Finite Group Databasebeta

← C2×#13080868 #15630625

Subgroups — C2×#13080868 #15630625

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×#10623226C211yesmaximal, characteristic, complemented
2C2×#10623208C211yesmaximal, characteristic, complemented
3#13080868C2116yesmaximal, direct product factor
4C2×#10622392C211yesmaximal, characteristic, complemented
5C2×#10622418C211yesmaximal, characteristic, complemented
6C2×#10622676C211yesmaximal, characteristic, complemented
7C2×#10622395C211yesmaximal, characteristic, complemented
8C2×#10622425C211yesmaximal, characteristic, complemented
9C2×#10622670C211yesmaximal, characteristic, complemented
10C2×#10622394C211yesmaximal, characteristic, complemented
11C2×#10622419C211yesmaximal, characteristic, complemented
12C2×C4×#4314C211yesmaximal, characteristic, complemented
13C2×#10622301C211yesmaximal, characteristic, complemented
14C2×#10622384C211yesmaximal, characteristic, complemented
15C2×#10622415C211yesmaximal, characteristic, complemented
16C2×C11×#488C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C2×C11×#125C2211yescharacteristic
20C2×C11×#124C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×#66991C2211yescharacteristic
24C22×#4323C2211yescharacteristic
25C22×#4314C2211yescharacteristic
26C22×#4313C2211yescharacteristic
27C22×#4313C2211yescharacteristic
28#10623226—24no—
29#10623226C2218yescomplemented
30#10623208—24no—
31#10623208C2218yescomplemented
32C2×#66951—21no—
33C2×#66948—21no—
34C2×#66948C2211yescharacteristic
35C2×#66948C2211yescharacteristic
36C2×#66947—21no—
37C2×#66946—21no—
38C2×#66945C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×#66938—21no—
41C2×#66937—21no—
42C2×(C22⋊D11)⋊C4—21no—
43C2×#66931—21no—
44C2×C4×D44C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic
47C11×#488C2218yescomplemented
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C4×C8×C11C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66881C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60#10622676C2218yescomplemented
61#10622670C2218yescomplemented
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622425C2218yescomplemented
68#10622419C2218yescomplemented
69#10622418C2218yescomplemented
70#10622415C2218yescomplemented
71#10622395C2218yescomplemented
72#10622394C2218yescomplemented
73#10622392C2218yescomplemented
74#10622384C2218yescomplemented
75C4×#4314C2218yescomplemented
76#10622301C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C22×C22⋊D11—21no—
80C22×C22⋊D11—21no—
81C23×Dic11—21no—
82C2×Q8×D11—22no—
83C2×Q8×D11—24no—
84C2×Q8×D11—42no—
85C2×Q8×D11C2314yes—
86C2×#4341—22no—
87C2×#4341—24no—
88C2×#4341—42no—
89C2×#4341C2314yes—
90C22×D44—21no—
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
99C22×Dic22—21no—
100C22×Dic22C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C11×#125—22no—
104C11×#125C2314yes—
105C11×#124—22no—
106C11×#124C2314yes—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C42×C11C2311yescharacteristic
114C2×C22⋊Dic11—21no—
115#66999—22no—
116#66999C2314yes—
117C2×#4325—42no—
118C2×#4325C2314yes—
119#66991—22no—
120#66991C2314yes—
121C2×#4323—42no—
122C2×#4323C2314yes—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4D411yescharacteristic
129C2×(C2×D11)⋊C4D411yescharacteristic
130C2×C4⋊Dic11D411yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C2×#4314—24no—
141C2×#4314C2314yes—
142C2×#4313—42no—
143C2×#4313—42no—
144C2×#4313C2314yes—
145C2×#4313C2314yes—
146#66951—28no—
147#66948—28no—
148#66948—22no—
149#66948—22no—
150#66948C2314yes—
151#66948C2314yes—
152#66947—28no—
153#66946—28no—
154#66945—22no—
155#66945C2314yes—
156C4⋊C4×D11—22no—
157C4⋊C4×D11C2314yes—
158#66938—28no—
159#66937—28no—
160(C22⋊D11)⋊C4—28no—
161#66931—28no—
162C4×D44—22no—
163C4×D44D414yes—
164C4×D44C2314yes—
165C4×D44C2314yes—
166C4×Dic22—22no—
167C4×Dic22C2314yes—
168C11×#103C2314yes—
169C11×#103C2314yes—
170C11×#102C2314yes—
171C11×#102C2314yes—
172C4×C8×C11C2314yes—
173#66899C2314yes—
174#66896C2314yes—
175#66885C2314yes—
176(C2×D11)⋊C8C2314yes—
177(C2×D11)⋊C8C2314yes—
178#66881C2314yes—
179#66880C2314yes—
180#66874C2314yes—
181#66874C2314yes—
182#66872C2314yes—
183#66871C2314yes—
184C4⋊(C11⋊C8)C2314yes—
185C2×#3326—111nomaximal, Sylow
186C24×C11—21no—
187C23×D11—21no—
188C23×D11C2×D411yescharacteristic
189C23×D11C2×D411yescharacteristic
190C2×Q8×C11—21no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11C2412yes—
194C2×D4×C11—21no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11C2412yes—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2411yescharacteristic
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—44no—
207C2×C22⋊D11—44no—
208C22×Dic11—24no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—44no—
213C22×Dic11C2×D411yescharacteristic
214C22×Dic11C2×D411yescharacteristic
215Q8×D11—28no—
216Q8×D11—44no—
217Q8×D11—48no—
218#4341—28no—
219#4341—44no—
220#4341—48no—
221C2×D44—24no—
222C2×D44—24no—
223C2×D44—21no—
224C2×D44—22no—
225C2×D44—22no—
226C2×D44—42no—
227C2×D44—44no—
228C2×D44—82no—
229C2×D44C2×D414yes—
230C2×D44C2412yes—
231C2×C4×D11—24no—
232C2×C4×D11—24no—
233C2×C4×D11—24no—
234C2×C4×D11—22no—
235C2×C4×D11—22no—
236C2×C4×D11—22no—
237C2×C4×D11—22no—
238C2×C4×D11—44no—
239C2×C4×D11—82no—
240C2×C4×D11—82no—
241C2×C4×D11C2×D412yes—
242C2×C4×D11C2×D412yes—
243C2×C4×D11C2412yes—
244C2×C4×D11C2412yes—
245C2×Dic22—24no—
246C2×Dic22—21no—
247C2×Dic22—22no—
248C2×Dic22—44no—
249C2×Dic22#4114yes—
250C2×Dic22C2412yes—
251C2×C8×C11—22no—
252C2×C8×C11—22no—
253C2×C8×C11C2412yes—
254C2×C8×C11C2412yes—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—24no—
258C11×C4⋊C4—24no—
259C11×C4⋊C4C2412yes—
260C11×C4⋊C4C2412yes—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—24no—
263C42×C11C2×D412yes—
264C42×C11C2412yes—
265C22⋊Dic11—24no—
266#4325—44no—
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)⋊C4—24no—
273(C2×D11)⋊C4C2×D414yes—
274(C2×D11)⋊C4C2×D414yes—
275C4⋊Dic11—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11C2×D414yes—
278C4⋊Dic11C2412yes—
279C4⋊Dic11C2412yes—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283C4×Dic11—24no—
284C4×Dic11—24no—
285C2×C11⋊C8—22no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8C2412yes—
288C2×C11⋊C8C2412yes—
289#4314—28no—
290#4313—44no—
291#4313—44no—
292C2×#553—111no—
293C2×#548—111no—
294#3326—1116no—
295C2×#488D1111yescharacteristic, complemented
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×#417—111no—
307C2×#419—111no—
308C23×C11—22no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11C22×D411yescharacteristic
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—42no—
321C22×D11—42no—
322C22×D11—42no—
323C22×D11C22×D412yes—
324C22×D11C22×D412yes—
325Q8×C11—22no—
326Q8×C11—22no—
327Q8×C11—42no—
328D4×C11—22no—
329D4×C11—22no—
330D4×C11—42no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—42no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4112yes—
343C2×C4×C11H(5,𝔽2)12yes—
344C2×C4×C11C2511yescharacteristic
345C22⋊D11—48no—
346C22⋊D11—48no—
347C2×Dic11—24no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—48no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11C22×D412yes—
357C2×Dic11C22×D412yes—
358D44—22no—
359D44—22no—
360D44—44no—
361D44—48no—
362D44—42no—
363D44—84no—
364C4×D11—24no—
365C4×D11—24no—
366C4×D11—22no—
367C4×D11—22no—
368C4×D11—22no—
369C4×D11—22no—
370C4×D11—48no—
371C4×D11—84no—
372C4×D11—84no—
373Dic22—24no—
374Dic22—22no—
375Dic22—48no—
376Dic22C2×#4114yes—
377C8×C11—22no—
378C8×C11—22no—
379C11⋊C8—22no—
380C11⋊C8—22no—
381C22×#41—111no—
382C23×Q8—111no—
383C22×SD16—111no—
384C22×SD16—111no—
385C22×D8—111no—
386C22×M16—111no—
387C22×M16—111no—
388#553—118no—
389#553—224no—
390#548—118no—
391#548—224no—
392C2×#126—221no—
393C2×#125C2×D1111yescharacteristic
394C2×#124—221no—
395C2×#124C2×D1111yescharacteristic
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⋊C4—111no—
411#488C2×D1118yescomplemented
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#417—118no—
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×C8C2×D1111yescharacteristic
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—84no—
445C22×C11#54612yes—
446C22×C11#57512yes—
447C22×C11#57712yes—
448C22×C11C23×D411yescharacteristic
449C2×D11—22no—
450C2×D11—22no—
451C2×D11—22no—
452C2×D11—22no—
453C2×D11—22no—
454C2×D11—22no—
455C2×D11—44no—
456C2×D11—44no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—84no—
461C4×C11—22no—
462C4×C11—22no—
463C4×C11—42no—
464C4×C11—42no—
465C4×C11—42no—
466C4×C11#54612yes—
467C4×C11C22×#4111yescharacteristic
468C4×C11C2×H(5,𝔽2)11yescharacteristic
469Dic11—24no—
470Dic11—22no—
471Dic11—22no—
472Dic11—42no—
473Dic11—42no—
474C2×#41—114no—
475C2×#41—222no—
476C2×#41—224no—
477C2×#41—442no—
478C22×Q8—114no—
479C22×Q8—111no—
480C22×Q8—221no—
481C22×Q8—222no—
482C22×Q8—224no—
483C22×Q8—442no—
484C22×Q8C22×D1111yescharacteristic
485C22×D4—111no—
486C22×D4—111no—
487C22×D4—221no—
488C22×D4—221no—
489C22×D4—221no—
490C22×D4—221no—
491C22×D4C22×D1111yescharacteristic
492C23×C4—111no—
493C23×C4—111no—
494C23×C4—221no—
495C23×C4—221no—
496C23×C4—221no—
497C23×C4—221no—
498C2×SD16—114no—
499C2×SD16—114no—
500C2×SD16—224no—
501C2×SD16—442no—
502C2×D8—114no—
503C2×D8—442no—
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—22no—
514#125C22×D1114yes—
515#124—22no—
516#124—228no—
517#124C22×D1114yes—
518#123—228no—
519C22⋊Q8—114no—
520C22⋊Q8—228no—
521C22⋊Q8—222no—
522#121—114no—
523#121—114no—
524#121—114no—
525#121—228no—
526#121—222no—
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—228no—
536C4×D4—228no—
537C4×D4—222no—
538#117—114no—
539#117—222no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—114no—
546C2×C4⋊C4—222no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C4⋊C4C22×D1111yescharacteristic
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—111no—
555C2×C22⋊C4—111no—
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—221no—
563C2×C42—221no—
564C2×C42C22×D1111yescharacteristic
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×C8C22×D1114yes—
582C2×C11—82no—
583C2×C11#332614yescomplemented
584C2×C11C2×#54611yescharacteristic
585C2×C11C2×#57511yescharacteristic
586C2×C11C2×#57711yescharacteristic
587D11—42no—
588D11—42no—
589D11—82no—
590C24—21no—
591C24—111no—
592C24—111no—
593C24—221no—
594#41—228no—
595#41—444no—
596#41—448no—
597C2×Q8—21no—
598C2×Q8—22no—
599C2×Q8—22no—
600C2×Q8—114no—
601C2×Q8—112no—
602C2×Q8—224no—
603C2×Q8—221no—
604C2×Q8—222no—
605C2×Q8—228no—
606C2×Q8—444no—
607C2×Q8—444no—
608C2×Q8—448no—
609C2×Q8C23×D1112yes—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—114no—
614C2×D4—112no—
615C2×D4—224no—
616C2×D4—224no—
617C2×D4—224no—
618C2×D4—224no—
619C2×D4—221no—
620C2×D4—222no—
621C2×D4—222no—
622C2×D4—442no—
623C2×D4—444no—
624C2×D4—444no—
625C2×D4—444no—
626C2×D4—882no—
627C2×D4C23×D1112yes—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—111no—
632C22×C4—111no—
633C22×C4—112no—
634C22×C4—112no—
635C22×C4—112no—
636C22×C4—112no—
637C22×C4—224no—
638C22×C4—224no—
639C22×C4—224no—
640C22×C4—221no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—224no—
648C22×C4—444no—
649C22×C4—444no—
650C22×C4—882no—
651C22×C4—882no—
652C22×C4D4×D1111yescharacteristic
653C22×C4D4×D1111yescharacteristic
654C22×C4C23×D1111yescharacteristic
655SD16—228no—
656SD16—444no—
657D8—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—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—114no—
673C4⋊C4—112no—
674C4⋊C4—112no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—221no—
678C4⋊C4—221no—
679C4⋊C4—224no—
680C4⋊C4C23×D1112yes—
681C4⋊C4C23×D1112yes—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—114no—
685C22⋊C4—114no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C42—224no—
693C42—224no—
694C42D4×D1112yes—
695C42C23×D1112yes—
696C11C2×#332611yescharacteristic, complemented, Sylow
697C23—22no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—112no—
702C23—112no—
703C23—222no—
704C23—222no—
705C23—222no—
706C23—222no—
707C23—222no—
708C23—222no—
709C23—222no—
710C23—442no—
711C23—442no—
712C23—442no—
713C23C2×D4×D1111yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—114no—
718Q8—222no—
719Q8—224no—
720Q8—448no—
721D4—22no—
722D4—22no—
723D4—42no—
724D4—222no—
725D4—222no—
726D4—444no—
727D4—448no—
728D4—448no—
729D4—448no—
730D4—442no—
731D4—884no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—112no—
741C2×C4—112no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—224no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—224no—
751C2×C4—224no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—448no—
755C2×C4—448no—
756C2×C4—442no—
757C2×C4—442no—
758C2×C4—884no—
759C2×C4—884no—
760C2×C4C2×D4×D1112yes—
761C2×C4C2×D4×D1112yes—
762C2×C4C2×D4×D1111yescharacteristic
763C2×C4#41×D1112yes—
764C2×C4#6704212yes—
765C2×C4C24×D1111yescharacteristic
766C8—22no—
767C8—22no—
768C8—222no—
769C8—222no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—84no—
774C22—222no—
775C22—222no—
776C22—222no—
777C22—222no—
778C22—222no—
779C22—222no—
780C22—444no—
781C22—444no—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—884no—
786C22#1062320712yes—
787C22#1062329912yes—
788C22#1062330112yes—
789C22C22×D4×D1111yescharacteristic
790C4—22no—
791C4—22no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—222no—
796C4—222no—
797C4—224no—
798C4—442no—
799C4—442no—
800C4#1062320712yes—
801C4C2×#41×D1111yescharacteristic
802C4C2×#6704211yescharacteristic
803C2—82no—
804C2—442no—
805C2—442no—
806C2—882no—
807C2#1308086814yesdirect product factor
808C2C2×#1062320711yescharacteristic
809C2C2×#1062329911yescharacteristic
810C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#488C2
socleC23×C11C22×D4
hypercenterC2×#488D11
hypocenterC11C2×#3326
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#10623226C2semidirect
2. C2×#10623208C2semidirect
3. #13080868C2direct (N × H)
4. C2×#10622392C2semidirect
5. C2×#10622418C2semidirect
6. C2×#10622676C2semidirect
7. C2×#10622395C2semidirect
8. C2×#10622425C2semidirect
9. C2×#10622670C2semidirect
10. C2×#10622394C2semidirect
11. C2×#10622419C2semidirect
12. C2×C4×#4314C2semidirect
13. C2×#10622301C2semidirect
14. C2×#10622384C2semidirect
15. C2×#10622415C2semidirect
16. C2×C11×#488C2semidirect
29. #10623226C22semidirect
31. #10623208C22semidirect
47. C11×#488C22semidirect
60. #10622676C22semidirect
61. #10622670C22semidirect
67. #10622425C22semidirect
68. #10622419C22semidirect
69. #10622418C22semidirect
70. #10622415C22semidirect
71. #10622395C22semidirect
72. #10622394C22semidirect
73. #10622392C22semidirect
74. #10622384C22semidirect
75. C4×#4314C22semidirect
76. #10622301C22semidirect
295. C2×#488D11semidirect
411. #488C2×D11semidirect
583. C2×C11#3326semidirect
696. C11C2×#3326semidirect
807. C2#13080868direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232262
C2×#106232082
#130808682
C2×#106223922
C2×#106224182
C2×#106226762
C2×#106223952
C2×#106224252
C2×#106226702
C2×#106223942
C2×#106224192
C2×C4×#43142
C2×#106223012
C2×#106223842
C2×#106224152
C2×C11×#4882
C2×#332611