Finite Group Databasebeta

← C2×#13080619 #15630472

Subgroups — C2×#13080619 #15630472

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×#10623108C211yesmaximal, characteristic, complemented
3#13080619C2116yesmaximal, direct product factor
4C2×#10622680C211yesmaximal, characteristic, complemented
5C2×#10622479C211yesmaximal, characteristic, complemented
6C2×#10622495C211yesmaximal, characteristic, complemented
7C2×#10622478C211yesmaximal, characteristic, complemented
8C2×#10622496C211yesmaximal, characteristic, complemented
9C2×#10622456C211yesmaximal, characteristic, complemented
10C2×#10622424C211yesmaximal, characteristic, complemented
11C2×#10622424C211yesmaximal, characteristic, complemented
12C2×#10622639C211yesmaximal, characteristic, complemented
13C2×#10622449C211yesmaximal, characteristic, complemented
14C2×#10622416C211yesmaximal, characteristic, complemented
15C2×#10622417C211yesmaximal, characteristic, complemented
16C2×C11×#479C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×#4343C2211yescharacteristic
19C2×C11×#125C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C22×D88C2211yescharacteristic
23C22×D88C2211yescharacteristic
24C22×#4313C2211yescharacteristic
25C22×C8×D11C2211yescharacteristic
26#10623226—24no—
27#10623226C2218yescomplemented
28#10623108—24no—
29#10623108C2218yescomplemented
30C2×#66951—21no—
31C2×#66948—21no—
32C2×#66948—21no—
33C2×#66948—21no—
34C2×#66948C2211yescharacteristic
35C2×#66948C2211yescharacteristic
36C2×#66948C2211yescharacteristic
37C2×#66948C2211yescharacteristic
38C2×#66947—21no—
39C2×#66946—21no—
40C2×#66945C2211yescharacteristic
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×#66927—21no—
43C2×#66927C2211yescharacteristic
44C2×C4×D44—21no—
45C2×C4×D44C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47C11×#479C2218yescomplemented
48C2×C11×#107C2211yescharacteristic
49C2×C11×#106C2211yescharacteristic
50C2×C11×C4⋊C8C2211yescharacteristic
51C2×C11×#103C2211yescharacteristic
52C2×C11×#103C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58#10622680C2218yescomplemented
59#10622639C2218yescomplemented
60C2×#66873C2211yescharacteristic
61C2×#66873C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×#66867C2211yescharacteristic
67#10622496C2218yescomplemented
68#10622495C2218yescomplemented
69#10622479C2218yescomplemented
70#10622478C2218yescomplemented
71#10622456C2218yescomplemented
72#10622449C2218yescomplemented
73#10622424C2218yescomplemented
74#10622424C2218yescomplemented
75#10622417C2218yescomplemented
76#10622416C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C2×#4343—22no—
79C2×#4343—22no—
80C2×#4343—24no—
81C2×#4343—24no—
82C2×#4343—42no—
83C2×#4343—42no—
84C2×#4343C2314yes—
85C2×#4343C2314yes—
86C22×D44—21no—
87C22×D44—21no—
88C22×D44—21no—
89C22×D44—21no—
90C22×D44—21no—
91C22×D44—21no—
92C22×D44—21no—
93C22×D44—21no—
94C22×D44D411yescharacteristic
95C22×D44C2311yescharacteristic
96C22×D44C2311yescharacteristic
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C22×C4×D11—21no—
100C22×C4×D11—21no—
101C22×C4×D11—21no—
102C22×C4×D11C2311yescharacteristic
103C22×C4×D11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C11×#125—22no—
107C11×#125C2314yes—
108C4×Q8×C11—22no—
109C4×Q8×C11C2314yes—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C42×C11—21no—
117C2×C42×C11C2311yescharacteristic
118C2×#4325—24no—
119C2×#4325C2314yes—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4D411yescharacteristic
127C2×(C2×D11)⋊C4D411yescharacteristic
128C2×C4⋊Dic11D411yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×Dic11⋊C4—21no—
131C2×C4×Dic11—21no—
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C2×D88—42no—
135C2×D88—42no—
136C2×D88C2314yes—
137C2×D88C2314yes—
138C2×#4313—42no—
139C2×#4313C2314yes—
140C2×C8×D11—42no—
141C2×C8×D11C2314yes—
142#66951—28no—
143#66948—28no—
144#66948—22no—
145#66948—22no—
146#66948—22no—
147#66948—22no—
148#66948—28no—
149#66948—28no—
150#66948C2314yes—
151#66948C2314yes—
152#66948C2314yes—
153#66948C2314yes—
154#66947—28no—
155#66946—28no—
156#66945—22no—
157#66945C2314yes—
158C4⋊C4×D11—22no—
159C4⋊C4×D11C2314yes—
160#66927—28no—
161#66927—22no—
162#66927C2314yes—
163C4×D44—22no—
164C4×D44—28no—
165C4×D44D414yes—
166C4×D44C2314yes—
167C4×D44C2314yes—
168C11×#107C2314yes—
169C11×#106C2314yes—
170C11×C4⋊C8C2314yes—
171C11×#103C2314yes—
172C11×#103C2314yes—
173#66899C2314yes—
174#66885C2314yes—
175#66885C2314yes—
176(C2×D11)⋊C8C2314yes—
177(C2×D11)⋊C8C2314yes—
178#66873C2314yes—
179#66873C2314yes—
180#66873C2314yes—
181#66873C2314yes—
182#66873C2314yes—
183#66871C2314yes—
184#66867C2314yes—
185C2×#3309—111nomaximal, Sylow
186C23×D11—21no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11C2×D411yescharacteristic
190C23×D11C2×D411yescharacteristic
191C2×Q8×C11—21no—
192C2×Q8×C11—22no—
193C2×Q8×C11#4114yes—
194C2×Q8×C11C2412yes—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C22×Dic11—21no—
203C22×Dic11C2×D411yescharacteristic
204C22×Dic11C2×D411yescharacteristic
205#4343—28no—
206#4343—28no—
207#4343—44no—
208#4343—44no—
209#4343—48no—
210#4343—48no—
211C2×D44—24no—
212C2×D44—24no—
213C2×D44—24no—
214C2×D44—24no—
215C2×D44—24no—
216C2×D44—24no—
217C2×D44—24no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—24no—
222C2×D44—22no—
223C2×D44—22no—
224C2×D44—22no—
225C2×D44—22no—
226C2×D44—22no—
227C2×D44—22no—
228C2×D44—42no—
229C2×D44—44no—
230C2×D44—44no—
231C2×D44—44no—
232C2×D44—44no—
233C2×D44—82no—
234C2×D44—82no—
235C2×D44—82no—
236C2×D44—82no—
237C2×D44C2×D414yes—
238C2×D44C2412yes—
239C2×D44C2412yes—
240C2×D44C2412yes—
241C2×C4×D11—24no—
242C2×C4×D11—24no—
243C2×C4×D11—24no—
244C2×C4×D11—24no—
245C2×C4×D11—22no—
246C2×C4×D11—22no—
247C2×C4×D11—22no—
248C2×C4×D11—22no—
249C2×C4×D11—44no—
250C2×C4×D11—44no—
251C2×C4×D11—82no—
252C2×C4×D11—82no—
253C2×C4×D11C2×D412yes—
254C2×C4×D11C2×D412yes—
255C2×C4×D11C2412yes—
256C2×C4×D11C2412yes—
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⋊C4—21no—
266C11×C4⋊C4—24no—
267C11×C4⋊C4C2412yes—
268C11×C4⋊C4C2412yes—
269C11×C4⋊C4C2412yes—
270C42×C11—24no—
271C42×C11C2×D412yes—
272C42×C11C2412yes—
273#4325—28no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4C2×D414yes—
281(C2×D11)⋊C4C2×D414yes—
282C4⋊Dic11—21no—
283C4⋊Dic11C2×D414yes—
284C4⋊Dic11C2412yes—
285Dic11⋊C4—24no—
286C4×Dic11—24no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8—22no—
289C2×C11⋊C8C2412yes—
290C2×C11⋊C8C2412yes—
291D88—44no—
292D88—44no—
293#4313—44no—
294C8×D11—44no—
295C2×#553—111no—
296C2×#550—111no—
297#3309—1116no—
298C2×#490—111no—
299C2×#482—111no—
300C2×#480—111no—
301C2×#479D1111yescharacteristic, complemented
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×C11C22×D411yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—42no—
322C22×D11—42no—
323C22×D11—42no—
324C22×D11—42no—
325C22×D11—42no—
326C22×D11—42no—
327C22×D11—42no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11C22×D412yes—
331C22×D11C22×D412yes—
332Q8×C11—24no—
333Q8×C11—22no—
334Q8×C11C2×#4114yes—
335C2×C4×C11—24no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—42no—
343C2×C4×C11—42no—
344C2×C4×C11—42no—
345C2×C4×C11C22×D412yes—
346C2×C4×C11C22×D412yes—
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11C2×#4112yes—
349C2×C4×C11H(5,𝔽2)12yes—
350C2×C4×C11C2511yescharacteristic
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—42no—
355C2×Dic11C22×D412yes—
356C2×Dic11C22×D412yes—
357D44—22no—
358D44—22no—
359D44—22no—
360D44—22no—
361D44—22no—
362D44—22no—
363D44—44no—
364D44—48no—
365D44—48no—
366D44—48no—
367D44—48no—
368D44—42no—
369D44—42no—
370D44—42no—
371D44—84no—
372D44—84no—
373D44—84no—
374D44—84no—
375C4×D11—24no—
376C4×D11—24no—
377C4×D11—22no—
378C4×D11—22no—
379C4×D11—22no—
380C4×D11—22no—
381C4×D11—48no—
382C4×D11—48no—
383C4×D11—84no—
384C4×D11—84no—
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—111no—
401C2×#127—221no—
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×Q8C2×D1111yescharacteristic
413C2×C4×D4—111no—
414C2×C4×D4—111no—
415C2×C4×D4—221no—
416C2×C4×D4—221no—
417C2×#117—111no—
418C22×C4⋊C4—111no—
419#490—118no—
420#482—118no—
421#480—118no—
422#479C2×D1118yescomplemented
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×#107C2×D1111yescharacteristic
432C2×#106C2×D1111yescharacteristic
433C2×C4⋊C8C2×D1111yescharacteristic
434#417—118no—
435#416—118no—
436C2×#103—111no—
437C2×#103C2×D1111yescharacteristic
438C2×#103C2×D1111yescharacteristic
439C2×#102—111no—
440C2×#102—111no—
441C2×#102—111no—
442C2×#102—111no—
443C2×#102—111no—
444C2×#102—111no—
445C2×#102—111no—
446C2×C22⋊C8—111no—
447C2×C22⋊C8—111no—
448C2×#97—111no—
449C22×C11#54612yes—
450C22×C11#57512yes—
451C22×C11#57612yes—
452C22×C11C23×D411yescharacteristic
453C2×D11—22no—
454C2×D11—22no—
455C2×D11—22no—
456C2×D11—22no—
457C2×D11—22no—
458C2×D11—22no—
459C2×D11—44no—
460C2×D11—44no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—42no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—84no—
471C2×D11—84no—
472C2×D11—84no—
473C4×C11—24no—
474C4×C11—22no—
475C4×C11—22no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11—42no—
479C4×C11#54612yes—
480C4×C11C22×#4111yescharacteristic
481C4×C11C2×H(5,𝔽2)11yescharacteristic
482Dic11—22no—
483Dic11—22no—
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×Q8C22×D1111yescharacteristic
494C22×D4—111no—
495C22×D4—111no—
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×D4—221no—
505C22×D4—221no—
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—114no—
527#127—228no—
528#127—222no—
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—222no—
542#121—222no—
543#121—228no—
544C4×Q8—22no—
545C4×Q8C22×D1114yes—
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—21no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—111no—
559C2×C4⋊C4—114no—
560C2×C4⋊C4—222no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4C22×D1111yescharacteristic
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—21no—
574C2×C42—221no—
575C2×C42C22×D1111yescharacteristic
576#107—114no—
577#107C22×D1114yes—
578#106C22×D1114yes—
579C4⋊C8C22×D1114yes—
580#103—114no—
581#103C22×D1114yes—
582#103C22×D1114yes—
583#102—114no—
584#102—114no—
585#102—114no—
586#102—114no—
587#102—114no—
588#102—114no—
589#102—114no—
590C22⋊C8—114no—
591C22⋊C8—114no—
592#97—114no—
593C2×C11#330914yescomplemented
594C2×C11C2×#54611yescharacteristic
595C2×C11C2×#57511yescharacteristic
596C2×C11C2×#57611yescharacteristic
597D11—42no—
598D11—42no—
599D11—82no—
600D11—82no—
601D11—82no—
602C24—111no—
603C24—111no—
604C24—221no—
605C24—221no—
606C24—221no—
607#41—228no—
608#41—228no—
609#41—444no—
610#41—444no—
611#41—448no—
612#41—448no—
613C2×Q8—21no—
614C2×Q8—22no—
615C2×Q8#434314yes—
616C2×Q8C23×D1112yes—
617C2×D4—114no—
618C2×D4—112no—
619C2×D4—112no—
620C2×D4—112no—
621C2×D4—224no—
622C2×D4—224no—
623C2×D4—224no—
624C2×D4—224no—
625C2×D4—224no—
626C2×D4—224no—
627C2×D4—221no—
628C2×D4—224no—
629C2×D4—221no—
630C2×D4—221no—
631C2×D4—224no—
632C2×D4—222no—
633C2×D4—222no—
634C2×D4—222no—
635C2×D4—222no—
636C2×D4—222no—
637C2×D4—222no—
638C2×D4—442no—
639C2×D4—444no—
640C2×D4—444no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—882no—
644C2×D4—882no—
645C2×D4—882no—
646C2×D4—882no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—111no—
652C22×C4—111no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—224no—
658C22×C4—224no—
659C22×C4—224no—
660C22×C4—222no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
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—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—114no—
693C4⋊C4—112no—
694C4⋊C4—224no—
695C4⋊C4—221no—
696C4⋊C4C23×D1112yes—
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—24no—
708C42—224no—
709C42D4×D1112yes—
710C42C23×D1112yes—
711C11C2×#330911yescharacteristic, complemented, Sylow
712C23—112no—
713C23—112no—
714C23—222no—
715C23—222no—
716C23—222no—
717C23—222no—
718C23—222no—
719C23—222no—
720C23—222no—
721C23—222no—
722C23—222no—
723C23—442no—
724C23—442no—
725C23—442no—
726C23—442no—
727C23—442no—
728C23—442no—
729C23—442no—
730C23—442no—
731C23—442no—
732C23C2×D4×D1111yescharacteristic
733Q8—24no—
734Q8—22no—
735Q8C2×#434314yes—
736D4—222no—
737D4—222no—
738D4—222no—
739D4—222no—
740D4—222no—
741D4—222no—
742D4—444no—
743D4—448no—
744D4—448no—
745D4—448no—
746D4—448no—
747D4—442no—
748D4—442no—
749D4—442no—
750D4—884no—
751D4—884no—
752D4—884no—
753D4—884no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—112no—
765C2×C4—112no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—224no—
769C2×C4—224no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—448no—
776C2×C4—448no—
777C2×C4—442no—
778C2×C4—884no—
779C2×C4—884no—
780C2×C4C2×D4×D1112yes—
781C2×C4C2×D4×D1112yes—
782C2×C4C2×D4×D1111yescharacteristic
783C2×C4C2×#434312yes—
784C2×C4#6704212yes—
785C2×C4C24×D1111yescharacteristic
786C8—22no—
787C8—22no—
788C8—222no—
789C8—222no—
790C22—222no—
791C22—222no—
792C22—222no—
793C22—222no—
794C22—222no—
795C22—222no—
796C22—444no—
797C22—444no—
798C22—442no—
799C22—442no—
800C22—442no—
801C22—442no—
802C22—442no—
803C22—442no—
804C22—442no—
805C22—442no—
806C22—442no—
807C22—884no—
808C22—884no—
809C22—884no—
810C22#1062316112yes—
811C22#1062330012yes—
812C22#1062330812yes—
813C22C22×D4×D1111yescharacteristic
814C4—24no—
815C4—22no—
816C4—22no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—222no—
821C4—222no—
822C4—442no—
823C4#1062316112yes—
824C4C22×#434311yescharacteristic
825C4C2×#6704211yescharacteristic
826C2—442no—
827C2—442no—
828C2—882no—
829C2—882no—
830C2—882no—
831C2#1308061914yesdirect product factor
832C2C2×#1062316111yescharacteristic
833C2C2×#1062330811yescharacteristic
834C2C2×#1062330011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#479C2
socleC23×C11C22×D4
hypercenterC2×#479D11
hypocenterC11C2×#3309
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#10623226C2semidirect
2. C2×#10623108C2semidirect
3. #13080619C2direct (N × H)
4. C2×#10622680C2semidirect
5. C2×#10622479C2semidirect
6. C2×#10622495C2semidirect
7. C2×#10622478C2semidirect
8. C2×#10622496C2semidirect
9. C2×#10622456C2semidirect
10. C2×#10622424C2semidirect
11. C2×#10622424C2semidirect
12. C2×#10622639C2semidirect
13. C2×#10622449C2semidirect
14. C2×#10622416C2semidirect
15. C2×#10622417C2semidirect
16. C2×C11×#479C2semidirect
27. #10623226C22semidirect
29. #10623108C22semidirect
47. C11×#479C22semidirect
58. #10622680C22semidirect
59. #10622639C22semidirect
67. #10622496C22semidirect
68. #10622495C22semidirect
69. #10622479C22semidirect
70. #10622478C22semidirect
71. #10622456C22semidirect
72. #10622449C22semidirect
73. #10622424C22semidirect
74. #10622424C22semidirect
75. #10622417C22semidirect
76. #10622416C22semidirect
301. C2×#479D11semidirect
422. #479C2×D11semidirect
593. C2×C11#3309semidirect
711. C11C2×#3309semidirect
831. C2#13080619direct (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×#106231082
#130806192
C2×#106226802
C2×#106224792
C2×#106224952
C2×#106224782
C2×#106224962
C2×#106224562
C2×#106224242
C2×#106226392
C2×#106224492
C2×#106224162
C2×#106224172
C2×C11×#4792
C2×#330911