacteristic
712C22×C83#58511yescharacteristic
713C22×C83#58511yescharacteristic
714C22×C83#58511yescharacteristic
715C2×D83—22no—
716C2×D83—22no—
717C2×D83—22no—
718C2×D83—41no—
719C2×D83—41no—
720C2×D83—41no—
721C2×D83—41no—
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—41no—
731C4×C83—41no—
732C4×C83—41no—
733C4×C83—41no—
734Dic83—22no—
735Dic83—22no—
736Dic83—22no—
737Dic83—22no—
738Dic83—22no—
739Dic83—22no—
740Dic83—22no—
741Dic83—22no—
742Dic83—41no—
743Dic83—41no—
744Dic83—41no—
745Dic83—41no—
746Dic83—41no—
747Dic83—41no—
748Dic83—41no—
749#34315—831nomaximal, Sylow
750C2×C83—24no—
751C2×C83—42no—
752C2×C83—42no—
753C2×C83C2×C4×#4111yescharacteristic
754C2×C83#342811yescharacteristic
755C2×C83C4×H(5,𝔽2)11yescharacteristic
756C2×C83#350511yescharacteristic
757C2×C83#351011yescharacteristic
758C2×C83#351311yescharacteristic
759C2×C83#352111yescharacteristic
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⋊Q8—831no—
785C4×#123—831no—
786#2298—831no—
787#2290—831no—
788C2×#388—831no—
789#2274—831no—
790#2273D8311yescharacteristic, complemented
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⋊Q8—831no—
802C2×#120—831no—
803C2×C4×Q8—831no—
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⋊C4C2×D8311yescharacteristic
817C22×C22⋊C4C2×D8311yescharacteristic
818C22×C22⋊C4C2×D8311yescharacteristic
819C22×C42—831no—
820C22×C42—831no—
821#391—831no—
822#391—831no—
823#391—831no—
824#390—831no—
825#390—831no—
826#390—831no—
827#389—831no—
828#389—831no—
829#389—831no—
830#389—831no—
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#387—831no—
874#387—831no—
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#385—831no—
890#385—831no—
891#383—831no—
892#383—831no—
893#382—831no—
894#381—831no—
895#381—831no—
896#381—831no—
897#380—831no—
898#380—831no—
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⋊C4—831no—
916C4×C4⋊C4—831no—
917C4×C4⋊C4—831no—
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⋊C4C2×D8311yescharacteristic
933C4×C22⋊C4C2×D8311yescharacteristic
934C4×C22⋊C4C2×D8311yescharacteristic
935C4×C22⋊C4C2×D8311yescharacteristic
936C4×C22⋊C4C2×D8311yescharacteristic
937C4×C22⋊C4C2×D8311yescharacteristic
938C4×C22⋊C4C2×D8311yescharacteristic
939C4×C22⋊C4C2×D8311yescharacteristic
940C4×C22⋊C4C2×D8311yescharacteristic
941C4×C22⋊C4C2×D8311yescharacteristic
942C4×C22⋊C4C2×D8311yescharacteristic
943C4×C22⋊C4C2×D8311yescharacteristic
944#376—831no—
945#376—831no—
946C2×#95—831no—
947C2×#95—831no—
948C43—831no—
949C25C22×D8311yescharacteristic
950C22×Q8—831no—
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×C4C22×D8311yescharacteristic
962C23×C4C22×D8311yescharacteristic
963C23×C4C22×D8311yescharacteristic
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⋊Q8—838no—
975#120—838no—
976C4×Q8—3322no—
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—831no—
1004C2×C4⋊C4—831no—
1005C2×C4⋊C4—831no—
1006C2×C4⋊C4—831no—
1007C2×C4⋊C4—831no—
1008C2×C4⋊C4—831no—
1009C2×C4⋊C4—831no—
1010C2×C4⋊C4—831no—
1011C2×C4⋊C4—831no—
1012C2×C4⋊C4—1664no—
1013C2×C22⋊C4—24no—
1014C2×C22⋊C4—24no—
1015C2×C22⋊C4—3322no—
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—831no—
1039C2×C22⋊C4—831no—
1040C2×C22⋊C4—831no—
1041C2×C22⋊C4—831no—
1042C2×C22⋊C4—831no—
1043C2×C22⋊C4C4×D8318yescomplemented
1044C2×C22⋊C4C22×D8311yescharacteristic
1045C2×C22⋊C4C22×D8311yescharacteristic
1046C2×C22⋊C4C22×D8311yescharacteristic
1047C2×C22⋊C4C22×D8311yescharacteristic
1048C2×C22⋊C4C22×D8311yescharacteristic
1049C2×C22⋊C4C22×D8311yescharacteristic
1050C2×C22⋊C4C22×D8311yescharacteristic
1051C2×C22⋊C4C22×D8311yescharacteristic
1052C2×C22⋊C4C22×D8311yescharacteristic
1053C2×C22⋊C4C22×D8311yescharacteristic
1054C2×C22⋊C4C22×D8311yescharacteristic
1055C2×C22⋊C4C22×D8311yescharacteristic
1056C2×C42—3322no—
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#95—831no—
1122#95—831no—
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—22no—
1132C24—22no—
1133C24—41no—
1134C24—41no—
1135C24—41no—
1136C24—41no—
1137C24—831no—
1138C24C2×C4×D8314yes—
1139C24C23×D8311yescharacteristic
1140C24C23×D8311yescharacteristic
1141C24C23×D8311yescharacteristic
1142C2×Q8—3321no—
1143C2×Q8—3321no—
1144C2×Q8—834no—
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—22no—
1157C22×C4—41no—
1158C22×C4—41no—
1159C22×C4—41no—
1160C22×C4—41no—
1161C22×C4—41no—
1162C22×C4—41no—
1163C22×C4—41no—
1164C22×C4—41no—
1165C22×C4—41no—
1166C22×C4—41no—
1167C22×C4—41no—
1168C22×C4—41no—
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—3321no—
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—831no—
1196C22×C4—831no—
1197C22×C4—1662no—
1198C22×C4—1662no—
1199C22×C4—1662no—
1200C22×C4—1662no—
1201C22×C4—1662no—
1202C22×C4—1662no—
1203C22×C4—1662no—
1204C22×C4—1662no—
1205C22×C4C2×C4×D8314yes—
1206C22×C4C2×C4×D8314yes—
1207C22×C4#1305059014yes—
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—3321no—
1221C4⋊C4—3321no—
1222C4⋊C4—3321no—
1223C4⋊C4—3321no—
1224C4⋊C4—3321no—
1225C4⋊C4—3321no—
1226C4⋊C4—3321no—
1227C4⋊C4—3321no—
1228C4⋊C4—834no—
1229C4⋊C4—834no—
1230C4⋊C4—834no—
1231C4⋊C4—834no—
1232C4⋊C4—834no—
1233C4⋊C4—834no—
1234C4⋊C4—834no—
1235C4⋊C4—834no—
1236C4⋊C4—1662no—
1237C4⋊C4—1662no—
1238C4⋊C4—1662no—
1239C4⋊C4—1662no—
1240C4⋊C4—1662no—
1241C4⋊C4—1662no—
1242C4⋊C4—1662no—
1243C4⋊C4—1662no—
1244C4⋊C4—1662no—
1245C4⋊C4—1662no—
1246C22⋊C4—22no—
1247C22⋊C4—22no—
1248C22⋊C4—22no—
1249C22⋊C4—22no—
1250C22⋊C4—22no—
1251C22⋊C4—22no—
1252C22⋊C4—22no—
1253C22⋊C4—3321no—
1254C22⋊C4—3321no—
1255C22⋊C4—3321no—
1256C22⋊C4—3321no—
1257C22⋊C4—3321no—
1258C22⋊C4—3321no—
1259C22⋊C4—3321no—
1260C22⋊C4—3321no—
1261C22⋊C4—3321no—
1262C22⋊C4—3321no—
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—834no—
1272C22⋊C4—834no—
1273C22⋊C4—1662no—
1274C22⋊C4—1662no—
1275C22⋊C4—1662no—
1276C22⋊C4—1662no—
1277C22⋊C4—1662no—
1278C22⋊C4—1662no—
1279C22⋊C4C2×C4×D8314yes—
1280C22⋊C4C2×C4×D8314yes—
1281C22⋊C4C2×C4×D8314yes—
1282C22⋊C4C2×C4×D8314yes—
1283C22⋊C4#1305059014yes—
1284C42—41no—
1285C42—41no—
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—834no—
1304C42—834no—
1305C42—834no—
1306C42—1662no—
1307C42—1662no—
1308C42—1662no—
1309C42—1662no—
1310C42—1662no—
1311C42—1662no—
1312C42—1662no—
1313C23—21no—
1314C23—21no—
1315C23—21no—
1316C23—21no—
1317C23—21no—
1318C23—21no—
1319C23—21no—
1320C23—21no—
1321C23—21no—
1322C23—21no—
1323C23—21no—
1324C23—21no—
1325C23—21no—
1326C23—21no—
1327C23—21no—
1328C23—21no—
1329C23—28no—
1330C23—44no—
1331C23—44no—
1332C23—82no—
1333C23—82no—
1334C23—82no—
1335C23—82no—
1336C23—832no—
1337C23—1661no—
1338C23—1661no—
1339C23—1661no—
1340C23—1661no—
1341C23—1661no—
1342C23—1661no—
1343C23C22×C4×D8312yes—
1344C23C22×C4×D8312yes—
1345C23C22×C4×D8312yes—
1346C23C2×#1305059012yes—
1347C23C2×#1305059012yes—
1348C23C24×D8311yescharacteristic
1349Q8—3324no—
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—44no—
1382C2×C4—44no—
1383C2×C4—44no—
1384C2×C4—82no—
1385C2×C4—82no—
1386C2×C4—82no—
1387C2×C4—3324no—
1388C2×C4—3324no—
1389C2×C4—3324no—
1390C2×C4—3324no—
1391C2×C4—3324no—
1392C2×C4—832no—
1393C2×C4—832no—
1394C2×C4—832no—
1395C2×C4—832no—
1396C2×C4—832no—
1397C2×C4—832no—
1398C2×C4—832no—
1399C2×C4—832no—
1400C2×C4—6642no—
1401C2×C4—1661no—
1402C2×C4—1661no—
1403C2×C4—1661no—
1404C2×C4—1661no—
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—1668no—
1423C2×C4—1661no—
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×C4—1661no—
1439C2×C4C22×C4×D8312yes—
1440C2×C4C22×C4×D8312yes—
1441C2×C4C22×C4×D8312yes—
1442C2×C4C22×C4×D8312yes—
1443C2×C4C2×#1305059012yes—
1444C2×C4C2×#1305059012yes—
1445C2×C4C2×#1305059012yes—
1446C2×C4C2×#1305059012yes—
1447C22—22no—
1448C22—22no—
1449C22—22no—
1450C22—22no—
1451C22—22no—
1452C22—22no—
1453C22—22no—
1454C22—22no—
1455C22—22no—
1456C22—22no—
1457C22—22no—
1458C22—22no—
1459C22—41no—
1460C22—41no—
1461C22—41no—
1462C22—41no—
1463C22—41no—
1464C22—41no—
1465C22—41no—
1466C22—41no—
1467C22—88no—
1468C22—3321no—
1469C22—3321no—
1470C22—3321no—
1471C22—3321no—
1472C22—1662no—
1473C22—1662no—
1474C22—1662no—
1475C22C4×#1305059014yes—
1476C22C23×C4×D8311yescharacteristic
1477C22C22×#1305059011yescharacteristic
1478C22C22×#1305059011yescharacteristic
1479C22H(5,𝔽2)×D8311yescharacteristic
1480C22#1912853611yescharacteristic
1481C22#1912853611yescharacteristic
1482C22#1912853611yescharacteristic
1483C4—22no—
1484C4—22no—
1485C4—22no—
1486C4—22no—
1487C4—22no—
1488C4—22no—
1489C4—22no—
1490C4—22no—
1491C4—41no—
1492C4—41no—
1493C4—41no—
1494C4—41no—
1495C4—3321no—
1496C4—3321no—
1497C4—3321no—
1498C4—3321no—
1499C4—3321no—
1500C4—3321no—
1501C4—3321no—
1502C4—1662no—
1503C4—1662no—
1504C4—1662no—
1505C4—1662no—
1506C4—1662no—
1507C4—1662no—
1508C4—1662no—
1509C4—1662no—
1510C2—24no—
1511C2—42no—
1512C2—42no—
1513C2—3322no—
1514C2C2×C4×#1305059011yescharacteristic
1515C2#2492066111yescharacteristic
1516C2#2492066711yescharacteristic
1517C2#2492129311yescharacteristic
1518C2#2492135411yescharacteristic
1519C2#2492139111yescharacteristic
1520C2#2492151911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2273C2
socle, cosocleC23×C83C25
prime radicalC2×#14581761C22
hypercenter#2273D83
hypocenterC83#34315
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2273

Complements

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

NH ≅ G/Ntype
2. #24910597C2semidirect
3. #24910594C2semidirect
4. #24910584C2semidirect
5. #24910584C2semidirect
6. #24910541C2semidirect
7. #24910535C2semidirect
8. #24910488C2semidirect
9. #24910457C2semidirect
11. #24910437C2semidirect
12. #24910397C2semidirect
13. #24910354C2semidirect
14. #24910317C2semidirect
15. #24910312C2semidirect
16. #24910308C2semidirect
17. #24910271C2semidirect
18. #24910253C2semidirect
19. #24910240C2semidirect
20. #24910219C2semidirect
21. #24910134C2semidirect
23. C4×#14581785C2semidirect
24. C4×#14581769C2semidirect
25. C4×#14581774C2semidirect
26. #24909959C2semidirect
27. #24909909C2semidirect
28. C2×#19127595C2semidirect
29. #24909818C2semidirect
30. C4×(C22⋊D83)⋊C4C2semidirect
31. C83×#2273C2semidirect
32. #19128377C4semidirect
42. C2×C4×Dic166C22semidirect
56. C2×C42×D83C22semidirect
57. #19127607C22semidirect
58. #19127605C22semidirect
59. #19127605C22semidirect
63. #19127599C22semidirect
64. #19127599C22semidirect
65. #19127599C22semidirect
66. #19127598C22semidirect
84. #19127593C22semidirect
85. #19127592C22semidirect
86. #19127592C22semidirect
87. #19127592C22semidirect
88. #19127592C22semidirect
89. #19127590C22semidirect
95. #19127588C22semidirect
96. #19127588C22semidirect
97. #19127588C22semidirect
98. #19127586C22semidirect
99. #19127586C22semidirect
100. #19127586C22semidirect
101. #19127586C22semidirect
102. #19127585C22semidirect
103. #19127585C22semidirect
104. #19127585C22semidirect
105. #19127585C22semidirect
106. #19127584C22semidirect
107. #19127584C22semidirect
108. #19127583C22semidirect
109. #19127583C22semidirect
110. #19127583C22semidirect
119. #19127575C22semidirect
120. #19127575C22semidirect
121. #19127575C22semidirect
127. #19127568C22semidirect
128. #19127568C22semidirect
129. #19127565C22semidirect
131. #19127563C22semidirect
136. C4×Dic83⋊C4C22semidirect
137. C4×Dic83⋊C4C22semidirect
138. C4×Dic83⋊C4C22semidirect
139. C4×Dic83⋊C4C22semidirect
140. C4×Dic83⋊C4C22semidirect
141. C4×Dic83⋊C4C22semidirect
142. C4×Dic83⋊C4C22semidirect
143. C4×Dic83⋊C4C22semidirect
144. C4×Dic83⋊C4C22semidirect
145. C4×C4⋊Dic83C22semidirect
146. C4×C4⋊Dic83C22semidirect
147. C4×C4⋊Dic83C22semidirect
148. #19127552C22semidirect
149. #19127552C22semidirect
150. #19127552C22semidirect
151. #19127552C22semidirect
152. #19127552C22semidirect
153. #19127552C22semidirect
158. C4×(C2×D83)⋊C4C22semidirect
159. C4×(C2×D83)⋊C4C22semidirect
160. C4×(C2×D83)⋊C4C22semidirect
166. #19127548C22semidirect
167. #19127548C22semidirect
168. #19127547C22semidirect
169. #19127547C22semidirect
172. C42×Dic83C22semidirect
199. #14581785C2×C4semidirect
200. #14581785C2×C4semidirect
201. #14581778C2×C4semidirect
202. #14581776C2×C4semidirect
203. #14581775C2×C4semidirect
204. #14581774C2×C4semidirect
205. #14581771C2×C4semidirect
206. #14581769C2×C4semidirect
211. C4×C22⋊D83C2×C4semidirect
213. (C22⋊D83)⋊C4C2×C4semidirect
215. #14581751C2×C4semidirect
217. #14581748C2×C4semidirect
246. C2×C22⋊Dic83C2×C4semidirect
341. C2×C22⋊C4×C83C2×C4semidirect
790. #2273D83semidirect
792. C83#34315semidirect
1043. C2×C22⋊C4C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191283772
#249105972
#249105942
#249105842
#249105412
#249105352
#249104882
#249104572
#249104422
#249104372
#249103972
#249103542
#249103172
#249103122
#249103082
#249102712
#249102532
#249102402
#249102192
#249101342
#249101212
C4×#145817852
C4×#145817692
C4×#145817742
#249099592
#249099092
C2×#191275952
#249098182
C4×(C22⋊D83)⋊C42
C83×#22732
#3431583