Finite Group Databasebeta

← C2×#13080594 #15630413

Subgroups — C2×#13080594 #15630413

Order 2816.

2190 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623096C211yesmaximal, characteristic, complemented
2C2×#10623082C211yesmaximal, characteristic, complemented
3#13080594C2116yesmaximal, direct product factor
4C2×#10622316C211yesmaximal, characteristic, complemented
5C2×#10622336C211yesmaximal, characteristic, complemented
6C2×#10622334C211yesmaximal, characteristic, complemented
7C2×#10622460C211yesmaximal, characteristic, complemented
8C2×#10622747C211yesmaximal, characteristic, complemented
9C2×#10622727C211yesmaximal, characteristic, complemented
10C2×#10622454C211yesmaximal, characteristic, complemented
11C2×#10622347C211yesmaximal, characteristic, complemented
12C2×#10622347C211yesmaximal, characteristic, complemented
13C2×#10622324C211yesmaximal, characteristic, complemented
14C2×#10622746C211yesmaximal, characteristic, complemented
15C2×#10622726C211yesmaximal, characteristic, complemented
16C2×C11×#435C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66992—21no—
23C2×#66991—21no—
24C2×#66983C2211yescharacteristic
25C2×#66983C2211yescharacteristic
26C2×#66979C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C2×#66977C2211yescharacteristic
29C2×#66977C2211yescharacteristic
30C22×D88C2211yescharacteristic
31C22×#4314C2211yescharacteristic
32C22×#4314C2211yescharacteristic
33#10623096—24no—
34#10623096C2218yescomplemented
35#10623082—24no—
36#10623082C2218yescomplemented
37C2×#66951—21no—
38C2×C4⋊C4×D11—21no—
39C2×#66936—21no—
40C2×#66936—21no—
41C2×#66936—21no—
42C2×(C22⋊D11)⋊C4—21no—
43C2×C4×D44C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C2×#66923C2211yescharacteristic
46C2×#66922C2211yescharacteristic
47C11×#435C2218yescomplemented
48C2×C11×C4⋊C8C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×C11×#97C2211yescharacteristic
52#10622747C2218yescomplemented
53#10622746C2218yescomplemented
54#10622727C2218yescomplemented
55#10622726C2218yescomplemented
56C2×#66885C2211yescharacteristic
57C2×#66885C2211yescharacteristic
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66881C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×#66880C2211yescharacteristic
65C2×#66880C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×#66880C2211yescharacteristic
69#10622460C2218yescomplemented
70#10622454C2218yescomplemented
71#10622347C2218yescomplemented
72#10622347C2218yescomplemented
73#10622336C2218yescomplemented
74#10622334C2218yescomplemented
75#10622324C2218yescomplemented
76#10622316C2218yescomplemented
77C22×D4×C11D411yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C23×Dic11—21no—
85C2×#4339—22no—
86C2×#4339—22no—
87C2×#4339—24no—
88C2×#4339—24no—
89C2×#4339—42no—
90C2×#4339—42no—
91C2×#4339C2314yes—
92C2×#4339C2314yes—
93C22×D44C2311yescharacteristic
94C22×D44C2311yescharacteristic
95C22×C4×D11—21no—
96C22×C4×D11—21no—
97C22×C4×D11—21no—
98C22×C4×D11—21no—
99C22×Dic22C2311yescharacteristic
100C22×Dic22C2311yescharacteristic
101C2×C11×M16—42no—
102C2×C11×M16C2314yes—
103C22×C8×C11—42no—
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2314yes—
109C4×D4×C11D414yes—
110C4×D4×C11C2314yes—
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C22⋊C4D411yescharacteristic
113C2×C11×C22⋊C4D411yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11—21no—
118#66992—28no—
119#66991—28no—
120#66983—22no—
121#66983—22no—
122#66983C2314yes—
123#66983C2314yes—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128#66979—22no—
129#66979C2314yes—
130C2×C4⋊Dic11—21no—
131C2×C4⋊Dic11—21no—
132C2×C4⋊Dic11—21no—
133C2×C4⋊Dic11—22no—
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2311yescharacteristic
138C2×C4⋊Dic11C2314yes—
139#66977—22no—
140#66977—22no—
141#66977C2314yes—
142#66977C2314yes—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×C4×Dic11—21no—
148C2×D88—24no—
149C2×D88C2314yes—
150C2×#4314—42no—
151C2×#4314—42no—
152C2×#4314C2314yes—
153C2×#4314C2314yes—
154#66951—28no—
155C4⋊C4×D11—28no—
156#66936—28no—
157#66936—28no—
158#66936—28no—
159(C22⋊D11)⋊C4—28no—
160C4×D44—22no—
161C4×D44—22no—
162C4×D44C2314yes—
163C4×D44C2314yes—
164#66923—22no—
165#66923C2314yes—
166#66922—22no—
167#66922C2314yes—
168C11×C4⋊C8C2314yes—
169C11×C22⋊C8C2314yes—
170C11×C22⋊C8C2314yes—
171C11×#97C2314yes—
172#66885C2314yes—
173#66885C2314yes—
174#66885C2314yes—
175#66885C2314yes—
176#66882C2314yes—
177#66881C2314yes—
178#66881C2314yes—
179#66880C2314yes—
180#66880C2314yes—
181#66880C2314yes—
182#66880C2314yes—
183#66880C2314yes—
184#66880C2314yes—
185C2×#3307—111nomaximal, Sylow
186C24×C11C2×D411yescharacteristic
187C24×C11C2×D411yescharacteristic
188C23×D11—21no—
189C23×D11—21no—
190C2×D4×C11—42no—
191C2×D4×C11C2×D414yes—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2411yescharacteristic
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—24no—
209C2×C22⋊D11—44no—
210C2×C22⋊D11—44no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—82no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—24no—
220C22×Dic11—82no—
221#4339—28no—
222#4339—28no—
223#4339—44no—
224#4339—44no—
225#4339—48no—
226#4339—48no—
227C2×D44—21no—
228C2×D44—21no—
229C2×D44—22no—
230C2×D44—22no—
231C2×D44—22no—
232C2×D44#4114yes—
233C2×D44C2412yes—
234C2×D44C2412yes—
235C2×C4×D11—24no—
236C2×C4×D11—24no—
237C2×C4×D11—24no—
238C2×C4×D11—24no—
239C2×C4×D11—44no—
240C2×C4×D11—44no—
241C2×C4×D11—44no—
242C2×C4×D11—82no—
243C2×Dic22—21no—
244C2×Dic22—21no—
245C2×Dic22—22no—
246C2×Dic22—22no—
247C2×Dic22—22no—
248C2×Dic22—22no—
249C2×Dic22C2412yes—
250C2×Dic22C2412yes—
251C11×M16—44no—
252C2×C8×C11—22no—
253C2×C8×C11—22no—
254C2×C8×C11—22no—
255C2×C8×C11—22no—
256C2×C8×C11—44no—
257C2×C8×C11C2412yes—
258C2×C8×C11C2412yes—
259C2×C8×C11C2412yes—
260C2×C8×C11C2412yes—
261C11×C4⋊C4C2×D414yes—
262C11×C22⋊C4C2×D414yes—
263C11×C22⋊C4C2×D414yes—
264C42×C11C2×D412yes—
265C42×C11C2412yes—
266C22⋊Dic11—24no—
267C22⋊Dic11—24no—
268C22⋊Dic11—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273C4⋊Dic11—24no—
274C4⋊Dic11—24no—
275C4⋊Dic11—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11—21no—
278C4⋊Dic11—21no—
279C4⋊Dic11—24no—
280C4⋊Dic11C2412yes—
281C4⋊Dic11C2412yes—
282C4⋊Dic11C2412yes—
283C4⋊Dic11C2412yes—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286Dic11⋊C4—24no—
287Dic11⋊C4—24no—
288C4×Dic11—24no—
289D88—28no—
290#4314—44no—
291#4314—44no—
292C2×#553—111no—
293C2×#547—111no—
294#3307—1116no—
295C2×#491—111no—
296C2×#485—111no—
297C2×#483—111no—
298C2×#478—111no—
299C2×#468—111no—
300C2×#465—111no—
301C2×#461—111no—
302C2×#449—111no—
303C2×#449—111no—
304C2×#442—111no—
305C2×#435D1111yescharacteristic, complemented
306C2×#417—111no—
307C2×#416—111no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11C22×D412yes—
315C23×C11C22×D412yes—
316C23×C11C22×D411yescharacteristic
317C22×D11—24no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—42no—
321C22×D11—42no—
322C22×D11—42no—
323C22×D11—42no—
324C22×D11—42no—
325D4×C11—44no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—24no—
331C2×C4×C11—24no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11C22×D412yes—
337C2×C4×C11C22×D412yes—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C2×#4112yes—
342C2×C4×C11H(5,𝔽2)12yes—
343C2×C4×C11C2511yescharacteristic
344C22⋊D11—48no—
345C22⋊D11—48no—
346C22⋊D11—48no—
347C22⋊D11—84no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11—84no—
361D44—24no—
362D44—22no—
363D44—22no—
364D44—22no—
365D44—42no—
366D44C2×#4114yes—
367C4×D11—48no—
368C4×D11—48no—
369C4×D11—48no—
370C4×D11—84no—
371Dic22—22no—
372Dic22—22no—
373Dic22—22no—
374Dic22—22no—
375Dic22—42no—
376Dic22—42no—
377C8×C11—22no—
378C8×C11—22no—
379C8×C11—22no—
380C8×C11—22no—
381C22×#41—111no—
382C22×#41—111no—
383C22×SD16—111no—
384C22×SD16—111no—
385C22×D8—111no—
386C22×M16C2×D1111yescharacteristic
387C23×C8C2×D1111yescharacteristic
388#553—118no—
389#553—224no—
390#547—118no—
391#547—224no—
392C2×C4⋊Q8—111no—
393C2×#126—221no—
394C2×#125—111no—
395C2×#123—221no—
396C2×#123—221no—
397C2×#123—221no—
398C2×C22⋊Q8—111no—
399C2×C22⋊Q8—111no—
400C2×#121—111no—
401C2×#121—111no—
402C2×#121—221no—
403C2×#121—221no—
404C2×C4×D4—111no—
405C2×C4×D4—111no—
406C2×C4×D4—221no—
407C2×C4×D4C2×D1111yescharacteristic
408C2×#117—111no—
409C22×C4⋊C4—111no—
410C22×C4⋊C4—221no—
411#491—118no—
412#485—118no—
413#483—118no—
414#478—118no—
415#468—118no—
416#465—118no—
417#461—118no—
418#449—118no—
419#449—118no—
420#442—118no—
421#435C2×D1118yescomplemented
422C2×#107—111no—
423C2×#106—111no—
424C2×#106—111no—
425C2×C4⋊C8C2×D1111yescharacteristic
426#417—118no—
427#416—118no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#103—111no—
433C2×#103—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×C22⋊C8C2×D1111yescharacteristic
439C2×C22⋊C8C2×D1111yescharacteristic
440C2×#97C2×D1111yescharacteristic
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—44no—
448C22×C11—44no—
449C22×C11#54612yes—
450C22×C11#57512yes—
451C22×C11#57712yes—
452C22×C11C23×D411yescharacteristic
453C2×D11—24no—
454C2×D11—48no—
455C2×D11—42no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—84no—
461C4×C11—22no—
462C4×C11—22no—
463C4×C11—22no—
464C4×C11—22no—
465C4×C11#54612yes—
466C4×C11C22×#4111yescharacteristic
467C4×C11C2×H(5,𝔽2)11yescharacteristic
468Dic11—42no—
469Dic11—42no—
470Dic11—42no—
471Dic11—42no—
472Dic11—42no—
473Dic11—42no—
474C2×#41—114no—
475C2×#41—114no—
476C2×#41—224no—
477C2×#41—224no—
478C2×#41—222no—
479C2×#41—222no—
480C2×#41—442no—
481C2×#41—442no—
482C22×Q8—111no—
483C22×Q8—111no—
484C22×D4—111no—
485C22×D4—111no—
486C22×D4—221no—
487C22×D4—221no—
488C22×D4—221no—
489C22×D4—221no—
490C22×D4D4411yescharacteristic
491C23×C4—221no—
492C23×C4—221no—
493C23×C4—221no—
494C23×C4—221no—
495C23×C4—221no—
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C2×SD16—114no—
499C2×SD16—114no—
500C2×SD16—442no—
501C2×SD16—442no—
502C2×D8—114no—
503C2×D8—224no—
504C2×M16—42no—
505C2×M16C22×D1114yes—
506C22×C8—42no—
507C22×C8C22×D1111yescharacteristic
508C22×C8C22×D1111yescharacteristic
509C22×C8C22×D1111yescharacteristic
510C22×C8C22×D1111yescharacteristic
511C22×C8C22×D1114yes—
512C4⋊Q8—114no—
513C4⋊Q8—222no—
514#126—228no—
515#125—114no—
516#125—222no—
517#123—228no—
518#123—228no—
519#123—228no—
520C22⋊Q8—114no—
521C22⋊Q8—114no—
522C22⋊Q8—222no—
523C22⋊Q8—222no—
524#121—114no—
525#121—114no—
526#121—228no—
527#121—228no—
528#121—222no—
529#121—222no—
530C4×D4—114no—
531C4×D4—114no—
532C4×D4—228no—
533C4×D4—222no—
534C4×D4—222no—
535C4×D4D4414yes—
536C4×D4C22×D1114yes—
537#117—114no—
538#117—222no—
539C2×C4⋊C4—111no—
540C2×C4⋊C4—111no—
541C2×C4⋊C4—114no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—221no—
545C2×C4⋊C4—222no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4—221no—
551C2×C4⋊C4—221no—
552C2×C4⋊C4—228no—
553C2×C4⋊C4D4411yescharacteristic
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4D4411yescharacteristic
562C2×C22⋊C4D4411yescharacteristic
563C2×C42—221no—
564C2×C42C22×D1111yescharacteristic
565#107—114no—
566#106—114no—
567#106—114no—
568C4⋊C8C22×D1114yes—
569#103—114no—
570#103—114no—
571#103—114no—
572#103—114no—
573#103—114no—
574#103—114no—
575#102—114no—
576#102—114no—
577#102—114no—
578#102—114no—
579C22⋊C8C22×D1114yes—
580C22⋊C8C22×D1114yes—
581#97C22×D1114yes—
582C2×C11—42no—
583C2×C11—42no—
584C2×C11#330714yescomplemented
585C2×C11C2×#54611yescharacteristic
586C2×C11C2×#57511yescharacteristic
587C2×C11C2×#57711yescharacteristic
588D11—44no—
589D11—82no—
590C24—221no—
591C24—221no—
592C24C2×D4411yescharacteristic
593C24C2×D4411yescharacteristic
594#41—228no—
595#41—228no—
596#41—444no—
597#41—444no—
598#41—448no—
599#41—448no—
600C2×Q8—112no—
601C2×Q8—112no—
602C2×Q8—221no—
603C2×Q8—221no—
604C2×Q8—222no—
605C2×Q8—222no—
606C2×Q8—222no—
607C2×Q8—222no—
608C2×D4—42no—
609C2×D4—114no—
610C2×D4—112no—
611C2×D4—112no—
612C2×D4—224no—
613C2×D4—224no—
614C2×D4—224no—
615C2×D4—224no—
616C2×D4—221no—
617C2×D4—221no—
618C2×D4—222no—
619C2×D4—222no—
620C2×D4—222no—
621C2×D4—444no—
622C2×D4—444no—
623C2×D4—444no—
624C2×D4—882no—
625C2×D4C2×D4414yes—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—221no—
631C22×C4—221no—
632C22×C4—221no—
633C22×C4—221no—
634C22×C4—221no—
635C22×C4—221no—
636C22×C4—224no—
637C22×C4—224no—
638C22×C4—224no—
639C22×C4—224no—
640C22×C4—224no—
641C22×C4—444no—
642C22×C4—444no—
643C22×C4—444no—
644C22×C4—882no—
645C22×C4—882no—
646C22×C4C2×D4412yes—
647C22×C4C2×D4412yes—
648C22×C4C2×D4411yescharacteristic
649C22×C4C2×D4411yescharacteristic
650C22×C4C2×D4411yescharacteristic
651C22×C4C2×D4411yescharacteristic
652C22×C4C23×D1112yes—
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655SD16—444no—
656SD16—444no—
657D8—228no—
658M16—44no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—44no—
664C2×C8C23×D1112yes—
665C2×C8C23×D1112yes—
666C2×C8C23×D1112yes—
667C2×C8C23×D1112yes—
668C4⋊C4—112no—
669C4⋊C4—112no—
670C4⋊C4—112no—
671C4⋊C4—112no—
672C4⋊C4—221no—
673C4⋊C4—221no—
674C4⋊C4—224no—
675C4⋊C4—221no—
676C4⋊C4—221no—
677C4⋊C4—224no—
678C4⋊C4—224no—
679C4⋊C4—224no—
680C4⋊C4—224no—
681C4⋊C4—224no—
682C4⋊C4—224no—
683C4⋊C4C2×D4414yes—
684C22⋊C4—224no—
685C22⋊C4—224no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4C2×D4414yes—
692C22⋊C4C2×D4414yes—
693C42—224no—
694C42C2×D4412yes—
695C42C23×D1112yes—
696C11C2×#330711yescharacteristic, complemented, Sylow
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—224no—
704C23—222no—
705C23—222no—
706C23—442no—
707C23—442no—
708C23—442no—
709C23—442no—
710C23—442no—
711C23C22×D4412yes—
712C23C22×D4412yes—
713C23C22×D4411yescharacteristic
714Q8—222no—
715Q8—222no—
716Q8—222no—
717Q8—222no—
718Q8—442no—
719Q8—442no—
720D4—44no—
721D4—114no—
722D4—224no—
723D4—222no—
724D4—222no—
725D4—222no—
726D4—448no—
727D4—448no—
728D4—448no—
729D4—442no—
730D4—884no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—448no—
748C2×C4—448no—
749C2×C4—448no—
750C2×C4—442no—
751C2×C4—442no—
752C2×C4—442no—
753C2×C4—442no—
754C2×C4—442no—
755C2×C4—442no—
756C2×C4—884no—
757C2×C4—884no—
758C2×C4C22×D4412yes—
759C2×C4C22×D4412yes—
760C2×C4C22×D4412yes—
761C2×C4C22×D4412yes—
762C2×C4C22×D4411yescharacteristic
763C2×C4#6703712yes—
764C2×C4#41×D1112yes—
765C2×C4C24×D1111yescharacteristic
766C8—22no—
767C8—22no—
768C8—22no—
769C8—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—224no—
779C22—448no—
780C22—442no—
781C22—442no—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—884no—
786C22#1062308512yes—
787C22#1062327912yes—
788C22#1062328212yes—
789C22C23×D4411yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—442no—
795C4—442no—
796C4—442no—
797C4—442no—
798C4—442no—
799C4—442no—
800C4#1062308512yes—
801C4C2×#6703711yescharacteristic
802C4C2×#41×D1111yescharacteristic
803C2—42no—
804C2—42no—
805C2—444no—
806C2—882no—
807C2#1308059414yesdirect product factor
808C2C2×#1062308511yescharacteristic
809C2C2×#1062327911yescharacteristic
810C2C2×#1062328211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
hypercenterC2×#435D11
hypocenterC11C2×#3307
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×#10623096C2semidirect
2. C2×#10623082C2semidirect
3. #13080594C2direct (N × H)
4. C2×#10622316C2semidirect
5. C2×#10622336C2semidirect
6. C2×#10622334C2semidirect
7. C2×#10622460C2semidirect
8. C2×#10622747C2semidirect
9. C2×#10622727C2semidirect
10. C2×#10622454C2semidirect
11. C2×#10622347C2semidirect
12. C2×#10622347C2semidirect
13. C2×#10622324C2semidirect
14. C2×#10622746C2semidirect
15. C2×#10622726C2semidirect
16. C2×C11×#435C2semidirect
34. #10623096C22semidirect
36. #10623082C22semidirect
47. C11×#435C22semidirect
52. #10622747C22semidirect
53. #10622746C22semidirect
54. #10622727C22semidirect
55. #10622726C22semidirect
69. #10622460C22semidirect
70. #10622454C22semidirect
71. #10622347C22semidirect
72. #10622347C22semidirect
73. #10622336C22semidirect
74. #10622334C22semidirect
75. #10622324C22semidirect
76. #10622316C22semidirect
305. C2×#435D11semidirect
421. #435C2×D11semidirect
584. C2×C11#3307semidirect
696. C11C2×#3307semidirect
807. C2#13080594direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230962
C2×#106230822
#130805942
C2×#106223162
C2×#106223362
C2×#106223342
C2×#106224602
C2×#106227472
C2×#106227272
C2×#106224542
C2×#106223472
C2×#106223242
C2×#106227462
C2×#106227262
C2×C11×#4352
C2×#330711