Finite Group Databasebeta

← C2×#13080839 #15630593

Subgroups — C2×#13080839 #15630593

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×#10623112C211yesmaximal, characteristic, complemented
2C2×#10623207C211yesmaximal, characteristic
3#13080839C2116yesmaximal, direct product factor
4C2×#10622669C211yesmaximal, characteristic, complemented
5C2×#10622390C211yesmaximal, characteristic, complemented
6C2×#10622427C211yesmaximal, characteristic, complemented
7C2×#10622460C211yesmaximal, characteristic, complemented
8C2×#10622802C211yesmaximal, characteristic, complemented
9C2×#10622787C211yesmaximal, characteristic, complemented
10C2×#10622800C211yesmaximal, characteristic, complemented
11C2×#10622782C211yesmaximal, characteristic, complemented
12C2×C4×#4325C211yesmaximal, characteristic, complemented
13C2×#10622451C211yesmaximal, characteristic, complemented
14C2×#10622416C211yesmaximal, characteristic, complemented
15C2×#10622383C211yesmaximal, 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×#66999C2211yescharacteristic
24C2×#66999C2211yescharacteristic
25C2×#66999C2211yescharacteristic, complemented
26C22×#4325C2211yescharacteristic
27C2×#66991C2211yescharacteristic
28C22×#4313C2211yescharacteristic
29C22×#4313C2211yescharacteristic, complemented
30#10623207—24no—
31#10623207C2218yes—
32#10623112—24no—
33#10623112C2218yescomplemented
34C2×#66947—21no—
35C2×#66945C2211yescharacteristic
36C2×C4⋊C4×D11C2211yescharacteristic, complemented
37C2×#66942—21no—
38C2×#66937—21no—
39C2×#66936—21no—
40C2×#66935—21no—
41C2×C22⋊C4×D11—21no—
42C2×#66929—21no—
43C2×C4×D44C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C2×#66925—21no—
46C2×#66923C2211yescharacteristic, complemented
47C11×#464C2218yescomplemented
48C2×C11×C4⋊C8C2211yescharacteristic, complemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic
51C2×#66899C2211yescharacteristic, complemented
52C2×#66899C2211yescharacteristic, complemented
53C2×#66899C2211yescharacteristic, complemented
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56#10622802C2218yescomplemented
57#10622800C2218yescomplemented
58#10622787C2218yescomplemented
59#10622782C2218yescomplemented
60C2×#66885C2211yescharacteristic
61C2×#66885C2211yescharacteristic
62C2×(C2×D11)⋊C8C2211yescharacteristic
63C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
64C2×#66882C2211yescharacteristic, complemented
65C2×#66881C2211yescharacteristic, complemented
66#10622669C2218yescomplemented
67C4×#4325C2218yescomplemented
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic, complemented
70C2×C4×C11⋊C8C2211yescharacteristic, complemented
71#10622460C2218yescomplemented
72#10622451C2218yescomplemented
73#10622427C2218yescomplemented
74#10622416C2218yescomplemented
75#10622390C2218yescomplemented
76#10622383C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C2×#4343—22no—
84C2×#4343—24no—
85C2×#4343—42no—
86C2×#4343C2314yes—
87C2×D4×D11—24no—
88C2×D4×D11—22no—
89C2×D4×D11—42no—
90C2×D4×D11C2314yes—
91C22×D44—21no—
92C22×D44D411yescharacteristic
93C22×D44C2311yescharacteristic
94C22×C4×D11—21no—
95C22×C4×D11—21no—
96C22×C4×D11—21no—
97C22×C4×D11C2311yescharacteristic
98C22×C4×D11C2311yescharacteristic
99C2×C11×Q16—42no—
100C2×C11×Q16C2314yescomplemented
101C2×C11×SD16—42no—
102C2×C11×SD16C2314yes—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C11×#124—22no—
106C11×#124C2314yes—
107C4×Q8×C11—22no—
108C4×Q8×C11C2314yescomplemented
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C42×C11—21no—
114C2×C42×C11C2311yescharacteristic
115C2×C22⋊Dic11—21no—
116#66999—22no—
117#66999—22no—
118#66999—22no—
119#66999C2314yes—
120#66999C2314yes—
121#66999C2314yescomplemented
122C2×#4325—24no—
123C2×#4325C2314yes—
124#66991—22no—
125#66991C2314yes—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4D411yescharacteristic
132C2×(C2×D11)⋊C4D411yescharacteristic
133C2×C4⋊Dic11D411yescharacteristic
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×C4×Dic11—21no—
144C22×C11⋊C8C2311yescharacteristic
145C22×C11⋊C8C2311yescharacteristic
146C2×#4313—42no—
147C2×#4313—42no—
148C2×#4313C2314yes—
149C2×#4313C2314yescomplemented
150#66947—28no—
151#66945—22no—
152#66945C2314yes—
153C4⋊C4×D11—22no—
154C4⋊C4×D11C2314yescomplemented
155#66942—28no—
156#66937—28no—
157#66936—28no—
158#66935—28no—
159C22⋊C4×D11—28no—
160#66929—28no—
161C4×D44—22no—
162C4×D44D414yes—
163C4×D44C2314yes—
164C4×D44C2314yes—
165#66925—28no—
166#66923—22no—
167#66923C2314yescomplemented
168C11×C4⋊C8C2314yescomplemented
169C11×#103C2314yescomplemented
170C11×#102C2314yes—
171#66899C2314yescomplemented
172#66899C2314yescomplemented
173#66899C2314yescomplemented
174#66896C2314yes—
175#66896C2314yes—
176#66885C2314yes—
177#66885C2314yes—
178(C2×D11)⋊C8C2314yes—
179(C2×D11)⋊C8C2314yescomplemented
180#66882C2314yescomplemented
181#66881C2314yescomplemented
182#66873C2314yes—
183#66872C2314yescomplemented
184C4×C11⋊C8C2314yescomplemented
185C2×#3323—111nomaximal, Sylow
186C24×C11—21no—
187C23×D11—21no—
188C23×D11—24no—
189C23×D11—44no—
190C23×D11—44no—
191C23×D11—82no—
192C23×D11C2×D411yescharacteristic
193C23×D11C2×D411yescharacteristic
194C2×Q8×C11—21no—
195C2×Q8×C11—21no—
196C2×Q8×C11—22no—
197C2×Q8×C11—22no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×Q8×C11C2412yes—
201C2×Q8×C11C2412yes—
202C2×D4×C11—21no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11C2412yes—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2411yescharacteristic
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—44no—
215C2×C22⋊D11—82no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221#4343—28no—
222#4343—44no—
223#4343—48no—
224D4×D11—28no—
225D4×D11—44no—
226D4×D11—48no—
227C2×D44—24no—
228C2×D44—21no—
229C2×D44—22no—
230C2×D44—42no—
231C2×D44—44no—
232C2×D44C2×D414yes—
233C2×D44#4114yes—
234C2×D44C2412yes—
235C2×C4×D11—24no—
236C2×C4×D11—24no—
237C2×C4×D11—24no—
238C2×C4×D11—22no—
239C2×C4×D11—22no—
240C2×C4×D11—22no—
241C2×C4×D11—22no—
242C2×C4×D11—44no—
243C2×C4×D11—44no—
244C2×C4×D11—82no—
245C2×C4×D11C2×D412yes—
246C2×C4×D11C2×D412yes—
247C2×C4×D11C2412yes—
248C2×C4×D11C2412yes—
249C11×Q16—44no—
250C11×SD16—44no—
251C2×C8×C11—22no—
252C2×C8×C11—22no—
253C2×C8×C11C2412yes—
254C2×C8×C11C2412yes—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4C2412yes—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—24no—
260C42×C11—24no—
261C42×C11C2×D412yes—
262C42×C11C2412yes—
263C22⋊Dic11—24no—
264#4325—28no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4C2×D414yes—
271(C2×D11)⋊C4C2×D414yes—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11—21no—
275C4⋊Dic11C2×D414yes—
276C4⋊Dic11C2412yes—
277C4⋊Dic11C2412yes—
278C4⋊Dic11C2412yes—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284Dic11⋊C4—24no—
285C4×Dic11—24no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8C2412yes—
289C2×C11⋊C8C2412yes—
290#4313—44no—
291#4313—44no—
292C2×#552—111no—
293C2×#546—111no—
294#3323—1116no—
295C2×#488—111no—
296C2×#481—111no—
297C2×#485—111no—
298C2×#478—111no—
299C2×#470—111no—
300C2×#468—111no—
301C2×#464D1111yescharacteristic, complemented
302C2×#452—111no—
303C2×#450—111no—
304C2×C4×SD16—111no—
305C2×#436—111no—
306C2×#417—111no—
307C2×#418—111no—
308C23×C11—22no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11C22×D411yescharacteristic
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—24no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—48no—
322C22×D11—48no—
323C22×D11—42no—
324C22×D11—42no—
325C22×D11—84no—
326C22×D11—816no—
327C22×D11C22×D412yes—
328C22×D11C22×D412yes—
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—42no—
334Q8×C11—42no—
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—42no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—42no—
344C2×C4×C11—42no—
345C2×C4×C11—42no—
346C2×C4×C11C22×D412yes—
347C2×C4×C11C22×D412yes—
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C2×#4112yes—
350C2×C4×C11H(5,𝔽2)12yes—
351C2×C4×C11C2511yescharacteristic
352C22⋊D11—48no—
353C22⋊D11—84no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11C22×D412yes—
363C2×Dic11C22×D412yes—
364D44—24no—
365D44—22no—
366D44—44no—
367D44—48no—
368D44C2×#4114yes—
369C4×D11—24no—
370C4×D11—24no—
371C4×D11—22no—
372C4×D11—22no—
373C4×D11—22no—
374C4×D11—22no—
375C4×D11—48no—
376C4×D11—48no—
377C4×D11—84no—
378C8×C11—22no—
379C8×C11—22no—
380C11⋊C8—22no—
381C11⋊C8—22no—
382C22×#41—111no—
383C23×D4—111no—
384C22×Q16C2×D1111yescharacteristic, complemented
385C22×SD16—111no—
386C22×SD16C2×D1111yescharacteristic
387C22×M16—111no—
388C22×M16—111no—
389#552—118no—
390#552—224no—
391#546—118no—
392#546—224no—
393C2×#126—221no—
394C2×#125—111no—
395C2×#125—221no—
396C2×#124C2×D1111yescharacteristic
397C2×#123—221no—
398C2×#123—221no—
399C2×C22⋊Q8—111no—
400C2×C22⋊Q8—111no—
401C2×C22⋊Q8—111no—
402C2×#121—111no—
403C2×#121—221no—
404C2×#120—221no—
405C2×C4×Q8C2×D1111yescharacteristic, complemented
406C2×C4×D4—111no—
407C2×C4×D4—111no—
408C2×#117—111no—
409C2×#117—221no—
410C22×C4⋊C4—111no—
411C22×C22⋊C4—221no—
412#488—118no—
413#485—118no—
414#481—118no—
415#478—118no—
416#470—118no—
417#468—118no—
418#464C2×D1118yescomplemented
419#452—118no—
420#450—118no—
421C4×SD16—118no—
422#436—118no—
423C2×#107—111no—
424C2×#106—111no—
425C2×#106—111no—
426C2×C4⋊C8C2×D1111yescharacteristic, complemented
427#418—118no—
428#417—118no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#103C2×D1111yescharacteristic, complemented
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×#102C2×D1111yescharacteristic
439C2×C22⋊C8—111no—
440C2×C22⋊C8—111no—
441C2×C4×C8—111no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—84no—
446C22×C11#54612yes—
447C22×C11#57512yes—
448C22×C11#57712yes—
449C22×C11C23×D411yescharacteristic
450C2×D11—24no—
451C2×D11—22no—
452C2×D11—22no—
453C2×D11—22no—
454C2×D11—22no—
455C2×D11—22no—
456C2×D11—22no—
457C2×D11—44no—
458C2×D11—44no—
459C2×D11—48no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—816no—
463C4×C11—22no—
464C4×C11—22no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11#54612yes—
469C4×C11C22×#4111yescharacteristic
470C4×C11C2×H(5,𝔽2)11yescharacteristic
471Dic11—22no—
472Dic11—22no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476C25—221no—
477C2×#41—114no—
478C2×#41—222no—
479C2×#41—224no—
480C2×#41—442no—
481C22×Q8C22×D1111yescharacteristic
482C22×Q8C22×D1111yescharacteristic
483C22×D4—114no—
484C22×D4—111no—
485C22×D4—111no—
486C22×D4—221no—
487C22×D4—222no—
488C22×D4—221no—
489C22×D4—224no—
490C22×D4—221no—
491C22×D4—442no—
492C22×D4C22×D1111yescharacteristic
493C23×C4—111no—
494C23×C4—111no—
495C23×C4—221no—
496C23×C4—221no—
497C23×C4—221no—
498C2×Q16—42no—
499C2×Q16C22×D1114yescomplemented
500C2×SD16—42no—
501C2×SD16—114no—
502C2×SD16—224no—
503C2×SD16C22×D1114yes—
504C2×M16—114no—
505C2×M16—114no—
506C2×M16—442no—
507C2×M16—442no—
508C22×C8—111no—
509C22×C8—111no—
510C22×C8C22×D1111yescharacteristic
511C22×C8C22×D1111yescharacteristic
512#126—228no—
513#125—114no—
514#125—228no—
515#125—222no—
516#124—22no—
517#124C22×D1114yes—
518#123—228no—
519#123—228no—
520C22⋊Q8—114no—
521C22⋊Q8—114no—
522C22⋊Q8—114no—
523C22⋊Q8—222no—
524C22⋊Q8—222no—
525C22⋊Q8—222no—
526#121—114no—
527#121—228no—
528#121—222no—
529#120—228no—
530C4×Q8—22no—
531C4×Q8C22×D1114yescomplemented
532C4×D4—114no—
533C4×D4—114no—
534C4×D4—114no—
535C4×D4—222no—
536#117—114no—
537#117—228no—
538#117—222no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—111no—
541C2×C4⋊C4—111no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—114no—
545C2×C4⋊C4—222no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4—221no—
551C2×C4⋊C4—221no—
552C2×C4⋊C4C22×D1111yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—111no—
556C2×C22⋊C4—111no—
557C2×C22⋊C4—228no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C42—21no—
565C2×C42—221no—
566C2×C42C22×D1111yescharacteristic
567#107—114no—
568#106—114no—
569#106—114no—
570C4⋊C8C22×D1114yescomplemented
571#103—114no—
572#103—114no—
573#103—114no—
574#103C22×D1114yescomplemented
575#102—114no—
576#102—114no—
577#102—114no—
578#102—114no—
579#102—114no—
580#102C22×D1114yes—
581C22⋊C8—114no—
582C22⋊C8—114no—
583C4×C8—114no—
584C2×C11—82no—
585C2×C11#332314yescomplemented
586C2×C11C2×#54611yescharacteristic
587C2×C11C2×#57511yescharacteristic
588C2×C11C2×#57711yescharacteristic
589D11—42no—
590D11—42no—
591D11—44no—
592C24—21no—
593C24—111no—
594C24—111no—
595C24—224no—
596C24—221no—
597C24—444no—
598C24—444no—
599C24—882no—
600#41—228no—
601#41—444no—
602#41—448no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8C23×D1112yes—
610C2×Q8C23×D1112yes—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—114no—
615C2×D4—114no—
616C2×D4—112no—
617C2×D4—224no—
618C2×D4—224no—
619C2×D4—228no—
620C2×D4—224no—
621C2×D4—221no—
622C2×D4—222no—
623C2×D4—442no—
624C2×D4—444no—
625C2×D4—444no—
626C2×D4—448no—
627C2×D4—444no—
628C2×D4—882no—
629C2×D4C23×D1112yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—111no—
634C22×C4—111no—
635C22×C4—112no—
636C22×C4—112no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—224no—
640C22×C4—224no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—224no—
649C22×C4—444no—
650C22×C4—444no—
651C22×C4—882no—
652C22×C4D4×D1111yescharacteristic
653C22×C4D4×D1111yescharacteristic
654C22×C4C23×D1111yescharacteristic
655Q16—44no—
656SD16—44no—
657SD16—228no—
658M16—444no—
659M16—444no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—112no—
663C2×C8—112no—
664C2×C8—222no—
665C2×C8—222no—
666C2×C8C23×D1112yes—
667C2×C8C23×D1112yes—
668C4⋊C4—24no—
669C4⋊C4—21no—
670C4⋊C4—114no—
671C4⋊C4—112no—
672C4⋊C4—112no—
673C4⋊C4—112no—
674C4⋊C4—224no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—224no—
678C4⋊C4—221no—
679C4⋊C4—221no—
680C4⋊C4—221no—
681C4⋊C4—224no—
682C4⋊C4—224no—
683C4⋊C4C23×D1112yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—114no—
687C22⋊C4—114no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C22⋊C4—224no—
693C22⋊C4—224no—
694C42—24no—
695C42—224no—
696C42D4×D1112yes—
697C42C23×D1112yes—
698C11C2×#332311yescharacteristic, complemented, Sylow
699C23—22no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—112no—
704C23—112no—
705C23—222no—
706C23—222no—
707C23—222no—
708C23—222no—
709C23—222no—
710C23—222no—
711C23—224no—
712C23—222no—
713C23—448no—
714C23—448no—
715C23—442no—
716C23—442no—
717C23—884no—
718C23—8816no—
719C23C2×D4×D1111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—42no—
725Q8—42no—
726D4—22no—
727D4—22no—
728D4—42no—
729D4—114no—
730D4—224no—
731D4—222no—
732D4—444no—
733D4—448no—
734D4—448no—
735D4—884no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—112no—
745C2×C4—112no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—224no—
749C2×C4—224no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—448no—
758C2×C4—448no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—884no—
763C2×C4C2×D4×D1112yes—
764C2×C4C2×D4×D1112yes—
765C2×C4C2×D4×D1111yescharacteristic
766C2×C4#6703712yes—
767C2×C4#41×D1112yes—
768C2×C4C24×D1111yescharacteristic
769C8—22no—
770C8—22no—
771C8—222no—
772C8—222no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—84no—
777C22—222no—
778C22—222no—
779C22—224no—
780C22—222no—
781C22—222no—
782C22—222no—
783C22—222no—
784C22—444no—
785C22—444no—
786C22—448no—
787C22—442no—
788C22—442no—
789C22—8816no—
790C22#1062314312yes—
791C22#1062329912yes—
792C22#1062330912yes—
793C22C22×D4×D1111yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—222no—
800C4—222no—
801C4—442no—
802C4—442no—
803C4—442no—
804C4#1062314312yes—
805C4C2×#6703711yescharacteristic
806C4C2×#41×D1111yescharacteristic
807C2—82no—
808C2—442no—
809C2—442no—
810C2—444no—
811C2#1308083914yesdirect product factor
812C2C2×#1062314311yescharacteristic
813C2C2×#1062329911yescharacteristic
814C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#464C2
socleC23×C11C22×D4
prime radicalC2×#10623207C2
hypercenterC2×#464D11
hypocenterC11C2×#3323
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×#10623112C2semidirect
3. #13080839C2direct (N × H)
4. C2×#10622669C2semidirect
5. C2×#10622390C2semidirect
6. C2×#10622427C2semidirect
7. C2×#10622460C2semidirect
8. C2×#10622802C2semidirect
9. C2×#10622787C2semidirect
10. C2×#10622800C2semidirect
11. C2×#10622782C2semidirect
12. C2×C4×#4325C2semidirect
13. C2×#10622451C2semidirect
14. C2×#10622416C2semidirect
15. C2×#10622383C2semidirect
16. C2×C11×#464C2semidirect
19. C22×C11×Q16C22semidirect
22. C2×C4×Q8×C11C22semidirect
25. C2×#66999C22semidirect
29. C22×#4313C22semidirect
33. #10623112C22semidirect
36. C2×C4⋊C4×D11C22semidirect
46. C2×#66923C22semidirect
47. C11×#464C22semidirect
48. C2×C11×C4⋊C8C22semidirect
49. C2×C11×#103C22semidirect
51. C2×#66899C22semidirect
52. C2×#66899C22semidirect
53. C2×#66899C22semidirect
56. #10622802C22semidirect
57. #10622800C22semidirect
58. #10622787C22semidirect
59. #10622782C22semidirect
63. C2×(C2×D11)⋊C8C22semidirect
64. C2×#66882C22semidirect
65. C2×#66881C22semidirect
66. #10622669C22semidirect
67. C4×#4325C22semidirect
69. C2×#66872C22semidirect
70. C2×C4×C11⋊C8C22semidirect
71. #10622460C22semidirect
72. #10622451C22semidirect
73. #10622427C22semidirect
74. #10622416C22semidirect
75. #10622390C22semidirect
76. #10622383C22semidirect
100. C2×C11×Q16C23semidirect
108. C4×Q8×C11C23semidirect
121. #66999C23semidirect
149. C2×#4313C23semidirect
154. C4⋊C4×D11C23semidirect
167. #66923C23semidirect
168. C11×C4⋊C8C23semidirect
169. C11×#103C23semidirect
171. #66899C23semidirect
172. #66899C23semidirect
173. #66899C23semidirect
179. (C2×D11)⋊C8C23semidirect
180. #66882C23semidirect
181. #66881C23semidirect
183. #66872C23semidirect
184. C4×C11⋊C8C23semidirect
301. C2×#464D11semidirect
384. C22×Q16C2×D11semidirect
405. C2×C4×Q8C2×D11semidirect
418. #464C2×D11semidirect
426. C2×C4⋊C8C2×D11semidirect
432. C2×#103C2×D11semidirect
499. C2×Q16C22×D11semidirect
531. C4×Q8C22×D11semidirect
570. C4⋊C8C22×D11semidirect
574. #103C22×D11semidirect
585. C2×C11#3323semidirect
698. C11C2×#3323semidirect
811. C2#13080839direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231122
C2×#106232072
#130808392
C2×#106226692
C2×#106223902
C2×#106224272
C2×#106224602
C2×#106228022
C2×#106227872
C2×#106228002
C2×#106227822
C2×C4×#43252
C2×#106224512
C2×#106224162
C2×#106223832
C2×C11×#4642
C2×#332311