Finite Group Databasebeta

← #14915039

Subgroups — #14915039

Order 2816.

3154 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623364C211yesmaximal, characteristic
2C2×#10623358C211yesmaximal, characteristic, complemented
3C2×#10623054C211yesmaximal, characteristic, complemented
4#13071659C212yesmaximal, complemented
5#13071652C212yesmaximal, complemented
6#13071648C212yesmaximal, complemented
7#13071641C212yesmaximal, complemented
8#13071637C212yesmaximal, complemented
9#13071630C212yesmaximal, complemented
10#13071626C212yesmaximal, complemented
11#13071619C212yesmaximal, complemented
12#13071317C214yesmaximal, complemented
13#13071232C211yesmaximal, characteristic, complemented
14#13071126C214yesmaximal, complemented
15#13071106C211yesmaximal, characteristic, complemented
16C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
17C11×#2297C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22#10623364C4116yescomplemented
23#10623358—28no—
24C2×#66999C2212yes—
25C2×Q8×Dic11C2212yes—
26C2×#66992C2214yes—
27C2×#66991C2212yes—
28C2×D4×Dic11C2212yes—
29C2×D4×Dic11C2214yes—
30C2×#66983C2212yes—
31C2×#66979C2211yescharacteristic
32C2×#66979C2212yes—
33C22×C4⋊Dic11C2212yes—
34C22×C4⋊Dic11C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C2×#66977C2212yes—
37C22×C4×Dic11C2212yes—
38#10623054—28no—
39C2×#66945C2212yes—
40C2×C4⋊C4×D11C2212yes—
41C2×(C22⋊D11)⋊C4C2214yes—
42C2×(C22⋊D11)⋊C4C2214yes—
43C2×C4×D44C2212yes—
44C2×C4×Dic22C2212yes—
45C11×#391C2211yescharacteristic
46C11×#391C2211yescharacteristic
47C11×#390C2211yescharacteristic
48C11×#390C2211yescharacteristic
49C11×#386C2212yes—
50C11×#386C2212yes—
51C4×C11×C22⋊C4C2212yes—
52C4×C11×C22⋊C4C2212yes—
53#10622826C2212yes—
54#10622826C2212yes—
55C2×C11⋊#95C2212yes—
56#10622586C2212yes—
57#10622586C2212yes—
58#10622571C2214yes—
59#10622570C2214yes—
60#10622569C2214yes—
61#10622559C2214yes—
62#10622558C2214yes—
63#10622557C2214yes—
64#10622555C2214yes—
65C22⋊C4×Dic11C2214yes—
66#10622552C2211yescharacteristic
67#10622552C2211yescharacteristic
68C4×(C2×D11)⋊C4C2212yes—
69C4×(C2×D11)⋊C4C2212yes—
70C4×C4⋊Dic11C2212yes—
71C4×C4⋊Dic11C2212yes—
72C4×C4⋊Dic11C2212yes—
73C4×C4⋊Dic11C2212yes—
74#10622542C2211yescharacteristic
75#10622542C2211yescharacteristic
76#10622541C2212yes—
77#10622541C2212yes—
78#10622283C2214yes—
79#10622282C2214yes—
80#10622281C2214yes—
81#10622279C2214yes—
82#10622268C2214yes—
83#10622265C2214yes—
84#10622262C2214yes—
85#10622260C2214yes—
86C2×C11×#41—24no—
87C2×C11×#41—24no—
88C2×C11×#41C2×C418yescomplemented
89C22×Q8×C11C2311yescharacteristic
90C22×D4×C11C2311yescharacteristic
91C22×D4×C11C2312yes—
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2312yes—
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C22×C22⋊D11C2312yes—
97C22×C22⋊D11C2314yes—
98C23×Dic11C2314yes—
99C23×Dic11C2312yes—
100C23×Dic11C2312yes—
101C2×#4339—24no—
102C2×#4339—24no—
103C2×#4339C2×C418yescomplemented
104C22×D44C2311yescharacteristic
105C22×C4×D11C2312yes—
106C22×C4×D11C2314yes—
107C22×Dic22C2311yescharacteristic
108C11×#117—24no—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C11×C22⋊C4C2312yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C42×C11—24no—
117C2×C42×C11C2312yes—
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C2×C42×C11C2311yescharacteristic
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125#66999C2×C4116yescomplemented
126Q8×Dic11—28no—
127#66992C2×C4132yescomplemented
128#66991C2×C4116yescomplemented
129D4×Dic11—216no—
130D4×Dic11—28no—
131#66983C2×C4116yescomplemented
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2312yes—
135C2×(C2×D11)⋊C4C2312yes—
136C2×(C2×D11)⋊C4C2312yes—
137C2×(C2×D11)⋊C4C2314yes—
138#66979—24no—
139#66979—28no—
140C2×C4⋊Dic11—28no—
141C2×C4⋊Dic11C2×C418yescomplemented
142C2×C4⋊Dic11D418yescomplemented
143C2×C4⋊Dic11C2314yes—
144C2×C4⋊Dic11C2311yescharacteristic
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2312yes—
147C2×C4⋊Dic11C2312yes—
148C2×C4⋊Dic11C2312yes—
149C2×C4⋊Dic11C2312yes—
150#66977C2×C4116yescomplemented
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×C4×Dic11—44no—
156C2×C4×Dic11C2314yes—
157C2×C4×Dic11C2314yes—
158C2×C4×Dic11C2314yes—
159C2×C4×Dic11C2312yes—
160C2×C4×Dic11C2314yes—
161#66945—28no—
162C4⋊C4×D11—28no—
163(C22⋊D11)⋊C4—216no—
164(C22⋊D11)⋊C4—48no—
165C4×D44—28no—
166C4×Dic22—28no—
167C11×#95C2312yes—
168C11×#95C2312yes—
169C11×#95C2312yes—
170C11×#95C2312yes—
171C11⋊#95C2312yes—
172C11⋊#95C2312yes—
173C11⋊#95C2312yes—
174C11⋊#95C2314yes—
175C11⋊#95C2314yes—
176C11⋊#95C2312yes—
177C11⋊#95C2314yes—
178C11⋊#95C2314yes—
179#34274—111nomaximal, Sylow
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11C2412yes—
183C11×#41—232no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11C22×C414yes—
187C2×D4×C11—24no—
188C2×D4×C11—24no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11C22×C414yes—
192C2×D4×C11C22×C418yes—
193C22×C4×C11—22no—
194C22×C4×C11—24no—
195C22×C4×C11—24no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—41no—
200C22×C4×C11—41no—
201C22×C4×C11C22×C418yes—
202C22×C4×C11C22×C414yes—
203C22×C4×C11C2×D414yes—
204C22×C4×C11#4114yes—
205C22×C4×C11C2411yescharacteristic
206C22×C4×C11C2411yescharacteristic
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2411yescharacteristic
211C22×C4×C11C2411yescharacteristic
212C22×C4×C11C2411yescharacteristic
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11C22×C418yes—
219C2×C22⋊D11C22×C4116yes—
220C22×Dic11—28no—
221C22×Dic11—42no—
222C22×Dic11—42no—
223C22×Dic11—42no—
224C22×Dic11—42no—
225C22×Dic11—44no—
226C22×Dic11—44no—
227C22×Dic11C22×C418yes—
228C22×Dic11C2×D418yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C22×Dic11C2414yes—
233C22×Dic11C2414yes—
234#4339—232no—
235C2×D44—22no—
236C2×D44—22no—
237C2×D44C22×C414yes—
238C2×C4×D11—28no—
239C2×C4×D11—24no—
240C2×C4×D11—24no—
241C2×C4×D11—44no—
242C2×C4×D11—44no—
243C2×C4×D11C22×C418yes—
244C2×Dic22—22no—
245C2×Dic22—22no—
246C2×Dic22C22×C414yes—
247C11×C4⋊C4—22no—
248C11×C4⋊C4—22no—
249C11×C22⋊C4—24no—
250C11×C22⋊C4—24no—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—42no—
253C11×C22⋊C4—42no—
254C42×C11—24no—
255C42×C11—22no—
256C42×C11—22no—
257C42×C11—22no—
258C42×C11—22no—
259C22⋊Dic11—28no—
260C22⋊Dic11—24no—
261C22⋊Dic11C22×C4116yes—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—42no—
266(C2×D11)⋊C4—42no—
267(C2×D11)⋊C4C22×C4116yes—
268C4⋊Dic11—28no—
269C4⋊Dic11—22no—
270C4⋊Dic11—22no—
271C4⋊Dic11C22×C418yes—
272C4⋊Dic11C22×C418yes—
273C4⋊Dic11C2×D418yes—
274C4⋊Dic11C2×D418yes—
275Dic11⋊C4—28no—
276Dic11⋊C4—44no—
277Dic11⋊C4—44no—
278Dic11⋊C4C22×C4116yes—
279C4×Dic11—28no—
280C4×Dic11—28no—
281C4×Dic11—24no—
282C4×Dic11—28no—
283C4×Dic11—44no—
284C2×#537—111no—
285C2×#520—111no—
286C2×#520—111no—
287#2363—112no—
288#2363—112no—
289#2362—112no—
290#2362—112no—
291#2361—112no—
292#2361—112no—
293#2360—112no—
294#2360—112no—
295#2325—114no—
296#2316—111no—
297C4×#121—114no—
298#2297—111no—
299#2297D1111yescharacteristic, complemented
300C2×C4×C4⋊C4—111no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11C23×C414yes—
312C23×C11C23×C412yes—
313C23×C11C22×D412yes—
314C23×C11C2×#4112yes—
315C23×C11C2511yescharacteristic
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11C23×C414yes—
323Q8×C11—28no—
324D4×C11—216no—
325D4×C11—28no—
326C2×C4×C11—28no—
327C2×C4×C11—22no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—22no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—216no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—22no—
346C2×C4×C11—44no—
347C2×C4×C11C4×D4116yescomplemented
348C2×C4×C11C23×C414yes—
349C2×C4×C11C23×C412yes—
350C2×C4×C11C23×C412yes—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C2×#4112yes—
354C2×C4×C11C2×#4112yes—
355C2×C4×C11H(5,𝔽2)12yes—
356C2×C4×C112−1+412yes—
357C22⋊D11—216no—
358C22⋊D11—416no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—24no—
362C2×Dic11—24no—
363C2×Dic11—24no—
364C2×Dic11—24no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—48no—
372C2×Dic11—48no—
373C2×Dic11—88no—
374C2×Dic11C23×C414yes—
375C2×Dic11C23×C418yes—
376C2×Dic11C22×D418yes—
377D44—28no—
378C4×D11—216no—
379C4×D11—88no—
380Dic22—28no—
381C22×#41—111no—
382C22×#41C2×D1111yescharacteristic
383#537—1116no—
384C2×C22⋊Q8—112no—
385C2×C22⋊Q8—112no—
386C2×#121—114no—
387C2×#121—112no—
388C2×#121—112no—
389#520—228no—
390#520—228no—
391C2×C4×Q8—112no—
392C2×C4×Q8—112no—
393C2×C4×D4—114no—
394C2×C4×D4—112no—
395C2×C4×D4—114no—
396C2×C4×D4—114no—
397C2×C4×D4—112no—
398C2×#117—111no—
399C2×#117—112no—
400C2×#117—112no—
401C2×#117C2×D1111yescharacteristic
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4—112no—
405C22×C4⋊C4—112no—
406C22×C42—112no—
407C22×C42C2×D1111yescharacteristic
408#391—111no—
409#391—111no—
410#391C2×D1111yescharacteristic
411#391C2×D1111yescharacteristic
412#390—114no—
413#390—111no—
414#390—111no—
415#390C2×D1111yescharacteristic
416#390C2×D1111yescharacteristic
417#389—112no—
418#389—112no—
419#389—112no—
420#389—112no—
421#389—114no—
422#388—114no—
423#388—114no—
424#388—114no—
425#388—114no—
426#387—114no—
427#387—114no—
428#386—112no—
429#386—112no—
430#386—114no—
431#386—114no—
432#386C2×D1112yes—
433#386C2×D1112yes—
434#385—114no—
435#385—114no—
436#380—114no—
437C4×C4⋊C4—112no—
438C4×C4⋊C4—112no—
439C4×C4⋊C4—112no—
440C4×C4⋊C4—112no—
441C4×C4⋊C4—114no—
442C4×C22⋊C4—114no—
443C4×C22⋊C4—112no—
444C4×C22⋊C4—112no—
445C4×C22⋊C4—114no—
446C4×C22⋊C4C2×D1112yes—
447C4×C22⋊C4C2×D1112yes—
448C2×#95—112no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—22no—
455C22×C11—24no—
456C22×C11—24no—
457C22×C11—24no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11C2×C4×D414yes—
463C22×C11C24×C411yescharacteristic
464C22×C11C23×D411yescharacteristic
465C22×C11C22×#4111yescharacteristic
466C22×C11C2×H(5,𝔽2)11yescharacteristic
467C22×C11C2×2−1+411yescharacteristic
468C22×C11#58511yescharacteristic
469C22×C11#58511yescharacteristic
470C2×D11—24no—
471C2×D11—24no—
472C2×D11—24no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C4×C11—24no—
478C4×C11—22no—
479C4×C11—22no—
480C4×C11—41no—
481C4×C11—41no—
482C4×C11—42no—
483C4×C11—42no—
484C4×C11C2×C4×D414yes—
485C4×C11C2×C4×D414yes—
486Dic11—24no—
487Dic11—28no—
488Dic11—28no—
489Dic11—42no—
490Dic11—42no—
491C2×#41—24no—
492C2×#41—24no—
493C2×#41—118no—
494C2×#41—224no—
495C2×#41—224no—
496C2×#41C4×D1118yescomplemented
497C22×Q8—111no—
498C22×Q8C22×D1111yescharacteristic
499C22×D4—112no—
500C22×D4—114no—
501C22×D4—111no—
502C22×D4C22×D1112yes—
503C22×D4C22×D1111yescharacteristic
504C23×C4—112no—
505C23×C4—112no—
506C23×C4—112no—
507C23×C4—114no—
508C23×C4—114no—
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1112yes—
511C23×C4C22×D1111yescharacteristic
512C23×C4C22×D1111yescharacteristic
513C22⋊Q8—1116no—
514C22⋊Q8—1116no—
515#121—1116no—
516#121—1132no—
517#121—1116no—
518C4×Q8—228no—
519C4×Q8—228no—
520C4×D4—228no—
521C4×D4—2216no—
522C4×D4—228no—
523C4×D4—2216no—
524C4×D4—448no—
525#117—24no—
526#117—228no—
527#117—228no—
528#117—224no—
529C2×C4⋊C4—118no—
530C2×C4⋊C4—118no—
531C2×C4⋊C4—112no—
532C2×C4⋊C4—112no—
533C2×C4⋊C4—112no—
534C2×C4⋊C4—112no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—111no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—111no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—114no—
542C2×C4⋊C4—228no—
543C2×C4⋊C4—228no—
544C2×C4⋊C4C22×D1111yescharacteristic
545C2×C4⋊C4C22×D1111yescharacteristic
546C2×C22⋊C4—114no—
547C2×C22⋊C4—114no—
548C2×C22⋊C4—112no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—112no—
552C2×C22⋊C4—112no—
553C2×C22⋊C4—112no—
554C2×C22⋊C4—112no—
555C2×C22⋊C4C22×D1112yes—
556C2×C22⋊C4C22×D1112yes—
557C2×C22⋊C4C22×D1112yes—
558C2×C22⋊C4C22×D1112yes—
559C2×C22⋊C4C22×D1112yes—
560C2×C42—24no—
561C2×C42—112no—
562C2×C42—114no—
563C2×C42—114no—
564C2×C42—114no—
565C2×C42—114no—
566C2×C42—444no—
567C2×C42C22×D1112yes—
568C2×C42C22×D1111yescharacteristic
569C2×C42C22×D1111yescharacteristic
570C2×C42C22×D1111yescharacteristic
571C2×C42C22×D1111yescharacteristic
572#95—114no—
573#95—114no—
574#95—112no—
575#95—112no—
576#95—114no—
577#95—114no—
578#95—112no—
579#95—112no—
580#95C22×D1112yes—
581#95C22×D1112yes—
582#95C22×D1112yes—
583#95C22×D1112yes—
584C2×C11—24no—
585C2×C11—44no—
586C2×C11C22×C4×D411yescharacteristic
587C2×C11C4×H(5,𝔽2)11yescharacteristic
588C2×C11C4×2−1+411yescharacteristic
589C2×C11#349211yescharacteristic
590C2×C11#349311yescharacteristic
591C2×C11#349611yescharacteristic
592C2×C11#349711yescharacteristic
593D11—44no—
594C24—112no—
595C24C23×D1112yes—
596C24C23×D1111yescharacteristic
597#41—232no—
598#41—2232no—
599C2×Q8—22no—
600C2×Q8—22no—
601C2×Q8—114no—
602C2×Q8—222no—
603C2×Q8—222no—
604C2×Q8C2×C4×D1114yes—
605C2×D4—24no—
606C2×D4—24no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—118no—
610C2×D4—1116no—
611C2×D4—114no—
612C2×D4—224no—
613C2×D4—224no—
614C2×D4—222no—
615C2×D4—222no—
616C2×D4—444no—
617C2×D4—444no—
618C2×D4C2×C4×D1118yes—
619C2×D4C2×C4×D1114yes—
620C22×C4—22no—
621C22×C4—24no—
622C22×C4—24no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—114no—
629C22×C4—112no—
630C22×C4—114no—
631C22×C4—118no—
632C22×C4—118no—
633C22×C4—118no—
634C22×C4—112no—
635C22×C4—112no—
636C22×C4—228no—
637C22×C4—228no—
638C22×C4—224no—
639C22×C4—224no—
640C22×C4—444no—
641C22×C4—444no—
642C22×C4—442no—
643C22×C4—442no—
644C22×C4—442no—
645C22×C4—442no—
646C22×C4—444no—
647C22×C4—444no—
648C22×C4C2×C4×D1118yes—
649C22×C4C2×C4×D1114yes—
650C22×C4D4×D1114yes—
651C22×C4#434114yes—
652C22×C4C23×D1111yescharacteristic
653C22×C4C23×D1111yescharacteristic
654C22×C4C23×D1112yes—
655C22×C4C23×D1112yes—
656C22×C4C23×D1112yes—
657C22×C4C23×D1111yescharacteristic
658C22×C4C23×D1111yescharacteristic
659C22×C4C23×D1111yescharacteristic
660C22×C4C23×D1111yescharacteristic
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—118no—
664C4⋊C4—118no—
665C4⋊C4—1116no—
666C4⋊C4—118no—
667C4⋊C4—118no—
668C4⋊C4—228no—
669C4⋊C4—228no—
670C4⋊C4—222no—
671C4⋊C4—222no—
672C4⋊C4—444no—
673C4⋊C4—444no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—1116no—
680C22⋊C4—1116no—
681C22⋊C4—228no—
682C22⋊C4—228no—
683C22⋊C4—224no—
684C22⋊C4—224no—
685C22⋊C4—224no—
686C22⋊C4—442no—
687C22⋊C4—442no—
688C42—24no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—228no—
694C42—228no—
695C42—224no—
696C42—228no—
697C42—444no—
698C11#3427411yescharacteristic, complemented, Sylow
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—114no—
710C23—222no—
711C23—222no—
712C23—222no—
713C23—222no—
714C23—222no—
715C23—222no—
716C23C22×C4×D1114yes—
717C23C22×C4×D1112yes—
718C23C2×D4×D1112yes—
719C23C2×#434112yes—
720C23C24×D1111yescharacteristic
721Q8—28no—
722Q8—228no—
723D4—216no—
724D4—28no—
725D4—2216no—
726D4—228no—
727D4—4416no—
728C2×C4—28no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—216no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—44no—
749C2×C4—118no—
750C2×C4—114no—
751C2×C4—118no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—224no—
755C2×C4—224no—
756C2×C4—224no—
757C2×C4—224no—
758C2×C4—2216no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—448no—
766C2×C4—448no—
767C2×C4—888no—
768C2×C4—888no—
769C2×C4(C22⋊D11)⋊C4116yescomplemented
770C2×C4C22×C4×D1114yes—
771C2×C4C22×C4×D1112yes—
772C2×C4C22×C4×D1112yes—
773C2×C4C2×D4×D1112yes—
774C2×C4C2×D4×D1112yes—
775C2×C4C2×#434112yes—
776C2×C4C2×#434112yes—
777C2×C4#6704212yes—
778C2×C4#6704312yes—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—224no—
793C22—224no—
794C22—224no—
795C22—442no—
796C22—442no—
797C22—442no—
798C22—442no—
799C22C2×(C22⋊D11)⋊C414yes—
800C22C23×C4×D1111yescharacteristic
801C22C22×D4×D1111yescharacteristic
802C22C22×#434111yescharacteristic
803C22C2×#6704211yescharacteristic
804C22C2×#6704311yescharacteristic
805C22#1062345311yescharacteristic
806C22#1062345311yescharacteristic
807C4—24no—
808C4—22no—
809C4—22no—
810C4—42no—
811C4—42no—
812C4—41no—
813C4—41no—
814C4—228no—
815C4—224no—
816C4—228no—
817C4—442no—
818C4—442no—
819C4C2×(C22⋊D11)⋊C414yes—
820C4C2×(C22⋊D11)⋊C414yes—
821C2—24no—
822C2—44no—
823C2—444no—
824C2C22×(C22⋊D11)⋊C411yescharacteristic
825C2C4×#6704211yescharacteristic
826C2C4×#6704311yescharacteristic
827C2#1308232211yescharacteristic
828C2#1308233311yescharacteristic
829C2#1308237811yescharacteristic
830C2#1308238211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2297C2
socle, cosocleC23×C11C25
prime radicalC2×#10623364C2
hypercenter#2297D11
hypocenterC11#34274
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. C2×#10623358C2semidirect
3. C2×#10623054C2semidirect
4. #13071659C2semidirect
5. #13071652C2semidirect
6. #13071648C2semidirect
7. #13071641C2semidirect
8. #13071637C2semidirect
9. #13071630C2semidirect
10. #13071626C2semidirect
11. #13071619C2semidirect
12. #13071317C2semidirect
13. #13071232C2semidirect
14. #13071126C2semidirect
15. #13071106C2semidirect
16. C2×C4×C4⋊Dic11C2semidirect
17. C11×#2297C2semidirect
22. #10623364C4semidirect
88. C2×C11×#41C2×C4semidirect
103. C2×#4339C2×C4semidirect
125. #66999C2×C4semidirect
127. #66992C2×C4semidirect
128. #66991C2×C4semidirect
131. #66983C2×C4semidirect
141. C2×C4⋊Dic11C2×C4semidirect
142. C2×C4⋊Dic11D4semidirect
150. #66977C2×C4semidirect
299. #2297D11semidirect
347. C2×C4×C11C4×D4semidirect
496. C2×#41C4×D11semidirect
698. C11#34274semidirect
769. C2×C4(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#106233642
C2×#106233582
C2×#106230542
#130716592
#130716522
#130716482
#130716412
#130716372
#130716302
#130716262
#130716192
#130713172
#130712322
#130711262
#130711062
C2×C4×C4⋊Dic112
C11×#22972
#3427411