Finite Group Databasebeta

← C2×#13080621 #15630474

Subgroups — C2×#13080621 #15630474

Order 2816.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623226C211yesmaximal, characteristic, complemented
2C2×#10623249C211yesmaximal, characteristic, complemented
3#13080621C2116yesmaximal, direct product factor
4C2×#10622397C211yesmaximal, characteristic, complemented
5C2×#10622387C211yesmaximal, characteristic, complemented
6C2×#10622676C211yesmaximal, characteristic, complemented
7C2×#10622395C211yesmaximal, characteristic, complemented
8C2×#10622388C211yesmaximal, characteristic, complemented
9C2×#10622685C211yesmaximal, characteristic, complemented
10C2×#10622394C211yesmaximal, characteristic, complemented
11C2×#10622394C211yesmaximal, characteristic, complemented
12C2×#10622323C211yesmaximal, characteristic, complemented
13C2×#10622319C211yesmaximal, characteristic, complemented
14C2×#10622384C211yesmaximal, characteristic, complemented
15C2×#10622385C211yesmaximal, characteristic, complemented
16C2×C11×#490C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C2×C11×#127C2211yescharacteristic
20C2×C11×#125C2211yescharacteristic
21C2×#66993—21no—
22C2×#66992—21no—
23C2×#66992—21no—
24C2×#66991C2211yescharacteristic
25C2×#66991C2211yescharacteristic
26C2×D4×Dic11—21no—
27C22×#4323C2211yescharacteristic
28C22×#4323C2211yescharacteristic
29C22×#4314C2211yescharacteristic
30C22×#4313C2211yescharacteristic
31C22×C8×D11C2211yescharacteristic
32#10623249—24no—
33#10623249C2218yescomplemented
34#10623226—24no—
35#10623226C2218yescomplemented
36C2×#66951—21no—
37C2×#66948—21no—
38C2×#66948C2211yescharacteristic
39C2×#66948C2211yescharacteristic
40C2×#66947—21no—
41C2×#66946—21no—
42C2×#66945C2211yescharacteristic
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic
47C11×#490C2218yescomplemented
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C11×#97C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66882C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60#10622685C2218yescomplemented
61#10622676C2218yescomplemented
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622397C2218yescomplemented
68#10622395C2218yescomplemented
69#10622394C2218yescomplemented
70#10622394C2218yescomplemented
71#10622388C2218yescomplemented
72#10622387C2218yescomplemented
73#10622385C2218yescomplemented
74#10622384C2218yescomplemented
75#10622323C2218yescomplemented
76#10622319C2218yescomplemented
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C23×Dic11—21no—
86C23×Dic11—21no—
87C2×#4341—22no—
88C2×#4341—22no—
89C2×#4341—24no—
90C2×#4341—24no—
91C2×#4341—42no—
92C2×#4341—42no—
93C2×#4341C2314yes—
94C2×#4341C2314yes—
95C22×D44—21no—
96C22×D44—21no—
97C22×D44D411yescharacteristic
98C22×D44C2311yescharacteristic
99C22×C4×D11—21no—
100C22×C4×D11—21no—
101C22×C4×D11C2311yescharacteristic
102C22×C4×D11C2311yescharacteristic
103C22×Dic22C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C11×#127—22no—
107C11×#127C2314yes—
108C11×#125—22no—
109C11×#125C2314yes—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117#66993—28no—
118#66992—28no—
119#66992—28no—
120#66991—22no—
121#66991—22no—
122#66991C2314yes—
123#66991C2314yes—
124D4×Dic11—28no—
125C2×#4323—42no—
126C2×#4323—42no—
127C2×#4323C2314yes—
128C2×#4323C2314yes—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4D411yescharacteristic
134C2×(C2×D11)⋊C4D411yescharacteristic
135C2×C4⋊Dic11D411yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2311yescharacteristic
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×C4×Dic11—21no—
141C2×C4×Dic11—21no—
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C2×#4314—24no—
145C2×#4314C2314yes—
146C2×#4313—42no—
147C2×#4313C2314yes—
148C2×C8×D11—42no—
149C2×C8×D11C2314yes—
150#66951—28no—
151#66948—28no—
152#66948—22no—
153#66948—22no—
154#66948C2314yes—
155#66948C2314yes—
156#66947—28no—
157#66946—28no—
158#66945—22no—
159#66945C2314yes—
160C4⋊C4×D11—22no—
161C4⋊C4×D11C2314yes—
162C4×D44—22no—
163C4×D44D414yes—
164C4×D44C2314yes—
165C4×D44C2314yes—
166C4×Dic22—22no—
167C4×Dic22C2314yes—
168C11×#102C2314yes—
169C11×#102C2314yes—
170C11×#102C2314yes—
171C11×#102C2314yes—
172C11×#97C2314yes—
173#66896C2314yes—
174#66896C2314yes—
175#66885C2314yes—
176(C2×D11)⋊C8C2314yes—
177(C2×D11)⋊C8C2314yes—
178#66882C2314yes—
179#66880C2314yes—
180#66874C2314yes—
181#66874C2314yes—
182#66872C2314yes—
183#66871C2314yes—
184C4⋊(C11⋊C8)C2314yes—
185C2×#3309—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C23×D11—21no—
189C23×D11C2×D411yescharacteristic
190C23×D11C2×D411yescharacteristic
191C2×D4×C11—24no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—24no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11—22no—
199C2×D4×C11—44no—
200C2×D4×C11—82no—
201C2×D4×C11C2412yes—
202C2×D4×C11C2412yes—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2411yescharacteristic
208C2×C22⋊D11—24no—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—82no—
215C2×C22⋊D11—82no—
216C22×Dic11—24no—
217C22×Dic11—24no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—44no—
222C22×Dic11—44no—
223C22×Dic11C2×D411yescharacteristic
224C22×Dic11C2×D411yescharacteristic
225#4341—28no—
226#4341—28no—
227#4341—44no—
228#4341—44no—
229#4341—48no—
230#4341—48no—
231C2×D44—24no—
232C2×D44—24no—
233C2×D44—21no—
234C2×D44—22no—
235C2×D44—22no—
236C2×D44—42no—
237C2×D44—44no—
238C2×D44—82no—
239C2×D44C2×D414yes—
240C2×D44C2412yes—
241C2×C4×D11—24no—
242C2×C4×D11—24no—
243C2×C4×D11—22no—
244C2×C4×D11—22no—
245C2×C4×D11—22no—
246C2×C4×D11—22no—
247C2×C4×D11—82no—
248C2×C4×D11—82no—
249C2×C4×D11C2×D412yes—
250C2×C4×D11C2×D412yes—
251C2×C4×D11C2412yes—
252C2×C4×D11C2412yes—
253C2×Dic22—21no—
254C2×Dic22—22no—
255C2×Dic22#4114yes—
256C2×Dic22C2412yes—
257C2×C8×C11—22no—
258C2×C8×C11—22no—
259C2×C8×C11C2412yes—
260C2×C8×C11C2412yes—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—24no—
264C11×C4⋊C4—24no—
265C11×C4⋊C4C2412yes—
266C11×C4⋊C4C2412yes—
267C42×C11C2×D412yes—
268C42×C11C2412yes—
269C22⋊Dic11—24no—
270C22⋊Dic11—24no—
271#4323—44no—
272#4323—44no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4C2×D414yes—
278(C2×D11)⋊C4C2×D414yes—
279C4⋊Dic11—21no—
280C4⋊Dic11—21no—
281C4⋊Dic11C2×D414yes—
282C4⋊Dic11C2412yes—
283C4⋊Dic11C2412yes—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286C4×Dic11—24no—
287C4×Dic11—24no—
288C2×C11⋊C8—22no—
289C2×C11⋊C8—22no—
290C2×C11⋊C8C2412yes—
291C2×C11⋊C8C2412yes—
292#4314—28no—
293#4313—44no—
294C8×D11—44no—
295C2×#553—111no—
296C2×#550—111no—
297#3309—1116no—
298C2×#490D1111yescharacteristic, complemented
299C2×#482—111no—
300C2×#480—111no—
301C2×#479—111no—
302C2×#469—111no—
303C2×#466—111no—
304C2×#459—111no—
305C2×#449—111no—
306C2×#449—111no—
307C2×#440—111no—
308C2×#435—111no—
309C2×#417—111no—
310C2×#416—111no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—42no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11C22×D411yescharacteristic
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—42no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11C22×D412yes—
331C22×D11C22×D412yes—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—48no—
337D4×C11—42no—
338D4×C11—42no—
339D4×C11—84no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—42no—
345C2×C4×C11—42no—
346C2×C4×C11C22×D412yes—
347C2×C4×C11C22×D412yes—
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C2×#4112yes—
350C2×C4×C11H(5,𝔽2)12yes—
351C2×C4×C11C2511yescharacteristic
352C22⋊D11—48no—
353C22⋊D11—48no—
354C22⋊D11—84no—
355C22⋊D11—84no—
356C2×Dic11—24no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—48no—
363C2×Dic11—48no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366C2×Dic11C22×D412yes—
367C2×Dic11C22×D412yes—
368D44—22no—
369D44—22no—
370D44—44no—
371D44—48no—
372D44—42no—
373D44—84no—
374C4×D11—24no—
375C4×D11—24no—
376C4×D11—22no—
377C4×D11—22no—
378C4×D11—22no—
379C4×D11—22no—
380C4×D11—84no—
381C4×D11—84no—
382Dic22—24no—
383Dic22—22no—
384Dic22C2×#4114yes—
385C8×C11—22no—
386C8×C11—22no—
387C11⋊C8—22no—
388C11⋊C8—22no—
389C22×#41—111no—
390C22×#41—111no—
391C22×SD16—111no—
392C22×D8—111no—
393C22×D8—111no—
394C22×M16—111no—
395C23×C8—111no—
396#553—118no—
397#553—224no—
398#550—118no—
399#550—224no—
400C2×#127—221no—
401C2×#127C2×D1111yescharacteristic
402C2×#126—221no—
403C2×#125C2×D1111yescharacteristic
404C2×#123—221no—
405C2×#121—111no—
406C2×#121—111no—
407C2×#121—111no—
408C2×#121—111no—
409C2×#121—221no—
410C2×#121—221no—
411C2×#121—221no—
412C2×C4×Q8—111no—
413C2×C4×D4—111no—
414C2×C4×D4—111no—
415C2×C4×D4—221no—
416C2×C4×D4—221no—
417C2×#117—111no—
418C22×C4⋊C4—111no—
419#490C2×D1118yescomplemented
420#482—118no—
421#480—118no—
422#479—118no—
423#469—118no—
424#466—118no—
425#459—118no—
426#449—118no—
427#449—118no—
428#440—118no—
429#435—118no—
430C2×#107—111no—
431C2×#107—111no—
432C2×#106—111no—
433C2×C4⋊C8—111no—
434#417—118no—
435#416—118no—
436C2×#103—111no—
437C2×#103—111no—
438C2×#103—111no—
439C2×#102—111no—
440C2×#102—111no—
441C2×#102—111no—
442C2×#102C2×D1111yescharacteristic
443C2×#102C2×D1111yescharacteristic
444C2×#102C2×D1111yescharacteristic
445C2×#102C2×D1111yescharacteristic
446C2×C22⋊C8—111no—
447C2×C22⋊C8—111no—
448C2×#97C2×D1111yescharacteristic
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—84no—
456C22×C11—84no—
457C22×C11#54612yes—
458C22×C11#57512yes—
459C22×C11#57612yes—
460C22×C11C23×D411yescharacteristic
461C2×D11—22no—
462C2×D11—22no—
463C2×D11—22no—
464C2×D11—22no—
465C2×D11—22no—
466C2×D11—22no—
467C2×D11—44no—
468C2×D11—44no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—84no—
473C4×C11—22no—
474C4×C11—22no—
475C4×C11—42no—
476C4×C11—42no—
477C4×C11#54612yes—
478C4×C11C22×#4111yescharacteristic
479C4×C11C2×H(5,𝔽2)11yescharacteristic
480Dic11—24no—
481Dic11—22no—
482Dic11—22no—
483Dic11—42no—
484Dic11—42no—
485C2×#41—114no—
486C2×#41—114no—
487C2×#41—222no—
488C2×#41—222no—
489C2×#41—224no—
490C2×#41—224no—
491C2×#41—442no—
492C2×#41—442no—
493C22×Q8—111no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—111no—
497C22×D4—111no—
498C22×D4—221no—
499C22×D4—221no—
500C22×D4—221no—
501C22×D4—221no—
502C22×D4—221no—
503C22×D4—221no—
504C22×D4C22×D1111yescharacteristic
505C22×D4C22×D1111yescharacteristic
506C23×C4—111no—
507C23×C4—111no—
508C23×C4—221no—
509C23×C4—221no—
510C23×C4—221no—
511C23×C4—221no—
512C2×SD16—114no—
513C2×SD16—224no—
514C2×D8—114no—
515C2×D8—114no—
516C2×D8—442no—
517C2×D8—442no—
518C2×M16—114no—
519C2×M16—442no—
520C22×C8—111no—
521C22×C8—111no—
522C22×C8—114no—
523C22×C8—442no—
524C22×C8C22×D1111yescharacteristic
525C22×C8C22×D1111yescharacteristic
526#127—22no—
527#127—228no—
528#127C22×D1114yes—
529#126—228no—
530#125—22no—
531#125C22×D1114yes—
532#123—228no—
533#121—114no—
534#121—114no—
535#121—114no—
536#121—114no—
537#121—228no—
538#121—228no—
539#121—222no—
540#121—222no—
541#121—228no—
542#121—222no—
543#121—222no—
544C4×Q8—114no—
545C4×Q8—222no—
546C4×D4—114no—
547C4×D4—114no—
548C4×D4—114no—
549C4×D4—228no—
550C4×D4—228no—
551C4×D4—222no—
552#117—114no—
553#117—222no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—111no—
559C2×C4⋊C4—114no—
560C2×C4⋊C4—222no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—221no—
563C2×C4⋊C4C22×D1111yescharacteristic
564C2×C4⋊C4C22×D1111yescharacteristic
565C2×C22⋊C4—111no—
566C2×C22⋊C4—111no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4—221no—
573C2×C42—221no—
574C2×C42—221no—
575C2×C42C22×D1111yescharacteristic
576#107—114no—
577#107—114no—
578#106—114no—
579C4⋊C8—114no—
580#103—114no—
581#103—114no—
582#103—114no—
583#102—114no—
584#102—114no—
585#102—114no—
586#102C22×D1114yes—
587#102C22×D1114yes—
588#102C22×D1114yes—
589#102C22×D1114yes—
590C22⋊C8—114no—
591C22⋊C8—114no—
592#97C22×D1114yes—
593C2×C11—82no—
594C2×C11—82no—
595C2×C11#330914yescomplemented
596C2×C11C2×#54611yescharacteristic
597C2×C11C2×#57511yescharacteristic
598C2×C11C2×#57611yescharacteristic
599D11—42no—
600D11—42no—
601D11—82no—
602C24—21no—
603C24—21no—
604C24—111no—
605C24—111no—
606C24—221no—
607#41—228no—
608#41—228no—
609#41—444no—
610#41—444no—
611#41—448no—
612#41—448no—
613C2×Q8—114no—
614C2×Q8—112no—
615C2×Q8—221no—
616C2×Q8—222no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—24no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—44no—
626C2×D4—82no—
627C2×D4—114no—
628C2×D4—112no—
629C2×D4—224no—
630C2×D4—224no—
631C2×D4—224no—
632C2×D4—224no—
633C2×D4—224no—
634C2×D4—224no—
635C2×D4—221no—
636C2×D4—222no—
637C2×D4—222no—
638C2×D4—442no—
639C2×D4—444no—
640C2×D4—444no—
641C2×D4—444no—
642C2×D4—882no—
643C2×D4—882no—
644C2×D4—882no—
645C2×D4C23×D1112yes—
646C2×D4C23×D1112yes—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—111no—
650C22×C4—111no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—224no—
656C22×C4—224no—
657C22×C4—224no—
658C22×C4—221no—
659C22×C4—222no—
660C22×C4—222no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—224no—
666C22×C4—444no—
667C22×C4—444no—
668C22×C4—882no—
669C22×C4—882no—
670C22×C4D4×D1111yescharacteristic
671C22×C4D4×D1111yescharacteristic
672C22×C4C23×D1111yescharacteristic
673SD16—228no—
674D8—444no—
675D8—444no—
676M16—444no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—112no—
680C2×C8—112no—
681C2×C8—222no—
682C2×C8—222no—
683C2×C8—444no—
684C2×C8C23×D1112yes—
685C2×C8C23×D1112yes—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—114no—
691C4⋊C4—112no—
692C4⋊C4—112no—
693C4⋊C4—224no—
694C4⋊C4—221no—
695C4⋊C4—221no—
696C4⋊C4—224no—
697C4⋊C4C23×D1112yes—
698C4⋊C4C23×D1112yes—
699C22⋊C4—114no—
700C22⋊C4—114no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C42—224no—
708C42—224no—
709C42D4×D1112yes—
710C42C23×D1112yes—
711C11C2×#330911yescharacteristic, complemented, Sylow
712C23—22no—
713C23—22no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—112no—
721C23—112no—
722C23—222no—
723C23—222no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—442no—
730C23—442no—
731C23—442no—
732C23C2×D4×D1111yescharacteristic
733Q8—114no—
734Q8—222no—
735Q8—224no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—48no—
741D4—42no—
742D4—42no—
743D4—84no—
744D4—222no—
745D4—222no—
746D4—444no—
747D4—448no—
748D4—448no—
749D4—448no—
750D4—442no—
751D4—884no—
752D4—884no—
753D4—884no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—112no—
761C2×C4—112no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—224no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—224no—
771C2×C4—224no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—448no—
775C2×C4—448no—
776C2×C4—442no—
777C2×C4—442no—
778C2×C4—884no—
779C2×C4—884no—
780C2×C4C2×D4×D1112yes—
781C2×C4C2×D4×D1112yes—
782C2×C4C2×D4×D1111yescharacteristic
783C2×C4#41×D1112yes—
784C2×C4#6704212yes—
785C2×C4C24×D1111yescharacteristic
786C8—22no—
787C8—22no—
788C8—222no—
789C8—222no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—84no—
797C22—84no—
798C22—222no—
799C22—222no—
800C22—222no—
801C22—222no—
802C22—222no—
803C22—222no—
804C22—444no—
805C22—444no—
806C22—442no—
807C22—442no—
808C22—442no—
809C22—884no—
810C22#1062320712yes—
811C22#1062330412yes—
812C22#1062330512yes—
813C22C22×D4×D1111yescharacteristic
814C4—22no—
815C4—22no—
816C4—42no—
817C4—42no—
818C4—222no—
819C4—222no—
820C4—224no—
821C4—442no—
822C4—442no—
823C4#1062320712yes—
824C4C2×#41×D1111yescharacteristic
825C4C2×#6704211yescharacteristic
826C2—82no—
827C2—82no—
828C2—442no—
829C2—442no—
830C2—882no—
831C2#1308062114yesdirect product factor
832C2C2×#1062320711yescharacteristic
833C2C2×#1062330411yescharacteristic
834C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#490C2
socleC23×C11C22×D4
hypercenterC2×#490D11
hypocenterC11C2×#3309
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#10623226C2semidirect
2. C2×#10623249C2semidirect
3. #13080621C2direct (N × H)
4. C2×#10622397C2semidirect
5. C2×#10622387C2semidirect
6. C2×#10622676C2semidirect
7. C2×#10622395C2semidirect
8. C2×#10622388C2semidirect
9. C2×#10622685C2semidirect
10. C2×#10622394C2semidirect
11. C2×#10622394C2semidirect
12. C2×#10622323C2semidirect
13. C2×#10622319C2semidirect
14. C2×#10622384C2semidirect
15. C2×#10622385C2semidirect
16. C2×C11×#490C2semidirect
33. #10623249C22semidirect
35. #10623226C22semidirect
47. C11×#490C22semidirect
60. #10622685C22semidirect
61. #10622676C22semidirect
67. #10622397C22semidirect
68. #10622395C22semidirect
69. #10622394C22semidirect
70. #10622394C22semidirect
71. #10622388C22semidirect
72. #10622387C22semidirect
73. #10622385C22semidirect
74. #10622384C22semidirect
75. #10622323C22semidirect
76. #10622319C22semidirect
298. C2×#490D11semidirect
419. #490C2×D11semidirect
595. C2×C11#3309semidirect
711. C11C2×#3309semidirect
831. C2#13080621direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232262
C2×#106232492
#130806212
C2×#106223972
C2×#106223872
C2×#106226762
C2×#106223952
C2×#106223882
C2×#106226852
C2×#106223942
C2×#106223232
C2×#106223192
C2×#106223842
C2×#106223852
C2×C11×#4902
C2×#330911