Finite Group Databasebeta

← C2×#13080623 #15630476

Subgroups — C2×#13080623 #15630476

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×#10623045C211yesmaximal, characteristic, complemented
2C2×#10623365C211yesmaximal, characteristic, complemented
3#13080623C2116yesmaximal, direct product factor
4C2×#10622377C211yesmaximal, characteristic, complemented
5C2×#10622392C211yesmaximal, characteristic, complemented
6C2×#10622580C211yesmaximal, characteristic, complemented
7C2×#10622412C211yesmaximal, characteristic, complemented
8C2×#10622748C211yesmaximal, characteristic, complemented
9C2×#10622388C211yesmaximal, characteristic, complemented
10C2×#10622399C211yesmaximal, characteristic, complemented
11C2×#10622424C211yesmaximal, characteristic, complemented
12C2×#10622851C211yesmaximal, characteristic, complemented
13C2×#10622430C211yesmaximal, characteristic, complemented
14C2×#10622740C211yesmaximal, characteristic, complemented
15C2×#10622417C211yesmaximal, characteristic, complemented
16C2×C11×#417C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4343C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21#10623365—24no—
22#10623365C2218yescomplemented
23C2×Q8×Dic11C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C2×#66993—21no—
26C2×#66993C2211yescharacteristic
27C2×#66991—21no—
28C2×#66991C2211yescharacteristic
29C22×#4323C2211yescharacteristic
30C2×#66983—21no—
31C2×#66983—21no—
32C2×#66983C2211yescharacteristic
33C2×#66983C2211yescharacteristic
34C2×C4×C22⋊D11—21no—
35C2×C4×C22⋊D11—21no—
36C2×C4×C22⋊D11C2211yescharacteristic
37C22×D88C2211yescharacteristic
38C22×C8×D11C2211yescharacteristic
39#10623045—24no—
40#10623045C2218yescomplemented
41C2×#66951—21no—
42C2×#66948C2211yescharacteristic
43C2×#66947—21no—
44C2×#66946C2211yescharacteristic
45C2×#66945C2211yescharacteristic
46C2×#66943C2211yescharacteristic
47C11×#417C2218yescomplemented
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52#10622851C2218yescomplemented
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622748C2218yescomplemented
57#10622740C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66879C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64#10622580C2218yescomplemented
65C2×#66873C2211yescharacteristic
66C2×#66873C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×#66871C2211yescharacteristic
69#10622430C2218yescomplemented
70#10622424C2218yescomplemented
71#10622417C2218yescomplemented
72#10622412C2218yescomplemented
73#10622399C2218yescomplemented
74#10622392C2218yescomplemented
75#10622388C2218yescomplemented
76#10622377C2218yescomplemented
77C2×C11×#41—22no—
78C2×C11×#41—24no—
79C2×C11×#41—42no—
80C2×C11×#41C2314yes—
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11D411yescharacteristic
93C2×#4343—22no—
94C2×#4343—24no—
95C2×#4343—42no—
96C2×#4343C2314yes—
97C22×D44—21no—
98C22×D44—21no—
99C22×D44C2311yescharacteristic
100C22×D44C2311yescharacteristic
101C22×C4×D11—21no—
102C22×C4×D11—21no—
103C22×C4×D11C2311yescharacteristic
104C2×C11×M16—42no—
105C2×C11×M16C2314yes—
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2314yes—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11D411yescharacteristic
115Q8×Dic11—22no—
116Q8×Dic11C2314yes—
117C2×#4325—24no—
118C2×#4325C2314yes—
119#66993—28no—
120#66993—22no—
121#66993C2314yes—
122#66991—22no—
123#66991—28no—
124#66991C2314yes—
125C2×#4323—42no—
126C2×#4323C2314yes—
127#66983—22no—
128#66983—22no—
129#66983—28no—
130#66983—28no—
131#66983C2314yes—
132#66983C2314yes—
133C4×C22⋊D11—28no—
134C4×C22⋊D11—28no—
135C4×C22⋊D11D414yes—
136C4×C22⋊D11C2314yes—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4D411yescharacteristic
143C2×C4⋊Dic11—21no—
144C2×C4⋊Dic11—21no—
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2311yescharacteristic
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4D411yescharacteristic
149C2×C4×Dic11—21no—
150C2×C4×Dic11—21no—
151C2×C4×Dic11C2311yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154C2×D88—42no—
155C2×D88C2314yes—
156C2×C8×D11—42no—
157C2×C8×D11C2314yes—
158#66951—28no—
159#66948—22no—
160#66948C2314yes—
161#66947—28no—
162#66946—22no—
163#66946C2314yes—
164#66945—22no—
165#66945C2314yes—
166#66943—22no—
167#66943C2314yes—
168C11×#103C2314yes—
169C11×#103C2314yes—
170C11×#102C2314yes—
171C11×#102C2314yes—
172#66899C2314yes—
173#66896C2314yes—
174C22⋊(C11⋊C8)C2314yes—
175#66885C2314yes—
176#66885C2314yes—
177(C2×D11)⋊C8C2314yes—
178#66881C2314yes—
179#66879C2314yes—
180Dic11⋊C8C2314yes—
181#66873C2314yes—
182#66873C2314yes—
183#66871C2314yes—
184#66871C2314yes—
185C2×#3309—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11C2×D411yescharacteristic
188C23×D11—21no—
189C23×D11—21no—
190C23×D11C2×D411yescharacteristic
191C11×#41—28no—
192C11×#41—44no—
193C11×#41—48no—
194C2×Q8×C11—21no—
195C2×Q8×C11—22no—
196C2×Q8×C11#4114yes—
197C2×Q8×C11C2412yes—
198C2×D4×C11—24no—
199C2×D4×C11—21no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—44no—
203C2×D4×C11C2412yes—
204C22×C4×C11—21no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—24no—
210C22×C4×C11—24no—
211C22×C4×C11—44no—
212C22×C4×C11—82no—
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2411yescharacteristic
217C2×C22⋊D11—24no—
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—42no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—82no—
226C2×C22⋊D11—82no—
227C2×C22⋊D11—82no—
228C2×C22⋊D11C2×D414yes—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11C2×D411yescharacteristic
232C22×Dic11C2×D411yescharacteristic
233C22×Dic11C2×D411yescharacteristic
234#4343—28no—
235#4343—44no—
236#4343—48no—
237C2×D44—24no—
238C2×D44—24no—
239C2×D44—21no—
240C2×D44—21no—
241C2×D44—22no—
242C2×D44—22no—
243C2×D44—22no—
244C2×D44—22no—
245C2×D44—44no—
246C2×D44—82no—
247C2×D44C2412yes—
248C2×D44C2412yes—
249C2×C4×D11—24no—
250C2×C4×D11—24no—
251C2×C4×D11—22no—
252C2×C4×D11—22no—
253C2×C4×D11—44no—
254C2×C4×D11—82no—
255C2×C4×D11C2×D412yes—
256C2×C4×D11C2412yes—
257C11×M16—44no—
258C2×C8×C11—22no—
259C2×C8×C11—22no—
260C2×C8×C11C2412yes—
261C2×C8×C11C2412yes—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—24no—
265C11×C4⋊C4C2412yes—
266C11×C4⋊C4C2412yes—
267C22⋊Dic11—24no—
268C22⋊Dic11C2×D414yes—
269#4325—28no—
270#4323—44no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4C2×D414yes—
277C4⋊Dic11—24no—
278C4⋊Dic11—24no—
279C4⋊Dic11—21no—
280C4⋊Dic11—21no—
281C4⋊Dic11C2412yes—
282C4⋊Dic11C2412yes—
283Dic11⋊C4—24no—
284Dic11⋊C4C2×D414yes—
285C4×Dic11—24no—
286C4×Dic11—24no—
287C4×Dic11C2×D412yes—
288C4×Dic11C2412yes—
289C2×C11⋊C8—22no—
290C2×C11⋊C8—22no—
291C2×C11⋊C8C2412yes—
292C2×C11⋊C8C2412yes—
293D88—44no—
294C8×D11—44no—
295C2×#553—111no—
296C2×#550—111no—
297#3309—1116no—
298C2×#490—111no—
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×#417D1111yescharacteristic, complemented
310C2×#416—111no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11C22×D412yes—
319C23×C11C22×D411yescharacteristic
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—42no—
326C22×D11—42no—
327C22×D11—42no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11C22×D412yes—
332Q8×C11—24no—
333Q8×C11—22no—
334Q8×C11C2×#4114yes—
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—48no—
338D4×C11—42no—
339C2×C4×C11—24no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—24no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—48no—
348C2×C4×C11—42no—
349C2×C4×C11—42no—
350C2×C4×C11—84no—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C2×#4112yes—
354C2×C4×C11H(5,𝔽2)12yes—
355C2×C4×C11C2511yescharacteristic
356C22⋊D11—44no—
357C22⋊D11—48no—
358C22⋊D11—48no—
359C22⋊D11—84no—
360C22⋊D11—84no—
361C22⋊D11—84no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—42no—
368C2×Dic11—42no—
369C2×Dic11C22×D412yes—
370C2×Dic11C22×D412yes—
371C2×Dic11C22×D412yes—
372D44—22no—
373D44—22no—
374D44—22no—
375D44—22no—
376D44—48no—
377D44—42no—
378D44—42no—
379D44—84no—
380C4×D11—24no—
381C4×D11—22no—
382C4×D11—22no—
383C4×D11—48no—
384C4×D11—84no—
385C8×C11—22no—
386C8×C11—22no—
387C11⋊C8—22no—
388C11⋊C8—22no—
389C22×#41—111no—
390C22×#41C2×D1111yescharacteristic
391C22×SD16—111no—
392C22×D8—111no—
393C22×D8—111no—
394C22×M16C2×D1111yescharacteristic
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×#125—111no—
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⋊C4C2×D1111yescharacteristic
419#490—118no—
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#417C2×D1118yescomplemented
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×#102C2×D1111yescharacteristic
445C2×#102C2×D1111yescharacteristic
446C2×C22⋊C8—111no—
447C2×C22⋊C8—111no—
448C2×#97—111no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—44no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
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—44no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—84no—
472C2×D11—84no—
473C4×C11—22no—
474C4×C11—24no—
475C4×C11—42no—
476C4×C11—42no—
477C4×C11#54612yes—
478C4×C11C22×#4111yescharacteristic
479C4×C11C2×H(5,𝔽2)11yescharacteristic
480Dic11—22no—
481Dic11—22no—
482Dic11—22no—
483Dic11—42no—
484Dic11—42no—
485C2×#41—22no—
486C2×#41—24no—
487C2×#41—42no—
488C2×#41—114no—
489C2×#41—222no—
490C2×#41—224no—
491C2×#41—442no—
492C2×#41C22×D1114yes—
493C22×Q8C22×D1111yescharacteristic
494C22×D4—21no—
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×D4C22×D1111yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—111no—
509C23×C4—221no—
510C23×C4—221no—
511C23×C4C22×D1111yescharacteristic
512C2×SD16—114no—
513C2×SD16—224no—
514C2×D8—114no—
515C2×D8—114no—
516C2×D8—442no—
517C2×D8—442no—
518C2×M16—42no—
519C2×M16C22×D1114yes—
520C22×C8—111no—
521C22×C8—111no—
522C22×C8—114no—
523C22×C8—442no—
524C22×C8C22×D1111yescharacteristic
525C22×C8C22×D1111yescharacteristic
526#127—114no—
527#127—222no—
528#127—228no—
529#126—228no—
530#125—114no—
531#125—222no—
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—228no—
541#121—222no—
542#121—222no—
543#121—222no—
544C4×Q8—114no—
545C4×Q8—222no—
546C4×D4—114no—
547C4×D4—114no—
548C4×D4—114no—
549C4×D4—222no—
550C4×D4—228no—
551C4×D4—228no—
552#117—114no—
553#117—222no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—111no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4C22×D1111yescharacteristic
563C2×C4⋊C4C22×D1111yescharacteristic
564C2×C4⋊C4C22×D1114yes—
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—111no—
574C2×C42—221no—
575C2×C42—221no—
576#107—114no—
577#107—114no—
578#106—114no—
579C4⋊C8—114no—
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#102C22×D1114yes—
589#102C22×D1114yes—
590C22⋊C8—114no—
591C22⋊C8—114no—
592#97—114no—
593C2×C11—42no—
594C2×C11—82no—
595C2×C11#330914yescomplemented
596C2×C11C2×#54611yescharacteristic
597C2×C11C2×#57511yescharacteristic
598C2×C11C2×#57611yescharacteristic
599D11—42no—
600D11—82no—
601D11—82no—
602C24—21no—
603C24—111no—
604C24—221no—
605C24—221no—
606C24D4×D1111yescharacteristic
607#41—28no—
608#41—44no—
609#41—48no—
610#41—228no—
611#41—444no—
612#41—448no—
613C2×Q8—21no—
614C2×Q8—22no—
615C2×Q8#433914yes—
616C2×Q8C23×D1112yes—
617C2×D4—24no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—44no—
622C2×D4—114no—
623C2×D4—112no—
624C2×D4—112no—
625C2×D4—224no—
626C2×D4—224no—
627C2×D4—224no—
628C2×D4—224no—
629C2×D4—224no—
630C2×D4—224no—
631C2×D4—224no—
632C2×D4—222no—
633C2×D4—222no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—222no—
637C2×D4—222no—
638C2×D4—444no—
639C2×D4—442no—
640C2×D4—444no—
641C2×D4—444no—
642C2×D4—882no—
643C2×D4—882no—
644C2×D4—882no—
645C2×D4—882no—
646C2×D4C23×D1112yes—
647C22×C4—21no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—24no—
653C22×C4—24no—
654C22×C4—44no—
655C22×C4—82no—
656C22×C4—111no—
657C22×C4—111no—
658C22×C4—111no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—224no—
662C22×C4—224no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—444no—
668C22×C4—882no—
669C22×C4D4×D1112yes—
670C22×C4D4×D1111yescharacteristic
671C22×C4C23×D1112yes—
672C22×C4C23×D1111yescharacteristic
673SD16—228no—
674D8—444no—
675D8—444no—
676M16—44no—
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—21no—
687C4⋊C4—21no—
688C4⋊C4—24no—
689C4⋊C4—114no—
690C4⋊C4—112no—
691C4⋊C4—112no—
692C4⋊C4—224no—
693C4⋊C4—224no—
694C4⋊C4—224no—
695C4⋊C4—221no—
696C4⋊C4—221no—
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—112no—
708C42—112no—
709C42—224no—
710C42—224no—
711C11C2×#330911yescharacteristic, complemented, Sylow
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—112no—
720C23—222no—
721C23—222no—
722C23—222no—
723C23—222no—
724C23—222no—
725C23—442no—
726C23—442no—
727C23—442no—
728C23—442no—
729C23—442no—
730C23—442no—
731C23C2×D4×D1112yes—
732C23C2×D4×D1111yescharacteristic
733Q8—24no—
734Q8—22no—
735Q8C2×#433914yes—
736D4—22no—
737D4—22no—
738D4—48no—
739D4—42no—
740D4—222no—
741D4—222no—
742D4—222no—
743D4—222no—
744D4—448no—
745D4—444no—
746D4—448no—
747D4—448no—
748D4—442no—
749D4—442no—
750D4—884no—
751D4—884no—
752D4—884no—
753D4—884no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—48no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—84no—
766C2×C4—112no—
767C2×C4—112no—
768C2×C4—112no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—224no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—448no—
778C2×C4—442no—
779C2×C4—442no—
780C2×C4—884no—
781C2×C4C2×#433912yes—
782C2×C4C2×D4×D1112yes—
783C2×C4C2×D4×D1111yescharacteristic
784C2×C4#6703712yes—
785C2×C4C24×D1111yescharacteristic
786C8—22no—
787C8—22no—
788C8—222no—
789C8—222no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—44no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—84no—
798C22—222no—
799C22—222no—
800C22—222no—
801C22—444no—
802C22—442no—
803C22—442no—
804C22—442no—
805C22—442no—
806C22—442no—
807C22—442no—
808C22—884no—
809C22—884no—
810C22#1062302112yes—
811C22#1062330512yes—
812C22#1062330812yes—
813C22C22×D4×D1111yescharacteristic
814C4—22no—
815C4—24no—
816C4—42no—
817C4—42no—
818C4—222no—
819C4—222no—
820C4—222no—
821C4—442no—
822C4—442no—
823C4#1062302112yes—
824C4C22×#433911yescharacteristic
825C4C2×#6703711yescharacteristic
826C2—42no—
827C2—82no—
828C2—442no—
829C2—882no—
830C2—882no—
831C2#1308062314yesdirect product factor
832C2C2×#1062302111yescharacteristic
833C2C2×#1062330811yescharacteristic
834C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
hypercenterC2×#417D11
hypocenterC11C2×#3309
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#10623045C2semidirect
2. C2×#10623365C2semidirect
3. #13080623C2direct (N × H)
4. C2×#10622377C2semidirect
5. C2×#10622392C2semidirect
6. C2×#10622580C2semidirect
7. C2×#10622412C2semidirect
8. C2×#10622748C2semidirect
9. C2×#10622388C2semidirect
10. C2×#10622399C2semidirect
11. C2×#10622424C2semidirect
12. C2×#10622851C2semidirect
13. C2×#10622430C2semidirect
14. C2×#10622740C2semidirect
15. C2×#10622417C2semidirect
16. C2×C11×#417C2semidirect
22. #10623365C22semidirect
40. #10623045C22semidirect
47. C11×#417C22semidirect
52. #10622851C22semidirect
56. #10622748C22semidirect
57. #10622740C22semidirect
64. #10622580C22semidirect
69. #10622430C22semidirect
70. #10622424C22semidirect
71. #10622417C22semidirect
72. #10622412C22semidirect
73. #10622399C22semidirect
74. #10622392C22semidirect
75. #10622388C22semidirect
76. #10622377C22semidirect
309. C2×#417D11semidirect
434. #417C2×D11semidirect
595. C2×C11#3309semidirect
711. C11C2×#3309semidirect
831. C2#13080623direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230452
C2×#106233652
#130806232
C2×#106223772
C2×#106223922
C2×#106225802
C2×#106224122
C2×#106227482
C2×#106223882
C2×#106223992
C2×#106224242
C2×#106228512
C2×#106224302
C2×#106227402
C2×#106224172
C2×C11×#4172
C2×#330911