Finite Group Databasebeta

← C2×#13079408 #15624337

Subgroups — C2×#13079408 #15624337

Order 2816.

2394 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic, complemented
2C2×#10623359C211yesmaximal, characteristic, complemented
3#13079408C2116yesmaximal, direct product factor
4C2×#10622428C211yesmaximal, characteristic, complemented
5C2×#10622658C211yesmaximal, characteristic, complemented
6C2×#10622350C211yesmaximal, characteristic, complemented
7C2×#10622397C211yesmaximal, characteristic, complemented
8C2×#10622801C211yesmaximal, characteristic, complemented
9C2×#10622388C211yesmaximal, characteristic, complemented
10C2×#10622420C211yesmaximal, characteristic, complemented
11C2×#10622784C211yesmaximal, characteristic, complemented
12C2×#10622800C211yesmaximal, characteristic, complemented
13C2×#10622851C211yesmaximal, characteristic, complemented
14C2×#10622785C211yesmaximal, characteristic, complemented
15C2×D11×C22⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#452C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4343C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×Q16C2211yescharacteristic, complemented
21C22×C11×SD16C2211yescharacteristic, complemented
22C2×C11×C22⋊Q8C2211yescharacteristic
23#10623359—24no—
24#10623359C2218yescomplemented
25C2×#66999C2211yescharacteristic
26C2×#66999C2211yescharacteristic
27C2×#66999C2211yescharacteristic
28C22×#4325C2211yescharacteristic, complemented
29C2×#66991C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×#66990—21no—
32C2×#66988—21no—
33C22×#4323C2211yescharacteristic, complemented
34C2×#66983C2211yescharacteristic
35C2×C4×C22⋊D11—21no—
36C2×C4×C22⋊D11—21no—
37C2×#66979C2211yescharacteristic
38C22×C8×D11C2211yescharacteristic
39C22×C8×D11C2211yescharacteristic
40#10623158—24no—
41#10623158C2218yescomplemented
42C2×#66948C2211yescharacteristic
43C2×#66947—21no—
44C2×#66946—21no—
45C2×#66945C2211yescharacteristic
46C2×#66935—21no—
47C2×(C22⋊D11)⋊C4—21no—
48C11×#452C2218yescomplemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic, complemented
51C2×C11×C22⋊C8C2211yescharacteristic
52#10622851C2218yescomplemented
53C2×#66899C2211yescharacteristic, complemented
54C2×#66899C2211yescharacteristic, complemented
55C2×#66899C2211yescharacteristic, complemented
56C2×#66896C2211yescharacteristic, complemented
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58#10622801C2218yescomplemented
59#10622800C2218yescomplemented
60#10622785C2218yescomplemented
61#10622784C2218yescomplemented
62C2×#66885C2211yescharacteristic, complemented
63C2×#66885C2211yescharacteristic, complemented
64C2×(C2×D11)⋊C8C2211yescharacteristic
65C2×(C2×D11)⋊C8C2211yescharacteristic
66C2×#66882C2211yescharacteristic, complemented
67C2×#66881C2211yescharacteristic, complemented
68#10622658C2218yescomplemented
69C2×#66872C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622428C2218yescomplemented
72#10622420C2218yescomplemented
73#10622397C2218yescomplemented
74#10622388C2218yescomplemented
75#10622350C2218yescomplemented
76D11×C22⋊C8C2218yescomplemented
77C24×D11D411yescharacteristic
78C2×C11×#41—22no—
79C2×C11×#41—42no—
80C2×C11×#41—42no—
81C2×C11×#41C2314yes—
82C22×Q8×C11C2311yescharacteristic
83C22×Q8×C11C2311yescharacteristic
84C22×D4×C11—21no—
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C23×Dic11D411yescharacteristic
92C2×#4343—22no—
93C2×#4343—42no—
94C2×#4343—42no—
95C2×#4343C2314yes—
96C22×D44—21no—
97C22×D44—21no—
98C22×D44C2311yescharacteristic
99C22×C4×D11—21no—
100C22×C4×D11—42no—
101C22×C4×D11—42no—
102C22×C4×D11D411yescharacteristic
103C22×C4×D11D411yescharacteristic
104C22×C4×D11D414yes—
105C22×C4×D11C2311yescharacteristic
106C22×C4×D11C2311yescharacteristic
107C22×C4×D11C2314yes—
108C2×C11×Q16—42no—
109C2×C11×Q16C2314yescomplemented
110C2×C11×SD16—42no—
111C2×C11×SD16C2314yescomplemented
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C11×C22⋊Q8—22no—
115C11×C22⋊Q8C2314yes—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C22⋊C4—21no—
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—21no—
122#66999—22no—
123#66999—22no—
124#66999—22no—
125#66999C2314yes—
126#66999C2314yes—
127#66999C2314yes—
128C2×#4325—42no—
129C2×#4325C2314yescomplemented
130#66991—22no—
131#66991—22no—
132#66991C2314yes—
133#66991C2314yes—
134#66990—28no—
135#66988—28no—
136C2×#4323—42no—
137C2×#4323C2314yescomplemented
138#66983—22no—
139#66983C2314yes—
140C4×C22⋊D11—28no—
141C4×C22⋊D11—28no—
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×(C2×D11)⋊C4—21no—
148#66979—22no—
149#66979C2314yes—
150C2×C4⋊Dic11C2311yescharacteristic
151C2×C4⋊Dic11C2311yescharacteristic
152C2×C4⋊Dic11C2311yescharacteristic
153C2×Dic11⋊C4—21no—
154C2×Dic11⋊C4—21no—
155C2×Dic11⋊C4—21no—
156C2×C4×Dic11—21no—
157C2×C4×Dic11—21no—
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C2×C8×D11—42no—
161C2×C8×D11—42no—
162C2×C8×D11C2314yes—
163C2×C8×D11C2314yes—
164#66948—22no—
165#66948C2314yes—
166#66947—28no—
167#66946—28no—
168#66945—22no—
169#66945C2314yes—
170#66935—28no—
171(C22⋊D11)⋊C4—28no—
172C11×#103C2314yescomplemented
173C11×#102C2314yescomplemented
174C11×C22⋊C8C2314yes—
175#66899C2314yescomplemented
176#66899C2314yescomplemented
177#66899C2314yescomplemented
178#66896C2314yescomplemented
179C22⋊(C11⋊C8)C2314yes—
180#66885C2314yescomplemented
181#66885C2314yescomplemented
182(C2×D11)⋊C8C2314yes—
183(C2×D11)⋊C8C2314yes—
184#66882C2314yescomplemented
185#66881C2314yescomplemented
186#66872C2314yescomplemented
187#66871C2314yescomplemented
188C2×#3191—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11C2×D411yescharacteristic
191C23×D11—24no—
192C23×D11—21no—
193C23×D11—42no—
194C23×D11—42no—
195C23×D11C2×D411yescharacteristic
196C23×D11C2×D411yescharacteristic
197C23×D11C2×D414yes—
198C11×#41—44no—
199C11×#41—44no—
200C11×#41—48no—
201C2×Q8×C11—21no—
202C2×Q8×C11—21no—
203C2×Q8×C11—22no—
204C2×Q8×C11—22no—
205C2×Q8×C11—22no—
206C2×Q8×C11—22no—
207C2×Q8×C11C2412yes—
208C2×Q8×C11C2412yes—
209C2×D4×C11—24no—
210C2×D4×C11—21no—
211C2×D4×C11—22no—
212C2×D4×C11—22no—
213C2×D4×C11—44no—
214C2×D4×C11C2412yes—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—24no—
221C22×C4×C11—44no—
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2411yescharacteristic
226C2×C22⋊D11—24no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—24no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—44no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—42no—
236C22×Dic11C2×D411yescharacteristic
237C22×Dic11C2×D411yescharacteristic
238C22×Dic11C2×D414yes—
239#4343—44no—
240#4343—44no—
241#4343—48no—
242C2×D44—24no—
243C2×D44—24no—
244C2×D44—21no—
245C2×D44—22no—
246C2×D44—22no—
247C2×D44—44no—
248C2×D44—44no—
249C2×D44C2412yes—
250C2×C4×D11—24no—
251C2×C4×D11—22no—
252C2×C4×D11—22no—
253C2×C4×D11—22no—
254C2×C4×D11—22no—
255C2×C4×D11—42no—
256C2×C4×D11—42no—
257C2×C4×D11—48no—
258C2×C4×D11—44no—
259C2×C4×D11—44no—
260C2×C4×D11—44no—
261C2×C4×D11C2×D412yes—
262C2×C4×D11C2×D412yes—
263C2×C4×D11C2×D414yes—
264C2×C4×D11C2×D414yes—
265C2×C4×D11C2412yes—
266C2×C4×D11C2412yes—
267C11×Q16—44no—
268C11×SD16—44no—
269C2×C8×C11—22no—
270C2×C8×C11—22no—
271C2×C8×C11C2412yes—
272C2×C8×C11C2412yes—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—24no—
275C11×C4⋊C4C2412yes—
276C11×C22⋊C4—24no—
277C22⋊Dic11—24no—
278C22⋊Dic11—24no—
279C22⋊Dic11—24no—
280#4325—44no—
281#4323—44no—
282(C2×D11)⋊C4—24no—
283(C2×D11)⋊C4—24no—
284(C2×D11)⋊C4—24no—
285(C2×D11)⋊C4—24no—
286(C2×D11)⋊C4—24no—
287(C2×D11)⋊C4—24no—
288C4⋊Dic11—21no—
289C4⋊Dic11—21no—
290C4⋊Dic11—21no—
291C4⋊Dic11C2412yes—
292C4⋊Dic11C2412yes—
293C4⋊Dic11C2412yes—
294Dic11⋊C4—24no—
295Dic11⋊C4—24no—
296Dic11⋊C4—24no—
297C4×Dic11—24no—
298C4×Dic11—24no—
299C2×C11⋊C8—22no—
300C2×C11⋊C8—22no—
301C2×C11⋊C8C2412yes—
302C2×C11⋊C8C2412yes—
303C8×D11—44no—
304C8×D11—44no—
305C2×#525—111no—
306C2×#525—111no—
307#3191—1116no—
308C2×#485—111no—
309C2×#485—111no—
310C2×#482—111no—
311C2×#482—111no—
312C2×#467—111no—
313C2×#466—111no—
314C2×#465—111no—
315C2×#465—111no—
316C2×#452—111no—
317C2×#452D1111yescharacteristic, complemented
318C2×#449—111no—
319C2×#449—111no—
320C22×C22⋊C8—111no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11—42no—
328C23×C11C22×D412yes—
329C23×C11C22×D411yescharacteristic
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—28no—
336C22×D11—22no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11—416no—
340C22×D11—42no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11#13514yes—
344C22×D11C22×D412yes—
345C22×D11C22×D412yes—
346Q8×C11—22no—
347Q8×C11—22no—
348Q8×C11—22no—
349Q8×C11—22no—
350Q8×C11—42no—
351Q8×C11—42no—
352D4×C11—22no—
353D4×C11—22no—
354D4×C11—48no—
355D4×C11—42no—
356C2×C4×C11—22no—
357C2×C4×C11—24no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—48no—
364C2×C4×C11—42no—
365C2×C4×C11—42no—
366C2×C4×C11—42no—
367C2×C4×C11C22×D412yes—
368C2×C4×C11C22×D411yescharacteristic
369C2×C4×C11H(5,𝔽2)12yes—
370C2×C4×C11H(5,𝔽2)12yes—
371C2×C4×C11C2511yescharacteristic
372C22⋊D11—48no—
373C22⋊D11—48no—
374C22⋊D11—48no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—44no—
381C2×Dic11—42no—
382C2×Dic11—42no—
383C2×Dic11—42no—
384C2×Dic11C22×D412yes—
385C2×Dic11C22×D412yes—
386D44—22no—
387D44—22no—
388D44—48no—
389D44—48no—
390D44—42no—
391C4×D11—24no—
392C4×D11—24no—
393C4×D11—22no—
394C4×D11—22no—
395C4×D11—22no—
396C4×D11—22no—
397C4×D11—44no—
398C4×D11—44no—
399C4×D11—48no—
400C8×C11—22no—
401C8×C11—22no—
402C11⋊C8—22no—
403C11⋊C8—22no—
404C22×#41—111no—
405C22×#41C2×D1111yescharacteristic
406C24×C4—111no—
407C22×Q16C2×D1111yescharacteristic, complemented
408C22×SD16—111no—
409C22×SD16C2×D1111yescharacteristic, complemented
410C22×D8—111no—
411C23×C8—111no—
412C23×C8—111no—
413#525—118no—
414#525—118no—
415#525—224no—
416#525—224no—
417C2×#123—221no—
418C2×#123—221no—
419C2×C22⋊Q8—111no—
420C2×C22⋊Q8—111no—
421C2×C22⋊Q8—111no—
422C2×C22⋊Q8C2×D1111yescharacteristic
423C2×#121—111no—
424C2×#121—111no—
425C2×#121—111no—
426C2×#121—111no—
427C2×#120—221no—
428C2×#120—221no—
429C2×C4×D4—221no—
430C2×C4×D4—221no—
431C2×C4×D4—221no—
432C2×C4×D4—221no—
433C2×#117—111no—
434C2×#117—111no—
435#485—118no—
436#485—118no—
437#482—118no—
438#482—118no—
439#467—118no—
440#466—118no—
441#465—118no—
442#465—118no—
443#452—118no—
444#452C2×D1118yescomplemented
445#449—118no—
446#449—118no—
447C2×#107—111no—
448C2×#107—111no—
449C2×#106—111no—
450C2×#106—111no—
451C2×#103—111no—
452C2×#103—111no—
453C2×#103—111no—
454C2×#103C2×D1111yescharacteristic, complemented
455C2×#102—111no—
456C2×#102—111no—
457C2×#102—111no—
458C2×#102C2×D1111yescharacteristic, complemented
459C2×C22⋊C8—111no—
460C2×C22⋊C8—111no—
461C2×C22⋊C8—111no—
462C2×C22⋊C8—118no—
463C2×C22⋊C8C2×D1111yescharacteristic
464C22×C11—22no—
465C22×C11—22no—
466C22×C11—22no—
467C22×C11—44no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—84no—
472C22×C11#53412yes—
473C22×C11C2×#13512yes—
474C22×C11#57512yes—
475C22×C11C23×D411yescharacteristic
476C2×D11—22no—
477C2×D11—28no—
478C2×D11—22no—
479C2×D11—22no—
480C2×D11—22no—
481C2×D11—22no—
482C2×D11—416no—
483C2×D11—44no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—84no—
488C2×D11C2×#13514yes—
489C4×C11—22no—
490C4×C11—42no—
491C4×C11—42no—
492C4×C11—42no—
493C4×C11#53412yes—
494C4×C11C2×H(5,𝔽2)11yescharacteristic
495C4×C11C2×H(5,𝔽2)11yescharacteristic
496Dic11—22no—
497Dic11—22no—
498Dic11—42no—
499Dic11—42no—
500Dic11—42no—
501C25—111no—
502C2×#41—22no—
503C2×#41—42no—
504C2×#41—42no—
505C2×#41—114no—
506C2×#41—222no—
507C2×#41—442no—
508C2×#41—442no—
509C2×#41C22×D1114yes—
510C22×Q8C22×D1111yescharacteristic
511C22×Q8C22×D1111yescharacteristic
512C22×D4—21no—
513C22×D4—111no—
514C22×D4—221no—
515C22×D4—221no—
516C22×D4—221no—
517C22×D4—221no—
518C22×D4—221no—
519C22×D4C22×D1111yescharacteristic
520C23×C4—21no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—111no—
525C23×C4—111no—
526C23×C4—114no—
527C23×C4—114no—
528C23×C4—221no—
529C23×C4—442no—
530C23×C4—442no—
531C23×C4C22×D1111yescharacteristic
532C2×Q16—42no—
533C2×Q16C22×D1114yescomplemented
534C2×SD16—42no—
535C2×SD16—114no—
536C2×SD16—442no—
537C2×SD16C22×D1114yescomplemented
538C2×D8—114no—
539C2×D8—442no—
540C22×C8—111no—
541C22×C8—111no—
542C22×C8—114no—
543C22×C8—114no—
544C22×C8—442no—
545C22×C8—442no—
546C22×C8C22×D1111yescharacteristic
547C22×C8C22×D1111yescharacteristic
548#123—228no—
549#123—228no—
550C22⋊Q8—22no—
551C22⋊Q8—114no—
552C22⋊Q8—114no—
553C22⋊Q8—114no—
554C22⋊Q8—222no—
555C22⋊Q8—222no—
556C22⋊Q8—222no—
557C22⋊Q8C22×D1114yes—
558#121—114no—
559#121—114no—
560#121—114no—
561#121—114no—
562#121—222no—
563#121—222no—
564#121—222no—
565#121—222no—
566#120—228no—
567#120—228no—
568C4×D4—228no—
569C4×D4—228no—
570C4×D4—228no—
571C4×D4—228no—
572#117—114no—
573#117—114no—
574#117—222no—
575#117—222no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—111no—
578C2×C4⋊C4—111no—
579C2×C4⋊C4—111no—
580C2×C4⋊C4—221no—
581C2×C4⋊C4—221no—
582C2×C4⋊C4—221no—
583C2×C4⋊C4C22×D1111yescharacteristic
584C2×C22⋊C4—21no—
585C2×C22⋊C4—221no—
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×C22⋊C4—221no—
593C2×C22⋊C4—221no—
594C2×C42—221no—
595C2×C42—221no—
596#107—114no—
597#107—114no—
598#106—114no—
599#106—114no—
600#103—114no—
601#103—114no—
602#103—114no—
603#103C22×D1114yescomplemented
604#102—114no—
605#102—114no—
606#102—114no—
607#102C22×D1114yescomplemented
608C22⋊C8—114no—
609C22⋊C8—114no—
610C22⋊C8—114no—
611C22⋊C8C22×D1114yes—
612C2×C11—42no—
613C2×C11—82no—
614C2×C11#319114yescomplemented
615C2×C11C2×#53411yescharacteristic
616C2×C11C22×#13511yescharacteristic
617C2×C11C2×#57511yescharacteristic
618D11—24no—
619D11—42no—
620D11—82no—
621C24—21no—
622C24—111no—
623C24—111no—
624C24—114no—
625C24—224no—
626C24—221no—
627C24—442no—
628C24—442no—
629C24D4×D1111yescharacteristic
630#41—44no—
631#41—44no—
632#41—48no—
633#41—444no—
634#41—444no—
635#41—448no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8C23×D1112yes—
643C2×Q8C23×D1112yes—
644C2×D4—24no—
645C2×D4—21no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—44no—
649C2×D4—112no—
650C2×D4—224no—
651C2×D4—224no—
652C2×D4—224no—
653C2×D4—224no—
654C2×D4—224no—
655C2×D4—221no—
656C2×D4—222no—
657C2×D4—222no—
658C2×D4—444no—
659C2×D4—444no—
660C2×D4—444no—
661C2×D4—444no—
662C2×D4—444no—
663C2×D4C23×D1112yes—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—24no—
670C22×C4—44no—
671C22×C4—111no—
672C22×C4—111no—
673C22×C4—114no—
674C22×C4—112no—
675C22×C4—112no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—114no—
679C22×C4—114no—
680C22×C4—224no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—448no—
689C22×C4—444no—
690C22×C4—444no—
691C22×C4—442no—
692C22×C4—442no—
693C22×C4—444no—
694C22×C4—442no—
695C22×C4D4×D1112yes—
696C22×C4D4×D1111yescharacteristic
697C22×C4C23×D1112yes—
698C22×C4C23×D1111yescharacteristic
699Q16—44no—
700SD16—44no—
701SD16—444no—
702D8—444no—
703C2×C8—22no—
704C2×C8—22no—
705C2×C8—112no—
706C2×C8—112no—
707C2×C8—222no—
708C2×C8—222no—
709C2×C8—444no—
710C2×C8—444no—
711C2×C8C23×D1112yes—
712C2×C8C23×D1112yes—
713C4⋊C4—24no—
714C4⋊C4—21no—
715C4⋊C4—112no—
716C4⋊C4—112no—
717C4⋊C4—112no—
718C4⋊C4—224no—
719C4⋊C4—224no—
720C4⋊C4—224no—
721C4⋊C4—221no—
722C4⋊C4—221no—
723C4⋊C4—221no—
724C4⋊C4C23×D1112yes—
725C22⋊C4—24no—
726C22⋊C4—224no—
727C22⋊C4—224no—
728C22⋊C4—224no—
729C22⋊C4—224no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—224no—
733C22⋊C4—224no—
734C22⋊C4—224no—
735C42—224no—
736C42—224no—
737C11C2×#319111yescharacteristic, complemented, Sylow
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—114no—
746C23—112no—
747C23—112no—
748C23—228no—
749C23—222no—
750C23—222no—
751C23—222no—
752C23—222no—
753C23—222no—
754C23—222no—
755C23—444no—
756C23—444no—
757C23—4416no—
758C23—442no—
759C23—442no—
760C23—442no—
761C23C2×D4×D1112yes—
762C23C2×D4×D1111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—22no—
766Q8—22no—
767Q8—42no—
768Q8—42no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—42no—
773D4—222no—
774D4—222no—
775D4—448no—
776D4—448no—
777D4—448no—
778D4—448no—
779D4—448no—
780D4—442no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—48no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—112no—
793C2×C4—112no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—224no—
797C2×C4—224no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—444no—
806C2×C4—444no—
807C2×C4—448no—
808C2×C4—444no—
809C2×C4—442no—
810C2×C4—442no—
811C2×C4—442no—
812C2×C4C2×D4×D1112yes—
813C2×C4C2×D4×D1111yescharacteristic
814C2×C4#6703712yes—
815C2×C4#6703712yes—
816C2×C4C24×D1111yescharacteristic
817C8—22no—
818C8—22no—
819C8—222no—
820C8—222no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—84no—
829C22—114no—
830C22—222no—
831C22—228no—
832C22—222no—
833C22—222no—
834C22—222no—
835C22—222no—
836C22—4416no—
837C22—444no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—884no—
842C22#1062312012yes—
843C22D11×#13512yes—
844C22#1062330812yes—
845C22C22×D4×D1111yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—222no—
851C4—222no—
852C4—442no—
853C4—442no—
854C4—442no—
855C4#1062312012yes—
856C4C2×#6703711yescharacteristic
857C4C2×#6703711yescharacteristic
858C2—42no—
859C2—82no—
860C2—224no—
861C2—442no—
862C2—882no—
863C2#1307940814yesdirect product factor
864C2C2×#1062312011yescharacteristic
865C2C2×D11×#13511yescharacteristic
866C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#452C2
socleC23×C11C22×D4
hypercenterC2×#452D11
hypocenterC11C2×#3191
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×#10623158C2semidirect
2. C2×#10623359C2semidirect
3. #13079408C2direct (N × H)
4. C2×#10622428C2semidirect
5. C2×#10622658C2semidirect
6. C2×#10622350C2semidirect
7. C2×#10622397C2semidirect
8. C2×#10622801C2semidirect
9. C2×#10622388C2semidirect
10. C2×#10622420C2semidirect
11. C2×#10622784C2semidirect
12. C2×#10622800C2semidirect
13. C2×#10622851C2semidirect
14. C2×#10622785C2semidirect
15. C2×D11×C22⋊C8C2semidirect
16. C2×C11×#452C2semidirect
20. C22×C11×Q16C22semidirect
21. C22×C11×SD16C22semidirect
24. #10623359C22semidirect
28. C22×#4325C22semidirect
33. C22×#4323C22semidirect
41. #10623158C22semidirect
48. C11×#452C22semidirect
49. C2×C11×#103C22semidirect
50. C2×C11×#102C22semidirect
52. #10622851C22semidirect
53. C2×#66899C22semidirect
54. C2×#66899C22semidirect
55. C2×#66899C22semidirect
56. C2×#66896C22semidirect
58. #10622801C22semidirect
59. #10622800C22semidirect
60. #10622785C22semidirect
61. #10622784C22semidirect
62. C2×#66885C22semidirect
63. C2×#66885C22semidirect
66. C2×#66882C22semidirect
67. C2×#66881C22semidirect
68. #10622658C22semidirect
69. C2×#66872C22semidirect
70. C2×#66871C22semidirect
71. #10622428C22semidirect
72. #10622420C22semidirect
73. #10622397C22semidirect
74. #10622388C22semidirect
75. #10622350C22semidirect
76. D11×C22⋊C8C22semidirect
109. C2×C11×Q16C23semidirect
111. C2×C11×SD16C23semidirect
129. C2×#4325C23semidirect
137. C2×#4323C23semidirect
172. C11×#103C23semidirect
173. C11×#102C23semidirect
175. #66899C23semidirect
176. #66899C23semidirect
177. #66899C23semidirect
178. #66896C23semidirect
180. #66885C23semidirect
181. #66885C23semidirect
184. #66882C23semidirect
185. #66881C23semidirect
186. #66872C23semidirect
187. #66871C23semidirect
317. C2×#452D11semidirect
407. C22×Q16C2×D11semidirect
409. C22×SD16C2×D11semidirect
444. #452C2×D11semidirect
454. C2×#103C2×D11semidirect
458. C2×#102C2×D11semidirect
533. C2×Q16C22×D11semidirect
537. C2×SD16C22×D11semidirect
603. #103C22×D11semidirect
607. #102C22×D11semidirect
614. C2×C11#3191semidirect
737. C11C2×#3191semidirect
863. C2#13079408direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×#106233592
#130794082
C2×#106224282
C2×#106226582
C2×#106223502
C2×#106223972
C2×#106228012
C2×#106223882
C2×#106224202
C2×#106227842
C2×#106228002
C2×#106228512
C2×#106227852
C2×D11×C22⋊C82
C2×C11×#4522
C2×#319111