Finite Group Databasebeta

← C2×#13080729 #15630365

Subgroups — C2×#13080729 #15630365

Order 2816.

2158 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
1C2×#10623074C211yesmaximal, characteristic, complemented
2C2×#10623083C211yesmaximal, characteristic
3#13080729C2116yesmaximal, direct product factor
4C2×#10622327C211yesmaximal, characteristic, complemented
5C2×#10622348C211yesmaximal, characteristic, complemented
6C2×#10622334C211yesmaximal, characteristic, complemented
7C2×#10622464C211yesmaximal, characteristic, complemented
8C2×#10622750C211yesmaximal, characteristic, complemented
9C2×#10622727C211yesmaximal, characteristic, complemented
10C2×#10622458C211yesmaximal, characteristic, complemented
11C2×#10622346C211yesmaximal, characteristic, complemented
12C2×#10622352C211yesmaximal, characteristic, complemented
13C2×#10622329C211yesmaximal, characteristic, complemented
14C2×#10622746C211yesmaximal, characteristic, complemented
15C22×#66880C211yesmaximal, characteristic, complemented
16C2×C11×#435C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66992—21no—
23C2×D4×Dic11—21no—
24C2×#66983C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C2×#66977C2211yescharacteristic
28C2×#66977C2211yescharacteristic
29C2×#66977C2211yescharacteristic
30C22×Dic44C2211yescharacteristic
31C22×Dic44C2211yescharacteristic
32C22×#4314C2211yescharacteristic
33#10623083—24no—
34#10623083C2218yes—
35#10623074—24no—
36#10623074C2218yescomplemented
37C2×#66949—21no—
38C2×#66943—21no—
39C2×#66938—21no—
40C2×(C22⋊D11)⋊C4—21no—
41C2×#66931—21no—
42C2×#66931—21no—
43C2×#66928C2211yescharacteristic
44C2×#66922C2211yescharacteristic
45C2×C4×Dic22C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic
47C11×#435C2218yescomplemented
48C2×C11×C4⋊C8C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×C11×#97C2211yescharacteristic
52#10622750C2218yescomplemented
53#10622746C2218yescomplemented
54#10622727C2218yescomplemented
55C2×#66885C2211yescharacteristic
56C2×#66885C2211yescharacteristic
57C2×#66885C2211yescharacteristic
58C2×#66881C2211yescharacteristic
59C2×#66881C2211yescharacteristic
60C2×#66881C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×#66880C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×#66880C2211yescharacteristic
65C2×#66880C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×#66880C2218yescomplemented
69#10622464C2218yescomplemented
70#10622458C2218yescomplemented
71#10622352C2218yescomplemented
72#10622348C2218yescomplemented
73#10622346C2218yescomplemented
74#10622334C2218yescomplemented
75#10622329C2218yescomplemented
76#10622327C2218yescomplemented
77C22×D4×C11D411yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C23×Dic11—21no—
83C23×Dic11—21no—
84C23×Dic11—21no—
85C2×#4339—22no—
86C2×#4339—24no—
87C2×#4339—42no—
88C2×#4339C2314yes—
89C22×D44C2311yescharacteristic
90C22×C4×D11—21no—
91C22×Dic22—24no—
92C22×Dic22—21no—
93C22×Dic22—22no—
94C22×Dic22—21no—
95C22×Dic22—42no—
96C22×Dic22C2311yescharacteristic
97C22×Dic22C2311yescharacteristic
98C22×Dic22C2314yes—
99C22×Dic22C2311yescharacteristic
100C2×C11×M16—42no—
101C2×C11×M16C2314yes—
102C22×C8×C11—42no—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2314yes—
108C4×D4×C11D414yes—
109C4×D4×C11C2314yes—
110C2×C11×C4⋊C4D411yescharacteristic
111C2×C11×C22⋊C4D411yescharacteristic
112C2×C11×C22⋊C4D411yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117#66992—28no—
118D4×Dic11—28no—
119#66983—22no—
120#66983C2314yes—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11—21no—
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11—22no—
128C2×C4⋊Dic11—22no—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2314yes—
134C2×C4⋊Dic11C2314yes—
135#66977—22no—
136#66977—22no—
137#66977—22no—
138#66977C2314yes—
139#66977C2314yes—
140#66977C2314yes—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×C4×Dic11—21no—
147C2×C4×Dic11—21no—
148C2×Dic44—24no—
149C2×Dic44—42no—
150C2×Dic44C2314yes—
151C2×Dic44C2314yes—
152C2×#4314—42no—
153C2×#4314C2314yes—
154#66949—28no—
155#66943—28no—
156#66938—28no—
157(C22⋊D11)⋊C4—28no—
158#66931—28no—
159#66931—28no—
160#66928—22no—
161#66928C2314yes—
162#66922—22no—
163#66922C2314yes—
164C4×Dic22—22no—
165C4×Dic22—22no—
166C4×Dic22C2314yes—
167C4×Dic22C2314yes—
168C11×C4⋊C8C2314yes—
169C11×C22⋊C8C2314yes—
170C11×C22⋊C8C2314yes—
171C11×#97C2314yes—
172#66885C2314yes—
173#66885C2314yes—
174#66885C2314yes—
175#66881C2314yes—
176#66881C2314yes—
177#66881C2314yes—
178#66880C2314yes—
179#66880C2314yes—
180#66880C2314yes—
181#66880C2314yes—
182#66880C2314yes—
183#66880C2314yes—
184#66880C2314yes—
185C2×#3316—111nomaximal, Sylow
186C24×C11C2×D411yescharacteristic
187C24×C11C2×D411yescharacteristic
188C23×D11—21no—
189C2×D4×C11—24no—
190C2×D4×C11C2×D414yes—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2411yescharacteristic
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—44no—
207C2×C22⋊D11—44no—
208C22×Dic11—21no—
209C22×Dic11—24no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—24no—
217C22×Dic11—24no—
218C22×Dic11—44no—
219C22×Dic11—82no—
220C22×Dic11—82no—
221#4339—28no—
222#4339—44no—
223#4339—48no—
224C2×D44—21no—
225C2×D44—22no—
226C2×D44—22no—
227C2×D44C2412yes—
228C2×C4×D11—24no—
229C2×C4×D11—44no—
230C2×Dic22—28no—
231C2×Dic22—21no—
232C2×Dic22—21no—
233C2×Dic22—21no—
234C2×Dic22—24no—
235C2×Dic22—24no—
236C2×Dic22—22no—
237C2×Dic22—22no—
238C2×Dic22—22no—
239C2×Dic22—22no—
240C2×Dic22—22no—
241C2×Dic22—44no—
242C2×Dic22—48no—
243C2×Dic22—44no—
244C2×Dic22—82no—
245C2×Dic22#4114yes—
246C2×Dic22C2412yes—
247C2×Dic22C2412yes—
248C2×Dic22C2412yes—
249C11×M16—44no—
250C2×C8×C11—22no—
251C2×C8×C11—22no—
252C2×C8×C11—22no—
253C2×C8×C11—22no—
254C2×C8×C11—44no—
255C2×C8×C11C2412yes—
256C2×C8×C11C2412yes—
257C2×C8×C11C2412yes—
258C2×C8×C11C2412yes—
259C11×C4⋊C4C2×D414yes—
260C11×C22⋊C4C2×D414yes—
261C11×C22⋊C4C2×D414yes—
262C42×C11C2×D412yes—
263C42×C11C2412yes—
264C22⋊Dic11—24no—
265C22⋊Dic11—24no—
266C22⋊Dic11—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11—24no—
275C4⋊Dic11—24no—
276C4⋊Dic11—24no—
277C4⋊Dic11C2412yes—
278C4⋊Dic11C2412yes—
279C4⋊Dic11C2412yes—
280C4⋊Dic11C2412yes—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286C4×Dic11—24no—
287C4×Dic11—24no—
288Dic44—28no—
289Dic44—44no—
290#4314—44no—
291C2×#554—111no—
292C2×#548—111no—
293#3316—1116no—
294C2×#489—111no—
295C2×#481—111no—
296C2×#483—111no—
297C2×#475—111no—
298C2×#470—111no—
299C2×#465—111no—
300C2×#464—111no—
301C2×#452—111no—
302C2×#451—111no—
303C2×#441—111no—
304C2×#435D1111yescharacteristic, complemented
305C2×#417—111no—
306C22×#103—111no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11#13714yes—
313C23×C11C22×D412yes—
314C23×C11C22×D412yes—
315C23×C11C22×D411yescharacteristic
316C22×D11—22no—
317C22×D11—42no—
318C22×D11—42no—
319C22×D11—42no—
320D4×C11—28no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—24no—
326C2×C4×C11—24no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×D412yes—
333C2×C4×C11C22×D412yes—
334C2×C4×C11C22×D412yes—
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C2×#4112yes—
337C2×C4×C11H(5,𝔽2)12yes—
338C2×C4×C11C2511yescharacteristic
339C22⋊D11—48no—
340C22⋊D11—48no—
341C2×Dic11—24no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—48no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—84no—
357C2×Dic11—84no—
358D44—22no—
359D44—22no—
360D44—42no—
361C4×D11—48no—
362Dic22—24no—
363Dic22—22no—
364Dic22—22no—
365Dic22—22no—
366Dic22—22no—
367Dic22—22no—
368Dic22—48no—
369Dic22—42no—
370Dic22—42no—
371Dic22—84no—
372Dic22C2×#4114yes—
373C8×C11—22no—
374C8×C11—22no—
375C8×C11—22no—
376C8×C11—22no—
377C22×#41—111no—
378C23×Q8—111no—
379C22×Q16—111no—
380C22×Q16—111no—
381C22×SD16—111no—
382C22×M16C2×D1111yescharacteristic
383C23×C8C2×D1111yescharacteristic
384#554—118no—
385#554—224no—
386#548—118no—
387#548—224no—
388C2×C4⋊Q8—111no—
389C2×#125—221no—
390C2×#124—111no—
391C2×#124—221no—
392C2×C22⋊Q8—111no—
393C2×C22⋊Q8—111no—
394C2×C22⋊Q8—111no—
395C2×C22⋊Q8—221no—
396C2×C22⋊Q8—221no—
397C2×C22⋊Q8—221no—
398C2×#121—111no—
399C2×#121—221no—
400C2×C4×Q8—111no—
401C2×C4×Q8—111no—
402C2×C4×D4—221no—
403C2×C4×D4—221no—
404C2×C4×D4C2×D1111yescharacteristic
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407#489—118no—
408#483—118no—
409#481—118no—
410#475—118no—
411#470—118no—
412#465—118no—
413#464—118no—
414#452—118no—
415#451—118no—
416#441—118no—
417#435C2×D1118yescomplemented
418C2×#106—111no—
419C2×#106—111no—
420C2×#106—111no—
421C2×C4⋊C8C2×D1111yescharacteristic
422#417—118no—
423C2×#103—111no—
424C2×#103—111no—
425C2×#103—111no—
426C2×#103—111no—
427C2×#103—111no—
428C2×#103—111no—
429C2×#103—118no—
430C2×#103—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×#102—111no—
434C2×C22⋊C8C2×D1111yescharacteristic
435C2×C22⋊C8C2×D1111yescharacteristic
436C2×#97C2×D1111yescharacteristic
437C22×C11—22no—
438C22×C11—28no—
439C22×C11—22no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—44no—
444C22×C11#54612yes—
445C22×C11C2×#13714yes—
446C22×C11C2×#13712yes—
447C22×C11#57712yes—
448C22×C11C23×D411yescharacteristic
449C2×D11—42no—
450C2×D11—42no—
451C2×D11—42no—
452C2×D11—84no—
453C4×C11—22no—
454C4×C11—22no—
455C4×C11—22no—
456C4×C11—22no—
457C4×C11#54612yes—
458C4×C11C22×#4111yescharacteristic
459C4×C11C2×H(5,𝔽2)11yescharacteristic
460Dic11—24no—
461Dic11—42no—
462Dic11—42no—
463Dic11—42no—
464Dic11—42no—
465Dic11—42no—
466Dic11—42no—
467C2×#41—114no—
468C2×#41—224no—
469C2×#41—222no—
470C2×#41—442no—
471C22×Q8—111no—
472C22×Q8—111no—
473C22×Q8—111no—
474C22×Q8—114no—
475C22×Q8—224no—
476C22×Q8—221no—
477C22×Q8—222no—
478C22×Q8—221no—
479C22×Q8—442no—
480C22×D4—111no—
481C22×D4—221no—
482C22×D4—221no—
483C22×D4D4411yescharacteristic
484C23×C4—221no—
485C23×C4—221no—
486C23×C4—221no—
487C23×C4—221no—
488C23×C4C22×D1111yescharacteristic
489C23×C4C22×D1111yescharacteristic
490C2×Q16—114no—
491C2×Q16—114no—
492C2×Q16—224no—
493C2×Q16—442no—
494C2×SD16—114no—
495C2×SD16—442no—
496C2×M16—42no—
497C2×M16C22×D1114yes—
498C22×C8—42no—
499C22×C8C22×D1111yescharacteristic
500C22×C8C22×D1111yescharacteristic
501C22×C8C22×D1111yescharacteristic
502C22×C8C22×D1111yescharacteristic
503C22×C8C22×D1114yes—
504C4⋊Q8—114no—
505C4⋊Q8—222no—
506#125—228no—
507#124—114no—
508#124—228no—
509#124—222no—
510C22⋊Q8—114no—
511C22⋊Q8—114no—
512C22⋊Q8—114no—
513C22⋊Q8—222no—
514C22⋊Q8—222no—
515C22⋊Q8—222no—
516C22⋊Q8—228no—
517C22⋊Q8—228no—
518C22⋊Q8—228no—
519#121—114no—
520#121—228no—
521#121—222no—
522C4×Q8—114no—
523C4×Q8—114no—
524C4×Q8—222no—
525C4×Q8—222no—
526C4×D4—228no—
527C4×D4—228no—
528C4×D4D4414yes—
529C4×D4C22×D1114yes—
530C2×C4⋊C4—111no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—111no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4—221no—
538C2×C4⋊C4—222no—
539C2×C4⋊C4—222no—
540C2×C4⋊C4—221no—
541C2×C4⋊C4—221no—
542C2×C4⋊C4—221no—
543C2×C4⋊C4—221no—
544C2×C4⋊C4—221no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4D4411yescharacteristic
547C2×C22⋊C4—221no—
548C2×C22⋊C4—221no—
549C2×C22⋊C4—221no—
550C2×C22⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4D4411yescharacteristic
554C2×C22⋊C4D4411yescharacteristic
555C2×C42—221no—
556C2×C42—221no—
557C2×C42C22×D1111yescharacteristic
558#106—114no—
559#106—114no—
560#106—114no—
561C4⋊C8C22×D1114yes—
562#103—114no—
563#103—114no—
564#103—114no—
565#103—114no—
566#103—114no—
567#103—114no—
568#103—114no—
569#102—114no—
570#102—114no—
571#102—114no—
572C22⋊C8C22×D1114yes—
573C22⋊C8C22×D1114yes—
574#97C22×D1114yes—
575C2×C11—24no—
576C2×C11—42no—
577C2×C11#331614yescomplemented
578C2×C11C2×#54611yescharacteristic
579C2×C11C22×#13711yescharacteristic
580C2×C11C2×#57711yescharacteristic
581D11—82no—
582C24—221no—
583C24C2×D4411yescharacteristic
584C24C2×D4411yescharacteristic
585#41—228no—
586#41—444no—
587#41—448no—
588C2×Q8—114no—
589C2×Q8—112no—
590C2×Q8—112no—
591C2×Q8—112no—
592C2×Q8—228no—
593C2×Q8—221no—
594C2×Q8—221no—
595C2×Q8—224no—
596C2×Q8—221no—
597C2×Q8—224no—
598C2×Q8—222no—
599C2×Q8—222no—
600C2×Q8—222no—
601C2×Q8—222no—
602C2×Q8—222no—
603C2×Q8—444no—
604C2×Q8—444no—
605C2×Q8—448no—
606C2×Q8—882no—
607C2×D4—24no—
608C2×D4—112no—
609C2×D4—224no—
610C2×D4—224no—
611C2×D4—221no—
612C2×D4—222no—
613C2×D4—222no—
614C2×D4—444no—
615C2×D4—444no—
616C2×D4C2×D4414yes—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—221no—
622C22×C4—224no—
623C22×C4—221no—
624C22×C4—221no—
625C22×C4—221no—
626C22×C4—221no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—224no—
630C22×C4—224no—
631C22×C4—224no—
632C22×C4—444no—
633C22×C4—444no—
634C22×C4—882no—
635C22×C4—882no—
636C22×C4C2×D4412yes—
637C22×C4C2×D4412yes—
638C22×C4C2×D4411yescharacteristic
639C22×C4C2×D4411yescharacteristic
640C22×C4C2×D4411yescharacteristic
641C22×C4C2×D4411yescharacteristic
642C22×C4C23×D1112yes—
643C22×C4C23×D1112yes—
644C22×C4C23×D1111yescharacteristic
645Q16—228no—
646Q16—444no—
647SD16—444no—
648M16—44no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—44no—
654C2×C8C23×D1112yes—
655C2×C8C23×D1112yes—
656C2×C8C23×D1112yes—
657C2×C8C23×D1112yes—
658C4⋊C4—112no—
659C4⋊C4—112no—
660C4⋊C4—112no—
661C4⋊C4—112no—
662C4⋊C4—221no—
663C4⋊C4—224no—
664C4⋊C4—224no—
665C4⋊C4—221no—
666C4⋊C4—221no—
667C4⋊C4—221no—
668C4⋊C4—224no—
669C4⋊C4—224no—
670C4⋊C4—224no—
671C4⋊C4—224no—
672C4⋊C4—224no—
673C4⋊C4—224no—
674C4⋊C4C2×D4414yes—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4C2×D4414yes—
682C22⋊C4C2×D4414yes—
683C42—224no—
684C42—224no—
685C42C2×D4412yes—
686C42C23×D1112yes—
687C11C2×#331611yescharacteristic, complemented, Sylow
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—222no—
694C23—442no—
695C23—442no—
696C23—442no—
697C23#6696214yes—
698C23C22×D4412yes—
699C23C22×D4412yes—
700C23C22×D4411yescharacteristic
701Q8—114no—
702Q8—224no—
703Q8—222no—
704Q8—222no—
705Q8—222no—
706Q8—222no—
707Q8—222no—
708Q8—448no—
709Q8—442no—
710Q8—442no—
711Q8—884no—
712D4—28no—
713D4—222no—
714D4—222no—
715D4—448no—
716D4—448no—
717D4—442no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—224no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—448no—
737C2×C4—448no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—884no—
745C2×C4—884no—
746C2×C4C22×D4412yes—
747C2×C4C22×D4412yes—
748C2×C4C22×D4412yes—
749C2×C4C22×D4412yes—
750C2×C4C22×D4411yescharacteristic
751C2×C4#6703712yes—
752C2×C4#41×D1112yes—
753C2×C4C24×D1111yescharacteristic
754C8—22no—
755C8—22no—
756C8—22no—
757C8—22no—
758C22—28no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—442no—
766C22—442no—
767C22—442no—
768C22—884no—
769C22#1062308512yes—
770C22C2×#6696214yes—
771C22C2×#6696212yes—
772C22#1062328212yes—
773C22C23×D4411yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—224no—
779C4—442no—
780C4—442no—
781C4—442no—
782C4—442no—
783C4—442no—
784C4—442no—
785C4#1062308512yes—
786C4C2×#6703711yescharacteristic
787C4C2×#41×D1111yescharacteristic
788C2—24no—
789C2—42no—
790C2—882no—
791C2#1308072914yesdirect product factor
792C2C2×#1062308511yescharacteristic
793C2C22×#6696211yescharacteristic
794C2C2×#1062328211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
prime radicalC2×#10623083C2
hypercenterC2×#435D11
hypocenterC11C2×#3316
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#10623074C2semidirect
3. #13080729C2direct (N × H)
4. C2×#10622327C2semidirect
5. C2×#10622348C2semidirect
6. C2×#10622334C2semidirect
7. C2×#10622464C2semidirect
8. C2×#10622750C2semidirect
9. C2×#10622727C2semidirect
10. C2×#10622458C2semidirect
11. C2×#10622346C2semidirect
12. C2×#10622352C2semidirect
13. C2×#10622329C2semidirect
14. C2×#10622746C2semidirect
15. C22×#66880C2semidirect
16. C2×C11×#435C2semidirect
36. #10623074C22semidirect
47. C11×#435C22semidirect
52. #10622750C22semidirect
53. #10622746C22semidirect
54. #10622727C22semidirect
68. C2×#66880C22semidirect
69. #10622464C22semidirect
70. #10622458C22semidirect
71. #10622352C22semidirect
72. #10622348C22semidirect
73. #10622346C22semidirect
74. #10622334C22semidirect
75. #10622329C22semidirect
76. #10622327C22semidirect
304. C2×#435D11semidirect
417. #435C2×D11semidirect
577. C2×C11#3316semidirect
687. C11C2×#3316semidirect
791. C2#13080729direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×#106230832
#130807292
C2×#106223272
C2×#106223482
C2×#106223342
C2×#106224642
C2×#106227502
C2×#106227272
C2×#106224582
C2×#106223462
C2×#106223522
C2×#106223292
C2×#106227462
C22×#668802
C2×C11×#4352
C2×#331611