Finite Group Databasebeta

← #14922660

Subgroups — #14922660

Order 2816.

3390 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623363C211yesmaximal, characteristic, complemented
2C2×#10623322C211yesmaximal, characteristic, complemented
3C2×#41×Dic11C211yesmaximal, characteristic, complemented
4#13072217C212yesmaximal, complemented
5#13072206C212yesmaximal, complemented
6#13072195C212yesmaximal, complemented
7#13072184C212yesmaximal, complemented
8#13072171C214yesmaximal, complemented
9#13072156C214yesmaximal, complemented
10#13071858C214yesmaximal, complemented
11C4×#66992C214yesmaximal, complemented
12#13071104C211yesmaximal, characteristic, complemented
13#13071098C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
15C2×C11×#525C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C11×#525—28no—
20C2×C11×#123C2212yes—
21C2×C11×C22⋊Q8C2212yes—
22C2×C11×#121C2212yes—
23C2×C11×#120C2212yes—
24C2×C4×D4×C11C2214yes—
25C2×C11×#117C2211yescharacteristic
26C2×#67006C2212yes—
27C22×C22⋊Dic11C2212yes—
28#10623363—28no—
29#41×Dic11—28no—
30C2×#67000C2211yescharacteristic, complemented
31C2×Q8×Dic11C2212yescomplemented
32C2×#66997C2211yescharacteristic, complemented
33C2×#66993C2211yescharacteristic, complemented
34C2×#66992C2214yes—
35C2×#66992C2214yes—
36C2×#66989C2211yescharacteristic, complemented
37C2×D4×Dic11C2214yes—
38C2×D4×Dic11C2212yescomplemented
39#10623322—28no—
40C2×#66983C2212yes—
41C2×#66982C2212yes—
42C2×C4×C22⋊D11C2214yes—
43C2×C4×C22⋊D11C2214yescomplemented
44C2×#66979C2211yescharacteristic
45C2×#66979C2212yescomplemented
46C2×#66977C2212yes—
47C22×C4×Dic11C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic
49C22×C4×Dic11C2212yescomplemented
50#10622836C2214yes—
51#10622835C2214yes—
52#10622833C2214yes—
53C4×C22⋊Dic11C2212yes—
54C4×C22⋊Dic11C2212yes—
55C4×C22⋊Dic11C2212yes—
56C4×C22⋊Dic11C2212yes—
57C2×C11⋊#95C2212yes—
58#10622607C2214yescomplemented
59#10622603C2214yescomplemented
60#10622601C2212yescomplemented
61#10622597C2214yescomplemented
62#10622587C2212yescomplemented
63#10622586C2212yescomplemented
64#10622586C2212yescomplemented
65#10622585C2214yescomplemented
66#10622574C2214yes—
67#10622572C2214yescomplemented
68#10622571C2214yes—
69#10622571C2214yescomplemented
70#10622570C2214yes—
71#10622565C2214yescomplemented
72#10622561C2214yes—
73#10622559C2214yes—
74#10622558C2214yes—
75#10622555C2214yescomplemented
76C4×(C2×D11)⋊C4C2212yescomplemented
77C4×(C2×D11)⋊C4C2212yescomplemented
78C4×Dic11⋊C4C2214yescomplemented
79C25×C11C2311yescharacteristic
80C2×C11×#41—24no—
81C2×C11×#41—24no—
82C2×C11×#41D418yescomplemented
83C22×Q8×C11C2311yescharacteristic
84C22×D4×C11C2314yes—
85C22×D4×C11C2312yes—
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11—24no—
88C23×C4×C11—24no—
89C23×C4×C11—24no—
90C23×C4×C11C2312yes—
91C23×C4×C11C2312yes—
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2312yes—
94C23×C4×C11C2311yescharacteristic
95C22×C22⋊D11C2312yes—
96C22×C22⋊D11C2314yes—
97C22×C22⋊D11C2314yes—
98C23×Dic11C2312yes—
99C23×Dic11C2312yes—
100C23×Dic11C2314yes—
101C2×#4339—24no—
102C2×#4339—24no—
103C2×#4339—24no—
104C22×D44C2311yescharacteristic
105C22×C4×D11C2312yes—
106C22×Dic22C2311yescharacteristic
107C11×#123—28no—
108C11×C22⋊Q8—28no—
109C11×#121—28no—
110C11×#120—28no—
111C4×D4×C11—216no—
112C11×#117—24no—
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C4⋊C4C2312yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2312yes—
118C2×C42×C11C2312yes—
119#67006—28no—
120C2×C22⋊Dic11—28no—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2312yes—
127C2×C22⋊Dic11C2312yes—
128C2×C22⋊Dic11C2312yes—
129#67000—24no—
130Q8×Dic11—28no—
131#66997—24no—
132#66993—24no—
133#66992—216no—
134#66992—216no—
135#66989—24no—
136D4×Dic11—216no—
137D4×Dic11—28no—
138#66983—28no—
139#66982—28no—
140C4×C22⋊D11—216no—
141C4×C22⋊D11—216no—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146#66979—28no—
147#66979D418yescomplemented
148C2×C4⋊Dic11C2314yes—
149C2×C4⋊Dic11C2312yes—
150#66977—28no—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×C4×Dic11—24no—
156C2×C4×Dic11—24no—
157C2×C4×Dic11—28no—
158C2×C4×Dic11C2312yes—
159C2×C4×Dic11C2311yescharacteristic
160C2×C4×Dic11C2311yescharacteristic
161C2×C4×Dic11C2312yes—
162C2×C4×Dic11C2311yescharacteristic
163C2×C4×Dic11C2311yescharacteristic
164C2×C4×Dic11C2314yes—
165C2×C4×Dic11C2312yes—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2312yes—
171C11⋊#95C2312yes—
172C11⋊#95C2312yes—
173C11⋊#95C2312yes—
174#34743—111nomaximal, Sylow
175C24×C11—24no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—42no—
180C24×C11C2412yes—
181C24×C11C2412yes—
182C24×C11C2411yescharacteristic
183C23×D11C2412yes—
184C11×#41—232no—
185C2×Q8×C11—22no—
186C2×Q8×C11—22no—
187C2×Q8×C11C2×D414yes—
188C2×D4×C11—24no—
189C2×D4×C11—24no—
190C2×D4×C11—28no—
191C2×D4×C11—28no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—44no—
195C2×D4×C11C2×D414yes—
196C2×D4×C11C2×D418yes—
197C22×C4×C11—24no—
198C22×C4×C11—24no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—24no—
203C22×C4×C11—24no—
204C22×C4×C11—24no—
205C22×C4×C11—24no—
206C22×C4×C11—24no—
207C22×C4×C11—24no—
208C22×C4×C11—416no—
209C22×C4×C11C2×D418yes—
210C22×C4×C11C2×D414yes—
211C22×C4×C11C2×D414yes—
212C22×C4×C11#4114yes—
213C22×C4×C11C2414yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2411yescharacteristic
217C22×C4×C11C2411yescharacteristic
218C2×C22⋊D11—28no—
219C2×C22⋊D11—28no—
220C2×C22⋊D11—28no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—28no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—44no—
227C22×Dic11—28no—
228C22×Dic11—28no—
229C22×Dic11—24no—
230C22×Dic11—24no—
231C22×Dic11—24no—
232C22×Dic11—24no—
233C22×Dic11—42no—
234C22×Dic11—42no—
235C22×Dic11—44no—
236C22×Dic11C2412yes—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C22×Dic11C2414yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242#4339—416no—
243C2×D44—22no—
244C2×D44—22no—
245C2×D44—22no—
246C2×C4×D11—24no—
247C2×C4×D11—24no—
248C2×C4×D11—24no—
249C2×Dic22—22no—
250C2×Dic22—22no—
251C2×Dic22—22no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—28no—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—28no—
256C11×C22⋊C4—28no—
257C42×C11—24no—
258C22⋊Dic11—28no—
259C22⋊Dic11—28no—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
262C22⋊Dic11—28no—
263C22⋊Dic11—24no—
264C22⋊Dic11C2×D418yes—
265C22⋊Dic11#4118yescomplemented
266(C2×D11)⋊C4—28no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—28no—
269(C2×D11)⋊C4—44no—
270C4⋊Dic11—28no—
271C4⋊Dic11C2×D418yes—
272Dic11⋊C4—28no—
273Dic11⋊C4—28no—
274Dic11⋊C4—28no—
275Dic11⋊C4—44no—
276C4×Dic11—28no—
277C4×Dic11—22no—
278C4×Dic11—22no—
279C4×Dic11—24no—
280C4×Dic11—24no—
281C4×Dic11—22no—
282C4×Dic11—22no—
283C4×Dic11C2×D418yes—
284C2×#532—111no—
285C2×#525—111no—
286C2×#525D1111yescharacteristic, complemented
287C2×C4×#41—111no—
288#2429—112no—
289#2428—112no—
290#2427—112no—
291#2426—112no—
292#2425—114no—
293#2424—114no—
294#2392—114no—
295C4×#121—114no—
296#2297—111no—
297#2296—111no—
298C2×C4×C22⋊C4—111no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—28no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—24no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—24no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—48no—
313C23×C11—48no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11C22×D412yes—
317C23×C11C22×D414yes—
318C23×C11C22×D412yes—
319C23×C11C2×#4112yes—
320C23×C11C2×#4114yes—
321C23×C11C2511yescharacteristic
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—24no—
325C22×D11—22no—
326C22×D11—24no—
327Q8×C11—28no—
328D4×C11—216no—
329D4×C11—28no—
330D4×C11—416no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—216no—
334C2×C4×C11—22no—
335C2×C4×C11—24no—
336C2×C4×C11—22no—
337C2×C4×C11—24no—
338C2×C4×C11—22no—
339C2×C4×C11—24no—
340C2×C4×C11—44no—
341C2×C4×C11—48no—
342C2×C4×C11—48no—
343C2×C4×C11#121116yescomplemented
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D412yes—
346C2×C4×C11C22×D414yes—
347C2×C4×C11C22×D412yes—
348C2×C4×C11C22×D412yes—
349C2×C4×C11C2×#4112yes—
350C2×C4×C11C2×#4112yes—
351C22⋊D11—416no—
352C22⋊D11—416no—
353C22⋊D11—48no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—24no—
357C2×Dic11—24no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—416no—
370C2×Dic11—48no—
371C2×Dic11—48no—
372C2×Dic11C22×D418yes—
373C2×Dic11C2×#4114yes—
374C2×Dic11C2×#4114yes—
375D44—44no—
376C4×D11—48no—
377Dic22—44no—
378C22×#41—111no—
379C22×#41C2×D1111yescharacteristic
380C24×C4C2×D1111yescharacteristic
381#532—228no—
382C2×C4⋊Q8—111no—
383C2×#127—111no—
384C2×#124—111no—
385C2×#124—111no—
386#525—28no—
387#525—228no—
388C2×#123—112no—
389C2×#123C2×D1112yes—
390C2×C22⋊Q8—112no—
391C2×C22⋊Q8C2×D1112yes—
392C2×#121—114no—
393C2×#121—114no—
394C2×#121—112no—
395C2×#121C2×D1112yes—
396C2×#120—112no—
397C2×#120C2×D1112yes—
398C4×#41—228no—
399C2×C4×Q8—112no—
400C2×C4×D4—114no—
401C2×C4×D4—112no—
402C2×C4×D4—114no—
403C2×C4×D4—114no—
404C2×C4×D4C2×D1114yes—
405C2×#117—111no—
406C2×#117—112no—
407C2×#117C2×D1111yescharacteristic
408C22×C22⋊C4—112no—
409C22×C42—111no—
410C22×C42—111no—
411C22×C42—112no—
412#398—114no—
413#397—114no—
414#396—114no—
415#396—114no—
416#394—114no—
417#394—114no—
418#394—114no—
419#392—114no—
420#391—112no—
421#390—112no—
422#390—114no—
423#389—114no—
424#389—112no—
425#389—112no—
426#388—114no—
427#388—114no—
428#386—114no—
429#386—114no—
430#386—114no—
431#385—114no—
432#380—114no—
433C4×C4⋊C4—114no—
434C4×C22⋊C4—112no—
435C4×C22⋊C4—112no—
436C4×C22⋊C4—112no—
437C4×C22⋊C4—112no—
438C4×C22⋊C4—112no—
439C4×C22⋊C4—112no—
440C2×#95—112no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—24no—
444C22×C11—24no—
445C22×C11—24no—
446C22×C11—24no—
447C22×C11—24no—
448C22×C11—28no—
449C22×C11—24no—
450C22×C11—416no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—44no—
458C22×C11C2×#12114yes—
459C22×C11C23×D411yescharacteristic
460C22×C11C23×D411yescharacteristic
461C22×C11C22×#4111yescharacteristic
462C22×C11C22×#4112yes—
463C22×C11#58512yes—
464C2×D11—42no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—44no—
468C2×D11—44no—
469C4×C11—24no—
470C4×C11—42no—
471C4×C11—44no—
472C4×C11C2×#12114yes—
473C4×C11C2×#12114yes—
474Dic11—24no—
475Dic11—28no—
476Dic11—24no—
477Dic11—42no—
478Dic11—42no—
479Dic11—42no—
480C25C22×D1111yescharacteristic
481C2×#41—24no—
482C2×#41—24no—
483C2×#41—224no—
484C2×#41—224no—
485C2×#41—224no—
486C2×#41C22⋊D1118yescomplemented
487C22×Q8—111no—
488C22×Q8C22×D1111yescharacteristic
489C22×D4—112no—
490C22×D4—114no—
491C22×D4—114no—
492C22×D4—111no—
493C22×D4C22×D1114yes—
494C22×D4C22×D1112yes—
495C22×D4C22×D1111yescharacteristic
496C23×C4—24no—
497C23×C4—24no—
498C23×C4—24no—
499C23×C4—112no—
500C23×C4—112no—
501C23×C4—114no—
502C23×C4—112no—
503C23×C4C22×D1112yes—
504C23×C4C22×D1111yescharacteristic
505C23×C4C22×D1112yes—
506C23×C4C22×D1112yes—
507C23×C4C22×D1111yescharacteristic
508C4⋊Q8—224no—
509#127—224no—
510#124—224no—
511#124—224no—
512#123—28no—
513#123—228no—
514C22⋊Q8—28no—
515C22⋊Q8—228no—
516#121—28no—
517#121—2216no—
518#121—228no—
519#121—2216no—
520#120—28no—
521#120—228no—
522C4×Q8—228no—
523C4×D4—216no—
524C4×D4—2216no—
525C4×D4—2216no—
526C4×D4—228no—
527C4×D4—2216no—
528#117—24no—
529#117—118no—
530#117—228no—
531C2×C4⋊C4—112no—
532C2×C4⋊C4—114no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4C22×D1112yes—
538C2×C4⋊C4C22×D1114yes—
539C2×C22⋊C4—112no—
540C2×C22⋊C4—112no—
541C2×C22⋊C4—112no—
542C2×C22⋊C4—112no—
543C2×C22⋊C4—112no—
544C2×C22⋊C4—114no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—114no—
547C2×C22⋊C4—114no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—228no—
552C2×C22⋊C4C22×D1112yes—
553C2×C22⋊C4C22×D1114yes—
554C2×C22⋊C4C22×D1114yes—
555C2×C42—112no—
556C2×C42—112no—
557C2×C42—114no—
558C2×C42—111no—
559C2×C42—111no—
560C2×C42—111no—
561C2×C42—112no—
562C2×C42—111no—
563C2×C42—228no—
564C2×C42—224no—
565C2×C42—224no—
566C2×C42C22×D1112yes—
567#95—112no—
568#95—112no—
569#95—112no—
570#95—112no—
571#95—114no—
572#95—114no—
573#95—114no—
574#95—114no—
575C2×C11—24no—
576C2×C11—44no—
577C2×C11—44no—
578C2×C11C22×#12111yescharacteristic
579C2×C11#344411yescharacteristic
580C2×C11#345511yescharacteristic
581C2×C11D4×#4112yes—
582C2×C11D4×#4112yes—
583D11—82no—
584C24—22no—
585C24—24no—
586C24—22no—
587C24—22no—
588C24—42no—
589C24—112no—
590C24C23×D1112yes—
591C24C23×D1112yes—
592C24C23×D1111yescharacteristic
593#41—232no—
594#41—4416no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—222no—
598C2×Q8—222no—
599C2×Q8—222no—
600C2×Q8C2×C22⋊D1114yes—
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—28no—
604C2×D4—28no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—44no—
608C2×D4—228no—
609C2×D4—228no—
610C2×D4—224no—
611C2×D4—224no—
612C2×D4—228no—
613C2×D4—228no—
614C2×D4—224no—
615C2×D4—222no—
616C2×D4—222no—
617C2×D4—222no—
618C2×D4—444no—
619C2×D4—444no—
620C2×D4C2×C22⋊D1118yes—
621C2×D4C2×C22⋊D1114yes—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—416no—
634C22×C4—112no—
635C22×C4—112no—
636C22×C4—114no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—228no—
641C22×C4—224no—
642C22×C4—224no—
643C22×C4—228no—
644C22×C4—224no—
645C22×C4—224no—
646C22×C4—224no—
647C22×C4—224no—
648C22×C4—224no—
649C22×C4—444no—
650C22×C4—442no—
651C22×C4—442no—
652C22×C4D4×D1114yes—
653C22×C4#434114yes—
654C22×C4C2×C22⋊D1118yes—
655C22×C4C2×C22⋊D1114yes—
656C22×C4C23×D1114yes—
657C22×C4C23×D1112yes—
658C22×C4C23×D1112yes—
659C22×C4C23×D1111yescharacteristic
660C22×C4C23×D1111yescharacteristic
661C4⋊C4—24no—
662C4⋊C4—28no—
663C4⋊C4—118no—
664C4⋊C4—228no—
665C4⋊C4—228no—
666C4⋊C4—228no—
667C4⋊C4—228no—
668C4⋊C4—444no—
669C22⋊C4—24no—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—118no—
673C22⋊C4—118no—
674C22⋊C4—228no—
675C22⋊C4—228no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—228no—
679C22⋊C4—228no—
680C22⋊C4—224no—
681C22⋊C4—228no—
682C22⋊C4—228no—
683C22⋊C4—444no—
684C42—24no—
685C42—118no—
686C42—228no—
687C42—222no—
688C42—222no—
689C42—224no—
690C42—224no—
691C42—222no—
692C42—222no—
693C11#3474311yescharacteristic, complemented, Sylow
694C23—22no—
695C23—22no—
696C23—28no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—24no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—48no—
708C23—48no—
709C23—44no—
710C23—44no—
711C23—222no—
712C23—222no—
713C23—224no—
714C23—224no—
715C23—222no—
716C23C2×D4×D1112yes—
717C23C2×#434112yes—
718C23#41×D1114yes—
719C23C22×C22⋊D1114yes—
720C23C22×C22⋊D1112yes—
721C23C24×D1111yescharacteristic
722Q8—28no—
723Q8—444no—
724D4—216no—
725D4—28no—
726D4—416no—
727D4—4416no—
728D4—4416no—
729D4—448no—
730D4—444no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—216no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—44no—
741C2×C4—48no—
742C2×C4—48no—
743C2×C4—118no—
744C2×C4—114no—
745C2×C4—114no—
746C2×C4—222no—
747C2×C4—224no—
748C2×C4—224no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—4416no—
762C2×C4—448no—
763C2×C4—448no—
764C2×C4—448no—
765C2×C4#66992116yescomplemented
766C2×C4C2×D4×D1112yes—
767C2×C4C2×D4×D1112yes—
768C2×C4C2×#434112yes—
769C2×C4C2×#434112yes—
770C2×C4C22×C22⋊D1114yes—
771C2×C4C22×C22⋊D1112yes—
772C2×C4C22×C22⋊D1112yes—
773C22—22no—
774C22—22no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—28no—
782C22—416no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—44no—
788C22—42no—
789C22—42no—
790C22—442no—
791C22—442no—
792C22—442no—
793C22—444no—
794C22—444no—
795C22C2×#6699214yes—
796C22C22×D4×D1111yescharacteristic
797C22C22×#434111yescharacteristic
798C22C2×#41×D1112yes—
799C22#1062345312yes—
800C22C23×C22⋊D1111yescharacteristic
801C4—24no—
802C4—42no—
803C4—44no—
804C4—224no—
805C4—228no—
806C4—224no—
807C4—442no—
808C4—442no—
809C4—442no—
810C4C2×#6699214yes—
811C4C2×#6699214yes—
812C2—24no—
813C2—44no—
814C2—44no—
815C2—882no—
816C2C22×#6699211yescharacteristic
817C2#1308190811yescharacteristic
818C2#1308200411yescharacteristic
819C2#1308209912yes—
820C2#41×C22⋊D1112yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#525C2
hypercenterC2×#525D11
hypocenterC11#34743
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#10623363C2semidirect
2. C2×#10623322C2semidirect
3. C2×#41×Dic11C2semidirect
4. #13072217C2semidirect
5. #13072206C2semidirect
6. #13072195C2semidirect
7. #13072184C2semidirect
8. #13072171C2semidirect
9. #13072156C2semidirect
10. #13071858C2semidirect
11. C4×#66992C2semidirect
12. #13071104C2semidirect
13. #13071098C2semidirect
14. C2×C4×C22⋊Dic11C2semidirect
15. C2×C11×#525C2semidirect
30. C2×#67000C22semidirect
31. C2×Q8×Dic11C22semidirect
32. C2×#66997C22semidirect
33. C2×#66993C22semidirect
36. C2×#66989C22semidirect
38. C2×D4×Dic11C22semidirect
43. C2×C4×C22⋊D11C22semidirect
45. C2×#66979C22semidirect
49. C22×C4×Dic11C22semidirect
58. #10622607C22semidirect
59. #10622603C22semidirect
60. #10622601C22semidirect
61. #10622597C22semidirect
62. #10622587C22semidirect
63. #10622586C22semidirect
64. #10622586C22semidirect
65. #10622585C22semidirect
67. #10622572C22semidirect
69. #10622571C22semidirect
71. #10622565C22semidirect
75. #10622555C22semidirect
76. C4×(C2×D11)⋊C4C22semidirect
77. C4×(C2×D11)⋊C4C22semidirect
78. C4×Dic11⋊C4C22semidirect
82. C2×C11×#41D4semidirect
147. #66979D4semidirect
265. C22⋊Dic11#41semidirect
286. C2×#525D11semidirect
343. C2×C4×C11#121semidirect
486. C2×#41C22⋊D11semidirect
693. C11#34743semidirect
765. C2×C4#66992semidirect

Maximal subgroups

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

subgroupindex
C2×#106233632
C2×#106233222
C2×#41×Dic112
#130722172
#130722062
#130721952
#130721842
#130721712
#130721562
#130718582
C4×#669922
#130711042
#130710982
C2×C4×C22⋊Dic112
C2×C11×#5252
#3474311