Finite Group Databasebeta

← C2×#13080735 #15630484

Subgroups — C2×#13080735 #15630484

Order 2816.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623173C211yesmaximal, characteristic, complemented
2C2×#10623365C211yesmaximal, characteristic
3#13080735C2116yesmaximal, direct product factor
4C2×#10622377C211yesmaximal, characteristic, complemented
5C2×#10622348C211yesmaximal, characteristic, complemented
6C2×#10622392C211yesmaximal, characteristic, complemented
7C2×#10622412C211yesmaximal, characteristic, complemented
8C2×#10622662C211yesmaximal, characteristic, complemented
9C2×#10622784C211yesmaximal, characteristic, complemented
10C2×#10622776C211yesmaximal, characteristic, complemented
11C2×#10622800C211yesmaximal, characteristic, complemented
12C2×#10622797C211yesmaximal, characteristic, complemented
13C2×#10622341C211yesmaximal, characteristic, complemented
14C2×#10622845C211yesmaximal, characteristic, complemented
15C2×#10622417C211yesmaximal, characteristic, complemented
16C2×C11×#452C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4343C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22#10623365—24no—
23#10623365C2218yes—
24C2×#66999C2211yescharacteristic
25C2×Q8×Dic11C2211yescharacteristic
26C2×Q8×Dic11C2211yescharacteristic
27C22×#4325C2211yescharacteristic
28C2×#66993—21no—
29C2×#66993C2211yescharacteristic
30C2×#66991—21no—
31C2×#66991C2211yescharacteristic
32C2×#66983—21no—
33C2×#66983C2211yescharacteristic
34C2×C4×C22⋊D11—21no—
35C2×C4×C22⋊D11C2211yescharacteristic
36C22×C4⋊Dic11C2211yescharacteristic
37C22×#4318C2211yescharacteristic
38C22×C8×D11C2211yescharacteristic
39#10623173—24no—
40#10623173C2218yescomplemented
41C2×#66951—21no—
42C2×#66945C2211yescharacteristic
43C2×#66943—21no—
44C2×#66943C2211yescharacteristic
45C2×#66939—21no—
46C2×#66930—21no—
47C11×#452C2218yescomplemented
48C2×C11×#103C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51#10622845C2218yescomplemented
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57#10622800C2218yescomplemented
58#10622797C2218yescomplemented
59#10622784C2218yescomplemented
60#10622776C2218yescomplemented
61C2×#66885C2211yescharacteristic
62C2×#66885C2211yescharacteristic
63C2×(C2×D11)⋊C8C2211yescharacteristic
64C2×#66881C2211yescharacteristic
65C2×#66881C2211yescharacteristic
66C2×#66879C2211yescharacteristic
67C2×Dic11⋊C8C2211yescharacteristic
68#10622662C2218yescomplemented
69C2×#66873C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622417C2218yescomplemented
72#10622412C2218yescomplemented
73#10622392C2218yescomplemented
74#10622377C2218yescomplemented
75#10622348C2218yescomplemented
76#10622341C2218yescomplemented
77C2×C11×#41—22no—
78C2×C11×#41—24no—
79C2×C11×#41—42no—
80C2×C11×#41C2314yes—
81C22×Q8×C11C2311yescharacteristic
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11—21no—
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11D411yescharacteristic
92C23×Dic11—21no—
93C2×#4343—22no—
94C2×#4343—24no—
95C2×#4343—42no—
96C2×#4343C2314yes—
97C22×D44—21no—
98C22×D44C2311yescharacteristic
99C22×C4×D11—21no—
100C22×C4×D11C2311yescharacteristic
101C2×C11×Q16—24no—
102C2×C11×Q16C2314yes—
103C2×C11×SD16—42no—
104C2×C11×SD16C2314yes—
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C11×C22⋊Q8—22no—
108C11×C22⋊Q8C2314yes—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11D411yescharacteristic
114#66999—22no—
115#66999C2314yes—
116Q8×Dic11—22no—
117Q8×Dic11—22no—
118Q8×Dic11C2314yes—
119Q8×Dic11C2314yes—
120C2×#4325—42no—
121C2×#4325C2314yes—
122#66993—28no—
123#66993—22no—
124#66993C2314yes—
125#66991—22no—
126#66991—28no—
127#66991C2314yes—
128#66983—22no—
129#66983—28no—
130#66983C2314yes—
131C4×C22⋊D11—28no—
132C4×C22⋊D11D414yes—
133C4×C22⋊D11C2314yes—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4D411yescharacteristic
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11—22no—
140C2×C4⋊Dic11—21no—
141C2×C4⋊Dic11—21no—
142C2×C4⋊Dic11—21no—
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2311yescharacteristic
145C2×C4⋊Dic11C2314yes—
146C2×C4⋊Dic11C2311yescharacteristic
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4D411yescharacteristic
150C2×C4×Dic11—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11—21no—
153C2×C4×Dic11C2311yescharacteristic
154C2×#4318—42no—
155C2×#4318C2314yes—
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158C2×C8×D11—42no—
159C2×C8×D11C2314yes—
160#66951—28no—
161#66945—22no—
162#66945C2314yes—
163#66943—28no—
164#66943—22no—
165#66943C2314yes—
166#66939—28no—
167#66930—28no—
168C11×#103C2314yes—
169C11×#102C2314yes—
170C11×C22⋊C8C2314yes—
171#66899C2314yes—
172#66899C2314yes—
173#66899C2314yes—
174#66896C2314yes—
175#66896C2314yes—
176#66885C2314yes—
177#66885C2314yes—
178(C2×D11)⋊C8C2314yes—
179#66881C2314yes—
180#66881C2314yes—
181#66879C2314yes—
182Dic11⋊C8C2314yes—
183#66873C2314yes—
184#66871C2314yes—
185C2×#3317—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11C2×D411yescharacteristic
188C23×D11—21no—
189C23×D11C2×D411yescharacteristic
190C11×#41—28no—
191C11×#41—44no—
192C11×#41—48no—
193C2×Q8×C11—21no—
194C2×Q8×C11—21no—
195C2×Q8×C11—22no—
196C2×Q8×C11—22no—
197C2×Q8×C11—22no—
198C2×Q8×C11#4114yes—
199C2×Q8×C11C2412yes—
200C2×Q8×C11C2412yes—
201C2×D4×C11—24no—
202C2×D4×C11—21no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—44no—
206C2×D4×C11C2412yes—
207C22×C4×C11—21no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—24no—
213C22×C4×C11—44no—
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2411yescharacteristic
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—42no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11—82no—
225C2×C22⋊D11—82no—
226C2×C22⋊D11—82no—
227C2×C22⋊D11C2×D414yes—
228C22×Dic11—24no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—44no—
233C22×Dic11C2×D411yescharacteristic
234C22×Dic11C2×D411yescharacteristic
235C22×Dic11C2×D411yescharacteristic
236#4343—28no—
237#4343—44no—
238#4343—48no—
239C2×D44—24no—
240C2×D44—21no—
241C2×D44—22no—
242C2×D44—22no—
243C2×D44—44no—
244C2×D44C2412yes—
245C2×C4×D11—24no—
246C2×C4×D11—22no—
247C2×C4×D11—22no—
248C2×C4×D11—44no—
249C2×C4×D11C2×D412yes—
250C2×C4×D11C2412yes—
251C11×Q16—28no—
252C11×SD16—44no—
253C2×C8×C11—22no—
254C2×C8×C11—22no—
255C2×C8×C11C2412yes—
256C2×C8×C11C2412yes—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—24no—
259C11×C4⋊C4C2412yes—
260C11×C22⋊C4—24no—
261C22⋊Dic11—24no—
262C22⋊Dic11C2×D414yes—
263#4325—44no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4C2×D414yes—
268C4⋊Dic11—24no—
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⋊C4C2×D414yes—
281C4×Dic11—24no—
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—
291C8×D11—44no—
292C2×#552—111no—
293C2×#550—111no—
294#3317—1116no—
295C2×#490—111no—
296C2×#481—111no—
297C2×#482—111no—
298C2×#479—111no—
299C2×#468—111no—
300C2×#465—111no—
301C2×#460—111no—
302C2×#452—111no—
303C2×#452D1111yescharacteristic, complemented
304C2×#441—111no—
305C2×#435—111no—
306C2×#417—111no—
307C2×#416—111no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—42no—
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—42no—
322C22×D11—42no—
323C22×D11—42no—
324C22×D11C22×D412yes—
325Q8×C11—24no—
326Q8×C11—22no—
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11—42no—
330Q8×C11C2×#4114yes—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—48no—
334D4×C11—42no—
335C2×C4×C11—24no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—24no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—48no—
344C2×C4×C11—42no—
345C2×C4×C11—42no—
346C2×C4×C11C22×D412yes—
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11C2×#4112yes—
349C2×C4×C11H(5,𝔽2)12yes—
350C2×C4×C11C2511yescharacteristic
351C22⋊D11—44no—
352C22⋊D11—48no—
353C22⋊D11—84no—
354C22⋊D11—84no—
355C22⋊D11—84no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—48no—
363C2×Dic11—42no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366C2×Dic11C22×D412yes—
367C2×Dic11C22×D412yes—
368C2×Dic11C22×D412yes—
369D44—22no—
370D44—22no—
371D44—48no—
372D44—42no—
373C4×D11—24no—
374C4×D11—22no—
375C4×D11—22no—
376C4×D11—48no—
377C8×C11—22no—
378C8×C11—22no—
379C11⋊C8—22no—
380C11⋊C8—22no—
381C22×#41—111no—
382C22×#41C2×D1111yescharacteristic
383C22×Q16C2×D1111yescharacteristic
384C22×SD16—111no—
385C22×SD16C2×D1111yescharacteristic
386C22×M16—111no—
387C23×C8—111no—
388#552—118no—
389#552—224no—
390#550—118no—
391#550—224no—
392C2×#127—111no—
393C2×#127—221no—
394C2×#126—221no—
395C2×#125—111no—
396C2×#125—221no—
397C2×#123—221no—
398C2×C22⋊Q8—111no—
399C2×C22⋊Q8C2×D1111yescharacteristic
400C2×#121—111no—
401C2×#121—111no—
402C2×#121—221no—
403C2×#121—221no—
404C2×C4×Q8—111no—
405C2×C4×Q8—111no—
406C2×C4×D4—111no—
407C2×C4×D4—221no—
408C2×#117—111no—
409C2×#117—221no—
410C22×C4⋊C4—111no—
411#490—118no—
412#482—118no—
413#481—118no—
414#479—118no—
415#468—118no—
416#465—118no—
417#460—118no—
418#452—118no—
419#452C2×D1118yescomplemented
420#441—118no—
421#435—118no—
422C2×#107—111no—
423C2×#106—111no—
424C2×#106—111no—
425C2×C4⋊C8—111no—
426#417—118no—
427#416—118no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103C2×D1111yescharacteristic
432C2×#102—111no—
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102C2×D1111yescharacteristic
438C2×C22⋊C8—111no—
439C2×C22⋊C8C2×D1111yescharacteristic
440C2×#97—111no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—44no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—84no—
449C22×C11#54612yes—
450C22×C11#57512yes—
451C22×C11#57712yes—
452C22×C11C23×D411yescharacteristic
453C2×D11—22no—
454C2×D11—22no—
455C2×D11—22no—
456C2×D11—44no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—84no—
461C4×C11—22no—
462C4×C11—24no—
463C4×C11—42no—
464C4×C11—42no—
465C4×C11#54612yes—
466C4×C11C22×#4111yescharacteristic
467C4×C11C2×H(5,𝔽2)11yescharacteristic
468Dic11—22no—
469Dic11—22no—
470Dic11—22no—
471Dic11—42no—
472Dic11—42no—
473Dic11—42no—
474C2×#41—22no—
475C2×#41—24no—
476C2×#41—42no—
477C2×#41—114no—
478C2×#41—222no—
479C2×#41—224no—
480C2×#41—442no—
481C2×#41C22×D1114yes—
482C22×Q8C22×D1111yescharacteristic
483C22×Q8C22×D1111yescharacteristic
484C22×D4—21no—
485C22×D4—111no—
486C22×D4—111no—
487C22×D4—221no—
488C22×D4—221no—
489C22×D4—221no—
490C22×D4—221no—
491C22×D4—221no—
492C22×D4C22×D1111yescharacteristic
493C23×C4—21no—
494C23×C4—111no—
495C23×C4—221no—
496C23×C4—221no—
497C23×C4C22×D1111yescharacteristic
498C2×Q16—24no—
499C2×Q16C22×D1114yes—
500C2×SD16—42no—
501C2×SD16—114no—
502C2×SD16—442no—
503C2×SD16C22×D1114yes—
504C2×M16—114no—
505C2×M16—442no—
506C22×C8—111no—
507C22×C8—111no—
508C22×C8—114no—
509C22×C8—442no—
510C22×C8C22×D1111yescharacteristic
511C22×C8C22×D1111yescharacteristic
512#127—114no—
513#127—222no—
514#127—228no—
515#126—228no—
516#125—114no—
517#125—222no—
518#125—228no—
519#123—228no—
520C22⋊Q8—22no—
521C22⋊Q8—114no—
522C22⋊Q8—222no—
523C22⋊Q8C22×D1114yes—
524#121—114no—
525#121—114no—
526#121—228no—
527#121—228no—
528#121—222no—
529#121—222no—
530C4×Q8—114no—
531C4×Q8—114no—
532C4×Q8—222no—
533C4×Q8—222no—
534C4×D4—114no—
535C4×D4—114no—
536C4×D4—228no—
537#117—114no—
538#117—228no—
539#117—222no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—111no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—114no—
545C2×C4⋊C4—111no—
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⋊C4—222no—
553C2×C4⋊C4C22×D1111yescharacteristic
554C2×C22⋊C4—21no—
555C2×C22⋊C4—111no—
556C2×C22⋊C4—111no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C42—111no—
562C2×C42—221no—
563C2×C42—221no—
564C2×C42—221no—
565#107—114no—
566#106—114no—
567#106—114no—
568C4⋊C8—114no—
569#103—114no—
570#103—114no—
571#103—114no—
572#103C22×D1114yes—
573#102—114no—
574#102—114no—
575#102—114no—
576#102—114no—
577#102—114no—
578#102C22×D1114yes—
579C22⋊C8—114no—
580C22⋊C8C22×D1114yes—
581#97—114no—
582C2×C11—42no—
583C2×C11—82no—
584C2×C11#331714yescomplemented
585C2×C11C2×#54611yescharacteristic
586C2×C11C2×#57511yescharacteristic
587C2×C11C2×#57711yescharacteristic
588D11—42no—
589D11—82no—
590C24—21no—
591C24—111no—
592C24—221no—
593C24D4×D1111yescharacteristic
594#41—28no—
595#41—44no—
596#41—48no—
597#41—228no—
598#41—444no—
599#41—448no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8#434114yes—
606C2×Q8C23×D1112yes—
607C2×Q8C23×D1112yes—
608C2×D4—24no—
609C2×D4—21no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—44no—
613C2×D4—114no—
614C2×D4—112no—
615C2×D4—224no—
616C2×D4—224no—
617C2×D4—224no—
618C2×D4—224no—
619C2×D4—224no—
620C2×D4—221no—
621C2×D4—222no—
622C2×D4—222no—
623C2×D4—444no—
624C2×D4—442no—
625C2×D4—444no—
626C2×D4—882no—
627C2×D4—882no—
628C2×D4—882no—
629C2×D4C23×D1112yes—
630C22×C4—21no—
631C22×C4—22no—
632C22×C4—22no—
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—444no—
651C22×C4D4×D1112yes—
652C22×C4D4×D1111yescharacteristic
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655Q16—28no—
656SD16—44no—
657SD16—444no—
658M16—444no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—112no—
662C2×C8—112no—
663C2×C8—222no—
664C2×C8—222no—
665C2×C8—444no—
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—
691C42—112no—
692C42—112no—
693C42—224no—
694C42—224no—
695C42—224no—
696C11C2×#331711yescharacteristic, complemented, Sylow
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—112no—
705C23—222no—
706C23—222no—
707C23—222no—
708C23—222no—
709C23—442no—
710C23—442no—
711C23—442no—
712C23C2×D4×D1112yes—
713C23C2×D4×D1111yescharacteristic
714Q8—24no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—42no—
719Q8C2×#434114yes—
720D4—22no—
721D4—22no—
722D4—48no—
723D4—42no—
724D4—222no—
725D4—222no—
726D4—448no—
727D4—444no—
728D4—448no—
729D4—442no—
730D4—884no—
731D4—884no—
732D4—884no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—48no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—112no—
745C2×C4—112no—
746C2×C4—112no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—224no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—448no—
757C2×C4—448no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4C2×D4×D1112yes—
762C2×C4C2×D4×D1111yescharacteristic
763C2×C4C2×#434112yes—
764C2×C4#6703712yes—
765C2×C4C24×D1111yescharacteristic
766C8—22no—
767C8—22no—
768C8—222no—
769C8—222no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—84no—
778C22—222no—
779C22—222no—
780C22—222no—
781C22—444no—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—884no—
786C22#1062312212yes—
787C22#1062330112yes—
788C22#1062330812yes—
789C22C22×D4×D1111yescharacteristic
790C4—22no—
791C4—24no—
792C4—42no—
793C4—42no—
794C4—222no—
795C4—222no—
796C4—222no—
797C4—442no—
798C4—442no—
799C4—442no—
800C4#1062312212yes—
801C4C22×#434111yescharacteristic
802C4C2×#6703711yescharacteristic
803C2—42no—
804C2—82no—
805C2—442no—
806C2—882no—
807C2#1308073514yesdirect product factor
808C2C2×#1062312211yescharacteristic
809C2C2×#1062330811yescharacteristic
810C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#452C2
socleC23×C11C22×D4
prime radicalC2×#10623365C2
hypercenterC2×#452D11
hypocenterC11C2×#3317
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. #13080735C2direct (N × H)
4. C2×#10622377C2semidirect
5. C2×#10622348C2semidirect
6. C2×#10622392C2semidirect
7. C2×#10622412C2semidirect
8. C2×#10622662C2semidirect
9. C2×#10622784C2semidirect
10. C2×#10622776C2semidirect
11. C2×#10622800C2semidirect
12. C2×#10622797C2semidirect
13. C2×#10622341C2semidirect
14. C2×#10622845C2semidirect
15. C2×#10622417C2semidirect
16. C2×C11×#452C2semidirect
40. #10623173C22semidirect
47. C11×#452C22semidirect
51. #10622845C22semidirect
57. #10622800C22semidirect
58. #10622797C22semidirect
59. #10622784C22semidirect
60. #10622776C22semidirect
68. #10622662C22semidirect
71. #10622417C22semidirect
72. #10622412C22semidirect
73. #10622392C22semidirect
74. #10622377C22semidirect
75. #10622348C22semidirect
76. #10622341C22semidirect
303. C2×#452D11semidirect
419. #452C2×D11semidirect
584. C2×C11#3317semidirect
696. C11C2×#3317semidirect
807. C2#13080735direct (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×#106233652
#130807352
C2×#106223772
C2×#106223482
C2×#106223922
C2×#106224122
C2×#106226622
C2×#106227842
C2×#106227762
C2×#106228002
C2×#106227972
C2×#106223412
C2×#106228452
C2×#106224172
C2×C11×#4522
C2×#331711