Finite Group Databasebeta

← C2×#13079696 #15625153

Subgroups — C2×#13079696 #15625153

Order 2816.

2022 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623114C211yesmaximal, characteristic, complemented
2C2×#10623206C211yesmaximal, characteristic
3#13079696C2116yesmaximal, direct product factor
4C2×#10622780C211yesmaximal, characteristic, complemented
5C2×#10622794C211yesmaximal, characteristic, complemented
6C2×#10622410C211yesmaximal, characteristic, complemented
7C2×#10622381C211yesmaximal, characteristic, complemented
8C2×#10622667C211yesmaximal, characteristic, complemented
9C2×#10622462C211yesmaximal, characteristic, complemented
10C2×#10622644C211yesmaximal, characteristic, complemented
11C2×#10622396C211yesmaximal, characteristic
12C2×#10622786C211yesmaximal, characteristic
13C2×#10622421C211yesmaximal, characteristic, complemented
14C2×#10622799C211yesmaximal, characteristic, complemented
15C2×#10622453C211yesmaximal, characteristic, complemented
16C2×C11×#464C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×#66999C2211yescharacteristic
24C2×#66997C2211yescharacteristic
25C2×#66997C2211yescharacteristic
26C22×#4326C2211yescharacteristic
27C22×#4326C2211yescharacteristic
28C22×#4326C2211yescharacteristic
29C2×#66989C2211yescharacteristic
30C22×#4324C2211yescharacteristic
31C22×Dic44C2211yescharacteristic
32C22×Dic44C2211yescharacteristic
33#10623206—24no—
34#10623206C2218yes—
35#10623114—24no—
36#10623114C2218yescomplemented
37C2×#66951—21no—
38C2×#66950C2211yescharacteristic
39C2×#66943C2211yescharacteristic
40C2×#66942—21no—
41C2×#66936—21no—
42C2×#66936—21no—
43C2×#66931—21no—
44C2×#66931—21no—
45C2×#66929—21no—
46C2×#66925C2211yescharacteristic
47C2×#66923—21no—
48C2×#66922C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic
50C11×#464C2218yescomplemented
51C2×C11×C4⋊C8C2211yescharacteristic
52C2×C11×#103C2211yescharacteristic
53C2×C11×#102C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56#10622799C2218yescomplemented
57#10622794C2218yescomplemented
58#10622786C2218yes—
59#10622780C2218yescomplemented
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×(C2×D11)⋊C8C2211yescharacteristic
62C2×#66880C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×#66879C2211yescharacteristic
65C2×C8×Dic11C2211yescharacteristic
66#10622667C2218yescomplemented
67#10622644C2218yescomplemented
68C2×#66874C2211yescharacteristic
69C2×#66874C2211yescharacteristic
70C2×C4⋊(C11⋊C8)C2211yescharacteristic
71#10622462C2218yescomplemented
72#10622453C2218yescomplemented
73#10622421C2218yescomplemented
74#10622410C2218yescomplemented
75#10622396C2218yes—
76#10622381C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C23×Dic11—21no—
82C2×Q8×D11—22no—
83C2×Q8×D11—42no—
84C2×Q8×D11—42no—
85C2×Q8×D11C2314yes—
86C2×#4341—22no—
87C2×#4341—42no—
88C2×#4341—42no—
89C2×#4341C2314yes—
90C22×C4×D11—21no—
91C22×C4×D11C2311yescharacteristic
92C22×Dic22—21no—
93C22×Dic22C2311yescharacteristic
94C22×Dic22C2311yescharacteristic
95C22×Dic22C2311yescharacteristic
96C2×C11×Q16—42no—
97C2×C11×Q16C2314yes—
98C2×C11×SD16—42no—
99C2×C11×SD16C2314yes—
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C11×#124—22no—
103C11×#124C2314yes—
104C4×Q8×C11—22no—
105C4×Q8×C11C2314yes—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C42×C11—21no—
111C2×C42×C11C2311yescharacteristic
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114#66999—22no—
115#66999C2314yes—
116#66997—22no—
117#66997—22no—
118#66997C2314yes—
119#66997C2314yes—
120C2×#4326—42no—
121C2×#4326—42no—
122C2×#4326—42no—
123C2×#4326C2314yes—
124C2×#4326C2314yes—
125C2×#4326C2314yes—
126#66989—22no—
127#66989C2314yes—
128C2×#4324—42no—
129C2×#4324C2314yes—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4D411yescharacteristic
133C2×(C2×D11)⋊C4D411yescharacteristic
134C2×C4⋊Dic11—21no—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11—21no—
137C2×C4⋊Dic11—21no—
138C2×C4⋊Dic11C2311yescharacteristic
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4D411yescharacteristic
147C2×Dic11⋊C4D411yescharacteristic
148C2×C4×Dic11—21no—
149C2×C4×Dic11C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C2×Dic44—42no—
153C2×Dic44—42no—
154C2×Dic44C2314yes—
155C2×Dic44C2314yes—
156#66951—28no—
157#66950—22no—
158#66950C2314yes—
159#66943—22no—
160#66943C2314yes—
161#66942—28no—
162#66936—28no—
163#66936—28no—
164#66931—28no—
165#66931—28no—
166#66929—28no—
167#66925D414yes—
168#66925C2314yes—
169#66923—28no—
170#66922—22no—
171#66922C2314yes—
172C4×Dic22—22no—
173C4×Dic22C2314yes—
174C11×C4⋊C8C2314yes—
175C11×#103C2314yes—
176C11×#102C2314yes—
177#66899C2314yes—
178#66896C2314yes—
179(C2×D11)⋊C8C2314yes—
180(C2×D11)⋊C8C2314yes—
181#66880C2314yes—
182#66880C2314yes—
183#66879C2314yes—
184C8×Dic11C2314yes—
185#66874C2314yes—
186#66874C2314yes—
187C4⋊(C11⋊C8)C2314yes—
188C2×#3223—111nomaximal, Sylow
189C24×C11—21no—
190C23×D11C2×D411yescharacteristic
191C2×Q8×C11—21no—
192C2×Q8×C11—21no—
193C2×Q8×C11—22no—
194C2×Q8×C11—22no—
195C2×Q8×C11—22no—
196C2×Q8×C11—22no—
197C2×Q8×C11C2412yes—
198C2×Q8×C11C2412yes—
199C2×D4×C11—21no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11C2412yes—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2411yescharacteristic
209C2×C22⋊D11—24no—
210C2×C22⋊D11—44no—
211C22×Dic11—24no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—44no—
217C22×Dic11C2×D411yescharacteristic
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D411yescharacteristic
220Q8×D11—44no—
221Q8×D11—44no—
222Q8×D11—48no—
223#4341—44no—
224#4341—44no—
225#4341—48no—
226C2×C4×D11—24no—
227C2×C4×D11—22no—
228C2×C4×D11—22no—
229C2×C4×D11—44no—
230C2×C4×D11C2×D412yes—
231C2×C4×D11C2412yes—
232C2×Dic22—24no—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22—21no—
236C2×Dic22—22no—
237C2×Dic22—22no—
238C2×Dic22—22no—
239C2×Dic22—22no—
240C2×Dic22—22no—
241C2×Dic22—22no—
242C2×Dic22—44no—
243C2×Dic22C2412yes—
244C2×Dic22C2412yes—
245C2×Dic22C2412yes—
246C11×Q16—44no—
247C11×SD16—44no—
248C2×C8×C11—22no—
249C2×C8×C11—22no—
250C2×C8×C11C2412yes—
251C2×C8×C11C2412yes—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4C2412yes—
255C11×C22⋊C4—24no—
256C11×C22⋊C4—24no—
257C42×C11—24no—
258C42×C11C2×D412yes—
259C42×C11C2412yes—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
262#4326—44no—
263#4326—44no—
264#4326—44no—
265#4324—44no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4C2×D414yes—
269(C2×D11)⋊C4C2×D414yes—
270C4⋊Dic11—24no—
271C4⋊Dic11—24no—
272C4⋊Dic11—21no—
273C4⋊Dic11—24no—
274C4⋊Dic11—24no—
275C4⋊Dic11C2412yes—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4C2×D414yes—
284Dic11⋊C4C2×D414yes—
285C4×Dic11—24no—
286C4×Dic11C2×D412yes—
287C4×Dic11C2412yes—
288C2×C11⋊C8—22no—
289C2×C11⋊C8—22no—
290C2×C11⋊C8C2412yes—
291C2×C11⋊C8C2412yes—
292Dic44—44no—
293Dic44—44no—
294C2×#541—111no—
295C2×#536—111no—
296#3223—1116no—
297C2×#497—111no—
298C2×#494—111no—
299C2×#491—111no—
300C2×#488—111no—
301C2×#464—111no—
302C2×#464D1111yescharacteristic, complemented
303C2×#462—111no—
304C2×#462—111no—
305C2×#452—111no—
306C2×#452—111no—
307C2×#451—111no—
308C2×#451—111no—
309C2×#433—111no—
310C23×C11—22no—
311C23×C11—42no—
312C23×C11—42no—
313C23×C11—42no—
314C23×C11C22×D411yescharacteristic
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11C22×D412yes—
319Q8×C11—22no—
320Q8×C11—22no—
321Q8×C11—22no—
322Q8×C11—22no—
323Q8×C11—42no—
324Q8×C11—42no—
325D4×C11—22no—
326D4×C11—22no—
327D4×C11—42no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11C22×D412yes—
337C2×C4×C11C22×D412yes—
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11H(5,𝔽2)12yes—
340C2×C4×C11H(5,𝔽2)12yes—
341C2×C4×C11C2511yescharacteristic
342C22⋊D11—48no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—48no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11C22×D412yes—
356C2×Dic11C22×D412yes—
357C2×Dic11C22×D412yes—
358C4×D11—24no—
359C4×D11—22no—
360C4×D11—22no—
361C4×D11—48no—
362Dic22—22no—
363Dic22—22no—
364Dic22—22no—
365Dic22—22no—
366Dic22—22no—
367Dic22—22no—
368Dic22—48no—
369Dic22—42no—
370Dic22—42no—
371Dic22—42no—
372C8×C11—22no—
373C8×C11—22no—
374C11⋊C8—22no—
375C11⋊C8—22no—
376C22×#41—111no—
377C23×Q8—111no—
378C22×Q16—111no—
379C22×Q16—111no—
380C22×Q16—111no—
381C22×Q16—111no—
382C22×Q16—111no—
383C22×Q16C2×D1111yescharacteristic
384C22×SD16—111no—
385C22×SD16C2×D1111yescharacteristic
386#541—118no—
387#541—224no—
388#536—118no—
389#536—224no—
390C2×C4⋊Q8—111no—
391C2×C4⋊Q8—111no—
392C2×C4⋊Q8—111no—
393C2×#126—221no—
394C2×#126—221no—
395C2×#125—111no—
396C2×#125—221no—
397C2×#125—221no—
398C2×#124—111no—
399C2×#124C2×D1111yescharacteristic
400C2×#123—221no—
401C2×#123—221no—
402C2×C22⋊Q8—111no—
403C2×C22⋊Q8—111no—
404C2×C22⋊Q8—221no—
405C2×C22⋊Q8—221no—
406C2×C4×Q8—111no—
407C2×C4×Q8C2×D1111yescharacteristic
408C2×#117—111no—
409#497—118no—
410#494—118no—
411#491—118no—
412#488—118no—
413#464—118no—
414#464C2×D1118yescomplemented
415#462—118no—
416#462—118no—
417#452—118no—
418#452—118no—
419#451—118no—
420#451—118no—
421#433—118no—
422C2×C4⋊C8—111no—
423C2×C4⋊C8C2×D1111yescharacteristic
424C2×#103—111no—
425C2×#103—111no—
426C2×#103—111no—
427C2×#103—111no—
428C2×#103—111no—
429C2×#103C2×D1111yescharacteristic
430C2×#102—111no—
431C2×#102C2×D1111yescharacteristic
432C2×C22⋊C8—111no—
433C2×C22⋊C8—111no—
434C2×#97—111no—
435C2×C4×C8—111no—
436C22×C11—42no—
437C22×C11—42no—
438C22×C11—42no—
439C22×C11—84no—
440C22×C11#53512yes—
441C22×C11#57812yes—
442C22×C11#57812yes—
443C22×C11C23×D411yescharacteristic
444C2×D11—22no—
445C2×D11—22no—
446C2×D11—22no—
447C2×D11—44no—
448C4×C11—22no—
449C4×C11—22no—
450C4×C11—42no—
451C4×C11—42no—
452C4×C11—42no—
453C4×C11#53512yes—
454C4×C11C2×H(5,𝔽2)11yescharacteristic
455C4×C11C2×H(5,𝔽2)11yescharacteristic
456Dic11—22no—
457Dic11—22no—
458Dic11—22no—
459Dic11—42no—
460Dic11—42no—
461Dic11—42no—
462Dic11—42no—
463C2×#41—114no—
464C2×#41—222no—
465C2×#41—442no—
466C2×#41—442no—
467C22×Q8—114no—
468C22×Q8—111no—
469C22×Q8—111no—
470C22×Q8—111no—
471C22×Q8—221no—
472C22×Q8—222no—
473C22×Q8—442no—
474C22×Q8—442no—
475C22×Q8C22×D1111yescharacteristic
476C22×Q8C22×D1111yescharacteristic
477C22×D4—221no—
478C22×D4C22×D1111yescharacteristic
479C23×C4—111no—
480C23×C4—221no—
481C23×C4—221no—
482C2×Q16—42no—
483C2×Q16—114no—
484C2×Q16—114no—
485C2×Q16—114no—
486C2×Q16—114no—
487C2×Q16—114no—
488C2×Q16—442no—
489C2×Q16—442no—
490C2×Q16—442no—
491C2×Q16—442no—
492C2×Q16—442no—
493C2×Q16C22×D1114yes—
494C2×SD16—42no—
495C2×SD16—114no—
496C2×SD16—442no—
497C2×SD16C22×D1114yes—
498C22×C8—111no—
499C22×C8—111no—
500C22×C8C22×D1111yescharacteristic
501C22×C8C22×D1111yescharacteristic
502C4⋊Q8—114no—
503C4⋊Q8—114no—
504C4⋊Q8—114no—
505C4⋊Q8—222no—
506C4⋊Q8—222no—
507C4⋊Q8—222no—
508#126—228no—
509#126—228no—
510#125—114no—
511#125—228no—
512#125—222no—
513#125—228no—
514#124—22no—
515#124—114no—
516#124—222no—
517#124C22×D1114yes—
518#123—228no—
519#123—228no—
520C22⋊Q8—114no—
521C22⋊Q8—114no—
522C22⋊Q8—228no—
523C22⋊Q8—228no—
524C22⋊Q8—222no—
525C22⋊Q8—222no—
526C4×Q8—22no—
527C4×Q8—114no—
528C4×Q8—222no—
529C4×Q8C22×D1114yes—
530#117—114no—
531#117—114no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—111no—
534C2×C4⋊C4—111no—
535C2×C4⋊C4—111no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4—221no—
538C2×C4⋊C4—221no—
539C2×C4⋊C4—221no—
540C2×C4⋊C4—221no—
541C2×C4⋊C4—221no—
542C2×C4⋊C4—221no—
543C2×C4⋊C4—221no—
544C2×C4⋊C4—221no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4C22×D1111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—111no—
551C2×C22⋊C4—111no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C42—21no—
557C2×C42—111no—
558C2×C42—221no—
559C2×C42C22×D1111yescharacteristic
560C4⋊C8—114no—
561C4⋊C8C22×D1114yes—
562#103—114no—
563#103—114no—
564#103—114no—
565#103—114no—
566#103—114no—
567#103C22×D1114yes—
568#102—114no—
569#102C22×D1114yes—
570C22⋊C8—114no—
571C22⋊C8—114no—
572#97—114no—
573C4×C8—114no—
574C2×C11—82no—
575C2×C11#322314yescomplemented
576C2×C11C2×#53511yescharacteristic
577C2×C11C2×#57811yescharacteristic
578C2×C11C2×#57811yescharacteristic
579D11—42no—
580C24—21no—
581C24—111no—
582#41—444no—
583#41—444no—
584#41—448no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—112no—
592C2×Q8—112no—
593C2×Q8—112no—
594C2×Q8—224no—
595C2×Q8—221no—
596C2×Q8—221no—
597C2×Q8—221no—
598C2×Q8—222no—
599C2×Q8—222no—
600C2×Q8—222no—
601C2×Q8—222no—
602C2×Q8—222no—
603C2×Q8—222no—
604C2×Q8—444no—
605C2×Q8—444no—
606C2×Q8—444no—
607C2×Q8—448no—
608C2×Q8C23×D1112yes—
609C2×Q8C23×D1112yes—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—224no—
614C2×D4—444no—
615C2×D4C23×D1112yes—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—111no—
620C22×C4—111no—
621C22×C4—111no—
622C22×C4—112no—
623C22×C4—112no—
624C22×C4—224no—
625C22×C4—224no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—221no—
629C22×C4—221no—
630C22×C4—221no—
631C22×C4—221no—
632C22×C4—444no—
633C22×C4—444no—
634C22×C4D4×D1111yescharacteristic
635C22×C4D4×D1111yescharacteristic
636C22×C4C23×D1111yescharacteristic
637Q16—44no—
638Q16—444no—
639Q16—444no—
640Q16—444no—
641Q16—444no—
642Q16—444no—
643SD16—44no—
644SD16—444no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—112no—
648C2×C8—112no—
649C2×C8—222no—
650C2×C8—222no—
651C2×C8C23×D1112yes—
652C2×C8C23×D1112yes—
653C4⋊C4—24no—
654C4⋊C4—21no—
655C4⋊C4—114no—
656C4⋊C4—114no—
657C4⋊C4—112no—
658C4⋊C4—224no—
659C4⋊C4—224no—
660C4⋊C4—224no—
661C4⋊C4—224no—
662C4⋊C4—224no—
663C4⋊C4—224no—
664C4⋊C4—224no—
665C4⋊C4—224no—
666C4⋊C4—221no—
667C4⋊C4—224no—
668C4⋊C4—224no—
669C4⋊C4—224no—
670C4⋊C4C23×D1112yes—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—114no—
674C22⋊C4—114no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C42—24no—
680C42—112no—
681C42—112no—
682C42—224no—
683C42D4×D1112yes—
684C42C23×D1112yes—
685C11C2×#322311yescharacteristic, complemented, Sylow
686C23—22no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—112no—
691C23—222no—
692C23—222no—
693C23—222no—
694C23C2×D4×D1111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—42no—
701Q8—222no—
702Q8—222no—
703Q8—222no—
704Q8—222no—
705Q8—222no—
706Q8—222no—
707Q8—448no—
708Q8—442no—
709Q8—442no—
710Q8—442no—
711D4—22no—
712D4—22no—
713D4—42no—
714D4—448no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—112no—
724C2×C4—112no—
725C2×C4—112no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—224no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—448no—
737C2×C4—448no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4C2×D4×D1112yes—
743C2×C4C2×D4×D1112yes—
744C2×C4C2×D4×D1111yescharacteristic
745C2×C4#6703712yes—
746C2×C4#6704212yes—
747C2×C4C24×D1111yescharacteristic
748C8—22no—
749C8—22no—
750C8—222no—
751C8—222no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—84no—
756C22—222no—
757C22—222no—
758C22—222no—
759C22—444no—
760C22#1062313812yes—
761C22#1062330212yes—
762C22#1062331012yes—
763C22C22×D4×D1111yescharacteristic
764C4—22no—
765C4—22no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—222no—
770C4—222no—
771C4—222no—
772C4—442no—
773C4—442no—
774C4—442no—
775C4—442no—
776C4#1062313812yes—
777C4C2×#6703711yescharacteristic
778C4C2×#6704211yescharacteristic
779C2—82no—
780C2—442no—
781C2#1307969614yesdirect product factor
782C2C2×#1062313811yescharacteristic
783C2C2×#1062330211yescharacteristic
784C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#464C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
hypercenterC2×#464D11
hypocenterC11C2×#3223
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#10623114C2semidirect
3. #13079696C2direct (N × H)
4. C2×#10622780C2semidirect
5. C2×#10622794C2semidirect
6. C2×#10622410C2semidirect
7. C2×#10622381C2semidirect
8. C2×#10622667C2semidirect
9. C2×#10622462C2semidirect
10. C2×#10622644C2semidirect
13. C2×#10622421C2semidirect
14. C2×#10622799C2semidirect
15. C2×#10622453C2semidirect
16. C2×C11×#464C2semidirect
36. #10623114C22semidirect
50. C11×#464C22semidirect
56. #10622799C22semidirect
57. #10622794C22semidirect
59. #10622780C22semidirect
66. #10622667C22semidirect
67. #10622644C22semidirect
71. #10622462C22semidirect
72. #10622453C22semidirect
73. #10622421C22semidirect
74. #10622410C22semidirect
76. #10622381C22semidirect
302. C2×#464D11semidirect
414. #464C2×D11semidirect
575. C2×C11#3223semidirect
685. C11C2×#3223semidirect
781. C2#13079696direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231142
C2×#106232062
#130796962
C2×#106227802
C2×#106227942
C2×#106224102
C2×#106223812
C2×#106226672
C2×#106224622
C2×#106226442
C2×#106223962
C2×#106227862
C2×#106224212
C2×#106227992
C2×#106224532
C2×C11×#4642
C2×#322311