Finite Group Databasebeta

← C2×#13080646 #15630437

Subgroups — C2×#13080646 #15630437

Order 2816.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623081C211yesmaximal, characteristic
2#13080646C2116yesmaximal, direct product factor
3C2×#10622702C211yesmaximal, characteristic, complemented
4C2×#10622609C211yesmaximal, characteristic, complemented
5C2×#10622616C211yesmaximal, characteristic, complemented
6C2×#10622697C211yesmaximal, characteristic, complemented
7C2×#10622665C211yesmaximal, characteristic, complemented
8C2×#10622661C211yesmaximal, characteristic, complemented
9C2×#10622641C211yesmaximal, characteristic, complemented
10C2×#10622660C211yesmaximal, characteristic, complemented
11C2×#10622659C211yesmaximal, characteristic, complemented
12C2×#10622639C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622614C211yesmaximal, characteristic, complemented
15C2×#10622615C211yesmaximal, characteristic, complemented
16C2×C11×#556C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C11×#556—24no—
20C11×#556C2218yescomplemented
21C2×C11×C4⋊Q8C2211yescharacteristic, complemented
22C2×C11×#126—21no—
23C2×C11×#126—21no—
24C2×C11×#124—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic, complemented
27C2×C4×Q8×C11—21no—
28C2×C4×Q8×C11C2211yescharacteristic, complemented
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C2×C11×#117C2211yescharacteristic, complemented
32C22×#4326C2211yescharacteristic, complemented
33C22×#4325C2211yescharacteristic
34C22×#4325C2211yescharacteristic
35C2×#66990—21no—
36C2×#66983C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38C22×#4318C2211yescharacteristic
39C23×C11⋊C8C2211yescharacteristic, complemented
40#10623081—24no—
41#10623081C2218yes—
42C2×#66947—21no—
43C2×#66937—21no—
44C2×C22⋊C4×D11—21no—
45C2×#66928C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47C2×#66899C2211yescharacteristic, complemented
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
50#10622702C2218yescomplemented
51#10622697C2218yescomplemented
52#10622665C2218yescomplemented
53#10622661C2218yescomplemented
54#10622660C2218yescomplemented
55#10622659C2218yescomplemented
56#10622641C2218yescomplemented
57#10622639C2218yescomplemented
58#10622624C2218yescomplemented
59#10622616C2218yescomplemented
60#10622615C2218yescomplemented
61#10622614C2218yescomplemented
62#10622609C2218yescomplemented
63C2×#66874C2211yescharacteristic, complemented
64C2×#66874C2211yescharacteristic, complemented
65C2×#66874C2211yescharacteristic, complemented
66C2×#66873C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66873C2211yescharacteristic
70C2×#66873C2211yescharacteristic
71C2×#66873C2211yescharacteristic
72C2×#66872C2211yescharacteristic, complemented
73C2×#66872C2211yescharacteristic, complemented
74C2×#66871C2211yescharacteristic, complemented
75C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
76C2×#66867C2211yescharacteristic, complemented
77C24×D11—21no—
78C22×Q8×C11—21no—
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11D411yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C2×#4339—22no—
86C2×#4339—24no—
87C2×#4339—42no—
88C2×#4339C2314yes—
89C22×D44—24no—
90C22×D44—21no—
91C22×D44—22no—
92C22×D44—42no—
93C22×D44C2311yescharacteristic
94C22×D44C2314yes—
95C22×D44C2311yescharacteristic
96C22×C4×D11—21no—
97C22×C4×D11—21no—
98C22×Dic22C2311yescharacteristic
99C11×C4⋊Q8—22no—
100C11×C4⋊Q8C2314yescomplemented
101C11×#126—28no—
102C11×#126—28no—
103C11×#124—28no—
104C11×C22⋊Q8—22no—
105C11×C22⋊Q8—22no—
106C11×C22⋊Q8C2314yes—
107C11×C22⋊Q8C2314yescomplemented
108C4×Q8×C11—28no—
109C4×Q8×C11—22no—
110C4×Q8×C11C2314yescomplemented
111C4×D4×C11D414yes—
112C4×D4×C11C2314yes—
113C11×#117—22no—
114C11×#117—22no—
115C11×#117C2314yes—
116C11×#117C2314yescomplemented
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4D411yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4—21no—
129C2×C11×C22⋊C4D411yescharacteristic
130C2×C11×C22⋊C4D411yescharacteristic
131C2×C42×C11—21no—
132C2×C42×C11—21no—
133C2×C42×C11—21no—
134C2×C42×C11C2311yescharacteristic
135C2×C22⋊Dic11—21no—
136C2×#4326—42no—
137C2×#4326C2314yescomplemented
138C2×#4325—24no—
139C2×#4325—42no—
140C2×#4325C2314yes—
141C2×#4325C2314yes—
142#66990—28no—
143#66983—22no—
144#66983C2314yes—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—21no—
149C2×C4⋊Dic11C2311yescharacteristic
150#66977—22no—
151#66977C2314yes—
152C2×Dic11⋊C4—21no—
153C2×#4318—42no—
154C2×#4318C2314yes—
155C22×C11⋊C8—42no—
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2314yescomplemented
161#66947—28no—
162#66937—28no—
163C22⋊C4×D11—28no—
164#66928—22no—
165#66928C2314yes—
166C4×D44—22no—
167C4×D44C2314yes—
168#66899C2314yescomplemented
169C22⋊(C11⋊C8)C2314yes—
170C22⋊(C11⋊C8)C2314yescomplemented
171#66874C2314yescomplemented
172#66874C2314yescomplemented
173#66874C2314yescomplemented
174#66873C2314yes—
175#66873C2314yes—
176#66873C2314yes—
177#66873C2314yes—
178#66873C2314yes—
179#66873C2314yes—
180#66872C2314yescomplemented
181#66872C2314yescomplemented
182#66871C2314yescomplemented
183C4⋊(C11⋊C8)C2314yescomplemented
184#66867C2314yescomplemented
185C2×#3311—111nomaximal, Sylow
186C24×C11C2×D411yescharacteristic
187C24×C11C2×D411yescharacteristic
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—24no—
191C23×D11—44no—
192C23×D11—44no—
193C23×D11—82no—
194C2×Q8×C11—21no—
195C2×Q8×C11—24no—
196C2×Q8×C11—22no—
197C2×Q8×C11—22no—
198C2×Q8×C11—44no—
199C2×Q8×C11C2412yes—
200C2×D4×C11—42no—
201C2×D4×C11C2×D414yes—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2411yescharacteristic
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—82no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225#4339—28no—
226#4339—44no—
227#4339—48no—
228C2×D44—28no—
229C2×D44—21no—
230C2×D44—21no—
231C2×D44—24no—
232C2×D44—22no—
233C2×D44—22no—
234C2×D44—22no—
235C2×D44—44no—
236C2×D44—44no—
237C2×D44—48no—
238C2×D44#4114yes—
239C2×D44C2412yes—
240C2×D44C2412yes—
241C2×C4×D11—24no—
242C2×C4×D11—24no—
243C2×C4×D11—44no—
244C2×C4×D11—82no—
245C2×Dic22—21no—
246C2×Dic22—22no—
247C2×Dic22—22no—
248C2×Dic22C2412yes—
249C11×C4⋊C4—24no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4C2×D414yes—
257C11×C4⋊C4C2412yes—
258C11×C4⋊C4C2412yes—
259C11×C4⋊C4C2412yes—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—24no—
263C11×C22⋊C4—24no—
264C11×C22⋊C4C2×D414yes—
265C11×C22⋊C4C2×D414yes—
266C42×C11—24no—
267C42×C11—24no—
268C42×C11—24no—
269C42×C11C2×D412yes—
270C42×C11C2412yes—
271C22⋊Dic11—24no—
272#4326—44no—
273#4325—28no—
274#4325—44no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279C4⋊Dic11—21no—
280C4⋊Dic11C2412yes—
281Dic11⋊C4—24no—
282#4318—44no—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8—22no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—44no—
288C2×C11⋊C8C2412yes—
289C2×C11⋊C8C2412yes—
290C2×C11⋊C8C2412yes—
291C2×C11⋊C8C2412yes—
292C2×#556D1111yescharacteristic, complemented
293C2×#546—111no—
294#3311—1116no—
295C2×#489—111no—
296C2×#485—111no—
297C2×#482—111no—
298C2×#476—111no—
299C2×#470—111no—
300C2×#465—111no—
301C2×#464—111no—
302C2×#452—111no—
303C2×#450—111no—
304C2×#440—111no—
305C2×#435—111no—
306C2×#418—111no—
307C2×#416—111no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11C22×D412yes—
315C23×C11C22×D412yes—
316C23×C11C22×D411yescharacteristic
317C22×D11—24no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—48no—
321C22×D11—42no—
322C22×D11—42no—
323C22×D11—48no—
324C22×D11—42no—
325C22×D11—42no—
326C22×D11—42no—
327C22×D11—84no—
328C22×D11—816no—
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—48no—
332Q8×C11—42no—
333D4×C11—44no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—24no—
339C2×C4×C11—24no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—42no—
349C2×C4×C11—42no—
350C2×C4×C11—42no—
351C2×C4×C11—42no—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C22×D412yes—
354C2×C4×C11C22×D412yes—
355C2×C4×C11C22×D412yes—
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C2×#4112yes—
358C2×C4×C11H(5,𝔽2)12yes—
359C2×C4×C11C2511yescharacteristic
360C22⋊D11—48no—
361C22⋊D11—84no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366D44—24no—
367D44—22no—
368D44—22no—
369D44—22no—
370D44—48no—
371D44—42no—
372D44C2×#4114yes—
373C4×D11—48no—
374C4×D11—84no—
375Dic22—22no—
376Dic22—22no—
377Dic22—42no—
378C11⋊C8—22no—
379C11⋊C8—22no—
380C11⋊C8—22no—
381C11⋊C8—22no—
382C22×#41—111no—
383C23×D4—111no—
384C22×Q16—111no—
385C22×SD16—111no—
386C22×SD16—111no—
387C22×M16—111no—
388C23×C8—111no—
389#556—24no—
390#556C2×D1118yescomplemented
391#546—118no—
392#546—224no—
393C2×C4⋊Q8C2×D1111yescharacteristic, complemented
394C2×#126—21no—
395C2×#126—21no—
396C2×#124—21no—
397C2×#124—111no—
398C2×#123—221no—
399C2×C22⋊Q8—111no—
400C2×C22⋊Q8C2×D1111yescharacteristic
401C2×C22⋊Q8C2×D1111yescharacteristic, complemented
402C2×#121—111no—
403C2×#121—221no—
404C2×#120—221no—
405C2×C4×Q8—21no—
406C2×C4×Q8C2×D1111yescharacteristic, complemented
407C2×C4×D4—111no—
408C2×C4×D4C2×D1111yescharacteristic
409C2×#117C2×D1111yescharacteristic
410C2×#117C2×D1111yescharacteristic, complemented
411C22×C22⋊C4—221no—
412#489—118no—
413#485—118no—
414#482—118no—
415#476—118no—
416#470—118no—
417#465—118no—
418#464—118no—
419#452—118no—
420#450—118no—
421#440—118no—
422#435—118no—
423C2×#107—111no—
424C2×#106—111no—
425C2×#106—111no—
426C2×C4⋊C8—111no—
427#418—118no—
428#416—118no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#103—111no—
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×#102—111no—
439C2×C22⋊C8—111no—
440C2×C22⋊C8—111no—
441C2×#97—111no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—44no—
449C22×C11—44no—
450C22×C11#54612yes—
451C22×C11#57512yes—
452C22×C11#57712yes—
453C22×C11C23×D411yescharacteristic
454C2×D11—24no—
455C2×D11—48no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—816no—
462C2×D11—84no—
463C4×C11—22no—
464C4×C11—22no—
465C4×C11—22no—
466C4×C11—22no—
467C4×C11—42no—
468C4×C11—42no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11#54612yes—
472C4×C11C22×#4111yescharacteristic
473C4×C11C2×H(5,𝔽2)11yescharacteristic
474Dic11—42no—
475Dic11—42no—
476C25—221no—
477C2×#41—114no—
478C2×#41—224no—
479C2×#41—222no—
480C2×#41—442no—
481C22×Q8—21no—
482C22×Q8—111no—
483C22×Q8C22×D1111yescharacteristic
484C22×D4—111no—
485C22×D4—111no—
486C22×D4—114no—
487C22×D4—224no—
488C22×D4—221no—
489C22×D4—221no—
490C22×D4—221no—
491C22×D4—222no—
492C22×D4—442no—
493C22×D4C22⋊D1111yescharacteristic
494C23×C4—221no—
495C23×C4—221no—
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C2×Q16—114no—
499C2×Q16—442no—
500C2×SD16—114no—
501C2×SD16—114no—
502C2×SD16—224no—
503C2×SD16—442no—
504C2×M16—114no—
505C2×M16—442no—
506C22×C8—111no—
507C22×C8—111no—
508C22×C8—111no—
509C22×C8—111no—
510C22×C8—114no—
511C22×C8—442no—
512C4⋊Q8—22no—
513C4⋊Q8C22×D1114yescomplemented
514#126—28no—
515#126—28no—
516#124—28no—
517#124—114no—
518#124—222no—
519#123—228no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522C22⋊Q8—114no—
523C22⋊Q8—222no—
524C22⋊Q8C22×D1114yes—
525C22⋊Q8C22×D1114yescomplemented
526#121—114no—
527#121—222no—
528#121—228no—
529#120—228no—
530C4×Q8—28no—
531C4×Q8—22no—
532C4×Q8C22×D1114yescomplemented
533C4×D4—114no—
534C4×D4—222no—
535C4×D4C22⋊D1114yes—
536C4×D4C22×D1114yes—
537#117—22no—
538#117—22no—
539#117C22×D1114yes—
540#117C22×D1114yescomplemented
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4C22⋊D1111yescharacteristic
548C2×C4⋊C4C22×D1111yescharacteristic
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—228no—
561C2×C22⋊C4C22⋊D1111yescharacteristic
562C2×C22⋊C4C22⋊D1111yescharacteristic
563C2×C42—21no—
564C2×C42—21no—
565C2×C42—21no—
566C2×C42C22×D1111yescharacteristic
567#107—114no—
568#106—114no—
569#106—114no—
570C4⋊C8—114no—
571#103—114no—
572#103—114no—
573#103—114no—
574#103—114no—
575#102—114no—
576#102—114no—
577#102—114no—
578#102—114no—
579#102—114no—
580#102—114no—
581C22⋊C8—114no—
582C22⋊C8—114no—
583#97—114no—
584C2×C11—42no—
585C2×C11—42no—
586C2×C11#331114yescomplemented
587C2×C11C2×#54611yescharacteristic
588C2×C11C2×#57511yescharacteristic
589C2×C11C2×#57711yescharacteristic
590D11—44no—
591D11—82no—
592C24—221no—
593C24—221no—
594C24—224no—
595C24—444no—
596C24—444no—
597C24—882no—
598C24C2×C22⋊D1111yescharacteristic
599C24C2×C22⋊D1111yescharacteristic
600#41—228no—
601#41—444no—
602#41—448no—
603C2×Q8—21no—
604C2×Q8—24no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—44no—
608C2×Q8—112no—
609C2×Q8—221no—
610C2×Q8—222no—
611C2×Q8—222no—
612C2×Q8C23×D1112yes—
613C2×D4—42no—
614C2×D4—114no—
615C2×D4—112no—
616C2×D4—112no—
617C2×D4—228no—
618C2×D4—224no—
619C2×D4—224no—
620C2×D4—222no—
621C2×D4—222no—
622C2×D4—222no—
623C2×D4—221no—
624C2×D4—224no—
625C2×D4—221no—
626C2×D4—444no—
627C2×D4—448no—
628C2×D4—444no—
629C2×D4—444no—
630C2×D4—882no—
631C2×D4C2×C22⋊D1114yes—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—221no—
641C22×C4—221no—
642C22×C4—224no—
643C22×C4—224no—
644C22×C4—444no—
645C22×C4—882no—
646C22×C4C2×C22⋊D1112yes—
647C22×C4C2×C22⋊D1112yes—
648C22×C4C2×C22⋊D1111yescharacteristic
649C22×C4C2×C22⋊D1111yescharacteristic
650C22×C4C2×C22⋊D1111yescharacteristic
651C22×C4C2×C22⋊D1111yescharacteristic
652C22×C4C23×D1112yes—
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655Q16—444no—
656SD16—228no—
657SD16—444no—
658M16—444no—
659C2×C8—112no—
660C2×C8—112no—
661C2×C8—112no—
662C2×C8—112no—
663C2×C8—222no—
664C2×C8—222no—
665C2×C8—222no—
666C2×C8—222no—
667C2×C8—444no—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—112no—
676C4⋊C4—221no—
677C4⋊C4—224no—
678C4⋊C4C2×C22⋊D1114yes—
679C4⋊C4C23×D1112yes—
680C4⋊C4C23×D1112yes—
681C4⋊C4C23×D1112yes—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4C2×C22⋊D1114yes—
692C22⋊C4C2×C22⋊D1114yes—
693C42—24no—
694C42—24no—
695C42—24no—
696C42C2×C22⋊D1112yes—
697C42C23×D1112yes—
698C11C2×#331111yescharacteristic, complemented, Sylow
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—224no—
706C23—222no—
707C23—222no—
708C23—448no—
709C23—448no—
710C23—442no—
711C23—442no—
712C23—442no—
713C23—442no—
714C23—442no—
715C23—884no—
716C23—8816no—
717C23C22×C22⋊D1112yes—
718C23C22×C22⋊D1112yes—
719C23C22×C22⋊D1111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—48no—
723Q8—42no—
724Q8—222no—
725Q8—222no—
726Q8—442no—
727D4—44no—
728D4—114no—
729D4—224no—
730D4—222no—
731D4—222no—
732D4—222no—
733D4—448no—
734D4—448no—
735D4—442no—
736D4—884no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—448no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—884no—
761C2×C4#41×D1112yes—
762C2×C4#6704212yes—
763C2×C4C22×C22⋊D1112yes—
764C2×C4C22×C22⋊D1112yes—
765C2×C4C22×C22⋊D1112yes—
766C2×C4C22×C22⋊D1112yes—
767C2×C4C22×C22⋊D1111yescharacteristic
768C2×C4C24×D1111yescharacteristic
769C8—222no—
770C8—222no—
771C8—222no—
772C8—222no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—44no—
780C22—44no—
781C22—224no—
782C22—448no—
783C22—442no—
784C22—442no—
785C22—442no—
786C22—442no—
787C22—442no—
788C22—8816no—
789C22—884no—
790C22#1062335312yes—
791C22#1062336012yes—
792C22#1062336812yes—
793C22C23×C22⋊D1111yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—442no—
803C4—442no—
804C4#1062336012yes—
805C4C2×#41×D1111yescharacteristic
806C4C2×#6704211yescharacteristic
807C2—42no—
808C2—42no—
809C2—444no—
810C2—882no—
811C2#1308064614yesdirect product factor
812C2C2×#1062336011yescharacteristic
813C2C2×#1062335311yescharacteristic
814C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC2×#10623081C2
hypercenterC2×#556D11
hypocenterC11C2×#3311
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. #13080646C2direct (N × H)
3. C2×#10622702C2semidirect
4. C2×#10622609C2semidirect
5. C2×#10622616C2semidirect
6. C2×#10622697C2semidirect
7. C2×#10622665C2semidirect
8. C2×#10622661C2semidirect
9. C2×#10622641C2semidirect
10. C2×#10622660C2semidirect
11. C2×#10622659C2semidirect
12. C2×#10622639C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622614C2semidirect
15. C2×#10622615C2semidirect
16. C2×C11×#556C2semidirect
20. C11×#556C22semidirect
21. C2×C11×C4⋊Q8C22semidirect
26. C2×C11×C22⋊Q8C22semidirect
28. C2×C4×Q8×C11C22semidirect
31. C2×C11×#117C22semidirect
32. C22×#4326C22semidirect
39. C23×C11⋊C8C22semidirect
47. C2×#66899C22semidirect
49. C2×C22⋊(C11⋊C8)C22semidirect
50. #10622702C22semidirect
51. #10622697C22semidirect
52. #10622665C22semidirect
53. #10622661C22semidirect
54. #10622660C22semidirect
55. #10622659C22semidirect
56. #10622641C22semidirect
57. #10622639C22semidirect
58. #10622624C22semidirect
59. #10622616C22semidirect
60. #10622615C22semidirect
61. #10622614C22semidirect
62. #10622609C22semidirect
63. C2×#66874C22semidirect
64. C2×#66874C22semidirect
65. C2×#66874C22semidirect
72. C2×#66872C22semidirect
73. C2×#66872C22semidirect
74. C2×#66871C22semidirect
75. C2×C4⋊(C11⋊C8)C22semidirect
76. C2×#66867C22semidirect
100. C11×C4⋊Q8C23semidirect
107. C11×C22⋊Q8C23semidirect
110. C4×Q8×C11C23semidirect
116. C11×#117C23semidirect
137. C2×#4326C23semidirect
160. C22×C11⋊C8C23semidirect
168. #66899C23semidirect
170. C22⋊(C11⋊C8)C23semidirect
171. #66874C23semidirect
172. #66874C23semidirect
173. #66874C23semidirect
180. #66872C23semidirect
181. #66872C23semidirect
182. #66871C23semidirect
183. C4⋊(C11⋊C8)C23semidirect
184. #66867C23semidirect
292. C2×#556D11semidirect
390. #556C2×D11semidirect
393. C2×C4⋊Q8C2×D11semidirect
401. C2×C22⋊Q8C2×D11semidirect
406. C2×C4×Q8C2×D11semidirect
410. C2×#117C2×D11semidirect
513. C4⋊Q8C22×D11semidirect
525. C22⋊Q8C22×D11semidirect
532. C4×Q8C22×D11semidirect
540. #117C22×D11semidirect
586. C2×C11#3311semidirect
698. C11C2×#3311semidirect
811. C2#13080646direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230812
#130806462
C2×#106227022
C2×#106226092
C2×#106226162
C2×#106226972
C2×#106226652
C2×#106226612
C2×#106226412
C2×#106226602
C2×#106226592
C2×#106226392
C2×#106226242
C2×#106226142
C2×#106226152
C2×C11×#5562
C2×#331111