Finite Group Databasebeta

← C2×#13079595 #15624996

Subgroups — C2×#13079595 #15624996

Order 2816.

2218 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623363C211yesmaximal, characteristic, complemented
2C2×#10623155C211yesmaximal, characteristic, complemented
3#13079595C2116yesmaximal, direct product factor
4C2×#10622804C211yesmaximal, characteristic, complemented
5C2×#10622781C211yesmaximal, characteristic, complemented
6C2×#10622413C211yesmaximal, characteristic, complemented
7C2×#10622381C211yesmaximal, characteristic, complemented
8C2×#10622795C211yesmaximal, characteristic, complemented
9C2×#10622776C211yesmaximal, characteristic, complemented
10C2×#10622431C211yesmaximal, characteristic, complemented
11C2×#10622399C211yesmaximal, characteristic, complemented
12C2×#10622660C211yesmaximal, characteristic, complemented
13C2×#10622347C211yesmaximal, characteristic, complemented
14C2×#10622851C211yesmaximal, characteristic, complemented
15C2×#10622331C211yesmaximal, characteristic, complemented
16C2×C11×#452C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22#10623363—24no—
23#10623363C2218yescomplemented
24C2×#67000C2211yescharacteristic
25C2×#67000C2211yescharacteristic
26C2×Q8×Dic11C2211yescharacteristic
27C2×#66997C2211yescharacteristic
28C22×#4326C2211yescharacteristic
29C22×#4325C2211yescharacteristic
30C22×#4325C2211yescharacteristic
31C2×#66993C2211yescharacteristic
32C2×#66992—21no—
33C2×#66992—21no—
34C2×#66989C2211yescharacteristic
35C22×#4323C2211yescharacteristic
36C2×#66983C2211yescharacteristic
37C2×C4×C22⋊D11—21no—
38C2×C4×C22⋊D11—21no—
39C22×C4×Dic11C2211yescharacteristic
40C22×D88C2211yescharacteristic
41C22×#4314C2211yescharacteristic
42#10623155—24no—
43#10623155C2218yescomplemented
44C2×#66951—21no—
45C2×#66946C2211yescharacteristic
46C2×#66945—21no—
47C2×#66943C2211yescharacteristic
48C2×#66939—21no—
49C2×(C22⋊D11)⋊C4—21no—
50C11×#452C2218yescomplemented
51C2×C11×#103C2211yescharacteristic
52C2×C11×#102C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54#10622851C2218yescomplemented
55C2×#66899C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58#10622804C2218yescomplemented
59#10622795C2218yescomplemented
60#10622781C2218yescomplemented
61#10622776C2218yescomplemented
62C2×#66885C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65C2×Dic11⋊C8C2211yescharacteristic
66C2×C8×Dic11C2211yescharacteristic
67C2×C8×Dic11C2211yescharacteristic
68#10622660C2218yescomplemented
69C2×#66874C2211yescharacteristic
70C2×#66873C2211yescharacteristic
71#10622431C2218yescomplemented
72#10622413C2218yescomplemented
73#10622399C2218yescomplemented
74#10622381C2218yescomplemented
75#10622347C2218yescomplemented
76#10622331C2218yescomplemented
77C2×C11×#41—22no—
78C2×C11×#41—42no—
79C2×C11×#41—42no—
80C2×C11×#41C2314yes—
81C22×Q8×C11C2311yescharacteristic
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11—21no—
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C23×Dic11D411yescharacteristic
92C23×Dic11D411yescharacteristic
93C2×#4339—22no—
94C2×#4339—42no—
95C2×#4339—42no—
96C2×#4339C2314yes—
97C22×D44C2311yescharacteristic
98C22×D44C2311yescharacteristic
99C22×C4×D11—21no—
100C22×C4×D11—21no—
101C22×Dic22C2311yescharacteristic
102C2×C11×Q16—42no—
103C2×C11×Q16C2314yes—
104C2×C11×SD16—42no—
105C2×C11×SD16C2314yes—
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C11×C22⋊Q8—22no—
109C11×C22⋊Q8C2314yes—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C22⋊C4—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115#67000—22no—
116#67000—22no—
117#67000C2314yes—
118#67000C2314yes—
119Q8×Dic11—22no—
120Q8×Dic11C2314yes—
121#66997—22no—
122#66997C2314yes—
123C2×#4326—42no—
124C2×#4326C2314yes—
125C2×#4325—42no—
126C2×#4325—42no—
127C2×#4325C2314yes—
128C2×#4325C2314yes—
129#66993—22no—
130#66993C2314yes—
131#66992—28no—
132#66992—28no—
133#66989—22no—
134#66989C2314yes—
135C2×#4323—42no—
136C2×#4323C2314yes—
137#66983—22no—
138#66983C2314yes—
139C4×C22⋊D11—28no—
140C4×C22⋊D11—28no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×C4⋊Dic11—21no—
148C2×C4⋊Dic11—21no—
149C2×C4⋊Dic11C2311yescharacteristic
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4—21no—
153C2×C4×Dic11—21no—
154C2×C4×Dic11D411yescharacteristic
155C2×C4×Dic11D411yescharacteristic
156C2×C4×Dic11D414yes—
157C2×C4×Dic11C2311yescharacteristic
158C2×C4×Dic11C2311yescharacteristic
159C2×C4×Dic11C2314yes—
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2311yescharacteristic
162C2×D88—42no—
163C2×D88C2314yes—
164C2×#4314—42no—
165C2×#4314C2314yes—
166#66951—28no—
167#66946—22no—
168#66946C2314yes—
169#66945—28no—
170#66943—22no—
171#66943C2314yes—
172#66939—28no—
173(C22⋊D11)⋊C4—28no—
174C11×#103C2314yes—
175C11×#102C2314yes—
176C11×C22⋊C8C2314yes—
177#66899C2314yes—
178#66896C2314yes—
179C22⋊(C11⋊C8)C2314yes—
180#66885C2314yes—
181#66880C2314yes—
182Dic11⋊C8C2314yes—
183Dic11⋊C8C2314yes—
184C8×Dic11C2314yes—
185C8×Dic11C2314yes—
186#66874C2314yes—
187#66873C2314yes—
188C2×#3212—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11C2×D411yescharacteristic
191C23×D11—21no—
192C23×D11—21no—
193C11×#41—44no—
194C11×#41—44no—
195C11×#41—48no—
196C2×Q8×C11—21no—
197C2×Q8×C11—21no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11C2412yes—
203C2×Q8×C11C2412yes—
204C2×D4×C11—24no—
205C2×D4×C11—21no—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11—44no—
209C2×D4×C11C2412yes—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—24no—
216C22×C4×C11—44no—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2411yescharacteristic
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—44no—
229C22×Dic11—24no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—42no—
233C22×Dic11C2×D414yes—
234C22×Dic11C2×D411yescharacteristic
235C22×Dic11C2×D411yescharacteristic
236C22×Dic11C2×D411yescharacteristic
237C22×Dic11C2×D414yes—
238C22×Dic11C2×D411yescharacteristic
239#4339—44no—
240#4339—44no—
241#4339—48no—
242C2×D44—21no—
243C2×D44—21no—
244C2×D44—22no—
245C2×D44—22no—
246C2×D44—22no—
247C2×D44—22no—
248C2×D44C2412yes—
249C2×D44C2412yes—
250C2×C4×D11—24no—
251C2×C4×D11—24no—
252C2×C4×D11—44no—
253C2×C4×D11—44no—
254C2×Dic22—21no—
255C2×Dic22—22no—
256C2×Dic22—22no—
257C2×Dic22C2412yes—
258C11×Q16—44no—
259C11×SD16—44no—
260C2×C8×C11—22no—
261C2×C8×C11—22no—
262C2×C8×C11C2412yes—
263C2×C8×C11C2412yes—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—24no—
266C11×C4⋊C4C2412yes—
267C11×C22⋊C4—24no—
268C22⋊Dic11—24no—
269C22⋊Dic11—24no—
270#4326—44no—
271#4325—44no—
272#4325—44no—
273#4323—44no—
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—
280C4⋊Dic11—24no—
281C4⋊Dic11—24no—
282C4⋊Dic11—21no—
283C4⋊Dic11C2412yes—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286Dic11⋊C4—24no—
287C4×Dic11—24no—
288C4×Dic11C2×D412yes—
289C4×Dic11C2×D414yes—
290C4×Dic11C2×D412yes—
291C4×Dic11C2×D414yes—
292C4×Dic11C2412yes—
293C4×Dic11C2412yes—
294C2×C11⋊C8—22no—
295C2×C11⋊C8—22no—
296C2×C11⋊C8C2412yes—
297C2×C11⋊C8C2412yes—
298D88—44no—
299#4314—44no—
300C2×#532—111no—
301C2×#529—111no—
302#3212—1116no—
303C2×#495—111no—
304C2×#495—111no—
305C2×#488—111no—
306C2×#488—111no—
307C2×#462—111no—
308C2×#460—111no—
309C2×#461—111no—
310C2×#459—111no—
311C2×#452—111no—
312C2×#452D1111yescharacteristic, complemented
313C2×#449—111no—
314C2×#449—111no—
315C2×#431—111no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11C22×D412yes—
324C23×C11C22×D411yescharacteristic
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—42no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333Q8×C11—22no—
334Q8×C11—22no—
335Q8×C11—22no—
336Q8×C11—22no—
337Q8×C11—42no—
338Q8×C11—42no—
339D4×C11—22no—
340D4×C11—22no—
341D4×C11—48no—
342D4×C11—42no—
343C2×C4×C11—22no—
344C2×C4×C11—24no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—48no—
351C2×C4×C11—42no—
352C2×C4×C11—42no—
353C2×C4×C11—42no—
354C2×C4×C11C22×D412yes—
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11H(5,𝔽2)12yes—
357C2×C4×C11H(5,𝔽2)12yes—
358C2×C4×C11C2511yescharacteristic
359C22⋊D11—48no—
360C22⋊D11—48no—
361C22⋊D11—48no—
362C22⋊D11—48no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—28no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—44no—
370C2×Dic11—42no—
371C2×Dic11—42no—
372C2×Dic11#13514yes—
373C2×Dic11C22×D412yes—
374C2×Dic11C22×D412yes—
375C2×Dic11C22×D412yes—
376C2×Dic11C22×D412yes—
377D44—22no—
378D44—22no—
379D44—22no—
380D44—22no—
381D44—42no—
382D44—42no—
383C4×D11—48no—
384C4×D11—48no—
385Dic22—22no—
386Dic22—22no—
387Dic22—42no—
388C8×C11—22no—
389C8×C11—22no—
390C11⋊C8—22no—
391C11⋊C8—22no—
392C22×#41—111no—
393C22×#41C2×D1111yescharacteristic
394C22×Q16—111no—
395C22×Q16C2×D1111yescharacteristic
396C22×SD16—111no—
397C22×SD16—111no—
398C22×SD16—111no—
399C22×SD16C2×D1111yescharacteristic
400C22×D8—111no—
401C22×D8—111no—
402#532—118no—
403#532—224no—
404C2×C4⋊Q8—111no—
405C2×#127—111no—
406#529—118no—
407#529—224no—
408C2×#126—221no—
409C2×#125—111no—
410C2×#124—111no—
411C2×#124—111no—
412C2×#124—111no—
413C2×#123—221no—
414C2×C22⋊Q8C2×D1111yescharacteristic
415C2×#121—111no—
416C2×#121—221no—
417C2×#121—221no—
418C2×C4×Q8—111no—
419C2×C4×D4—111no—
420C2×C4×D4—221no—
421C2×C4×D4—221no—
422C2×C4×D4—221no—
423C2×#117—221no—
424C22×C42—111no—
425#495—118no—
426#495—118no—
427#488—118no—
428#488—118no—
429#462—118no—
430#461—118no—
431#460—118no—
432#459—118no—
433#452—118no—
434#452C2×D1118yescomplemented
435#449—118no—
436#449—118no—
437#431—118no—
438C2×C4⋊C8—111no—
439C2×C4⋊C8—111no—
440C2×#103—111no—
441C2×#103—111no—
442C2×#103—111no—
443C2×#103C2×D1111yescharacteristic
444C2×#102—111no—
445C2×#102—111no—
446C2×#102—111no—
447C2×#102C2×D1111yescharacteristic
448C2×C22⋊C8—111no—
449C2×C22⋊C8C2×D1111yescharacteristic
450C2×C4×C8—111no—
451C2×C4×C8—111no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—22no—
455C22×C11—44no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—84no—
460C22×C11#53512yes—
461C22×C11C2×#13512yes—
462C22×C11#57512yes—
463C22×C11C23×D411yescharacteristic
464C2×D11—42no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—84no—
471C2×D11—84no—
472C4×C11—22no—
473C4×C11—42no—
474C4×C11—42no—
475C4×C11—42no—
476C4×C11#53512yes—
477C4×C11C2×H(5,𝔽2)11yescharacteristic
478C4×C11C2×H(5,𝔽2)11yescharacteristic
479Dic11—22no—
480Dic11—22no—
481Dic11—22no—
482Dic11—42no—
483Dic11—42no—
484Dic11C2×#13514yes—
485C2×#41—22no—
486C2×#41—42no—
487C2×#41—42no—
488C2×#41—114no—
489C2×#41—222no—
490C2×#41—442no—
491C2×#41—442no—
492C2×#41C22×D1114yes—
493C22×Q8—111no—
494C22×Q8C22×D1111yescharacteristic
495C22×Q8C22×D1111yescharacteristic
496C22×D4—21no—
497C22×D4—111no—
498C22×D4—111no—
499C22×D4—221no—
500C22×D4—221no—
501C22×D4—221no—
502C22×D4—221no—
503C22×D4C22×D1111yescharacteristic
504C23×C4—21no—
505C23×C4—111no—
506C23×C4—111no—
507C23×C4—221no—
508C23×C4—221no—
509C23×C4C22×D1111yescharacteristic
510C2×Q16—42no—
511C2×Q16—114no—
512C2×Q16—442no—
513C2×Q16C22×D1114yes—
514C2×SD16—42no—
515C2×SD16—114no—
516C2×SD16—114no—
517C2×SD16—114no—
518C2×SD16—442no—
519C2×SD16—442no—
520C2×SD16—442no—
521C2×SD16C22×D1114yes—
522C2×D8—114no—
523C2×D8—114no—
524C2×D8—442no—
525C2×D8—442no—
526C22×C8—111no—
527C22×C8—111no—
528C22×C8C22×D1111yescharacteristic
529C22×C8C22×D1111yescharacteristic
530C4⋊Q8—114no—
531C4⋊Q8—222no—
532#127—114no—
533#127—222no—
534#126—228no—
535#125—114no—
536#125—222no—
537#124—114no—
538#124—114no—
539#124—114no—
540#124—222no—
541#124—222no—
542#124—222no—
543#123—228no—
544C22⋊Q8—22no—
545C22⋊Q8C22×D1114yes—
546#121—114no—
547#121—228no—
548#121—228no—
549#121—222no—
550C4×Q8—114no—
551C4×Q8—222no—
552C4×D4—114no—
553C4×D4—222no—
554C4×D4—228no—
555C4×D4—228no—
556C4×D4—228no—
557#117—228no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—111no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—221no—
563C2×C4⋊C4—221no—
564C2×C4⋊C4—221no—
565C2×C4⋊C4C22×D1111yescharacteristic
566C2×C22⋊C4—21no—
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×C22⋊C4—221no—
574C2×C22⋊C4—221no—
575C2×C42—111no—
576C2×C42—111no—
577C2×C42—114no—
578C2×C42—111no—
579C2×C42—111no—
580C2×C42—114no—
581C2×C42—221no—
582C4⋊C8—114no—
583C4⋊C8—114no—
584#103—114no—
585#103—114no—
586#103—114no—
587#103C22×D1114yes—
588#102—114no—
589#102—114no—
590#102—114no—
591#102C22×D1114yes—
592C22⋊C8—114no—
593C22⋊C8C22×D1114yes—
594C4×C8—114no—
595C4×C8—114no—
596C2×C11—42no—
597C2×C11—82no—
598C2×C11#321214yescomplemented
599C2×C11C2×#53511yescharacteristic
600C2×C11C22×#13511yescharacteristic
601C2×C11C2×#57511yescharacteristic
602D11—82no—
603D11—82no—
604C24—21no—
605C24—221no—
606C24—221no—
607C24D4×D1111yescharacteristic
608#41—44no—
609#41—44no—
610#41—48no—
611#41—444no—
612#41—444no—
613#41—448no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—22no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—112no—
621C2×Q8—221no—
622C2×Q8—222no—
623C2×Q8—222no—
624C2×Q8C23×D1112yes—
625C2×Q8C23×D1112yes—
626C2×D4—24no—
627C2×D4—21no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—44no—
631C2×D4—112no—
632C2×D4—112no—
633C2×D4—224no—
634C2×D4—224no—
635C2×D4—224no—
636C2×D4—224no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—222no—
640C2×D4—222no—
641C2×D4—222no—
642C2×D4—222no—
643C2×D4—444no—
644C2×D4—444no—
645C2×D4—444no—
646C2×D4—444no—
647C2×D4C23×D1112yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—44no—
655C22×C4—111no—
656C22×C4—114no—
657C22×C4—111no—
658C22×C4—111no—
659C22×C4—111no—
660C22×C4—114no—
661C22×C4—224no—
662C22×C4—224no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—224no—
666C22×C4—444no—
667C22×C4—444no—
668C22×C4—442no—
669C22×C4D4×D1112yes—
670C22×C4D4×D1111yescharacteristic
671C22×C4C23×D1112yes—
672C22×C4C23×D1111yescharacteristic
673Q16—44no—
674Q16—444no—
675SD16—44no—
676SD16—444no—
677SD16—444no—
678SD16—444no—
679D8—444no—
680D8—444no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—112no—
684C2×C8—112no—
685C2×C8—222no—
686C2×C8—222no—
687C2×C8C23×D1112yes—
688C2×C8C23×D1112yes—
689C4⋊C4—24no—
690C4⋊C4—21no—
691C4⋊C4—112no—
692C4⋊C4—224no—
693C4⋊C4—224no—
694C4⋊C4—224no—
695C4⋊C4—224no—
696C4⋊C4—224no—
697C4⋊C4—221no—
698C4⋊C4C23×D1112yes—
699C22⋊C4—24no—
700C22⋊C4—224no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C42—114no—
709C42—114no—
710C42—112no—
711C42—112no—
712C42—112no—
713C42—112no—
714C42—224no—
715C11C2×#321211yescharacteristic, complemented, Sylow
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—222no—
724C23—222no—
725C23—442no—
726C23—442no—
727C23—442no—
728C23—442no—
729C23—442no—
730C23—442no—
731C23C2×D4×D1112yes—
732C23C2×D4×D1111yescharacteristic
733Q8—22no—
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8—42no—
738Q8—42no—
739Q8—222no—
740Q8—222no—
741Q8—442no—
742D4—22no—
743D4—22no—
744D4—48no—
745D4—42no—
746D4—222no—
747D4—222no—
748D4—222no—
749D4—222no—
750D4—448no—
751D4—448no—
752D4—448no—
753D4—448no—
754D4—442no—
755D4—442no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—48no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—114no—
768C2×C4—112no—
769C2×C4—112no—
770C2×C4—112no—
771C2×C4—112no—
772C2×C4—228no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—448no—
779C2×C4—448no—
780C2×C4—444no—
781C2×C4—442no—
782C2×C4—442no—
783C2×C4C2×D4×D1112yes—
784C2×C4C2×D4×D1111yescharacteristic
785C2×C4#6703712yes—
786C2×C4#6703712yes—
787C2×C4C24×D1111yescharacteristic
788C8—22no—
789C8—22no—
790C8—222no—
791C8—222no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—44no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—84no—
800C22—442no—
801C22—442no—
802C22—442no—
803C22—442no—
804C22—442no—
805C22—442no—
806C22—884no—
807C22—884no—
808C22#1062312312yes—
809C22D11×#13512yes—
810C22#1062330812yes—
811C22C22×D4×D1111yescharacteristic
812C4—22no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—114no—
817C4—222no—
818C4—222no—
819C4—222no—
820C4—442no—
821C4—442no—
822C4#1062312312yes—
823C4C2×#6703711yescharacteristic
824C4C2×#6703711yescharacteristic
825C2—42no—
826C2—82no—
827C2—882no—
828C2—882no—
829C2#1307959514yesdirect product factor
830C2C2×#1062312311yescharacteristic
831C2C2×D11×#13511yescharacteristic
832C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#452C2
socleC23×C11C22×D4
hypercenterC2×#452D11
hypocenterC11C2×#3212
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#10623363C2semidirect
2. C2×#10623155C2semidirect
3. #13079595C2direct (N × H)
4. C2×#10622804C2semidirect
5. C2×#10622781C2semidirect
6. C2×#10622413C2semidirect
7. C2×#10622381C2semidirect
8. C2×#10622795C2semidirect
9. C2×#10622776C2semidirect
10. C2×#10622431C2semidirect
11. C2×#10622399C2semidirect
12. C2×#10622660C2semidirect
13. C2×#10622347C2semidirect
14. C2×#10622851C2semidirect
15. C2×#10622331C2semidirect
16. C2×C11×#452C2semidirect
23. #10623363C22semidirect
43. #10623155C22semidirect
50. C11×#452C22semidirect
54. #10622851C22semidirect
58. #10622804C22semidirect
59. #10622795C22semidirect
60. #10622781C22semidirect
61. #10622776C22semidirect
68. #10622660C22semidirect
71. #10622431C22semidirect
72. #10622413C22semidirect
73. #10622399C22semidirect
74. #10622381C22semidirect
75. #10622347C22semidirect
76. #10622331C22semidirect
312. C2×#452D11semidirect
434. #452C2×D11semidirect
598. C2×C11#3212semidirect
715. C11C2×#3212semidirect
829. C2#13079595direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233632
C2×#106231552
#130795952
C2×#106228042
C2×#106227812
C2×#106224132
C2×#106223812
C2×#106227952
C2×#106227762
C2×#106224312
C2×#106223992
C2×#106226602
C2×#106223472
C2×#106228512
C2×#106223312
C2×C11×#4522
C2×#321211