Finite Group Databasebeta

← C2×#13080825 #15630579

Subgroups — C2×#13080825 #15630579

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×#10623173C211yesmaximal, characteristic, complemented
2C2×#10623360C211yesmaximal, characteristic
3#13080825C2116yesmaximal, direct product factor
4C2×#10622413C211yesmaximal, characteristic, complemented
5C2×#10622348C211yesmaximal, characteristic, complemented
6C2×#10622428C211yesmaximal, characteristic, complemented
7C2×#10622376C211yesmaximal, characteristic, complemented
8C2×#10622802C211yesmaximal, characteristic, complemented
9C2×#10622662C211yesmaximal, characteristic, complemented
10C2×#10622798C211yesmaximal, characteristic, complemented
11C2×#10622782C211yesmaximal, characteristic, complemented
12C2×SD16×Dic11C211yesmaximal, characteristic, complemented
13C2×#10622342C211yesmaximal, characteristic, complemented
14C2×#10622845C211yesmaximal, characteristic, complemented
15C2×#10622383C211yesmaximal, characteristic, complemented
16C2×C11×#452C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic, complemented
20C22×C11×SD16C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic, complemented
22#10623360—24no—
23#10623360C2218yes—
24C2×#67000C2211yescharacteristic
25C2×#66999C2211yescharacteristic
26C2×#66999C2211yescharacteristic
27C2×Q8×Dic11C2211yescharacteristic, complemented
28C22×#4325C2211yescharacteristic
29C2×#66992—21no—
30C2×#66990—21no—
31C2×D4×Dic11C2211yescharacteristic
32C2×#66983C2211yescharacteristic
33C2×#66982—21no—
34C2×C4×C22⋊D11C2211yescharacteristic
35C22×(C2×D11)⋊C4—21no—
36C22×C4⋊Dic11C2211yescharacteristic, complemented
37C22×#4318C2211yescharacteristic, complemented
38C22×#4313C2211yescharacteristic
39#10623173—24no—
40#10623173C2218yescomplemented
41C2×#66951—21no—
42C2×#66945C2211yescharacteristic
43C2×#66943—21no—
44C2×#66943C2211yescharacteristic, complemented
45C2×#66939—21no—
46C2×#66930—21no—
47C11×#452C2218yescomplemented
48C2×C11×#103C2211yescharacteristic, complemented
49C2×C11×#102C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic, complemented
51#10622845C2218yescomplemented
52C2×#66899C2211yescharacteristic, complemented
53C2×#66899C2211yescharacteristic, complemented
54C2×#66899C2211yescharacteristic, complemented
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57#10622802C2218yescomplemented
58#10622798C2218yescomplemented
59#10622782C2218yescomplemented
60SD16×Dic11C2218yescomplemented
61C2×#66885C2211yescharacteristic
62C2×#66885C2211yescharacteristic
63C2×(C2×D11)⋊C8C2211yescharacteristic
64C2×#66881C2211yescharacteristic, complemented
65C2×#66881C2211yescharacteristic, complemented
66C2×Dic11⋊C8C2211yescharacteristic, complemented
67C2×C8×Dic11C2211yescharacteristic, complemented
68#10622662C2218yescomplemented
69C2×#66873C2211yescharacteristic
70C2×#66871C2211yescharacteristic, complemented
71#10622428C2218yescomplemented
72#10622413C2218yescomplemented
73#10622383C2218yescomplemented
74#10622376C2218yescomplemented
75#10622348C2218yescomplemented
76#10622342C2218yescomplemented
77C24×D11—21no—
78C2×C11×#41—22no—
79C2×C11×#41—24no—
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⋊D11D411yescharacteristic
91C23×Dic11—21no—
92C23×Dic11—21no—
93C2×D4×D11—24no—
94C2×D4×D11—22no—
95C2×D4×D11—42no—
96C2×D4×D11C2314yes—
97C22×D44C2311yescharacteristic
98C22×C4×D11C2311yescharacteristic
99C2×C11×Q16—42no—
100C2×C11×Q16C2314yescomplemented
101C2×C11×SD16—24no—
102C2×C11×SD16C2314yes—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C11×C22⋊Q8—22no—
106C11×C22⋊Q8C2314yescomplemented
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11D411yescharacteristic
112#67000—22no—
113#67000C2314yes—
114#66999—22no—
115#66999—22no—
116#66999C2314yes—
117#66999C2314yes—
118Q8×Dic11—22no—
119Q8×Dic11C2314yescomplemented
120C2×#4325—42no—
121C2×#4325C2314yes—
122#66992—28no—
123#66990—28no—
124D4×Dic11—22no—
125D4×Dic11C2314yes—
126#66983—22no—
127#66983C2314yes—
128#66982—28no—
129C4×C22⋊D11D414yes—
130C4×C22⋊D11C2314yes—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—28no—
138C2×(C2×D11)⋊C4D411yescharacteristic
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11—22no—
141C2×C4⋊Dic11—21no—
142C2×C4⋊Dic11—21no—
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2311yescharacteristic
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2314yescomplemented
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4D411yescharacteristic
151C2×C4×Dic11—21no—
152C2×C4×Dic11—21no—
153C2×C4×Dic11C2311yescharacteristic
154C2×#4318—42no—
155C2×#4318C2314yescomplemented
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158C2×#4313—42no—
159C2×#4313C2314yes—
160#66951—28no—
161#66945—22no—
162#66945C2314yes—
163#66943—28no—
164#66943—22no—
165#66943C2314yescomplemented
166#66939—28no—
167#66930—28no—
168C11×#103C2314yescomplemented
169C11×#102C2314yes—
170C11×C22⋊C8C2314yescomplemented
171#66899C2314yescomplemented
172#66899C2314yescomplemented
173#66899C2314yescomplemented
174#66896C2314yes—
175#66896C2314yes—
176#66885C2314yes—
177#66885C2314yes—
178(C2×D11)⋊C8C2314yes—
179#66881C2314yescomplemented
180#66881C2314yescomplemented
181Dic11⋊C8C2314yescomplemented
182C8×Dic11C2314yescomplemented
183#66873C2314yes—
184#66871C2314yescomplemented
185C2×#3323—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11C2×D411yescharacteristic
188C23×D11—21no—
189C23×D11—24no—
190C23×D11—44no—
191C23×D11—44no—
192C23×D11—82no—
193C23×D11C2×D411yescharacteristic
194C11×#41—28no—
195C11×#41—44no—
196C11×#41—48no—
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—24no—
206C2×D4×C11—21no—
207C2×D4×C11—22no—
208C2×D4×C11—44no—
209C2×D4×C11#4114yes—
210C2×D4×C11C2412yes—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—24no—
217C22×C4×C11—44no—
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2411yescharacteristic
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—42no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—82no—
227C2×C22⋊D11C2×D414yes—
228C22×Dic11—24no—
229C22×Dic11—24no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—44no—
234C22×Dic11—82no—
235C22×Dic11C2×D411yescharacteristic
236C22×Dic11C2×D411yescharacteristic
237C22×Dic11C2×D411yescharacteristic
238D4×D11—28no—
239D4×D11—44no—
240D4×D11—48no—
241C2×D44—21no—
242C2×D44—22no—
243C2×D44—22no—
244C2×D44C2412yes—
245C2×C4×D11—22no—
246C2×C4×D11—22no—
247C2×C4×D11C2×D412yes—
248C2×C4×D11C2412yes—
249C11×Q16—44no—
250C11×SD16—28no—
251C2×C8×C11—22no—
252C2×C8×C11—22no—
253C2×C8×C11C2412yes—
254C2×C8×C11C2412yes—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—24no—
257C11×C4⋊C4C2412yes—
258C11×C22⋊C4—24no—
259C22⋊Dic11—24no—
260C22⋊Dic11C2×D414yes—
261#4325—44no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4C2×D414yes—
269C4⋊Dic11—24no—
270C4⋊Dic11—24no—
271C4⋊Dic11—24no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11—21no—
275C4⋊Dic11C2412yes—
276C4⋊Dic11C2412yes—
277C4⋊Dic11C2412yes—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4C2×D414yes—
282C4×Dic11—24no—
283C4×Dic11—24no—
284C4×Dic11C2×D412yes—
285C4×Dic11C2412yes—
286#4318—44no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8—22no—
289C2×C11⋊C8C2412yes—
290C2×C11⋊C8C2412yes—
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×#464—111no—
302C2×#452D1111yescharacteristic, complemented
303C2×#450—111no—
304C2×C4×SD16—111no—
305C2×#436—111no—
306C2×#417—111no—
307C2×#418—111no—
308C23×C11—24no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—42no—
314C23×C11—42no—
315C23×C11C22×D412yes—
316C23×C11C22×D411yescharacteristic
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—42no—
326C22×D11—84no—
327C22×D11—816no—
328C22×D11C22×D412yes—
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—42no—
334Q8×C11—42no—
335D4×C11—24no—
336D4×C11—22no—
337D4×C11—48no—
338D4×C11C2×#4114yes—
339C2×C4×C11—22no—
340C2×C4×C11—24no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—48no—
347C2×C4×C11—42no—
348C2×C4×C11—42no—
349C2×C4×C11—42no—
350C2×C4×C11C22×D412yes—
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C2×#4112yes—
353C2×C4×C11H(5,𝔽2)12yes—
354C2×C4×C11C2511yescharacteristic
355C22⋊D11—44no—
356C22⋊D11—48no—
357C22⋊D11—84no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—48no—
365C2×Dic11—42no—
366C2×Dic11—42no—
367C2×Dic11—42no—
368C2×Dic11—84no—
369C2×Dic11C22×D412yes—
370C2×Dic11C22×D412yes—
371C2×Dic11C22×D412yes—
372D44—22no—
373D44—22no—
374D44—42no—
375C4×D11—24no—
376C4×D11—22no—
377C4×D11—22no—
378C8×C11—22no—
379C8×C11—22no—
380C11⋊C8—22no—
381C11⋊C8—22no—
382C22×#41C2×D1111yescharacteristic
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×#124—111no—
397C2×#123—221no—
398C2×#123—221no—
399C2×C22⋊Q8—111no—
400C2×C22⋊Q8—111no—
401C2×C22⋊Q8C2×D1111yescharacteristic, complemented
402C2×#121—111no—
403C2×#121—221no—
404C2×#120—221no—
405C2×C4×Q8—111no—
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#464—118no—
419#452C2×D1118yescomplemented
420#450—118no—
421C4×SD16—118no—
422#436—118no—
423C2×#107—111no—
424C2×#106—111no—
425C2×#106—111no—
426C2×C4⋊C8—111no—
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⋊C8C2×D1111yescharacteristic, complemented
441C2×C4×C8—111no—
442C22×C11—22no—
443C22×C11—24no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—48no—
447C22×C11—44no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11#54612yes—
451C22×C11#57512yes—
452C22×C11#57712yes—
453C22×C11C23×D411yescharacteristic
454C2×D11—22no—
455C2×D11—22no—
456C2×D11—22no—
457C2×D11—44no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—816no—
462C2×D11—84no—
463C4×C11—22no—
464C4×C11—42no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11#54612yes—
468C4×C11C22×#4111yescharacteristic
469C4×C11C2×H(5,𝔽2)11yescharacteristic
470Dic11—22no—
471Dic11—22no—
472Dic11—22no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476C25—221no—
477C2×#41—22no—
478C2×#41—24no—
479C2×#41—42no—
480C2×#41C22×D1114yes—
481C22×Q8C22×D1111yescharacteristic
482C22×Q8C22×D1111yescharacteristic
483C22×D4—21no—
484C22×D4—111no—
485C22×D4—114no—
486C22×D4—111no—
487C22×D4—222no—
488C22×D4—221no—
489C22×D4—224no—
490C22×D4—221no—
491C22×D4—442no—
492C22×D4C22×D1111yescharacteristic
493C23×C4—21no—
494C23×C4—111no—
495C23×C4—221no—
496C23×C4—221no—
497C23×C4C22×D1111yescharacteristic
498C2×Q16—42no—
499C2×Q16C22×D1114yescomplemented
500C2×SD16—24no—
501C2×SD16—114no—
502C2×SD16—442no—
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—222no—
515#125—228no—
516#124—114no—
517#124—222no—
518#123—228no—
519#123—228no—
520C22⋊Q8—22no—
521C22⋊Q8—114no—
522C22⋊Q8—114no—
523C22⋊Q8—222no—
524C22⋊Q8—222no—
525C22⋊Q8C22×D1114yescomplemented
526#121—114no—
527#121—228no—
528#121—222no—
529#120—228no—
530C4×Q8—114no—
531C4×Q8—222no—
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—114no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4—221no—
551C2×C4⋊C4—222no—
552C2×C4⋊C4C22×D1111yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—111no—
555C2×C22⋊C4—111no—
556C2×C22⋊C4—228no—
557C2×C22⋊C4—221no—
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—111no—
565C2×C42—221no—
566C2×C42—221no—
567#107—114no—
568#106—114no—
569#106—114no—
570C4⋊C8—114no—
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⋊C8C22×D1114yescomplemented
583C4×C8—114no—
584C2×C11—44no—
585C2×C11—42no—
586C2×C11#332314yescomplemented
587C2×C11C2×#54611yescharacteristic
588C2×C11C2×#57511yescharacteristic
589C2×C11C2×#57711yescharacteristic
590D11—42no—
591D11—82no—
592C24—21no—
593C24—111no—
594C24—224no—
595C24—221no—
596C24—444no—
597C24—444no—
598C24—882no—
599C24D4×D1111yescharacteristic
600#41—28no—
601#41—44no—
602#41—48no—
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—24no—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—44no—
615C2×D4—114no—
616C2×D4—112no—
617C2×D4—224no—
618C2×D4—228no—
619C2×D4—224no—
620C2×D4—221no—
621C2×D4—222no—
622C2×D4—222no—
623C2×D4—444no—
624C2×D4—448no—
625C2×D4—442no—
626C2×D4—444no—
627C2×D4—882no—
628C2×D4#434114yes—
629C2×D4C23×D1112yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—24no—
636C22×C4—44no—
637C22×C4—111no—
638C22×C4—111no—
639C22×C4—111no—
640C22×C4—112no—
641C22×C4—112no—
642C22×C4—224no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—224no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—444no—
650C22×C4—882no—
651C22×C4D4×D1112yes—
652C22×C4D4×D1111yescharacteristic
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655Q16—44no—
656SD16—28no—
657SD16—444no—
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—224no—
679C4⋊C4—221no—
680C4⋊C4—221no—
681C4⋊C4—224no—
682C4⋊C4—221no—
683C4⋊C4C23×D1112yes—
684C22⋊C4—24no—
685C22⋊C4—114no—
686C22⋊C4—114no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C22⋊C4—224no—
693C22⋊C4—224no—
694C42—112no—
695C42—112no—
696C42—224no—
697C42—224no—
698C11C2×#332311yescharacteristic, complemented, Sylow
699C23—22no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—22no—
704C23—42no—
705C23—42no—
706C23—112no—
707C23—222no—
708C23—222no—
709C23—222no—
710C23—222no—
711C23—448no—
712C23—448no—
713C23—442no—
714C23—442no—
715C23—442no—
716C23—884no—
717C23—8816no—
718C23C2×D4×D1112yes—
719C23C2×D4×D1111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—42no—
725Q8—42no—
726D4—24no—
727D4—22no—
728D4—48no—
729D4—222no—
730D4—222no—
731D4—444no—
732D4—448no—
733D4—442no—
734D4—884no—
735D4C2×#434114yes—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—48no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—112no—
748C2×C4—112no—
749C2×C4—112no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—224no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—448no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4—884no—
764C2×C4C2×D4×D1112yes—
765C2×C4C2×D4×D1111yescharacteristic
766C2×C4C2×#434112yes—
767C2×C4#6703712yes—
768C2×C4C24×D1111yescharacteristic
769C8—22no—
770C8—22no—
771C8—222no—
772C8—222no—
773C22—22no—
774C22—24no—
775C22—22no—
776C22—22no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—48no—
781C22—222no—
782C22—222no—
783C22—222no—
784C22—444no—
785C22—442no—
786C22—442no—
787C22—442no—
788C22—8816no—
789C22—884no—
790C22#1062312212yes—
791C22#1062330112yes—
792C22#1062330812yes—
793C22C22×D4×D1111yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—222no—
799C4—222no—
800C4—222no—
801C4—442no—
802C4—442no—
803C4—442no—
804C4#1062312212yes—
805C4C22×#434111yescharacteristic
806C4C2×#6703711yescharacteristic
807C2—42no—
808C2—44no—
809C2—442no—
810C2—882no—
811C2#1308082514yesdirect product factor
812C2C2×#1062312211yescharacteristic
813C2C2×#1062330811yescharacteristic
814C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#452C2
socleC23×C11C22×D4
prime radicalC2×#10623360C2
hypercenterC2×#452D11
hypocenterC11C2×#3323
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×#10623173C2semidirect
3. #13080825C2direct (N × H)
4. C2×#10622413C2semidirect
5. C2×#10622348C2semidirect
6. C2×#10622428C2semidirect
7. C2×#10622376C2semidirect
8. C2×#10622802C2semidirect
9. C2×#10622662C2semidirect
10. C2×#10622798C2semidirect
11. C2×#10622782C2semidirect
12. C2×SD16×Dic11C2semidirect
13. C2×#10622342C2semidirect
14. C2×#10622845C2semidirect
15. C2×#10622383C2semidirect
16. C2×C11×#452C2semidirect
19. C22×C11×Q16C22semidirect
21. C2×C11×C22⋊Q8C22semidirect
27. C2×Q8×Dic11C22semidirect
36. C22×C4⋊Dic11C22semidirect
37. C22×#4318C22semidirect
40. #10623173C22semidirect
44. C2×#66943C22semidirect
47. C11×#452C22semidirect
48. C2×C11×#103C22semidirect
50. C2×C11×C22⋊C8C22semidirect
51. #10622845C22semidirect
52. C2×#66899C22semidirect
53. C2×#66899C22semidirect
54. C2×#66899C22semidirect
57. #10622802C22semidirect
58. #10622798C22semidirect
59. #10622782C22semidirect
60. SD16×Dic11C22semidirect
64. C2×#66881C22semidirect
65. C2×#66881C22semidirect
66. C2×Dic11⋊C8C22semidirect
67. C2×C8×Dic11C22semidirect
68. #10622662C22semidirect
70. C2×#66871C22semidirect
71. #10622428C22semidirect
72. #10622413C22semidirect
73. #10622383C22semidirect
74. #10622376C22semidirect
75. #10622348C22semidirect
76. #10622342C22semidirect
100. C2×C11×Q16C23semidirect
106. C11×C22⋊Q8C23semidirect
119. Q8×Dic11C23semidirect
146. C2×C4⋊Dic11C23semidirect
155. C2×#4318C23semidirect
165. #66943C23semidirect
168. C11×#103C23semidirect
170. C11×C22⋊C8C23semidirect
171. #66899C23semidirect
172. #66899C23semidirect
173. #66899C23semidirect
179. #66881C23semidirect
180. #66881C23semidirect
181. Dic11⋊C8C23semidirect
182. C8×Dic11C23semidirect
184. #66871C23semidirect
302. C2×#452D11semidirect
384. C22×Q16C2×D11semidirect
401. C2×C22⋊Q8C2×D11semidirect
419. #452C2×D11semidirect
432. C2×#103C2×D11semidirect
440. C2×C22⋊C8C2×D11semidirect
499. C2×Q16C22×D11semidirect
525. C22⋊Q8C22×D11semidirect
574. #103C22×D11semidirect
582. C22⋊C8C22×D11semidirect
586. C2×C11#3323semidirect
698. C11C2×#3323semidirect
811. C2#13080825direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231732
C2×#106233602
#130808252
C2×#106224132
C2×#106223482
C2×#106224282
C2×#106223762
C2×#106228022
C2×#106226622
C2×#106227982
C2×#106227822
C2×SD16×Dic112
C2×#106223422
C2×#106228452
C2×#106223832
C2×C11×#4522
C2×#332311