Finite Group Databasebeta

← C2×#13080870 #15630627

Subgroups — C2×#13080870 #15630627

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×#10623045C211yesmaximal, characteristic, complemented
2C2×#10623362C211yesmaximal, characteristic, complemented
3#13080870C2116yesmaximal, direct product factor
4C2×#10622381C211yesmaximal, characteristic, complemented
5C2×#10622397C211yesmaximal, characteristic, complemented
6C2×#10622584C211yesmaximal, characteristic, complemented
7C2×#10622409C211yesmaximal, characteristic, complemented
8C2×#10622395C211yesmaximal, characteristic, complemented
9C2×#10622747C211yesmaximal, characteristic, complemented
10C2×#10622400C211yesmaximal, characteristic, complemented
11C2×#10622851C211yesmaximal, characteristic, complemented
12C2×#10622419C211yesmaximal, characteristic, complemented
13C2×#10622401C211yesmaximal, characteristic, complemented
14C2×#10622741C211yesmaximal, characteristic, complemented
15C2×#10622415C211yesmaximal, characteristic, complemented
16C2×C11×#417C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21#10623362—24no—
22#10623362C2218yescomplemented
23C2×Q8×Dic11C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C2×#66991—21no—
26C2×#66991C2211yescharacteristic
27C2×#66989—21no—
28C2×#66989C2211yescharacteristic
29C22×#4323C2211yescharacteristic
30C2×#66983—21no—
31C2×#66983C2211yescharacteristic
32C2×C4×C22⋊D11—21no—
33C2×C4×C22⋊D11—21no—
34C2×C4×C22⋊D11C2211yescharacteristic
35C2×#66977—21no—
36C2×#66977C2211yescharacteristic
37C22×#4314C2211yescharacteristic
38C22×#4313C2211yescharacteristic
39#10623045—24no—
40#10623045C2218yescomplemented
41C2×#66951—21no—
42C2×#66948C2211yescharacteristic
43C2×#66947—21no—
44C2×#66946C2211yescharacteristic
45C2×#66945C2211yescharacteristic
46C2×#66943C2211yescharacteristic
47C11×#417C2218yescomplemented
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52#10622851C2218yescomplemented
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622747C2218yescomplemented
57#10622741C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×(C2×D11)⋊C8C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×Dic11⋊C8C2211yescharacteristic
63C2×C8×Dic11C2211yescharacteristic
64#10622584C2218yescomplemented
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69#10622419C2218yescomplemented
70#10622415C2218yescomplemented
71#10622409C2218yescomplemented
72#10622401C2218yescomplemented
73#10622400C2218yescomplemented
74#10622397C2218yescomplemented
75#10622395C2218yescomplemented
76#10622381C2218yescomplemented
77C2×C11×#41—22no—
78C2×C11×#41—24no—
79C2×C11×#41—42no—
80C2×C11×#41C2314yes—
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C22×C22⋊D11D411yescharacteristic
90C2×Q8×D11—22no—
91C2×Q8×D11—24no—
92C2×Q8×D11—42no—
93C2×Q8×D11C2314yes—
94C22×D44—21no—
95C22×D44C2311yescharacteristic
96C22×C4×D11—21no—
97C22×C4×D11—21no—
98C22×C4×D11C2311yescharacteristic
99C22×Dic22—21no—
100C22×Dic22C2311yescharacteristic
101C2×C11×M16—42no—
102C2×C11×M16C2314yes—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2314yes—
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11D411yescharacteristic
115Q8×Dic11—22no—
116Q8×Dic11C2314yes—
117C2×#4325—24no—
118C2×#4325C2314yes—
119#66991—28no—
120#66991—22no—
121#66991C2314yes—
122#66989—28no—
123#66989—22no—
124#66989C2314yes—
125C2×#4323—42no—
126C2×#4323C2314yes—
127#66983—22no—
128#66983—28no—
129#66983C2314yes—
130C4×C22⋊D11—28no—
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)⋊C4—21no—
138C2×(C2×D11)⋊C4D411yescharacteristic
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11—21no—
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143#66977—22no—
144#66977—28no—
145#66977C2314yes—
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4D411yescharacteristic
149C2×C4×Dic11—21no—
150C2×C4×Dic11—21no—
151C2×C4×Dic11C2311yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154C2×#4314—42no—
155C2×#4314C2314yes—
156C2×#4313—42no—
157C2×#4313C2314yes—
158#66951—28no—
159#66948—22no—
160#66948C2314yes—
161#66947—28no—
162#66946—22no—
163#66946C2314yes—
164#66945—22no—
165#66945C2314yes—
166#66943—22no—
167#66943C2314yes—
168C11×#103C2314yes—
169C11×#103C2314yes—
170C11×#102C2314yes—
171C11×#102C2314yes—
172#66899C2314yes—
173#66896C2314yes—
174C22⋊(C11⋊C8)C2314yes—
175#66885C2314yes—
176(C2×D11)⋊C8C2314yes—
177#66882C2314yes—
178#66880C2314yes—
179Dic11⋊C8C2314yes—
180C8×Dic11C2314yes—
181#66874C2314yes—
182#66874C2314yes—
183#66872C2314yes—
184#66872C2314yes—
185C2×#3326—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—22no—
195C2×Q8×C11#4114yes—
196C2×Q8×C11C2412yes—
197C2×D4×C11—24no—
198C2×D4×C11—21no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—44no—
202C2×D4×C11C2412yes—
203C22×C4×C11—21no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—24no—
209C22×C4×C11—24no—
210C22×C4×C11—44no—
211C22×C4×C11—82no—
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2411yescharacteristic
216C2×C22⋊D11—24no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—42no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11C2×D414yes—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11C2×D411yescharacteristic
226C22×Dic11C2×D411yescharacteristic
227C22×Dic11C2×D411yescharacteristic
228Q8×D11—28no—
229Q8×D11—44no—
230Q8×D11—48no—
231C2×D44—24no—
232C2×D44—21no—
233C2×D44—22no—
234C2×D44—22no—
235C2×D44—82no—
236C2×D44C2412yes—
237C2×C4×D11—24no—
238C2×C4×D11—24no—
239C2×C4×D11—22no—
240C2×C4×D11—22no—
241C2×C4×D11—44no—
242C2×C4×D11—82no—
243C2×C4×D11C2×D412yes—
244C2×C4×D11C2412yes—
245C2×Dic22—24no—
246C2×Dic22—21no—
247C2×Dic22—22no—
248C2×Dic22—22no—
249C2×Dic22—44no—
250C2×Dic22C2412yes—
251C11×M16—44no—
252C2×C8×C11—22no—
253C2×C8×C11—22no—
254C2×C8×C11C2412yes—
255C2×C8×C11C2412yes—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—24no—
259C11×C4⋊C4C2412yes—
260C11×C4⋊C4C2412yes—
261C22⋊Dic11—24no—
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264C22⋊Dic11—24no—
265C22⋊Dic11C2×D414yes—
266#4325—28no—
267#4323—44no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4C2×D414yes—
273C4⋊Dic11—24no—
274C4⋊Dic11—24no—
275C4⋊Dic11—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11C2412yes—
278C4⋊Dic11C2412yes—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4C2×D414yes—
282C4×Dic11—24no—
283C4×Dic11—24no—
284C4×Dic11C2×D412yes—
285C4×Dic11C2412yes—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8C2412yes—
289C2×C11⋊C8C2412yes—
290#4314—44no—
291#4313—44no—
292C2×#553—111no—
293C2×#548—111no—
294#3326—1116no—
295C2×#488—111no—
296C2×#482—111no—
297C2×#483—111no—
298C2×#479—111no—
299C2×#469—111no—
300C2×#468—111no—
301C2×#463—111no—
302C2×#449—111no—
303C2×#448—111no—
304C2×C4×SD16—111no—
305C2×#436—111no—
306C2×#417D1111yescharacteristic, complemented
307C2×#419—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×C11C2×#4114yes—
328D4×C11—22no—
329D4×C11—22no—
330D4×C11—48no—
331D4×C11—42no—
332C2×C4×C11—24no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—24no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—48no—
341C2×C4×C11—42no—
342C2×C4×C11—42no—
343C2×C4×C11—84no—
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C2×#4112yes—
347C2×C4×C11H(5,𝔽2)12yes—
348C2×C4×C11C2511yescharacteristic
349C22⋊D11—44no—
350C22⋊D11—48no—
351C22⋊D11—48no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11C22×D412yes—
362C2×Dic11C22×D412yes—
363C2×Dic11C22×D412yes—
364D44—22no—
365D44—22no—
366D44—42no—
367D44—84no—
368C4×D11—24no—
369C4×D11—22no—
370C4×D11—22no—
371C4×D11—48no—
372C4×D11—84no—
373Dic22—22no—
374Dic22—22no—
375Dic22—48no—
376Dic22—42no—
377C8×C11—22no—
378C8×C11—22no—
379C11⋊C8—22no—
380C11⋊C8—22no—
381C22×#41C2×D1111yescharacteristic
382C23×Q8—111no—
383C22×SD16—111no—
384C22×SD16—111no—
385C22×D8—111no—
386C22×M16—111no—
387C22×M16C2×D1111yescharacteristic
388#553—118no—
389#553—224no—
390#548—118no—
391#548—224no—
392C2×#126—221no—
393C2×#125—111no—
394C2×#124—111no—
395C2×#124—221no—
396C2×#123—221no—
397C2×C22⋊Q8—111no—
398C2×C22⋊Q8—221no—
399C2×#121—111no—
400C2×#121—111no—
401C2×#121—111no—
402C2×#121—221no—
403C2×#121—221no—
404C2×C4×Q8—111no—
405C2×C4×D4—111no—
406C2×C4×D4—111no—
407C2×C4×D4—221no—
408C2×C4×D4—221no—
409C2×#117—111no—
410C22×C4⋊C4C2×D1111yescharacteristic
411#488—118no—
412#483—118no—
413#482—118no—
414#479—118no—
415#469—118no—
416#468—118no—
417#463—118no—
418#449—118no—
419#448—118no—
420C4×SD16—118no—
421#436—118no—
422C2×#107—111no—
423C2×#106—111no—
424C2×#106—111no—
425C2×C4⋊C8—111no—
426#419—118no—
427#417C2×D1118yescomplemented
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#103C2×D1111yescharacteristic
433C2×#103C2×D1111yescharacteristic
434C2×#102—111no—
435C2×#102—111no—
436C2×#102C2×D1111yescharacteristic
437C2×#102C2×D1111yescharacteristic
438C2×C22⋊C8—111no—
439C2×C22⋊C8—111no—
440C2×C4×C8—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×#41C22×D1114yes—
478C22×Q8—114no—
479C22×Q8—111no—
480C22×Q8—221no—
481C22×Q8—222no—
482C22×Q8—224no—
483C22×Q8—442no—
484C22×Q8C22×D1111yescharacteristic
485C22×D4—21no—
486C22×D4—111no—
487C22×D4—111no—
488C22×D4—221no—
489C22×D4—221no—
490C22×D4—221no—
491C22×D4C22×D1111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—111no—
495C23×C4—221no—
496C23×C4—221no—
497C23×C4C22×D1111yescharacteristic
498C2×SD16—114no—
499C2×SD16—114no—
500C2×SD16—224no—
501C2×SD16—442no—
502C2×D8—114no—
503C2×D8—442no—
504C2×M16—42no—
505C2×M16—114no—
506C2×M16—442no—
507C2×M16C22×D1114yes—
508C22×C8—111no—
509C22×C8—111no—
510C22×C8C22×D1111yescharacteristic
511C22×C8C22×D1111yescharacteristic
512#126—228no—
513#125—114no—
514#125—222no—
515#124—114no—
516#124—222no—
517#124—228no—
518#123—228no—
519C22⋊Q8—114no—
520C22⋊Q8—228no—
521C22⋊Q8—222no—
522#121—114no—
523#121—114no—
524#121—114no—
525#121—222no—
526#121—228no—
527#121—222no—
528#121—228no—
529#121—222no—
530C4×Q8—114no—
531C4×Q8—222no—
532C4×D4—114no—
533C4×D4—114no—
534C4×D4—114no—
535C4×D4—222no—
536C4×D4—228no—
537C4×D4—228no—
538#117—114no—
539#117—222no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C4⋊C4C22×D1114yes—
552C2×C22⋊C4—111no—
553C2×C22⋊C4—111no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C42—111no—
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#103—114no—
573#103C22×D1114yes—
574#103C22×D1114yes—
575#102—114no—
576#102—114no—
577#102C22×D1114yes—
578#102C22×D1114yes—
579C22⋊C8—114no—
580C22⋊C8—114no—
581C4×C8—114no—
582C2×C11—42no—
583C2×C11—82no—
584C2×C11#332614yescomplemented
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—
597C2×Q8—21no—
598C2×Q8—22no—
599C2×Q8—112no—
600C2×Q8—224no—
601C2×Q8—221no—
602C2×Q8—228no—
603C2×Q8—222no—
604C2×Q8—222no—
605C2×Q8—444no—
606C2×Q8—444no—
607C2×Q8—448no—
608C2×Q8#433914yes—
609C2×Q8C23×D1112yes—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—44no—
615C2×D4—114no—
616C2×D4—112no—
617C2×D4—224no—
618C2×D4—224no—
619C2×D4—224no—
620C2×D4—222no—
621C2×D4—221no—
622C2×D4—222no—
623C2×D4—442no—
624C2×D4—444no—
625C2×D4—444no—
626C2×D4—882no—
627C2×D4C23×D1112yes—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—44no—
636C22×C4—82no—
637C22×C4—111no—
638C22×C4—111no—
639C22×C4—111no—
640C22×C4—112no—
641C22×C4—112no—
642C22×C4—224no—
643C22×C4—224no—
644C22×C4—222no—
645C22×C4—222no—
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
655SD16—228no—
656SD16—444no—
657D8—444no—
658M16—44no—
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—21no—
669C4⋊C4—21no—
670C4⋊C4—24no—
671C4⋊C4—114no—
672C4⋊C4—112no—
673C4⋊C4—112no—
674C4⋊C4—224no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—221no—
678C4⋊C4—221no—
679C4⋊C4—224no—
680C4⋊C4C23×D1112yes—
681C4⋊C4C23×D1112yes—
682C22⋊C4—114no—
683C22⋊C4—114no—
684C22⋊C4—224no—
685C22⋊C4—224no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C42—112no—
693C42—112no—
694C42—224no—
695C42—224no—
696C11C2×#332611yescharacteristic, 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—222no—
717Q8—222no—
718Q8—448no—
719Q8—442no—
720Q8C2×#433914yes—
721D4—22no—
722D4—22no—
723D4—48no—
724D4—42no—
725D4—222no—
726D4—222no—
727D4—444no—
728D4—448no—
729D4—448no—
730D4—442no—
731D4—884no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—48no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—84no—
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—442no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—884no—
761C2×C4C2×#433912yes—
762C2×C4C2×D4×D1112yes—
763C2×C4C2×D4×D1111yescharacteristic
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#1062302112yes—
787C22#1062330612yes—
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#1062302112yes—
801C4C22×#433911yescharacteristic
802C4C2×#6703711yescharacteristic
803C2—42no—
804C2—82no—
805C2—442no—
806C2—882no—
807C2#1308087014yesdirect product factor
808C2C2×#1062302111yescharacteristic
809C2C2×#1062330811yescharacteristic
810C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
hypercenterC2×#417D11
hypocenterC11C2×#3326
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#10623045C2semidirect
2. C2×#10623362C2semidirect
3. #13080870C2direct (N × H)
4. C2×#10622381C2semidirect
5. C2×#10622397C2semidirect
6. C2×#10622584C2semidirect
7. C2×#10622409C2semidirect
8. C2×#10622395C2semidirect
9. C2×#10622747C2semidirect
10. C2×#10622400C2semidirect
11. C2×#10622851C2semidirect
12. C2×#10622419C2semidirect
13. C2×#10622401C2semidirect
14. C2×#10622741C2semidirect
15. C2×#10622415C2semidirect
16. C2×C11×#417C2semidirect
22. #10623362C22semidirect
40. #10623045C22semidirect
47. C11×#417C22semidirect
52. #10622851C22semidirect
56. #10622747C22semidirect
57. #10622741C22semidirect
64. #10622584C22semidirect
69. #10622419C22semidirect
70. #10622415C22semidirect
71. #10622409C22semidirect
72. #10622401C22semidirect
73. #10622400C22semidirect
74. #10622397C22semidirect
75. #10622395C22semidirect
76. #10622381C22semidirect
306. C2×#417D11semidirect
427. #417C2×D11semidirect
584. C2×C11#3326semidirect
696. C11C2×#3326semidirect
807. C2#13080870direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230452
C2×#106233622
#130808702
C2×#106223812
C2×#106223972
C2×#106225842
C2×#106224092
C2×#106223952
C2×#106227472
C2×#106224002
C2×#106228512
C2×#106224192
C2×#106224012
C2×#106227412
C2×#106224152
C2×C11×#4172
C2×#332611