Finite Group Databasebeta

← C2×#13079709 #15625127

Subgroups — C2×#13079709 #15625127

Order 2816.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623092C211yesmaximal, characteristic, complemented
2C2×#10623205C211yesmaximal, characteristic, complemented
3#13079709C2116yesmaximal, direct product factor
4C2×#10622767C211yesmaximal, characteristic, complemented
5C2×#10622781C211yesmaximal, characteristic, complemented
6C2×#10622408C211yesmaximal, characteristic, complemented
7C2×#10622373C211yesmaximal, characteristic, complemented
8C2×#10622667C211yesmaximal, characteristic, complemented
9C2×#10622461C211yesmaximal, characteristic, complemented
10C2×#10622628C211yesmaximal, characteristic, complemented
11C2×#10622423C211yesmaximal, characteristic, complemented
12C2×#10622785C211yesmaximal, characteristic, complemented
13C2×#10622389C211yesmaximal, characteristic, complemented
14C2×#10622769C211yesmaximal, characteristic, complemented
15C2×#10622453C211yesmaximal, characteristic, complemented
16C2×C11×#463C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic, complemented
20C22×C11×D8C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic, complemented
23C2×#67000C2211yescharacteristic
24C22×#4326C2211yescharacteristic, complemented
25C2×#66993C2211yescharacteristic
26C2×#66991C2211yescharacteristic
27C2×#66989C2211yescharacteristic, complemented
28C22×#4324C2211yescharacteristic
29C22×#4323C2211yescharacteristic
30C22×#4323C2211yescharacteristic, complemented
31C2×#66982—21no—
32C2×#66977—21no—
33C22×#4314C2211yescharacteristic
34C22×#4314C2211yescharacteristic, complemented
35#10623205—24no—
36#10623205C2218yescomplemented
37#10623092—24no—
38#10623092C2218yescomplemented
39C2×#66950C2211yescharacteristic
40C2×#66941C2211yescharacteristic, complemented
41C2×#66938—21no—
42C2×#66937—21no—
43C2×#66937—21no—
44C2×#66935—21no—
45C2×#66935—21no—
46C2×#66932—21no—
47C2×#66927C2211yescharacteristic
48C2×#66925C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic, complemented
50C11×#463C2218yescomplemented
51C2×C11×C4⋊C8C2211yescharacteristic, complemented
52C2×C11×#103C2211yescharacteristic, complemented
53C2×C11×#102C2211yescharacteristic
54C2×#66899C2211yescharacteristic, complemented
55C2×#66896C2211yescharacteristic
56#10622785C2218yescomplemented
57#10622781C2218yescomplemented
58#10622769C2218yescomplemented
59#10622767C2218yescomplemented
60C2×#66885C2211yescharacteristic
61C2×#66885C2211yescharacteristic, complemented
62C2×(C2×D11)⋊C8C2211yescharacteristic
63C2×(C2×D11)⋊C8C2211yescharacteristic
64C2×#66879C2211yescharacteristic, complemented
65C2×C8×Dic11C2211yescharacteristic, complemented
66#10622667C2218yescomplemented
67#10622628C2218yescomplemented
68C2×#66873C2211yescharacteristic
69C2×#66873C2211yescharacteristic, complemented
70C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
71#10622461C2218yescomplemented
72#10622453C2218yescomplemented
73#10622423C2218yescomplemented
74#10622408C2218yescomplemented
75#10622389C2218yescomplemented
76#10622373C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C2×#4343—22no—
87C2×#4343—42no—
88C2×#4343—42no—
89C2×#4343C2314yes—
90C2×D4×D11—22no—
91C2×D4×D11—42no—
92C2×D4×D11—42no—
93C2×D4×D11C2314yes—
94C22×D44—21no—
95C22×D44—21no—
96C22×D44—21no—
97C22×D44C2311yescharacteristic
98C22×D44C2311yescharacteristic
99C22×C4×D11—21no—
100C22×C4×D11C2311yescharacteristic
101C22×Dic22—21no—
102C22×Dic22C2311yescharacteristic
103C2×C11×SD16—42no—
104C2×C11×SD16C2314yescomplemented
105C2×C11×D8—42no—
106C2×C11×D8C2314yes—
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C11×#124—22no—
110C11×#124C2314yes—
111C4×D4×C11—22no—
112C4×D4×C11C2314yescomplemented
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C42×C11C2311yescharacteristic
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11—21no—
121#67000—22no—
122#67000C2314yes—
123C2×#4326—42no—
124C2×#4326C2314yescomplemented
125#66993—22no—
126#66993C2314yes—
127#66991—22no—
128#66991C2314yes—
129#66989—22no—
130#66989C2314yescomplemented
131C2×#4324—42no—
132C2×#4324C2314yes—
133C2×#4323—42no—
134C2×#4323—42no—
135C2×#4323C2314yes—
136C2×#4323C2314yescomplemented
137#66982—28no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4D411yescharacteristic
142C2×(C2×D11)⋊C4D411yescharacteristic
143C2×C4⋊Dic11—21no—
144C2×C4⋊Dic11C2311yescharacteristic
145#66977—28no—
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4D411yescharacteristic
149C2×Dic11⋊C4D411yescharacteristic
150C2×C4×Dic11—21no—
151C2×C4×Dic11C2311yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154C2×#4314—42no—
155C2×#4314—42no—
156C2×#4314C2314yes—
157C2×#4314C2314yescomplemented
158#66950—22no—
159#66950C2314yes—
160#66941—22no—
161#66941C2314yescomplemented
162#66938—28no—
163#66937—28no—
164#66937—28no—
165#66935—28no—
166#66935—28no—
167#66932—28no—
168#66927—22no—
169#66927C2314yes—
170#66925D414yes—
171#66925C2314yes—
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×#3224—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—24no—
194C23×D11—44no—
195C23×D11—82no—
196C23×D11—82no—
197C23×D11C2×D411yescharacteristic
198C2×Q8×C11—21no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11C2412yes—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—22no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11C2412yes—
209C2×D4×C11C2412yes—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—24no—
213C22×C4×C11—82no—
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2411yescharacteristic
217C2×C22⋊D11—24no—
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—82no—
223C2×C22⋊D11—82no—
224C2×C22⋊D11—82no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230#4343—44no—
231#4343—44no—
232#4343—48no—
233D4×D11—44no—
234D4×D11—44no—
235D4×D11—48no—
236C2×D44—24no—
237C2×D44—21no—
238C2×D44—21no—
239C2×D44—24no—
240C2×D44—24no—
241C2×D44—22no—
242C2×D44—22no—
243C2×D44—22no—
244C2×D44—22no—
245C2×D44—44no—
246C2×D44—82no—
247C2×D44—82no—
248C2×D44C2412yes—
249C2×D44C2412yes—
250C2×C4×D11—24no—
251C2×C4×D11—22no—
252C2×C4×D11—22no—
253C2×C4×D11—44no—
254C2×C4×D11C2×D412yes—
255C2×C4×D11C2412yes—
256C2×Dic22—24no—
257C2×Dic22—21no—
258C2×Dic22—22no—
259C2×Dic22—22no—
260C2×Dic22—82no—
261C2×Dic22C2412yes—
262C11×SD16—44no—
263C11×D8—44no—
264C2×C8×C11—22no—
265C2×C8×C11—22no—
266C2×C8×C11C2412yes—
267C2×C8×C11C2412yes—
268C11×C4⋊C4—21no—
269C11×C4⋊C4C2412yes—
270C11×C22⋊C4—24no—
271C11×C22⋊C4—24no—
272C11×C22⋊C4—24no—
273C42×C11C2×D412yes—
274C42×C11C2412yes—
275C22⋊Dic11—24no—
276C22⋊Dic11—24no—
277C22⋊Dic11—24no—
278#4326—44no—
279#4324—44no—
280#4323—44no—
281#4323—44no—
282(C2×D11)⋊C4—24no—
283(C2×D11)⋊C4—24no—
284(C2×D11)⋊C4—24no—
285(C2×D11)⋊C4C2×D414yes—
286(C2×D11)⋊C4C2×D414yes—
287C4⋊Dic11—24no—
288C4⋊Dic11—21no—
289C4⋊Dic11C2412yes—
290Dic11⋊C4—24no—
291Dic11⋊C4—24no—
292Dic11⋊C4C2×D414yes—
293Dic11⋊C4C2×D414yes—
294C4×Dic11—24no—
295C4×Dic11C2×D412yes—
296C4×Dic11C2412yes—
297C2×C11⋊C8—22no—
298C2×C11⋊C8—22no—
299C2×C11⋊C8C2412yes—
300C2×C11⋊C8C2412yes—
301#4314—44no—
302#4314—44no—
303C2×#542—111no—
304C2×#535—111no—
305#3224—1116no—
306C2×#496—111no—
307C2×#495—111no—
308C2×#489—111no—
309C2×#486—111no—
310C2×#464—111no—
311C2×#460—111no—
312C2×#463D1111yescharacteristic, complemented
313C2×#459—111no—
314C2×#452—111no—
315C2×#449—111no—
316C2×#450—111no—
317C2×#447—111no—
318C2×#433—111no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11C22×D411yescharacteristic
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—48no—
334C22×D11—42no—
335C22×D11—42no—
336C22×D11—42no—
337C22×D11—42no—
338C22×D11—42no—
339C22×D11—42no—
340C22×D11—84no—
341C22×D11—84no—
342C22×D11—816no—
343C22×D11C22×D412yes—
344Q8×C11—22no—
345Q8×C11—22no—
346Q8×C11—42no—
347D4×C11—22no—
348D4×C11—22no—
349D4×C11—22no—
350D4×C11—22no—
351D4×C11—42no—
352D4×C11—42no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—42no—
358C2×C4×C11—42no—
359C2×C4×C11—84no—
360C2×C4×C11C22×D412yes—
361C2×C4×C11C22×D412yes—
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11H(5,𝔽2)12yes—
364C2×C4×C11H(5,𝔽2)12yes—
365C2×C4×C11C2511yescharacteristic
366C22⋊D11—48no—
367C22⋊D11—84no—
368C22⋊D11—84no—
369C22⋊D11—84no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—42no—
376C2×Dic11—42no—
377C2×Dic11C22×D412yes—
378C2×Dic11C22×D412yes—
379C2×Dic11C22×D412yes—
380D44—22no—
381D44—22no—
382D44—22no—
383D44—22no—
384D44—48no—
385D44—42no—
386D44—42no—
387D44—84no—
388D44—84no—
389C4×D11—24no—
390C4×D11—22no—
391C4×D11—22no—
392C4×D11—48no—
393Dic22—22no—
394Dic22—22no—
395Dic22—42no—
396Dic22—84no—
397C8×C11—22no—
398C8×C11—22no—
399C11⋊C8—22no—
400C11⋊C8—22no—
401C22×#41—111no—
402C23×D4—111no—
403C22×Q16—111no—
404C22×SD16—111no—
405C22×SD16—111no—
406C22×SD16—111no—
407C22×SD16C2×D1111yescharacteristic, complemented
408C22×D8—111no—
409C22×D8—111no—
410C22×D8C2×D1111yescharacteristic
411#542—118no—
412#542—224no—
413#535—118no—
414#535—224no—
415C2×C4⋊Q8—111no—
416C2×#127—111no—
417C2×#127—111no—
418C2×#126—221no—
419C2×#124—111no—
420C2×#124—111no—
421C2×#124—221no—
422C2×#124C2×D1111yescharacteristic
423C2×#123—221no—
424C2×C22⋊Q8—111no—
425C2×C22⋊Q8—221no—
426C2×#121—111no—
427C2×#121—221no—
428C2×#121—221no—
429C2×#120—221no—
430C2×#120—221no—
431C2×C4×Q8—111no—
432C2×C4×D4C2×D1111yescharacteristic, complemented
433C2×#117—111no—
434#496—118no—
435#495—118no—
436#489—118no—
437#486—118no—
438#464—118no—
439#463C2×D1118yescomplemented
440#460—118no—
441#459—118no—
442#452—118no—
443#450—118no—
444#449—118no—
445#447—118no—
446#433—118no—
447C2×C4⋊C8—111no—
448C2×C4⋊C8C2×D1111yescharacteristic, complemented
449C2×#103—111no—
450C2×#103C2×D1111yescharacteristic, complemented
451C2×#102—111no—
452C2×#102—111no—
453C2×#102—111no—
454C2×#102—111no—
455C2×#102—111no—
456C2×#102C2×D1111yescharacteristic
457C2×C22⋊C8—111no—
458C2×C22⋊C8—111no—
459C2×#97—111no—
460C2×C4×C8—111no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—84no—
468C22×C11—84no—
469C22×C11#53512yes—
470C22×C11#57612yes—
471C22×C11#57712yes—
472C22×C11C23×D411yescharacteristic
473C2×D11—22no—
474C2×D11—22no—
475C2×D11—22no—
476C2×D11—44no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—816no—
484C2×D11—84no—
485C2×D11—84no—
486C4×C11—22no—
487C4×C11—22no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11#53512yes—
491C4×C11C2×H(5,𝔽2)11yescharacteristic
492C4×C11C2×H(5,𝔽2)11yescharacteristic
493Dic11—22no—
494Dic11—22no—
495Dic11—22no—
496Dic11—42no—
497Dic11—42no—
498C25—221no—
499C2×#41—114no—
500C2×#41—222no—
501C2×#41—442no—
502C2×#41—442no—
503C22×Q8—111no—
504C22×Q8—221no—
505C22×Q8C22×D1111yescharacteristic
506C22×D4—114no—
507C22×D4—111no—
508C22×D4—111no—
509C22×D4—221no—
510C22×D4—222no—
511C22×D4—221no—
512C22×D4—221no—
513C22×D4—221no—
514C22×D4—221no—
515C22×D4—221no—
516C22×D4—221no—
517C22×D4—442no—
518C22×D4—442no—
519C22×D4C22×D1111yescharacteristic
520C22×D4C22×D1111yescharacteristic
521C23×C4—21no—
522C23×C4—111no—
523C23×C4—221no—
524C2×Q16—114no—
525C2×Q16—442no—
526C2×SD16—42no—
527C2×SD16—114no—
528C2×SD16—114no—
529C2×SD16—114no—
530C2×SD16—442no—
531C2×SD16—442no—
532C2×SD16—442no—
533C2×SD16C22×D1114yescomplemented
534C2×D8—42no—
535C2×D8—114no—
536C2×D8—114no—
537C2×D8—442no—
538C2×D8—442no—
539C2×D8C22×D1114yes—
540C22×C8—111no—
541C22×C8—111no—
542C22×C8C22×D1111yescharacteristic
543C22×C8C22×D1111yescharacteristic
544C4⋊Q8—114no—
545C4⋊Q8—222no—
546#127—114no—
547#127—114no—
548#127—222no—
549#127—222no—
550#126—228no—
551#124—22no—
552#124—114no—
553#124—114no—
554#124—222no—
555#124—222no—
556#124—228no—
557#124C22×D1114yes—
558#123—228no—
559C22⋊Q8—114no—
560C22⋊Q8—222no—
561C22⋊Q8—228no—
562#121—114no—
563#121—228no—
564#121—228no—
565#121—222no—
566#120—228no—
567#120—228no—
568C4×Q8—114no—
569C4×Q8—222no—
570C4×D4—22no—
571C4×D4C22×D1114yescomplemented
572#117—114no—
573#117—114no—
574C2×C4⋊C4—111no—
575C2×C4⋊C4—111no—
576C2×C4⋊C4—111no—
577C2×C4⋊C4—221no—
578C2×C4⋊C4—221no—
579C2×C4⋊C4—221no—
580C2×C4⋊C4C22×D1111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—111no—
585C2×C22⋊C4—111no—
586C2×C22⋊C4—221no—
587C2×C22⋊C4—221no—
588C2×C22⋊C4—221no—
589C2×C22⋊C4—221no—
590C2×C22⋊C4—221no—
591C2×C22⋊C4—221no—
592C2×C42—111no—
593C2×C42—221no—
594C2×C42C22×D1111yescharacteristic
595C4⋊C8—114no—
596C4⋊C8C22×D1114yescomplemented
597#103—114no—
598#103C22×D1114yescomplemented
599#102—114no—
600#102—114no—
601#102—114no—
602#102—114no—
603#102—114no—
604#102C22×D1114yes—
605C22⋊C8—114no—
606C22⋊C8—114no—
607#97—114no—
608C4×C8—114no—
609C2×C11—82no—
610C2×C11—82no—
611C2×C11#322414yescomplemented
612C2×C11C2×#53511yescharacteristic
613C2×C11C2×#57611yescharacteristic
614C2×C11C2×#57711yescharacteristic
615D11—42no—
616D11—82no—
617D11—82no—
618C24—21no—
619C24—21no—
620C24—111no—
621C24—224no—
622C24—221no—
623C24—221no—
624C24—444no—
625C24—882no—
626C24—882no—
627#41—444no—
628#41—444no—
629#41—448no—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—22no—
633C2×Q8—112no—
634C2×Q8—224no—
635C2×Q8—221no—
636C2×Q8—222no—
637C2×Q8—222no—
638C2×Q8—882no—
639C2×Q8C23×D1112yes—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—112no—
647C2×D4—112no—
648C2×D4—224no—
649C2×D4—224no—
650C2×D4—224no—
651C2×D4—224no—
652C2×D4—224no—
653C2×D4—221no—
654C2×D4—221no—
655C2×D4—224no—
656C2×D4—224no—
657C2×D4—222no—
658C2×D4—222no—
659C2×D4—222no—
660C2×D4—222no—
661C2×D4—444no—
662C2×D4—444no—
663C2×D4—444no—
664C2×D4—448no—
665C2×D4—444no—
666C2×D4—882no—
667C2×D4—882no—
668C2×D4—882no—
669C2×D4—882no—
670C2×D4—882no—
671C2×D4C23×D1112yes—
672C2×D4C23×D1112yes—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—82no—
677C22×C4—111no—
678C22×C4—111no—
679C22×C4—111no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—224no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—444no—
688C22×C4D4×D1111yescharacteristic
689C22×C4D4×D1111yescharacteristic
690C22×C4C23×D1111yescharacteristic
691Q16—444no—
692SD16—44no—
693SD16—444no—
694SD16—444no—
695SD16—444no—
696D8—44no—
697D8—444no—
698D8—444no—
699C2×C8—22no—
700C2×C8—22no—
701C2×C8—112no—
702C2×C8—112no—
703C2×C8—222no—
704C2×C8—222no—
705C2×C8C23×D1112yes—
706C2×C8C23×D1112yes—
707C4⋊C4—21no—
708C4⋊C4—114no—
709C4⋊C4—114no—
710C4⋊C4—112no—
711C4⋊C4—224no—
712C4⋊C4—224no—
713C4⋊C4—221no—
714C4⋊C4—224no—
715C4⋊C4C23×D1112yes—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—114no—
720C22⋊C4—114no—
721C22⋊C4—224no—
722C22⋊C4—224no—
723C22⋊C4—224no—
724C22⋊C4—224no—
725C22⋊C4—224no—
726C22⋊C4—224no—
727C42—112no—
728C42—112no—
729C42—224no—
730C42D4×D1112yes—
731C42C23×D1112yes—
732C11C2×#322411yescharacteristic, complemented, Sylow
733C23—22no—
734C23—22no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—112no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—448no—
748C23—442no—
749C23—442no—
750C23—442no—
751C23—442no—
752C23—442no—
753C23—442no—
754C23—884no—
755C23—884no—
756C23—8816no—
757C23C2×D4×D1111yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—42no—
761Q8—222no—
762Q8—222no—
763Q8—442no—
764Q8—884no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—42no—
770D4—42no—
771D4—222no—
772D4—222no—
773D4—222no—
774D4—222no—
775D4—448no—
776D4—448no—
777D4—442no—
778D4—442no—
779D4—884no—
780D4—884no—
781D4—884no—
782D4—884no—
783D4—884no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—84no—
791C2×C4—112no—
792C2×C4—112no—
793C2×C4—112no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—224no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—448no—
803C2×C4—442no—
804C2×C4—442no—
805C2×C4C2×D4×D1112yes—
806C2×C4C2×D4×D1112yes—
807C2×C4C2×D4×D1111yescharacteristic
808C2×C4#6703712yes—
809C2×C4#6704212yes—
810C2×C4C24×D1111yescharacteristic
811C8—22no—
812C8—22no—
813C8—222no—
814C8—222no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—84no—
822C22—84no—
823C22—222no—
824C22—222no—
825C22—222no—
826C22—444no—
827C22—442no—
828C22—442no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—8816no—
834C22—884no—
835C22—884no—
836C22#1062313812yes—
837C22#1062330112yes—
838C22#1062330512yes—
839C22C22×D4×D1111yescharacteristic
840C4—22no—
841C4—22no—
842C4—42no—
843C4—42no—
844C4—222no—
845C4—222no—
846C4—222no—
847C4—442no—
848C4—442no—
849C4#1062313812yes—
850C4C2×#6703711yescharacteristic
851C4C2×#6704211yescharacteristic
852C2—82no—
853C2—82no—
854C2—442no—
855C2—882no—
856C2—882no—
857C2#1307970914yesdirect product factor
858C2C2×#1062313811yescharacteristic
859C2C2×#1062330511yescharacteristic
860C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#463C2
socleC23×C11C22×D4
hypercenterC2×#463D11
hypocenterC11C2×#3224
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#10623092C2semidirect
2. C2×#10623205C2semidirect
3. #13079709C2direct (N × H)
4. C2×#10622767C2semidirect
5. C2×#10622781C2semidirect
6. C2×#10622408C2semidirect
7. C2×#10622373C2semidirect
8. C2×#10622667C2semidirect
9. C2×#10622461C2semidirect
10. C2×#10622628C2semidirect
11. C2×#10622423C2semidirect
12. C2×#10622785C2semidirect
13. C2×#10622389C2semidirect
14. C2×#10622769C2semidirect
15. C2×#10622453C2semidirect
16. C2×C11×#463C2semidirect
19. C22×C11×SD16C22semidirect
22. C2×C4×D4×C11C22semidirect
24. C22×#4326C22semidirect
27. C2×#66989C22semidirect
30. C22×#4323C22semidirect
34. C22×#4314C22semidirect
36. #10623205C22semidirect
38. #10623092C22semidirect
40. C2×#66941C22semidirect
49. C2×C4×Dic22C22semidirect
50. C11×#463C22semidirect
51. C2×C11×C4⋊C8C22semidirect
52. C2×C11×#103C22semidirect
54. C2×#66899C22semidirect
56. #10622785C22semidirect
57. #10622781C22semidirect
58. #10622769C22semidirect
59. #10622767C22semidirect
61. C2×#66885C22semidirect
64. C2×#66879C22semidirect
65. C2×C8×Dic11C22semidirect
66. #10622667C22semidirect
67. #10622628C22semidirect
69. C2×#66873C22semidirect
70. C2×C4⋊(C11⋊C8)C22semidirect
71. #10622461C22semidirect
72. #10622453C22semidirect
73. #10622423C22semidirect
74. #10622408C22semidirect
75. #10622389C22semidirect
76. #10622373C22semidirect
104. C2×C11×SD16C23semidirect
112. C4×D4×C11C23semidirect
124. C2×#4326C23semidirect
130. #66989C23semidirect
136. C2×#4323C23semidirect
157. C2×#4314C23semidirect
161. #66941C23semidirect
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
312. C2×#463D11semidirect
407. C22×SD16C2×D11semidirect
432. C2×C4×D4C2×D11semidirect
439. #463C2×D11semidirect
448. C2×C4⋊C8C2×D11semidirect
450. C2×#103C2×D11semidirect
533. C2×SD16C22×D11semidirect
571. C4×D4C22×D11semidirect
596. C4⋊C8C22×D11semidirect
598. #103C22×D11semidirect
611. C2×C11#3224semidirect
732. C11C2×#3224semidirect
857. C2#13079709direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230922
C2×#106232052
#130797092
C2×#106227672
C2×#106227812
C2×#106224082
C2×#106223732
C2×#106226672
C2×#106224612
C2×#106226282
C2×#106224232
C2×#106227852
C2×#106223892
C2×#106227692
C2×#106224532
C2×C11×#4632
C2×#322411