Finite Group Databasebeta

← C2×#24910233 #35563277

Subgroups — C2×#24910233 #35563277

Order 21248.

2614 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581785C211yesmaximal, characteristic
2#24910233C2116yesmaximal, direct product factor
3C2×#19127596C211yesmaximal, characteristic, complemented
4C2×#19127596C211yesmaximal, characteristic, complemented
5C2×#19127594C211yesmaximal, characteristic
6C2×#19127589C211yesmaximal, characteristic
7C2×#19127589C211yesmaximal, characteristic
8C2×#19127588C211yesmaximal, characteristic, complemented
9C2×#19127584C211yesmaximal, characteristic, complemented
10C2×#19127583C211yesmaximal, characteristic, complemented
11C2×#19127574C211yesmaximal, characteristic
12C2×#19127566C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
14C2×#19127552C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic83C211yesmaximal, characteristic
16C2×#385×C83C211yesmaximal, characteristic
17C2×#14581785C4116yescomplemented
18C2×#14581785C2218yes—
19C22×C4⋊Dic83C2211yescharacteristic
20C22×C4⋊Dic83C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×Dic83⋊C4C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×C22⋊Dic83C2211yescharacteristic
28C22×C22⋊Dic83C2211yescharacteristic
29C22×C22⋊Dic83C2211yescharacteristic
30C22×C22⋊Dic83C2211yescharacteristic
31C22×C4×Dic83C2211yescharacteristic
32C22×C4×Dic83C2211yescharacteristic
33C22×C4×Dic83C2211yescharacteristic
34C22×C4×Dic83C2211yescharacteristic
35C22×C4×Dic83C2211yescharacteristic
36C22×C4×Dic83C2211yescharacteristic
37#19127596C2218yescomplemented
38#19127596C2218yescomplemented
39#19127594C2218yes—
40#19127589C2218yes—
41#19127589C2218yes—
42#19127588C2218yescomplemented
43#19127584C2218yescomplemented
44#19127583C2218yescomplemented
45#19127574C2218yes—
46#19127566C2218yescomplemented
47C4⋊C4×Dic83C2218yescomplemented
48#19127552C2218yescomplemented
49C4×C22⋊Dic83C2218yes—
50C2×C83⋊#95C2211yescharacteristic
51C2×C83⋊#95C2211yescharacteristic
52C2×C83⋊#95C2211yescharacteristic
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C24×C4×C83C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63C22×C22⋊C4×C83C2211yescharacteristic
64C22×C22⋊C4×C83C2211yescharacteristic
65#385×C83C2218yes—
66C2×#95×C83C2211yescharacteristic
67C2×#95×C83C2211yescharacteristic
68C23×Dic83C2311yescharacteristic
69C23×Dic83C2311yescharacteristic
70C23×Dic83C2311yescharacteristic
71C23×Dic83C2311yescharacteristic
72C23×Dic83C2311yescharacteristic
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76#14581785C2×C4164yescomplemented
77C2×C4⋊Dic83—42no—
78C2×C4⋊Dic83C2×C418yescomplemented
79C2×C4⋊Dic83C2314yes—
80C2×C4⋊Dic83C2314yes—
81C2×Dic83⋊C4—24no—
82C2×Dic83⋊C4—24no—
83C2×Dic83⋊C4—42no—
84C2×Dic83⋊C4—42no—
85C2×Dic83⋊C4C2×C418yescomplemented
86C2×Dic83⋊C4C2×C418yescomplemented
87C2×Dic83⋊C4C2314yes—
88C2×Dic83⋊C4C2314yes—
89C2×Dic83⋊C4C2314yes—
90C2×Dic83⋊C4C2314yes—
91C2×Dic83⋊C4C2314yes—
92C2×Dic83⋊C4C2314yes—
93C2×C22⋊Dic83—24no—
94C2×C22⋊Dic83—42no—
95C2×C22⋊Dic83C2×C418yes—
96C2×C22⋊Dic83C2×C418yes—
97C2×C22⋊Dic83C2314yes—
98C2×C22⋊Dic83C2314yes—
99C2×C22⋊Dic83C2314yes—
100C2×C22⋊Dic83C2314yes—
101C2×C4×Dic83—24no—
102C2×C4×Dic83—42no—
103C2×C4×Dic83—42no—
104C2×C4×Dic83—42no—
105C2×C4×Dic83—42no—
106C2×C4×Dic83C2×C418yescomplemented
107C2×C4×Dic83C2314yes—
108C2×C4×Dic83C2314yes—
109C2×C4×Dic83C2314yes—
110C2×C4×Dic83C2314yes—
111C2×C4×Dic83C2314yes—
112C2×C4×Dic83C2314yes—
113C83⋊#95C2314yes—
114C83⋊#95C2314yes—
115C83⋊#95C2314yes—
116C83⋊#95C2314yes—
117C83⋊#95C2314yes—
118C83⋊#95C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C25×C83C2311yescharacteristic
124C23×C4×C83—24no—
125C23×C4×C83—42no—
126C23×C4×C83—42no—
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C23×C4×C83C2314yes—
134C2×C4⋊C4×C83—24no—
135C2×C4⋊C4×C83—42no—
136C2×C4⋊C4×C83C2314yes—
137C2×C4⋊C4×C83C2314yes—
138C2×C22⋊C4×C83—42no—
139C2×C22⋊C4×C83C2×C418yes—
140C2×C22⋊C4×C83C2314yes—
141C2×C22⋊C4×C83C2314yes—
142#95×C83C2314yes—
143#95×C83C2314yes—
144C22×Dic83—22no—
145C22×Dic83—22no—
146C22×Dic83—22no—
147C22×Dic83—22no—
148C22×Dic83—22no—
149C22×Dic83—22no—
150C22×Dic83—22no—
151C22×Dic83—22no—
152C22×Dic83—22no—
153C22×Dic83—22no—
154C22×Dic83—22no—
155C22×Dic83—22no—
156C22×Dic83—22no—
157C22×Dic83—22no—
158C22×Dic83—22no—
159C22×Dic83—22no—
160C22×Dic83—22no—
161C22×Dic83—22no—
162C22×Dic83—22no—
163C22×Dic83C22×C414yes—
164C22×Dic83C22×C414yes—
165C22×Dic83C22×C414yes—
166C22×Dic83C22×C414yes—
167C22×Dic83#4114yes—
168C22×Dic83C2412yes—
169C22×Dic83C2412yes—
170C22×Dic83C2412yes—
171C22×Dic83C2412yes—
172C22×Dic83C2412yes—
173C22×Dic83C2412yes—
174C22×Dic83C2412yes—
175C22×Dic83C2412yes—
176C4⋊Dic83—44no—
177C4⋊Dic83C22×C4116yescomplemented
178Dic83⋊C4—28no—
179Dic83⋊C4—28no—
180Dic83⋊C4—44no—
181Dic83⋊C4—44no—
182Dic83⋊C4C22×C4116yescomplemented
183Dic83⋊C4C22×C4116yescomplemented
184C22⋊Dic83—28no—
185C22⋊Dic83—44no—
186C22⋊Dic83C22×C4116yes—
187C22⋊Dic83C22×C4116yes—
188C4×Dic83—28no—
189C4×Dic83—44no—
190C4×Dic83—44no—
191C4×Dic83—44no—
192C4×Dic83—44no—
193C4×Dic83C22×C4116yescomplemented
194C24×C83—22no—
195C24×C83—22no—
196C24×C83—22no—
197C24×C83—22no—
198C24×C83—22no—
199C24×C83—22no—
200C24×C83C22×C414yes—
201C24×C83C2412yes—
202C24×C83C2411yescharacteristic
203C22×C4×C83—22no—
204C22×C4×C83—22no—
205C22×C4×C83—22no—
206C22×C4×C83—22no—
207C22×C4×C83—22no—
208C22×C4×C83—22no—
209C22×C4×C83—22no—
210C22×C4×C83—22no—
211C22×C4×C83—22no—
212C22×C4×C83—22no—
213C22×C4×C83—22no—
214C22×C4×C83—22no—
215C22×C4×C83—22no—
216C22×C4×C83—22no—
217C22×C4×C83—22no—
218C22×C4×C83—28no—
219C22×C4×C83—44no—
220C22×C4×C83—44no—
221C22×C4×C83—416no—
222C22×C4×C83C22×C414yes—
223C22×C4×C83C22×C414yes—
224C22×C4×C83#4114yes—
225C22×C4×C83C2412yes—
226C22×C4×C83C2412yes—
227C22×C4×C83C2412yes—
228C22×C4×C83C2412yes—
229C22×C4×C83C2412yes—
230C22×C4×C83C2412yes—
231C4⋊C4×C83—28no—
232C4⋊C4×C83—44no—
233C22⋊C4×C83—44no—
234C22⋊C4×C83C22×C4116yes—
235C23×C83—28no—
236C23×C83—28no—
237C23×C83—28no—
238C23×C83—22no—
239C23×C83—22no—
240C23×C83—22no—
241C23×C83—22no—
242C23×C83—22no—
243C23×C83—22no—
244C23×C83—44no—
245C23×C83—44no—
246C23×C83—44no—
247C23×C83—44no—
248C23×C83C23×C414yes—
249C23×C83C23×C412yes—
250C23×C83C2×#4112yes—
251C23×C83C2×#4112yes—
252C23×C83H(5,𝔽2)12yes—
253C23×C83H(5,𝔽2)12yes—
254C23×C832−1+412yes—
255C23×C832−1+412yes—
256C23×C83C2511yescharacteristic
257C2×C4×C83—28no—
258C2×C4×C83—28no—
259C2×C4×C83—28no—
260C2×C4×C83—22no—
261C2×C4×C83—22no—
262C2×C4×C83—22no—
263C2×C4×C83—22no—
264C2×C4×C83—22no—
265C2×C4×C83—22no—
266C2×C4×C83—22no—
267C2×C4×C83—22no—
268C2×C4×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—22no—
274C2×C4×C83—22no—
275C2×C4×C83—416no—
276C2×C4×C83—44no—
277C2×C4×C83—44no—
278C2×C4×C83—44no—
279C2×C4×C83C23×C414yes—
280C2×C4×C83C23×C414yes—
281C2×C4×C83C2×#4114yes—
282C2×Dic83—28no—
283C2×Dic83—28no—
284C2×Dic83—28no—
285C2×Dic83—28no—
286C2×Dic83—28no—
287C2×Dic83—22no—
288C2×Dic83—22no—
289C2×Dic83—22no—
290C2×Dic83—22no—
291C2×Dic83—22no—
292C2×Dic83—22no—
293C2×Dic83—22no—
294C2×Dic83—22no—
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—44no—
307C2×Dic83—44no—
308C2×Dic83—44no—
309C2×Dic83C23×C414yes—
310C2×Dic83C23×C414yes—
311C2×Dic83C23×C414yes—
312C2×Dic83C23×C414yes—
313C2×Dic83C2×#4114yes—
314C22×C83—24no—
315C22×C83—24no—
316C22×C83—24no—
317C22×C83—416no—
318C22×C83—42no—
319C22×C83—42no—
320C22×C83—42no—
321C22×C83—42no—
322C22×C83C4×#4114yes—
323C22×C83#52014yes—
324C22×C83#52014yes—
325C22×C83#53814yes—
326C22×C83#53914yes—
327C22×C83#54114yes—
328C22×C83#54214yes—
329C22×C83C24×C411yescharacteristic
330C22×C83C22×#4111yescharacteristic
331C22×C83C22×#4111yescharacteristic
332C22×C83C2×H(5,𝔽2)11yescharacteristic
333C22×C83C2×H(5,𝔽2)11yescharacteristic
334C22×C83C2×2−1+411yescharacteristic
335C22×C83C2×2−1+411yescharacteristic
336C4×C83—24no—
337C4×C83—24no—
338C4×C83—24no—
339C4×C83—42no—
340C4×C83—42no—
341C4×C83—42no—
342Dic83—24no—
343Dic83—24no—
344Dic83—24no—
345Dic83—24no—
346Dic83—24no—
347Dic83—42no—
348Dic83—42no—
349Dic83—42no—
350C2×#2334—831nomaximal, Sylow
351C2×C83—44no—
352C2×C83#233418yescomplemented
353C2×C83C2×C4×#4111yescharacteristic
354C2×C83C2×#52011yescharacteristic
355C2×C83C2×#52011yescharacteristic
356C2×C83C2×#53811yescharacteristic
357C2×C83C2×#53911yescharacteristic
358C2×C83C2×#54111yescharacteristic
359C2×C83C2×#54211yescharacteristic
360C22×#126—831no—
361#2334—8316no—
362C2×#389—831no—
363C2×#389—831no—
364C2×#388—831no—
365C2×#388—831no—
366C2×#388—831no—
367C2×#387—831no—
368C2×#387—831no—
369C2×#387—831no—
370C2×#385—831no—
371C2×#385D8311yescharacteristic
372C2×#382—831no—
373C2×C4×C4⋊C4—831no—
374C2×C4×C4⋊C4—831no—
375C2×C4×C22⋊C4—831no—
376C83C2×#233411yescharacteristic, complemented, Sylow
377C24×C4C2×D8311yescharacteristic
378C2×#126—8316no—
379C2×#126—838no—
380C22×C4⋊C4—831no—
381C22×C4⋊C4—831no—
382C22×C4⋊C4—831no—
383C22×C4⋊C4—831no—
384C22×C4⋊C4—831no—
385C22×C4⋊C4—831no—
386C22×C4⋊C4—831no—
387C22×C4⋊C4—831no—
388C22×C4⋊C4C2×D8311yescharacteristic
389C22×C4⋊C4C2×D8311yescharacteristic
390C22×C22⋊C4—831no—
391C22×C22⋊C4—831no—
392C22×C22⋊C4—831no—
393C22×C22⋊C4—831no—
394C22×C22⋊C4C2×D8311yescharacteristic
395C22×C22⋊C4C2×D8311yescharacteristic
396C22×C42—831no—
397C22×C42—831no—
398C22×C42—831no—
399C22×C42—831no—
400C22×C42—831no—
401C22×C42—831no—
402#389—838no—
403#389—838no—
404#388—838no—
405#388—838no—
406#388—838no—
407#387—838no—
408#387—838no—
409#387—838no—
410#385—838no—
411#385C2×D8318yes—
412#382—838no—
413C4×C4⋊C4—838no—
414C4×C4⋊C4—838no—
415C4×C22⋊C4—838no—
416C2×#95—831no—
417C2×#95—831no—
418C2×#95—831no—
419C2×#95—831no—
420C2×#95—831no—
421C2×#95—831no—
422C2×#95—831no—
423C2×#95—831no—
424C2×#95—831no—
425C2×#95—831no—
426C2×#95C2×D8311yescharacteristic
427C2×#95C2×D8311yescharacteristic
428C25C22×D8311yescharacteristic
429C23×C4—24no—
430C23×C4—42no—
431C23×C4—42no—
432C23×C4—831no—
433C23×C4—831no—
434C23×C4—831no—
435C23×C4—831no—
436C23×C4—831no—
437C23×C4—831no—
438C23×C4—831no—
439C23×C4—831no—
440C23×C4C22×D8311yescharacteristic
441C23×C4C22×D8311yescharacteristic
442C23×C4C22×D8311yescharacteristic
443C23×C4C22×D8311yescharacteristic
444C23×C4C22×D8311yescharacteristic
445C23×C4C22×D8311yescharacteristic
446C23×C4C22×D8314yes—
447#126—8364no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—3322no—
451C2×C4⋊C4—3322no—
452C2×C4⋊C4—3322no—
453C2×C4⋊C4—834no—
454C2×C4⋊C4—834no—
455C2×C4⋊C4—834no—
456C2×C4⋊C4—838no—
457C2×C4⋊C4—838no—
458C2×C4⋊C4—838no—
459C2×C4⋊C4—834no—
460C2×C4⋊C4—834no—
461C2×C4⋊C4—834no—
462C2×C4⋊C4—834no—
463C2×C4⋊C4—834no—
464C2×C4⋊C4—1664no—
465C2×C4⋊C4—1664no—
466C2×C4⋊C4C22×D8314yes—
467C2×C4⋊C4C22×D8314yes—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—3322no—
470C2×C22⋊C4—834no—
471C2×C22⋊C4—838no—
472C2×C22⋊C4—838no—
473C2×C22⋊C4—834no—
474C2×C22⋊C4—834no—
475C2×C22⋊C4—834no—
476C2×C22⋊C4—1664no—
477C2×C22⋊C4C4×D8318yes—
478C2×C22⋊C4C22×D8314yes—
479C2×C22⋊C4C22×D8314yes—
480C2×C42—3322no—
481C2×C42—3322no—
482C2×C42—3322no—
483C2×C42—3322no—
484C2×C42—834no—
485C2×C42—834no—
486C2×C42—834no—
487C2×C42—834no—
488C2×C42—838no—
489C2×C42—834no—
490C2×C42—834no—
491C2×C42—1664no—
492#95—834no—
493#95—834no—
494#95—834no—
495#95—834no—
496#95—834no—
497#95—834no—
498#95—834no—
499#95—834no—
500#95—834no—
501#95—834no—
502#95C22×D8314yes—
503#95C22×D8314yes—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24C2×C4×D8314yes—
511C24C23×D8312yes—
512C24C23×D8311yescharacteristic
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—28no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—416no—
532C22×C4—834no—
533C22×C4—834no—
534C22×C4—834no—
535C22×C4—834no—
536C22×C4—834no—
537C22×C4—832no—
538C22×C4—832no—
539C22×C4—832no—
540C22×C4—832no—
541C22×C4—832no—
542C22×C4—832no—
543C22×C4—832no—
544C22×C4—832no—
545C22×C4—1662no—
546C22×C4—1662no—
547C22×C4—1662no—
548C22×C4—1662no—
549C22×C4—1662no—
550C22×C4—1662no—
551C22×C4—1662no—
552C22×C4—1662no—
553C22×C4—1662no—
554C22×C4—1662no—
555C22×C4—1662no—
556C22×C4—1662no—
557C22×C4—1662no—
558C22×C4—1662no—
559C22×C4—1662no—
560C22×C4—1662no—
561C22×C4—1662no—
562C22×C4—1662no—
563C22×C4—1662no—
564C22×C4C2×C4×D8314yes—
565C22×C4C2×C4×D8314yes—
566C22×C4#1305058914yes—
567C22×C4C23×D8312yes—
568C22×C4C23×D8312yes—
569C22×C4C23×D8312yes—
570C22×C4C23×D8312yes—
571C22×C4C23×D8312yes—
572C22×C4C23×D8312yes—
573C4⋊C4—28no—
574C4⋊C4—44no—
575C4⋊C4—3324no—
576C4⋊C4—3324no—
577C4⋊C4—3324no—
578C4⋊C4—8316no—
579C4⋊C4—8316no—
580C4⋊C4—8316no—
581C4⋊C4—1668no—
582C4⋊C4—1668no—
583C22⋊C4—44no—
584C22⋊C4—3324no—
585C22⋊C4—8316no—
586C22⋊C4—8316no—
587C22⋊C4—1668no—
588C22⋊C4C2×C4×D83116yes—
589C42—3324no—
590C42—3324no—
591C42—3324no—
592C42—3324no—
593C42—8316no—
594C42—1668no—
595C23—28no—
596C23—28no—
597C23—28no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23C22×C4×D8314yes—
609C23C22×C4×D8312yes—
610C23#41×D8312yes—
611C23C2×#1305058912yes—
612C23#1458183712yes—
613C23#1458183712yes—
614C23#1458183912yes—
615C23#1458184012yes—
616C23C24×D8311yescharacteristic
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—28no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—416no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—3324no—
640C2×C4—3324no—
641C2×C4—3324no—
642C2×C4—834no—
643C2×C4—834no—
644C2×C4—834no—
645C2×C4—834no—
646C2×C4—834no—
647C2×C4—1662no—
648C2×C4—1662no—
649C2×C4—1662no—
650C2×C4—1662no—
651C2×C4—1662no—
652C2×C4—1662no—
653C2×C4—1662no—
654C2×C4—1662no—
655C2×C4—1662no—
656C2×C4—1668no—
657C2×C4—1668no—
658C2×C4—1668no—
659C2×C4—1668no—
660C2×C4—1662no—
661C2×C4—1662no—
662C2×C4—1662no—
663C2×C4—1662no—
664C2×C4—1662no—
665C2×C4—1662no—
666C2×C4—1662no—
667C2×C4—1662no—
668C2×C4—1662no—
669C2×C4—1662no—
670C2×C4—1668no—
671C2×C4C22×C4×D8314yes—
672C2×C4C22×C4×D8314yes—
673C2×C4C2×#1305058914yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—42no—
678C22—416no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22C4×#1305058914yes—
683C22#1912818014yes—
684C22#1912818214yes—
685C22#1912828614yes—
686C22#1912829414yes—
687C22#1912831114yes—
688C22#1912832114yes—
689C22C23×C4×D8311yescharacteristic
690C22C2×#41×D8311yescharacteristic
691C22C22×#1305058911yescharacteristic
692C22C2×#1458183711yescharacteristic
693C22C2×#1458183711yescharacteristic
694C22C2×#1458183911yescharacteristic
695C22C2×#1458184011yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—3322no—
703C4—3322no—
704C4—3322no—
705C4—1664no—
706C4—1664no—
707C4—1664no—
708C4—1664no—
709C4—1664no—
710C2—44no—
711C2#2491023318yesdirect product factor
712C2C2×C4×#1305058911yescharacteristic
713C2C2×#1912818011yescharacteristic
714C2C2×#1912818211yescharacteristic
715C2C2×#1912828611yescharacteristic
716C2C2×#1912829411yescharacteristic
717C2C2×#1912831111yescharacteristic
718C2C2×#1912832111yescharacteristic
subgroupG/H
centerC24C23×D83
commutatorC22×C83C24×C4
FrattiniC23C24×D83
FittingC2×#385×C83C2
socleC24×C83C24
prime radicalC25×C83C23
cosocleC23×C83C25
hypercenterC2×#385D83
hypocenterC83C2×#2334
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #24910233C2direct (N × H)
3. C2×#19127596C2semidirect
4. C2×#19127596C2semidirect
8. C2×#19127588C2semidirect
9. C2×#19127584C2semidirect
10. C2×#19127583C2semidirect
12. C2×#19127566C2semidirect
13. C2×C4⋊C4×Dic83C2semidirect
14. C2×#19127552C2semidirect
17. C2×#14581785C4semidirect
37. #19127596C22semidirect
38. #19127596C22semidirect
42. #19127588C22semidirect
43. #19127584C22semidirect
44. #19127583C22semidirect
46. #19127566C22semidirect
47. C4⋊C4×Dic83C22semidirect
48. #19127552C22semidirect
76. #14581785C2×C4semidirect
78. C2×C4⋊Dic83C2×C4semidirect
85. C2×Dic83⋊C4C2×C4semidirect
86. C2×Dic83⋊C4C2×C4semidirect
106. C2×C4×Dic83C2×C4semidirect
177. C4⋊Dic83C22×C4semidirect
182. Dic83⋊C4C22×C4semidirect
183. Dic83⋊C4C22×C4semidirect
193. C4×Dic83C22×C4semidirect
352. C2×C83#2334semidirect
376. C83C2×#2334semidirect
711. C2#24910233direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817852
#249102332
C2×#191275962
C2×#191275942
C2×#191275892
C2×#191275882
C2×#191275842
C2×#191275832
C2×#191275742
C2×#191275662
C2×C4⋊C4×Dic832
C2×#191275522
C2×C4×C22⋊Dic832
C2×#385×C832
C2×#233483