Finite Group Databasebeta

← C2×#13079685 #15625113

Subgroups — C2×#13079685 #15625113

Order 2816.

2214 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623114C211yesmaximal, characteristic, complemented
2C2×#10623205C211yesmaximal, characteristic
3#13079685C2116yesmaximal, direct product factor
4C2×#10622803C211yesmaximal, characteristic, complemented
5C2×#10622788C211yesmaximal, characteristic, complemented
6C2×#10622377C211yesmaximal, characteristic, complemented
7C2×#10622413C211yesmaximal, characteristic, complemented
8C2×#10622667C211yesmaximal, characteristic, complemented
9C2×#10622461C211yesmaximal, characteristic, complemented
10C2×#10622640C211yesmaximal, characteristic, complemented
11C2×#10622423C211yesmaximal, characteristic, complemented
12C2×#10622800C211yesmaximal, characteristic, complemented
13C2×#10622389C211yesmaximal, characteristic, complemented
14C2×#10622782C211yesmaximal, characteristic, complemented
15C2×#10622453C211yesmaximal, characteristic, complemented
16C2×C11×#464C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic, complemented
20C22×C11×SD16C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic, complemented
23C2×#67000C2211yescharacteristic
24C2×#66999C2211yescharacteristic
25C2×#66997C2211yescharacteristic, complemented
26C22×#4326C2211yescharacteristic, complemented
27C22×#4325C2211yescharacteristic
28C22×#4325C2211yescharacteristic, complemented
29C2×#66993C2211yescharacteristic
30C22×#4324C2211yescharacteristic
31C22×#4314C2211yescharacteristic
32C22×#4314C2211yescharacteristic, complemented
33#10623205—24no—
34#10623205C2218yes—
35#10623114—24no—
36#10623114C2218yescomplemented
37C2×#66951—21no—
38C2×#66950C2211yescharacteristic
39C2×#66943C2211yescharacteristic, complemented
40C2×#66942—21no—
41C2×#66937—21no—
42C2×#66937—21no—
43C2×#66935—21no—
44C2×#66935—21no—
45C2×#66929—21no—
46C2×#66927C2211yescharacteristic
47C2×#66925C2211yescharacteristic
48C2×#66923—21no—
49C2×C4×Dic22C2211yescharacteristic, complemented
50C11×#464C2218yescomplemented
51C2×C11×C4⋊C8C2211yescharacteristic, complemented
52C2×C11×#103C2211yescharacteristic, complemented
53C2×C11×#102C2211yescharacteristic
54C2×#66899C2211yescharacteristic, complemented
55C2×#66896C2211yescharacteristic
56#10622803C2218yescomplemented
57#10622800C2218yescomplemented
58#10622788C2218yescomplemented
59#10622782C2218yescomplemented
60C2×#66885C2211yescharacteristic
61C2×#66885C2211yescharacteristic, complemented
62C2×(C2×D11)⋊C8C2211yescharacteristic
63C2×(C2×D11)⋊C8C2211yescharacteristic
64C2×#66879C2211yescharacteristic, complemented
65C2×C8×Dic11C2211yescharacteristic, complemented
66#10622667C2218yescomplemented
67#10622640C2218yescomplemented
68C2×#66873C2211yescharacteristic
69C2×#66873C2211yescharacteristic, complemented
70C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
71#10622461C2218yescomplemented
72#10622453C2218yescomplemented
73#10622423C2218yescomplemented
74#10622413C2218yescomplemented
75#10622389C2218yescomplemented
76#10622377C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C2×#4343—22no—
85C2×#4343—42no—
86C2×#4343—42no—
87C2×#4343C2314yes—
88C2×D4×D11—22no—
89C2×D4×D11—42no—
90C2×D4×D11—42no—
91C2×D4×D11C2314yes—
92C22×D44—21no—
93C22×D44—21no—
94C22×D44—21no—
95C22×D44C2311yescharacteristic
96C22×D44C2311yescharacteristic
97C22×C4×D11—21no—
98C22×C4×D11C2311yescharacteristic
99C22×Dic22C2311yescharacteristic
100C2×C11×Q16—42no—
101C2×C11×Q16C2314yescomplemented
102C2×C11×SD16—42no—
103C2×C11×SD16C2314yes—
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C11×#124—22no—
107C11×#124C2314yes—
108C4×Q8×C11—22no—
109C4×Q8×C11C2314yescomplemented
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C42×C11—21no—
115C2×C42×C11C2311yescharacteristic
116#67000—22no—
117#67000C2314yes—
118#66999—22no—
119#66999C2314yes—
120#66997—22no—
121#66997C2314yescomplemented
122C2×#4326—42no—
123C2×#4326C2314yescomplemented
124C2×#4325—42no—
125C2×#4325—42no—
126C2×#4325C2314yes—
127C2×#4325C2314yescomplemented
128#66993—22no—
129#66993C2314yes—
130C2×#4324—42no—
131C2×#4324C2314yes—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4D411yescharacteristic
137C2×(C2×D11)⋊C4D411yescharacteristic
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11C2311yescharacteristic
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4D411yescharacteristic
147C2×Dic11⋊C4D411yescharacteristic
148C2×C4×Dic11—21no—
149C2×C4×Dic11C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C2×#4314—42no—
153C2×#4314—42no—
154C2×#4314C2314yes—
155C2×#4314C2314yescomplemented
156#66951—28no—
157#66950—22no—
158#66950C2314yes—
159#66943—22no—
160#66943C2314yescomplemented
161#66942—28no—
162#66937—28no—
163#66937—28no—
164#66935—28no—
165#66935—28no—
166#66929—28no—
167#66927—22no—
168#66927C2314yes—
169#66925D414yes—
170#66925C2314yes—
171#66923—28no—
172C4×Dic22—22no—
173C4×Dic22C2314yescomplemented
174C11×C4⋊C8C2314yescomplemented
175C11×#103C2314yescomplemented
176C11×#102C2314yes—
177#66899C2314yescomplemented
178#66896C2314yes—
179#66885C2314yes—
180#66885C2314yescomplemented
181(C2×D11)⋊C8C2314yes—
182(C2×D11)⋊C8C2314yes—
183#66879C2314yescomplemented
184C8×Dic11C2314yescomplemented
185#66873C2314yes—
186#66873C2314yescomplemented
187C4⋊(C11⋊C8)C2314yescomplemented
188C2×#3222—111nomaximal, Sylow
189C24×C11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—24no—
193C23×D11—44no—
194C23×D11—82no—
195C23×D11—82no—
196C23×D11C2×D411yescharacteristic
197C2×Q8×C11—21no—
198C2×Q8×C11—21no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11—22no—
203C2×Q8×C11C2412yes—
204C2×Q8×C11C2412yes—
205C2×D4×C11—21no—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11C2412yes—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2411yescharacteristic
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—44no—
219C2×C22⋊D11—82no—
220C2×C22⋊D11—82no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11C2×D411yescharacteristic
224C22×Dic11C2×D411yescharacteristic
225C22×Dic11C2×D411yescharacteristic
226#4343—44no—
227#4343—44no—
228#4343—48no—
229D4×D11—44no—
230D4×D11—44no—
231D4×D11—48no—
232C2×D44—24no—
233C2×D44—21no—
234C2×D44—21no—
235C2×D44—24no—
236C2×D44—24no—
237C2×D44—22no—
238C2×D44—22no—
239C2×D44—22no—
240C2×D44—22no—
241C2×D44—44no—
242C2×D44—82no—
243C2×D44—82no—
244C2×D44C2412yes—
245C2×D44C2412yes—
246C2×C4×D11—24no—
247C2×C4×D11—22no—
248C2×C4×D11—22no—
249C2×C4×D11—44no—
250C2×C4×D11C2×D412yes—
251C2×C4×D11C2412yes—
252C2×Dic22—21no—
253C2×Dic22—22no—
254C2×Dic22—22no—
255C2×Dic22C2412yes—
256C11×Q16—44no—
257C11×SD16—44no—
258C2×C8×C11—22no—
259C2×C8×C11—22no—
260C2×C8×C11C2412yes—
261C2×C8×C11C2412yes—
262C11×C4⋊C4—24no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4C2412yes—
265C11×C22⋊C4—24no—
266C11×C22⋊C4—24no—
267C42×C11—24no—
268C42×C11C2×D412yes—
269C42×C11C2412yes—
270#4326—44no—
271#4325—44no—
272#4325—44no—
273#4324—44no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4C2×D414yes—
279(C2×D11)⋊C4C2×D414yes—
280C4⋊Dic11—24no—
281C4⋊Dic11—24no—
282C4⋊Dic11—21no—
283C4⋊Dic11C2412yes—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286Dic11⋊C4—24no—
287Dic11⋊C4—24no—
288Dic11⋊C4—24no—
289Dic11⋊C4C2×D414yes—
290Dic11⋊C4C2×D414yes—
291C4×Dic11—24no—
292C4×Dic11C2×D412yes—
293C4×Dic11C2412yes—
294C2×C11⋊C8—22no—
295C2×C11⋊C8—22no—
296C2×C11⋊C8C2412yes—
297C2×C11⋊C8C2412yes—
298#4314—44no—
299#4314—44no—
300C2×#541—111no—
301C2×#535—111no—
302#3222—1116no—
303C2×#497—111no—
304C2×#492—111no—
305C2×#490—111no—
306C2×#488—111no—
307C2×#464—111no—
308C2×#464D1111yescharacteristic, complemented
309C2×#460—111no—
310C2×#460—111no—
311C2×#452—111no—
312C2×#452—111no—
313C2×#450—111no—
314C2×#450—111no—
315C2×#433—111no—
316C23×C11—22no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11C22×D411yescharacteristic
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—48no—
327C22×D11—42no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—84no—
334C22×D11—84no—
335C22×D11—816no—
336C22×D11C22×D412yes—
337Q8×C11—22no—
338Q8×C11—22no—
339Q8×C11—22no—
340Q8×C11—22no—
341Q8×C11—42no—
342Q8×C11—42no—
343D4×C11—22no—
344D4×C11—22no—
345D4×C11—42no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—42no—
352C2×C4×C11—42no—
353C2×C4×C11—42no—
354C2×C4×C11C22×D412yes—
355C2×C4×C11C22×D412yes—
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11H(5,𝔽2)12yes—
358C2×C4×C11H(5,𝔽2)12yes—
359C2×C4×C11C2511yescharacteristic
360C22⋊D11—48no—
361C22⋊D11—84no—
362C22⋊D11—84no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—42no—
369C2×Dic11—42no—
370C2×Dic11C22×D412yes—
371C2×Dic11C22×D412yes—
372C2×Dic11C22×D412yes—
373D44—22no—
374D44—22no—
375D44—22no—
376D44—22no—
377D44—48no—
378D44—42no—
379D44—42no—
380D44—84no—
381D44—84no—
382C4×D11—24no—
383C4×D11—22no—
384C4×D11—22no—
385C4×D11—48no—
386Dic22—22no—
387Dic22—22no—
388Dic22—42no—
389C8×C11—22no—
390C8×C11—22no—
391C11⋊C8—22no—
392C11⋊C8—22no—
393C22×#41—111no—
394C23×D4—111no—
395C22×Q16—111no—
396C22×Q16C2×D1111yescharacteristic, complemented
397C22×SD16—111no—
398C22×SD16—111no—
399C22×SD16—111no—
400C22×SD16—111no—
401C22×SD16—111no—
402C22×SD16C2×D1111yescharacteristic
403#541—118no—
404#541—224no—
405#535—118no—
406#535—224no—
407C2×C4⋊Q8—111no—
408C2×#127—111no—
409C2×#127—111no—
410C2×#126—221no—
411C2×#126—221no—
412C2×#125—111no—
413C2×#125—221no—
414C2×#125—221no—
415C2×#124—111no—
416C2×#124C2×D1111yescharacteristic
417C2×C22⋊Q8—111no—
418C2×C22⋊Q8—111no—
419C2×#121—221no—
420C2×#121—221no—
421C2×#120—221no—
422C2×#120—221no—
423C2×C4×Q8—111no—
424C2×C4×Q8C2×D1111yescharacteristic, complemented
425C2×#117—111no—
426#497—118no—
427#492—118no—
428#490—118no—
429#488—118no—
430#464—118no—
431#464C2×D1118yescomplemented
432#460—118no—
433#460—118no—
434#452—118no—
435#452—118no—
436#450—118no—
437#450—118no—
438#433—118no—
439C2×C4⋊C8—111no—
440C2×C4⋊C8C2×D1111yescharacteristic, complemented
441C2×#103—111no—
442C2×#103C2×D1111yescharacteristic, complemented
443C2×#102—111no—
444C2×#102—111no—
445C2×#102—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102C2×D1111yescharacteristic
449C2×C22⋊C8—111no—
450C2×C22⋊C8—111no—
451C2×#97—111no—
452C2×C4×C8—111no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—84no—
457C22×C11#53512yes—
458C22×C11#57712yes—
459C22×C11#57712yes—
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—816no—
472C2×D11—84no—
473C2×D11—84no—
474C4×C11—22no—
475C4×C11—22no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11—42no—
479C4×C11#53512yes—
480C4×C11C2×H(5,𝔽2)11yescharacteristic
481C4×C11C2×H(5,𝔽2)11yescharacteristic
482Dic11—22no—
483Dic11—22no—
484Dic11—22no—
485Dic11—42no—
486Dic11—42no—
487C25—221no—
488C2×#41—114no—
489C2×#41—222no—
490C2×#41—442no—
491C2×#41—442no—
492C22×Q8—111no—
493C22×Q8C22×D1111yescharacteristic
494C22×Q8C22×D1111yescharacteristic
495C22×D4—114no—
496C22×D4—111no—
497C22×D4—111no—
498C22×D4—221no—
499C22×D4—222no—
500C22×D4—221no—
501C22×D4—221no—
502C22×D4—221no—
503C22×D4—221no—
504C22×D4—221no—
505C22×D4—442no—
506C22×D4—442no—
507C22×D4C22×D1111yescharacteristic
508C23×C4—111no—
509C23×C4—221no—
510C2×Q16—42no—
511C2×Q16—114no—
512C2×Q16—442no—
513C2×Q16C22×D1114yescomplemented
514C2×SD16—42no—
515C2×SD16—114no—
516C2×SD16—114no—
517C2×SD16—114no—
518C2×SD16—114no—
519C2×SD16—114no—
520C2×SD16—442no—
521C2×SD16—442no—
522C2×SD16—442no—
523C2×SD16—442no—
524C2×SD16—442no—
525C2×SD16C22×D1114yes—
526C22×C8—111no—
527C22×C8—111no—
528C22×C8C22×D1111yescharacteristic
529C22×C8C22×D1111yescharacteristic
530C4⋊Q8—114no—
531C4⋊Q8—222no—
532#127—114no—
533#127—114no—
534#127—222no—
535#127—222no—
536#126—228no—
537#126—228no—
538#125—114no—
539#125—228no—
540#125—222no—
541#125—228no—
542#124—22no—
543#124—114no—
544#124—222no—
545#124C22×D1114yes—
546C22⋊Q8—114no—
547C22⋊Q8—114no—
548C22⋊Q8—222no—
549C22⋊Q8—222no—
550#121—228no—
551#121—228no—
552#120—228no—
553#120—228no—
554C4×Q8—22no—
555C4×Q8—114no—
556C4×Q8—222no—
557C4×Q8C22×D1114yescomplemented
558#117—114no—
559#117—114no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—111no—
562C2×C4⋊C4—111no—
563C2×C4⋊C4—111no—
564C2×C4⋊C4—221no—
565C2×C4⋊C4—221no—
566C2×C4⋊C4—221no—
567C2×C4⋊C4—221no—
568C2×C4⋊C4—221no—
569C2×C4⋊C4—221no—
570C2×C4⋊C4—221no—
571C2×C4⋊C4C22×D1111yescharacteristic
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—111no—
575C2×C22⋊C4—111no—
576C2×C22⋊C4—221no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C22⋊C4—221no—
580C2×C42—21no—
581C2×C42—111no—
582C2×C42—221no—
583C2×C42C22×D1111yescharacteristic
584C4⋊C8—114no—
585C4⋊C8C22×D1114yescomplemented
586#103—114no—
587#103C22×D1114yescomplemented
588#102—114no—
589#102—114no—
590#102—114no—
591#102—114no—
592#102—114no—
593#102C22×D1114yes—
594C22⋊C8—114no—
595C22⋊C8—114no—
596#97—114no—
597C4×C8—114no—
598C2×C11—82no—
599C2×C11#322214yescomplemented
600C2×C11C2×#53511yescharacteristic
601C2×C11C2×#57711yescharacteristic
602C2×C11C2×#57711yescharacteristic
603D11—42no—
604D11—82no—
605D11—82no—
606C24—21no—
607C24—111no—
608C24—224no—
609C24—221no—
610C24—221no—
611C24—444no—
612C24—882no—
613C24—882no—
614#41—444no—
615#41—444no—
616#41—448no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—22no—
620C2×Q8—22no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—112no—
624C2×Q8—221no—
625C2×Q8—222no—
626C2×Q8—222no—
627C2×Q8C23×D1112yes—
628C2×Q8C23×D1112yes—
629C2×D4—21no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—112no—
633C2×D4—112no—
634C2×D4—224no—
635C2×D4—224no—
636C2×D4—224no—
637C2×D4—224no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—224no—
641C2×D4—224no—
642C2×D4—222no—
643C2×D4—222no—
644C2×D4—222no—
645C2×D4—222no—
646C2×D4—444no—
647C2×D4—444no—
648C2×D4—444no—
649C2×D4—448no—
650C2×D4—444no—
651C2×D4—882no—
652C2×D4—882no—
653C2×D4—882no—
654C2×D4—882no—
655C2×D4C23×D1112yes—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—111no—
660C22×C4—111no—
661C22×C4—111no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—224no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—444no—
670C22×C4D4×D1111yescharacteristic
671C22×C4D4×D1111yescharacteristic
672C22×C4C23×D1111yescharacteristic
673Q16—44no—
674Q16—444no—
675SD16—44no—
676SD16—444no—
677SD16—444no—
678SD16—444no—
679SD16—444no—
680SD16—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—114no—
692C4⋊C4—114no—
693C4⋊C4—112no—
694C4⋊C4—224no—
695C4⋊C4—224no—
696C4⋊C4—224no—
697C4⋊C4—224no—
698C4⋊C4—224no—
699C4⋊C4—224no—
700C4⋊C4—221no—
701C4⋊C4—224no—
702C4⋊C4C23×D1112yes—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—114no—
706C22⋊C4—114no—
707C22⋊C4—224no—
708C22⋊C4—224no—
709C22⋊C4—224no—
710C22⋊C4—224no—
711C42—24no—
712C42—112no—
713C42—112no—
714C42—224no—
715C42D4×D1112yes—
716C42C23×D1112yes—
717C11C2×#322211yescharacteristic, complemented, Sylow
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—112no—
723C23—222no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—448no—
729C23—442no—
730C23—442no—
731C23—442no—
732C23—442no—
733C23—442no—
734C23—442no—
735C23—884no—
736C23—884no—
737C23—8816no—
738C23C2×D4×D1111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—22no—
743Q8—42no—
744Q8—42no—
745Q8—222no—
746Q8—222no—
747Q8—442no—
748D4—22no—
749D4—22no—
750D4—42no—
751D4—222no—
752D4—222no—
753D4—222no—
754D4—222no—
755D4—448no—
756D4—448no—
757D4—442no—
758D4—442no—
759D4—884no—
760D4—884no—
761D4—884no—
762D4—884no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—112no—
772C2×C4—112no—
773C2×C4—112no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—224no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—448no—
783C2×C4—442no—
784C2×C4—442no—
785C2×C4C2×D4×D1112yes—
786C2×C4C2×D4×D1112yes—
787C2×C4C2×D4×D1111yescharacteristic
788C2×C4#6703712yes—
789C2×C4#6704212yes—
790C2×C4C24×D1111yescharacteristic
791C8—22no—
792C8—22no—
793C8—222no—
794C8—222no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—84no—
799C22—222no—
800C22—222no—
801C22—222no—
802C22—444no—
803C22—442no—
804C22—442no—
805C22—442no—
806C22—442no—
807C22—442no—
808C22—442no—
809C22—8816no—
810C22—884no—
811C22—884no—
812C22#1062313812yes—
813C22#1062330112yes—
814C22#1062330912yes—
815C22C22×D4×D1111yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—222no—
822C4—222no—
823C4—222no—
824C4—442no—
825C4—442no—
826C4#1062313812yes—
827C4C2×#6703711yescharacteristic
828C4C2×#6704211yescharacteristic
829C2—82no—
830C2—442no—
831C2—882no—
832C2—882no—
833C2#1307968514yesdirect product factor
834C2C2×#1062313811yescharacteristic
835C2C2×#1062330111yescharacteristic
836C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#464C2
socleC23×C11C22×D4
prime radicalC2×#10623205C2
hypercenterC2×#464D11
hypocenterC11C2×#3222
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#10623114C2semidirect
3. #13079685C2direct (N × H)
4. C2×#10622803C2semidirect
5. C2×#10622788C2semidirect
6. C2×#10622377C2semidirect
7. C2×#10622413C2semidirect
8. C2×#10622667C2semidirect
9. C2×#10622461C2semidirect
10. C2×#10622640C2semidirect
11. C2×#10622423C2semidirect
12. C2×#10622800C2semidirect
13. C2×#10622389C2semidirect
14. C2×#10622782C2semidirect
15. C2×#10622453C2semidirect
16. C2×C11×#464C2semidirect
19. C22×C11×Q16C22semidirect
22. C2×C4×Q8×C11C22semidirect
25. C2×#66997C22semidirect
26. C22×#4326C22semidirect
28. C22×#4325C22semidirect
32. C22×#4314C22semidirect
36. #10623114C22semidirect
39. C2×#66943C22semidirect
49. C2×C4×Dic22C22semidirect
50. C11×#464C22semidirect
51. C2×C11×C4⋊C8C22semidirect
52. C2×C11×#103C22semidirect
54. C2×#66899C22semidirect
56. #10622803C22semidirect
57. #10622800C22semidirect
58. #10622788C22semidirect
59. #10622782C22semidirect
61. C2×#66885C22semidirect
64. C2×#66879C22semidirect
65. C2×C8×Dic11C22semidirect
66. #10622667C22semidirect
67. #10622640C22semidirect
69. C2×#66873C22semidirect
70. C2×C4⋊(C11⋊C8)C22semidirect
71. #10622461C22semidirect
72. #10622453C22semidirect
73. #10622423C22semidirect
74. #10622413C22semidirect
75. #10622389C22semidirect
76. #10622377C22semidirect
101. C2×C11×Q16C23semidirect
109. C4×Q8×C11C23semidirect
121. #66997C23semidirect
123. C2×#4326C23semidirect
127. C2×#4325C23semidirect
155. C2×#4314C23semidirect
160. #66943C23semidirect
173. C4×Dic22C23semidirect
174. C11×C4⋊C8C23semidirect
175. C11×#103C23semidirect
177. #66899C23semidirect
180. #66885C23semidirect
183. #66879C23semidirect
184. C8×Dic11C23semidirect
186. #66873C23semidirect
187. C4⋊(C11⋊C8)C23semidirect
308. C2×#464D11semidirect
396. C22×Q16C2×D11semidirect
424. C2×C4×Q8C2×D11semidirect
431. #464C2×D11semidirect
440. C2×C4⋊C8C2×D11semidirect
442. C2×#103C2×D11semidirect
513. C2×Q16C22×D11semidirect
557. C4×Q8C22×D11semidirect
585. C4⋊C8C22×D11semidirect
587. #103C22×D11semidirect
599. C2×C11#3222semidirect
717. C11C2×#3222semidirect
833. C2#13079685direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231142
C2×#106232052
#130796852
C2×#106228032
C2×#106227882
C2×#106223772
C2×#106224132
C2×#106226672
C2×#106224612
C2×#106226402
C2×#106224232
C2×#106228002
C2×#106223892
C2×#106227822
C2×#106224532
C2×C11×#4642
C2×#322211