Finite Group Databasebeta

← C2×#24910605 #35566985

Subgroups — C2×#24910605 #35566985

Order 21248.

2870 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581774C211yesmaximal, characteristic
2#24910605C2116yesmaximal, direct product factor
3C2×#19127601C211yesmaximal, characteristic
4C2×#19127599C211yesmaximal, characteristic, complemented
5C2×#19127598C211yesmaximal, characteristic, complemented
6C2×#19127595C211yesmaximal, characteristic, complemented
7C2×#19127593C211yesmaximal, characteristic, complemented
8C2×#19127592C211yesmaximal, characteristic, complemented
9C2×#19127584C211yesmaximal, characteristic, complemented
10C2×#19127582C211yesmaximal, characteristic, complemented
11C2×#19127578C211yesmaximal, characteristic
12C2×#19127576C211yesmaximal, characteristic, complemented
13C2×#19127573C211yesmaximal, characteristic, complemented
14C2×#19127560C211yesmaximal, characteristic, complemented
15C2×#19127558C211yesmaximal, characteristic, complemented
16C2×#388×C83C211yesmaximal, characteristic, complemented
17C23×C22⋊D83C2211yescharacteristic
18C24×Dic83C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C2×#14581774C4116yescomplemented
21C2×#14581774C2218yes—
22C22×C4⋊Dic83C2211yescharacteristic
23C22×C4⋊Dic83C2211yescharacteristic
24C22×C4⋊Dic83C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2211yescharacteristic
29C22×Dic83⋊C4C2211yescharacteristic
30C22×C22⋊Dic83C2211yescharacteristic
31C22×C22⋊Dic83C2211yescharacteristic
32C22×(C2×D83)⋊C4C2211yescharacteristic
33C22×(C2×D83)⋊C4C2211yescharacteristic
34C22×(C2×D83)⋊C4C2211yescharacteristic
35C22×(C2×D83)⋊C4C2211yescharacteristic
36C22×(C2×D83)⋊C4C2211yescharacteristic
37C22×C4×Dic83C2211yescharacteristic
38C22×C4×Dic83C2211yescharacteristic
39#19127601C2218yes—
40#19127599C2218yescomplemented
41#19127598C2218yescomplemented
42#19127595C2218yescomplemented
43#19127593C2218yescomplemented
44#19127592C2218yescomplemented
45#19127584C2218yescomplemented
46#19127582C2218yescomplemented
47#19127578C2218yes—
48#19127576C2218yescomplemented
49#19127573C2218yescomplemented
50#19127560C2218yescomplemented
51#19127558C2218yescomplemented
52C2×C83⋊#95C2211yescharacteristic
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C22×C4⋊C4×C83C2211yescharacteristic
61C22×C22⋊C4×C83C2211yescharacteristic
62C22×C22⋊C4×C83C2211yescharacteristic
63C22×C22⋊C4×C83C2211yescharacteristic
64C22×C42×C83C2211yescharacteristic
65#388×C83C2218yescomplemented
66C2×#95×C83C2211yescharacteristic
67C2×#95×C83C2211yescharacteristic
68C24×D83C2311yescharacteristic
69C22×C22⋊D83—42no—
70C22×C22⋊D83—42no—
71C22×C22⋊D83C2×C418yes—
72C22×C22⋊D83C2314yes—
73C23×Dic83—42no—
74C23×Dic83—42no—
75C23×Dic83—42no—
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2314yes—
84C22×C4×D83—42no—
85C22×C4×D83—42no—
86C22×C4×D83C2×C418yescomplemented
87C22×C4×D83C2314yes—
88#14581774C2×C4164yescomplemented
89C2×C4⋊Dic83—42no—
90C2×C4⋊Dic83—42no—
91C2×C4⋊Dic83C2×C418yescomplemented
92C2×C4⋊Dic83C2314yes—
93C2×C4⋊Dic83C2314yes—
94C2×C4⋊Dic83C2314yes—
95C2×Dic83⋊C4—42no—
96C2×Dic83⋊C4—42no—
97C2×Dic83⋊C4—42no—
98C2×Dic83⋊C4—42no—
99C2×Dic83⋊C4C2×C418yescomplemented
100C2×Dic83⋊C4C2314yes—
101C2×Dic83⋊C4C2314yes—
102C2×Dic83⋊C4C2314yes—
103C2×Dic83⋊C4C2314yes—
104C2×Dic83⋊C4C2314yes—
105C2×C22⋊Dic83—42no—
106C2×C22⋊Dic83C2×C418yes—
107C2×C22⋊Dic83C2314yes—
108C2×C22⋊Dic83C2314yes—
109C2×(C2×D83)⋊C4—42no—
110C2×(C2×D83)⋊C4—42no—
111C2×(C2×D83)⋊C4—42no—
112C2×(C2×D83)⋊C4—42no—
113C2×(C2×D83)⋊C4C2×C418yescomplemented
114C2×(C2×D83)⋊C4C2314yes—
115C2×(C2×D83)⋊C4C2314yes—
116C2×(C2×D83)⋊C4C2314yes—
117C2×(C2×D83)⋊C4C2314yes—
118C2×(C2×D83)⋊C4C2314yes—
119C2×C4×Dic83—42no—
120C2×C4×Dic83—42no—
121C2×C4×Dic83C2314yes—
122C2×C4×Dic83C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2314yes—
129C83⋊#95C2314yes—
130C83⋊#95C2314yes—
131C25×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C23×C4×C83C2311yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C2×C4⋊C4×C83—42no—
139C2×C4⋊C4×C83C2314yes—
140C2×C22⋊C4×C83—42no—
141C2×C22⋊C4×C83—42no—
142C2×C22⋊C4×C83C2×C418yes—
143C2×C22⋊C4×C83C2314yes—
144C2×C22⋊C4×C83C2314yes—
145C2×C22⋊C4×C83C2314yes—
146C2×C42×C83—42no—
147C2×C42×C83C2314yes—
148#95×C83C2314yes—
149#95×C83C2314yes—
150C23×D83—22no—
151C23×D83—22no—
152C23×D83—22no—
153C23×D83—22no—
154C23×D83—22no—
155C23×D83—22no—
156C23×D83C22×C414yes—
157C23×D83C2412yes—
158C2×C22⋊D83—416no—
159C2×C22⋊D83—44no—
160C2×C22⋊D83—44no—
161C2×C22⋊D83C22×C4116yes—
162C22×Dic83—22no—
163C22×Dic83—22no—
164C22×Dic83—22no—
165C22×Dic83—22no—
166C22×Dic83—22no—
167C22×Dic83—22no—
168C22×Dic83—22no—
169C22×Dic83—22no—
170C22×Dic83—22no—
171C22×Dic83—22no—
172C22×Dic83—22no—
173C22×Dic83—22no—
174C22×Dic83—22no—
175C22×Dic83—22no—
176C22×Dic83—22no—
177C22×Dic83—22no—
178C22×Dic83—22no—
179C22×Dic83—22no—
180C22×Dic83—44no—
181C22×Dic83—44no—
182C22×Dic83—44no—
183C22×Dic83—416no—
184C22×Dic83C22×C414yes—
185C22×Dic83C22×C414yes—
186C22×Dic83C22×C414yes—
187C22×Dic83C2412yes—
188C22×Dic83C2412yes—
189C22×Dic83C2412yes—
190C22×Dic83C2412yes—
191C22×Dic83C2412yes—
192C22×Dic83C2412yes—
193C22×Dic83C2412yes—
194C2×C4×D83—416no—
195C2×C4×D83—44no—
196C2×C4×D83—44no—
197C2×C4×D83C22×C4116yescomplemented
198C4⋊Dic83—44no—
199C4⋊Dic83—44no—
200C4⋊Dic83C22×C4116yescomplemented
201Dic83⋊C4—44no—
202Dic83⋊C4—44no—
203Dic83⋊C4—44no—
204Dic83⋊C4—44no—
205Dic83⋊C4C22×C4116yescomplemented
206C22⋊Dic83—44no—
207C22⋊Dic83C22×C4116yes—
208(C2×D83)⋊C4—44no—
209(C2×D83)⋊C4—44no—
210(C2×D83)⋊C4—44no—
211(C2×D83)⋊C4—44no—
212(C2×D83)⋊C4C22×C4116yescomplemented
213C4×Dic83—44no—
214C4×Dic83—44no—
215C24×C83—22no—
216C24×C83—22no—
217C24×C83—22no—
218C24×C83—22no—
219C24×C83—22no—
220C24×C83—22no—
221C24×C83C22×C414yes—
222C24×C83C2412yes—
223C24×C83C2411yescharacteristic
224C22×C4×C83—22no—
225C22×C4×C83—22no—
226C22×C4×C83—22no—
227C22×C4×C83—22no—
228C22×C4×C83—22no—
229C22×C4×C83—22no—
230C22×C4×C83—22no—
231C22×C4×C83—22no—
232C22×C4×C83—22no—
233C22×C4×C83—22no—
234C22×C4×C83—22no—
235C22×C4×C83—22no—
236C22×C4×C83—22no—
237C22×C4×C83—22no—
238C22×C4×C83—22no—
239C22×C4×C83—22no—
240C22×C4×C83C22×C414yes—
241C22×C4×C83C22×C414yes—
242C22×C4×C83C2412yes—
243C22×C4×C83C2412yes—
244C22×C4×C83C2412yes—
245C22×C4×C83C2412yes—
246C22×C4×C83C2412yes—
247C22×C4×C83C2412yes—
248C4⋊C4×C83—44no—
249C22⋊C4×C83—44no—
250C22⋊C4×C83—44no—
251C22⋊C4×C83C22×C4116yes—
252C42×C83—44no—
253C23×C83—28no—
254C23×C83—28no—
255C23×C83—28no—
256C23×C83—22no—
257C23×C83—22no—
258C23×C83—22no—
259C23×C83—22no—
260C23×C83—22no—
261C23×C83—22no—
262C23×C83—44no—
263C23×C83—44no—
264C23×C83—44no—
265C23×C83—44no—
266C23×C83C23×C414yes—
267C23×C83C23×C412yes—
268C23×C83H(5,𝔽2)12yes—
269C23×C83H(5,𝔽2)12yes—
270C23×C83H(5,𝔽2)12yes—
271C23×C83H(5,𝔽2)12yes—
272C23×C832−1+412yes—
273C23×C832−1+412yes—
274C23×C83C2511yescharacteristic
275C22×D83—28no—
276C22×D83—28no—
277C22×D83—28no—
278C22×D83—22no—
279C22×D83—22no—
280C22×D83—22no—
281C22×D83—22no—
282C22×D83—22no—
283C22×D83—22no—
284C22×D83—44no—
285C22×D83—44no—
286C22×D83—44no—
287C22×D83—44no—
288C22×D83C23×C414yes—
289C2×C4×C83—28no—
290C2×C4×C83—28no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
294C2×C4×C83—22no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—22no—
304C2×C4×C83—22no—
305C2×C4×C83—22no—
306C2×C4×C83—22no—
307C2×C4×C83—44no—
308C2×C4×C83—44no—
309C2×C4×C83—44no—
310C2×C4×C83—44no—
311C2×C4×C83C23×C414yes—
312C2×C4×C83C23×C414yes—
313C22⋊D83—416no—
314C2×Dic83—28no—
315C2×Dic83—28no—
316C2×Dic83—28no—
317C2×Dic83—22no—
318C2×Dic83—22no—
319C2×Dic83—22no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—22no—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—22no—
327C2×Dic83—22no—
328C2×Dic83—22no—
329C2×Dic83—22no—
330C2×Dic83—22no—
331C2×Dic83—22no—
332C2×Dic83—22no—
333C2×Dic83—22no—
334C2×Dic83—22no—
335C2×Dic83—416no—
336C2×Dic83—44no—
337C2×Dic83—44no—
338C2×Dic83—44no—
339C2×Dic83—44no—
340C2×Dic83C23×C414yes—
341C2×Dic83C23×C414yes—
342C2×Dic83C23×C414yes—
343C4×D83—416no—
344C22×C83—24no—
345C22×C83—24no—
346C22×C83—24no—
347C22×C83—416no—
348C22×C83—42no—
349C22×C83—42no—
350C22×C83—42no—
351C22×C83—42no—
352C22×C83#51814yes—
353C22×C83#52014yes—
354C22×C83#52014yes—
355C22×C83#56014yes—
356C22×C83#56214yes—
357C22×C83#56214yes—
358C22×C83#56314yes—
359C22×C83C24×C411yescharacteristic
360C22×C83C2×H(5,𝔽2)11yescharacteristic
361C22×C83C2×H(5,𝔽2)11yescharacteristic
362C22×C83C2×H(5,𝔽2)11yescharacteristic
363C22×C83C2×H(5,𝔽2)11yescharacteristic
364C22×C83C2×2−1+411yescharacteristic
365C22×C83C2×2−1+411yescharacteristic
366C2×D83—24no—
367C2×D83—24no—
368C2×D83—24no—
369C2×D83—416no—
370C2×D83—42no—
371C2×D83—42no—
372C2×D83—42no—
373C2×D83—42no—
374C4×C83—24no—
375C4×C83—24no—
376C4×C83—42no—
377C4×C83—42no—
378C4×C83—42no—
379C4×C83—42no—
380Dic83—24no—
381Dic83—24no—
382Dic83—24no—
383Dic83—42no—
384Dic83—42no—
385Dic83—42no—
386Dic83—42no—
387C2×#2376—831nomaximal, Sylow
388C2×C83—44no—
389C2×C83#237618yescomplemented
390C2×C83C2×#51811yescharacteristic
391C2×C83C2×#52011yescharacteristic
392C2×C83C2×#52011yescharacteristic
393C2×C83C2×#56011yescharacteristic
394C2×C83C2×#56211yescharacteristic
395C2×C83C2×#56211yescharacteristic
396C2×C83C2×#56311yescharacteristic
397D83—44no—
398C22×#123—831no—
399#2376—8316no—
400C2×#390—831no—
401C2×#389—831no—
402C2×#389—831no—
403C2×#388—831no—
404C2×#388—831no—
405C2×#388—831no—
406C2×#388D8311yescharacteristic, complemented
407C2×#387—831no—
408C2×#387—831no—
409C2×#386—831no—
410C2×#385—831no—
411C2×#385—831no—
412C2×#380—831no—
413C2×#380—831no—
414C83C2×#237611yescharacteristic, complemented, Sylow
415C23×D4—831no—
416C24×C4—831no—
417C24×C4—831no—
418C2×#123—8316no—
419C2×#123—838no—
420C22×C4⋊C4—831no—
421C22×C4⋊C4—831no—
422C22×C4⋊C4—831no—
423C22×C4⋊C4—831no—
424C22×C4⋊C4—831no—
425C22×C4⋊C4—831no—
426C22×C4⋊C4—831no—
427C22×C4⋊C4—831no—
428C22×C4⋊C4C2×D8311yescharacteristic
429C22×C22⋊C4—831no—
430C22×C22⋊C4—831no—
431C22×C22⋊C4—831no—
432C22×C22⋊C4—831no—
433C22×C22⋊C4—831no—
434C22×C22⋊C4—831no—
435C22×C22⋊C4—831no—
436C22×C22⋊C4C2×D8311yescharacteristic
437C22×C22⋊C4C2×D8311yescharacteristic
438C22×C22⋊C4C2×D8311yescharacteristic
439C22×C42—831no—
440C22×C42—831no—
441C22×C42C2×D8311yescharacteristic
442#390—838no—
443#389—838no—
444#389—838no—
445#388—838no—
446#388—838no—
447#388—838no—
448#388C2×D8318yescomplemented
449#387—838no—
450#387—838no—
451#386—838no—
452#385—838no—
453#385—838no—
454#380—838no—
455#380—838no—
456C2×#95—831no—
457C2×#95—831no—
458C2×#95—831no—
459C2×#95—831no—
460C2×#95—831no—
461C2×#95—831no—
462C2×#95—831no—
463C2×#95—831no—
464C2×#95C2×D8311yescharacteristic
465C2×#95C2×D8311yescharacteristic
466C25—831no—
467C25C22×D8311yescharacteristic
468C22×D4—3322no—
469C22×D4—3322no—
470C22×D4—838no—
471C22×D4—834no—
472C23×C4—3322no—
473C23×C4—3322no—
474C23×C4—3322no—
475C23×C4—3322no—
476C23×C4—3322no—
477C23×C4—834no—
478C23×C4—838no—
479C23×C4—834no—
480C23×C4—831no—
481C23×C4—831no—
482C23×C4—831no—
483C23×C4—831no—
484C23×C4—831no—
485C23×C4—831no—
486C23×C4—831no—
487C23×C4C22×D8311yescharacteristic
488C23×C4C22×D8311yescharacteristic
489C23×C4C22×D8311yescharacteristic
490C23×C4C22×D8311yescharacteristic
491C23×C4C22×D8311yescharacteristic
492C23×C4C22×D8311yescharacteristic
493#123—8364no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—3322no—
496C2×C4⋊C4—3322no—
497C2×C4⋊C4—3322no—
498C2×C4⋊C4—3322no—
499C2×C4⋊C4—3322no—
500C2×C4⋊C4—3322no—
501C2×C4⋊C4—834no—
502C2×C4⋊C4—834no—
503C2×C4⋊C4—834no—
504C2×C4⋊C4—834no—
505C2×C4⋊C4—834no—
506C2×C4⋊C4—834no—
507C2×C4⋊C4—838no—
508C2×C4⋊C4—838no—
509C2×C4⋊C4—834no—
510C2×C4⋊C4—834no—
511C2×C4⋊C4C22×D8314yes—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—3322no—
515C2×C22⋊C4—3322no—
516C2×C22⋊C4—3322no—
517C2×C22⋊C4—3322no—
518C2×C22⋊C4—3322no—
519C2×C22⋊C4—834no—
520C2×C22⋊C4—834no—
521C2×C22⋊C4—834no—
522C2×C22⋊C4—834no—
523C2×C22⋊C4—834no—
524C2×C22⋊C4—838no—
525C2×C22⋊C4—834no—
526C2×C22⋊C4—838no—
527C2×C22⋊C4—834no—
528C2×C22⋊C4C4×D8318yes—
529C2×C22⋊C4C22×D8314yes—
530C2×C22⋊C4C22×D8314yes—
531C2×C22⋊C4C22×D8314yes—
532C2×C42—42no—
533C2×C42—3322no—
534C2×C42—3322no—
535C2×C42—834no—
536C2×C42—834no—
537C2×C42C22×D8314yes—
538#95—834no—
539#95—834no—
540#95—834no—
541#95—834no—
542#95—834no—
543#95—834no—
544#95—834no—
545#95—834no—
546#95C22×D8314yes—
547#95C22×D8314yes—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—834no—
555C24—832no—
556C24—1662no—
557C24—1662no—
558C24—1662no—
559C24—1662no—
560C24—1662no—
561C24—1662no—
562C24C2×C4×D8314yes—
563C24C23×D8312yes—
564C24C23×D8311yescharacteristic
565C2×D4—33216no—
566C2×D4—3324no—
567C2×D4—3324no—
568C2×D4—8316no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—33216no—
586C22×C4—3324no—
587C22×C4—3324no—
588C22×C4—33216no—
589C22×C4—3324no—
590C22×C4—3324no—
591C22×C4—3324no—
592C22×C4—8316no—
593C22×C4—834no—
594C22×C4—834no—
595C22×C4—834no—
596C22×C4—832no—
597C22×C4—832no—
598C22×C4—832no—
599C22×C4—832no—
600C22×C4—832no—
601C22×C4—832no—
602C22×C4—832no—
603C22×C4—1662no—
604C22×C4—1662no—
605C22×C4—1662no—
606C22×C4—1662no—
607C22×C4—1662no—
608C22×C4—1662no—
609C22×C4—1662no—
610C22×C4—1662no—
611C22×C4—1662no—
612C22×C4—1662no—
613C22×C4—1662no—
614C22×C4—1662no—
615C22×C4—1662no—
616C22×C4—1662no—
617C22×C4—1662no—
618C22×C4—1662no—
619C22×C4—1662no—
620C22×C4—1662no—
621C22×C4C2×C4×D8314yes—
622C22×C4C2×C4×D8314yes—
623C22×C4C23×D8312yes—
624C22×C4C23×D8312yes—
625C22×C4C23×D8312yes—
626C22×C4C23×D8312yes—
627C22×C4C23×D8312yes—
628C22×C4C23×D8312yes—
629C4⋊C4—44no—
630C4⋊C4—3324no—
631C4⋊C4—3324no—
632C4⋊C4—3324no—
633C4⋊C4—3324no—
634C4⋊C4—3324no—
635C4⋊C4—3324no—
636C4⋊C4—8316no—
637C4⋊C4—8316no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—3324no—
641C22⋊C4—3324no—
642C22⋊C4—3324no—
643C22⋊C4—3324no—
644C22⋊C4—3324no—
645C22⋊C4—8316no—
646C22⋊C4—8316no—
647C22⋊C4C2×C4×D83116yes—
648C42—44no—
649C42—3324no—
650C42—3324no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—3324no—
665C23—3324no—
666C23—3324no—
667C23—3324no—
668C23—834no—
669C23—1668no—
670C23—1668no—
671C23—1668no—
672C23—1662no—
673C23—1662no—
674C23—1662no—
675C23—1662no—
676C23—1662no—
677C23—1662no—
678C23C22×C4×D8314yes—
679C23C22×C4×D8312yes—
680C23#1458183712yes—
681C23#1458183712yes—
682C23#1458183812yes—
683C23#1458183812yes—
684C23#1458183912yes—
685C23#1458183912yes—
686C23C24×D8311yescharacteristic
687D4—33216no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—33216no—
711C2×C4—33216no—
712C2×C4—3324no—
713C2×C4—3324no—
714C2×C4—3324no—
715C2×C4—3324no—
716C2×C4—834no—
717C2×C4—834no—
718C2×C4—834no—
719C2×C4—1662no—
720C2×C4—1662no—
721C2×C4—1662no—
722C2×C4—1662no—
723C2×C4—1662no—
724C2×C4—1662no—
725C2×C4—1662no—
726C2×C4—1662no—
727C2×C4—1662no—
728C2×C4—1662no—
729C2×C4—1662no—
730C2×C4—1662no—
731C2×C4—1668no—
732C2×C4—1668no—
733C2×C4—1668no—
734C2×C4—1662no—
735C2×C4—1662no—
736C2×C4—1662no—
737C2×C4—1662no—
738C2×C4—1662no—
739C2×C4—1662no—
740C2×C4C22×C4×D8314yes—
741C2×C4C22×C4×D8314yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—416no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—33216no—
751C22—3322no—
752C22—3322no—
753C22—3322no—
754C22—3322no—
755C22—1664no—
756C22—1664no—
757C22—1664no—
758C22#1912817314yes—
759C22#1912818014yes—
760C22#1912818114yes—
761C22#1912844114yes—
762C22#1912844514yes—
763C22#1912844614yes—
764C22#1912845314yes—
765C22C23×C4×D8311yescharacteristic
766C22C2×#1458183711yescharacteristic
767C22C2×#1458183711yescharacteristic
768C22C2×#1458183811yescharacteristic
769C22C2×#1458183811yescharacteristic
770C22C2×#1458183911yescharacteristic
771C22C2×#1458183911yescharacteristic
772C4—24no—
773C4—24no—
774C4—42no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—3322no—
779C4—3322no—
780C4—3322no—
781C4—3322no—
782C4—1664no—
783C4—1664no—
784C4—1664no—
785C2—44no—
786C2—3324no—
787C2#2491060518yesdirect product factor
788C2C2×#1912817311yescharacteristic
789C2C2×#1912818011yescharacteristic
790C2C2×#1912818111yescharacteristic
791C2C2×#1912844111yescharacteristic
792C2C2×#1912844511yescharacteristic
793C2C2×#1912844611yescharacteristic
794C2C2×#1912845311yescharacteristic
subgroupG/H
centerC24C23×D83
commutatorC22×C83C24×C4
FrattiniC23C24×D83
FittingC2×#388×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
cosocleC23×C83C25
hypercenterC2×#388D83
hypocenterC83C2×#2376
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #24910605C2direct (N × H)
4. C2×#19127599C2semidirect
5. C2×#19127598C2semidirect
6. C2×#19127595C2semidirect
7. C2×#19127593C2semidirect
8. C2×#19127592C2semidirect
9. C2×#19127584C2semidirect
10. C2×#19127582C2semidirect
12. C2×#19127576C2semidirect
13. C2×#19127573C2semidirect
14. C2×#19127560C2semidirect
15. C2×#19127558C2semidirect
16. C2×#388×C83C2semidirect
20. C2×#14581774C4semidirect
40. #19127599C22semidirect
41. #19127598C22semidirect
42. #19127595C22semidirect
43. #19127593C22semidirect
44. #19127592C22semidirect
45. #19127584C22semidirect
46. #19127582C22semidirect
48. #19127576C22semidirect
49. #19127573C22semidirect
50. #19127560C22semidirect
51. #19127558C22semidirect
65. #388×C83C22semidirect
86. C22×C4×D83C2×C4semidirect
88. #14581774C2×C4semidirect
91. C2×C4⋊Dic83C2×C4semidirect
99. C2×Dic83⋊C4C2×C4semidirect
113. C2×(C2×D83)⋊C4C2×C4semidirect
197. C2×C4×D83C22×C4semidirect
200. C4⋊Dic83C22×C4semidirect
205. Dic83⋊C4C22×C4semidirect
212. (C2×D83)⋊C4C22×C4semidirect
389. C2×C83#2376semidirect
406. C2×#388D83semidirect
414. C83C2×#2376semidirect
448. #388C2×D83semidirect
787. C2#24910605direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817742
#249106052
C2×#191276012
C2×#191275992
C2×#191275982
C2×#191275952
C2×#191275932
C2×#191275922
C2×#191275842
C2×#191275822
C2×#191275782
C2×#191275762
C2×#191275732
C2×#191275602
C2×#191275582
C2×#388×C832
C2×#237683