Finite Group Databasebeta

← C2×#13080807 #15630528

Subgroups — C2×#13080807 #15630528

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×#10623094C211yesmaximal, characteristic, complemented
2C2×#10623107C211yesmaximal, characteristic, complemented
3#13080807C2116yesmaximal, direct product factor
4C2×#10622327C211yesmaximal, characteristic, complemented
5C2×#10622501C211yesmaximal, characteristic, complemented
6C2×#10622498C211yesmaximal, characteristic, complemented
7C2×#10622633C211yesmaximal, characteristic, complemented
8C2×#10622395C211yesmaximal, characteristic, complemented
9C2×#10622391C211yesmaximal, characteristic, complemented
10C2×#10622629C211yesmaximal, characteristic, complemented
11C2×#10622785C211yesmaximal, characteristic, complemented
12C2×#10622783C211yesmaximal, characteristic, complemented
13C2×#10622319C211yesmaximal, characteristic, complemented
14C2×#10622415C211yesmaximal, characteristic, complemented
15C2×#10622417C211yesmaximal, characteristic, complemented
16C2×C11×#440C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66991C2211yescharacteristic
23C2×#66991C2211yescharacteristic
24C22×#4324C2211yescharacteristic
25C22×#4323C2211yescharacteristic
26C2×#66983—21no—
27C2×#66979—21no—
28C22×#4313C2211yescharacteristic
29C22×C8×D11C2211yescharacteristic
30#10623107—24no—
31#10623107C2218yescomplemented
32#10623094—24no—
33#10623094C2218yescomplemented
34C2×#66950—21no—
35C2×#66950C2211yescharacteristic
36C2×#66948—21no—
37C2×#66948C2211yescharacteristic
38C2×#66945C2211yescharacteristic
39C2×#66945C2211yescharacteristic
40C2×#66938—21no—
41C2×#66938—21no—
42C2×#66928—21no—
43C2×#66928C2211yescharacteristic
44C2×C4×D44—21no—
45C2×C4×D44C2211yescharacteristic
46C2×#66922C2211yescharacteristic
47C11×#440C2218yescomplemented
48C2×C11×#107C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#97C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54#10622785C2218yescomplemented
55#10622783C2218yescomplemented
56C2×#66885C2211yescharacteristic
57C2×#66885C2211yescharacteristic
58C2×(C2×D11)⋊C8C2211yescharacteristic
59C2×(C2×D11)⋊C8C2211yescharacteristic
60C2×#66880C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62#10622633C2218yescomplemented
63#10622629C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×C4⋊(C11⋊C8)C2211yescharacteristic
69#10622501C2218yescomplemented
70#10622498C2218yescomplemented
71#10622417C2218yescomplemented
72#10622415C2218yescomplemented
73#10622395C2218yescomplemented
74#10622391C2218yescomplemented
75#10622327C2218yescomplemented
76#10622319C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C2×#4343—22no—
83C2×#4343—24no—
84C2×#4343—42no—
85C2×#4343C2314yes—
86C2×Q8×D11—22no—
87C2×Q8×D11—24no—
88C2×Q8×D11—42no—
89C2×Q8×D11C2314yes—
90C22×D44—21no—
91C22×D44—21no—
92C22×D44D411yescharacteristic
93C22×D44C2311yescharacteristic
94C22×C4×D11—21no—
95C22×C4×D11—21no—
96C22×C4×D11C2311yescharacteristic
97C22×C4×D11C2311yescharacteristic
98C22×Dic22—21no—
99C22×Dic22—21no—
100C22×Dic22C2311yescharacteristic
101C2×C11×SD16—24no—
102C2×C11×SD16C2314yes—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C4×Q8×C11—22no—
106C4×Q8×C11C2314yes—
107C4×D4×C11—22no—
108C4×D4×C11C2314yes—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C22⋊C4—21no—
113C2×C42×C11—21no—
114C2×C42×C11C2311yescharacteristic
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117#66991—22no—
118#66991—22no—
119#66991C2314yes—
120#66991C2314yes—
121C2×#4324—42no—
122C2×#4324C2314yes—
123C2×#4323—42no—
124C2×#4323C2314yes—
125#66983—28no—
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)⋊C4—21no—
132C2×(C2×D11)⋊C4D411yescharacteristic
133C2×(C2×D11)⋊C4D411yescharacteristic
134#66979—28no—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11—21no—
137C2×C4⋊Dic11D411yescharacteristic
138C2×C4⋊Dic11C2311yescharacteristic
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4×Dic11—21no—
141C2×C4×Dic11—21no—
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C2×#4313—42no—
145C2×#4313C2314yes—
146C2×C8×D11—42no—
147C2×C8×D11C2314yes—
148#66950—22no—
149#66950—28no—
150#66950C2314yes—
151#66948—28no—
152#66948—22no—
153#66948C2314yes—
154#66945—22no—
155#66945—22no—
156#66945C2314yes—
157#66945C2314yes—
158#66938—28no—
159#66938—28no—
160#66928—22no—
161#66928—28no—
162#66928C2314yes—
163C4×D44—28no—
164C4×D44D414yes—
165C4×D44C2314yes—
166#66922—22no—
167#66922C2314yes—
168C11×#107C2314yes—
169C11×#103C2314yes—
170C11×#102C2314yes—
171C11×#97C2314yes—
172#66899C2314yes—
173#66899C2314yes—
174#66885C2314yes—
175#66885C2314yes—
176(C2×D11)⋊C8C2314yes—
177(C2×D11)⋊C8C2314yes—
178#66880C2314yes—
179#66880C2314yes—
180#66874C2314yes—
181#66873C2314yes—
182#66872C2314yes—
183#66872C2314yes—
184C4⋊(C11⋊C8)C2314yes—
185C2×#3321—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#4114yes—
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×C11—24no—
202C22×C4×C11—44no—
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2411yescharacteristic
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—82no—
209C2×C22⋊D11—82no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11C2×D411yescharacteristic
214C22×Dic11C2×D411yescharacteristic
215#4343—28no—
216#4343—44no—
217#4343—48no—
218Q8×D11—28no—
219Q8×D11—44no—
220Q8×D11—48no—
221C2×D44—24no—
222C2×D44—24no—
223C2×D44—21no—
224C2×D44—22no—
225C2×D44—22no—
226C2×D44—42no—
227C2×D44—44no—
228C2×D44—44no—
229C2×D44C2×D414yes—
230C2×D44C2412yes—
231C2×C4×D11—24no—
232C2×C4×D11—24no—
233C2×C4×D11—22no—
234C2×C4×D11—22no—
235C2×C4×D11—22no—
236C2×C4×D11—22no—
237C2×C4×D11—44no—
238C2×C4×D11—44no—
239C2×C4×D11C2×D412yes—
240C2×C4×D11C2×D412yes—
241C2×C4×D11C2412yes—
242C2×C4×D11C2412yes—
243C2×Dic22—24no—
244C2×Dic22—21no—
245C2×Dic22—24no—
246C2×Dic22—22no—
247C2×Dic22—22no—
248C2×Dic22—44no—
249C2×Dic22—82no—
250C2×Dic22C2412yes—
251C11×SD16—28no—
252C2×C8×C11—22no—
253C2×C8×C11—22no—
254C2×C8×C11C2412yes—
255C2×C8×C11C2412yes—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—24no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4C2412yes—
260C11×C4⋊C4C2412yes—
261C11×C22⋊C4—24no—
262C42×C11—24no—
263C42×C11C2×D412yes—
264C42×C11C2412yes—
265C22⋊Dic11—24no—
266C22⋊Dic11—24no—
267#4324—44no—
268#4323—44no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4C2×D414yes—
276(C2×D11)⋊C4C2×D414yes—
277C4⋊Dic11—24no—
278C4⋊Dic11—21no—
279C4⋊Dic11—21no—
280C4⋊Dic11—24no—
281C4⋊Dic11C2×D414yes—
282C4⋊Dic11C2412yes—
283C4⋊Dic11C2412yes—
284C4×Dic11—24no—
285C4×Dic11—24no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8C2412yes—
289C2×C11⋊C8C2412yes—
290#4313—44no—
291C8×D11—44no—
292C2×#555—111no—
293C2×#548—111no—
294#3321—1116no—
295C2×#489—111no—
296C2×#485—111no—
297C2×#482—111no—
298C2×#475—111no—
299C2×#469—111no—
300C2×#465—111no—
301C2×#463—111no—
302C2×#449—111no—
303C2×#448—111no—
304C2×#440D1111yescharacteristic, complemented
305C2×#435—111no—
306C2×#419—111no—
307C2×#416—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—24no—
326Q8×C11—22no—
327Q8×C11C2×#4114yes—
328D4×C11—22no—
329D4×C11—22no—
330D4×C11—42no—
331C2×C4×C11—24no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—48no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×D412yes—
342C2×C4×C11C22×D411yescharacteristic
343C2×C4×C11C2×#4112yes—
344C2×C4×C11H(5,𝔽2)12yes—
345C2×C4×C11C2511yescharacteristic
346C22⋊D11—84no—
347C22⋊D11—84no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11C22×D412yes—
357C2×Dic11C22×D412yes—
358D44—22no—
359D44—22no—
360D44—44no—
361D44—48no—
362D44—48no—
363D44—42no—
364C4×D11—24no—
365C4×D11—24no—
366C4×D11—22no—
367C4×D11—22no—
368C4×D11—22no—
369C4×D11—22no—
370C4×D11—48no—
371C4×D11—48no—
372Dic22—22no—
373Dic22—22no—
374Dic22—48no—
375Dic22—42no—
376Dic22—84no—
377C8×C11—22no—
378C8×C11—22no—
379C11⋊C8—22no—
380C11⋊C8—22no—
381C22×#41—111no—
382C23×Q8—111no—
383C22×SD16—111no—
384C22×SD16C2×D1111yescharacteristic
385C22×D8—111no—
386C22×M16—111no—
387C23×C8—111no—
388#555—118no—
389#555—224no—
390#548—118no—
391#548—224no—
392C2×C4⋊Q8—111no—
393C2×#124—111no—
394C2×#124—221no—
395C2×#124—221no—
396C2×#124—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×Q8C2×D1111yescharacteristic
405C2×C4×D4—111no—
406C2×C4×D4—221no—
407C2×C4×D4C2×D1111yescharacteristic
408C2×#117—111no—
409C2×#117—111no—
410C2×#117—221no—
411#489—118no—
412#485—118no—
413#482—118no—
414#475—118no—
415#469—118no—
416#465—118no—
417#463—118no—
418#449—118no—
419#448—118no—
420#440C2×D1118yescomplemented
421#435—118no—
422C2×#107C2×D1111yescharacteristic
423C2×#106—111no—
424C2×#106—111no—
425C2×C4⋊C8—111no—
426#419—118no—
427#416—118no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#103—111no—
433C2×#103C2×D1111yescharacteristic
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102C2×D1111yescharacteristic
438C2×C22⋊C8—111no—
439C2×C22⋊C8—111no—
440C2×#97C2×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—24no—
462C4×C11—22no—
463C4×C11—22no—
464C4×C11—42no—
465C4×C11—42no—
466C4×C11#54612yes—
467C4×C11C22×#4111yescharacteristic
468C4×C11C2×H(5,𝔽2)11yescharacteristic
469Dic11—22no—
470Dic11—22no—
471Dic11—42no—
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—221no—
483C22×Q8—224no—
484C22×Q8—442no—
485C22×Q8C22×D1111yescharacteristic
486C22×D4—111no—
487C22×D4—111no—
488C22×D4—221no—
489C22×D4—221no—
490C22×D4—221no—
491C22×D4—221no—
492C22×D4C22×D1111yescharacteristic
493C23×C4—21no—
494C23×C4—111no—
495C23×C4—111no—
496C23×C4—221no—
497C23×C4—221no—
498C2×SD16—24no—
499C2×SD16—114no—
500C2×SD16—442no—
501C2×SD16C22×D1114yes—
502C2×D8—114no—
503C2×D8—442no—
504C2×M16—114no—
505C2×M16—442no—
506C22×C8—111no—
507C22×C8—111no—
508C22×C8—114no—
509C22×C8—442no—
510C22×C8C22×D1111yescharacteristic
511C22×C8C22×D1111yescharacteristic
512C4⋊Q8—114no—
513C4⋊Q8—222no—
514#124—114no—
515#124—228no—
516#124—228no—
517#124—228no—
518#124—222no—
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—228no—
528#121—222no—
529#121—222no—
530C4×Q8—22no—
531C4×Q8C22×D1114yes—
532C4×D4—22no—
533C4×D4—114no—
534C4×D4—114no—
535C4×D4—228no—
536C4×D4C22×D1114yes—
537#117—114no—
538#117—114no—
539#117—222no—
540#117—222no—
541#117—228no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4C22×D1111yescharacteristic
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C22⋊C4—21no—
551C2×C22⋊C4—111no—
552C2×C22⋊C4—111no—
553C2×C22⋊C4—221no—
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×C42—21no—
562C2×C42—221no—
563C2×C42—221no—
564C2×C42C22×D1111yescharacteristic
565#107C22×D1114yes—
566#106—114no—
567#106—114no—
568C4⋊C8—114no—
569#103—114no—
570#103—114no—
571#103—114no—
572#103—114no—
573#103—114no—
574#103C22×D1114yes—
575#102—114no—
576#102—114no—
577#102—114no—
578#102C22×D1114yes—
579C22⋊C8—114no—
580C22⋊C8—114no—
581#97C22×D1114yes—
582C2×C11—82no—
583C2×C11#332114yescomplemented
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—112no—
600C2×Q8—224no—
601C2×Q8—221no—
602C2×Q8—224no—
603C2×Q8—228no—
604C2×Q8—222no—
605C2×Q8—222no—
606C2×Q8—444no—
607C2×Q8—444no—
608C2×Q8—448no—
609C2×Q8—882no—
610C2×Q8#433914yes—
611C2×Q8C23×D1112yes—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—114no—
616C2×D4—112no—
617C2×D4—224no—
618C2×D4—224no—
619C2×D4—224no—
620C2×D4—224no—
621C2×D4—222no—
622C2×D4—221no—
623C2×D4—222no—
624C2×D4—442no—
625C2×D4—444no—
626C2×D4—444no—
627C2×D4—882no—
628C2×D4—882no—
629C2×D4C23×D1112yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—24no—
634C22×C4—44no—
635C22×C4—111no—
636C22×C4—111no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—224no—
642C22×C4—224no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—221no—
650C22×C4—444no—
651C22×C4—444no—
652C22×C4D4×D1111yescharacteristic
653C22×C4D4×D1111yescharacteristic
654C22×C4C23×D1111yescharacteristic
655SD16—28no—
656SD16—444no—
657D8—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—21no—
671C4⋊C4—114no—
672C4⋊C4—112no—
673C4⋊C4—112no—
674C4⋊C4—224no—
675C4⋊C4—221no—
676C4⋊C4—221no—
677C4⋊C4—224no—
678C4⋊C4C23×D1112yes—
679C4⋊C4C23×D1112yes—
680C22⋊C4—24no—
681C22⋊C4—114no—
682C22⋊C4—114no—
683C22⋊C4—224no—
684C22⋊C4—224no—
685C22⋊C4—224no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C42—24no—
692C42—224no—
693C42—224no—
694C42D4×D1112yes—
695C42C23×D1112yes—
696C11C2×#332111yescharacteristic, 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—24no—
715Q8—22no—
716Q8—222no—
717Q8—222no—
718Q8—448no—
719Q8—442no—
720Q8—884no—
721Q8C2×#433914yes—
722D4—22no—
723D4—22no—
724D4—42no—
725D4—222no—
726D4—222no—
727D4—444no—
728D4—448no—
729D4—448no—
730D4—442no—
731D4—884no—
732D4—884no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—48no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—112no—
743C2×C4—112no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—224no—
747C2×C4—224no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—448no—
756C2×C4—448no—
757C2×C4—442no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4C2×#433912yes—
761C2×C4C2×D4×D1112yes—
762C2×C4C2×D4×D1112yes—
763C2×C4C2×D4×D1111yescharacteristic
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#1062308112yes—
787C22#1062330412yes—
788C22#1062330912yes—
789C22C22×D4×D1111yescharacteristic
790C4—24no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—222no—
796C4—222no—
797C4—442no—
798C4—442no—
799C4—442no—
800C4#1062308112yes—
801C4C22×#433911yescharacteristic
802C4C2×#6704211yescharacteristic
803C2—82no—
804C2—442no—
805C2—442no—
806C2—882no—
807C2#1308080714yesdirect product factor
808C2C2×#1062308111yescharacteristic
809C2C2×#1062330411yescharacteristic
810C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
hypercenterC2×#440D11
hypocenterC11C2×#3321
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#10623094C2semidirect
2. C2×#10623107C2semidirect
3. #13080807C2direct (N × H)
4. C2×#10622327C2semidirect
5. C2×#10622501C2semidirect
6. C2×#10622498C2semidirect
7. C2×#10622633C2semidirect
8. C2×#10622395C2semidirect
9. C2×#10622391C2semidirect
10. C2×#10622629C2semidirect
11. C2×#10622785C2semidirect
12. C2×#10622783C2semidirect
13. C2×#10622319C2semidirect
14. C2×#10622415C2semidirect
15. C2×#10622417C2semidirect
16. C2×C11×#440C2semidirect
31. #10623107C22semidirect
33. #10623094C22semidirect
47. C11×#440C22semidirect
54. #10622785C22semidirect
55. #10622783C22semidirect
62. #10622633C22semidirect
63. #10622629C22semidirect
69. #10622501C22semidirect
70. #10622498C22semidirect
71. #10622417C22semidirect
72. #10622415C22semidirect
73. #10622395C22semidirect
74. #10622391C22semidirect
75. #10622327C22semidirect
76. #10622319C22semidirect
304. C2×#440D11semidirect
420. #440C2×D11semidirect
583. C2×C11#3321semidirect
696. C11C2×#3321semidirect
807. C2#13080807direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230942
C2×#106231072
#130808072
C2×#106223272
C2×#106225012
C2×#106224982
C2×#106226332
C2×#106223952
C2×#106223912
C2×#106226292
C2×#106227852
C2×#106227832
C2×#106223192
C2×#106224152
C2×#106224172
C2×C11×#4402
C2×#332111