Finite Group Databasebeta

← C2×#13079697 #15625154

Subgroups — C2×#13079697 #15625154

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×#10623156C211yesmaximal, characteristic, complemented
2C2×#10623356C211yesmaximal, characteristic
3#13079697C2116yesmaximal, direct product factor
4C2×#10622780C211yesmaximal, characteristic, complemented
5C2×#10622794C211yesmaximal, characteristic, complemented
6C2×#10622410C211yesmaximal, characteristic, complemented
7C2×#10622381C211yesmaximal, characteristic, complemented
8C2×#10622380C211yesmaximal, characteristic, complemented
9C2×#10622779C211yesmaximal, characteristic, complemented
10C2×#10622406C211yesmaximal, characteristic, complemented
11C2×#10622795C211yesmaximal, characteristic, complemented
12C2×#10622852C211yesmaximal, characteristic
13C2×#10622352C211yesmaximal, characteristic, complemented
14C2×#10622663C211yesmaximal, characteristic, complemented
15C2×#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#452C211yesmaximal, characteristic
17C22×C11×#41C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22#10623356—24no—
23#10623356C2218yes—
24C2×Q8×Dic11C2211yescharacteristic
25C2×#66997C2211yescharacteristic
26C2×#66997C2211yescharacteristic
27C2×#66997C2211yescharacteristic
28C22×#4326C2211yescharacteristic
29C22×#4326C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C2×#66989C2211yescharacteristic
32C2×#66989C2211yescharacteristic
33C2×#66988—21no—
34C2×#66988—21no—
35C22×#4324C2211yescharacteristic
36C2×#66979C2211yescharacteristic
37C2×#66977—21no—
38C2×#66977—21no—
39C2×#66977C2211yescharacteristic
40C22×Dic44C2211yescharacteristic
41C22×Dic44C2211yescharacteristic
42#10623156—24no—
43#10623156C2218yescomplemented
44C2×#66943—21no—
45C2×#66943C2211yescharacteristic
46C2×#66942—21no—
47C2×#66940C2211yescharacteristic
48C2×#66932—21no—
49C2×#66932—21no—
50C11×#452C2218yes—
51C2×C11×#103C2211yescharacteristic
52C2×C11×#102C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic
54#10622852C2218yes—
55C2×#66899C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58#10622795C2218yescomplemented
59#10622794C2218yescomplemented
60#10622780C2218yescomplemented
61#10622779C2218yescomplemented
62C2×#66880C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×#66879C2211yescharacteristic
65C2×Dic11⋊C8C2211yescharacteristic
66C2×Dic11⋊C8C2211yescharacteristic
67C2×C8×Dic11C2211yescharacteristic
68#10622663C2218yescomplemented
69C2×#66874C2211yescharacteristic
70C2×#66874C2211yescharacteristic
71#10622410C2218yescomplemented
72#10622406C2218yescomplemented
73#10622381C2218yescomplemented
74#10622380C2218yescomplemented
75#10622352C2218yescomplemented
76#10622333C2218yescomplemented
77C2×C11×#41—22no—
78C2×C11×#41—42no—
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
87C23×Dic11—21no—
88C22×Dic22—21no—
89C22×Dic22—22no—
90C22×Dic22—42no—
91C22×Dic22—42no—
92C22×Dic22C2311yescharacteristic
93C22×Dic22C2311yescharacteristic
94C22×Dic22C2311yescharacteristic
95C22×Dic22C2314yes—
96C2×C11×Q16—42no—
97C2×C11×Q16C2314yes—
98C2×C11×SD16—42no—
99C2×C11×SD16C2314yes—
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C11×C22⋊Q8—22no—
103C11×C22⋊Q8C2314yes—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C22⋊C4—21no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11D411yescharacteristic
113C2×C22⋊Dic11D411yescharacteristic
114Q8×Dic11—22no—
115Q8×Dic11C2314yes—
116#66997—22no—
117#66997—22no—
118#66997—22no—
119#66997C2314yes—
120#66997C2314yes—
121#66997C2314yes—
122C2×#4326—42no—
123C2×#4326—42no—
124C2×#4326—42no—
125C2×#4326C2314yes—
126C2×#4326C2314yes—
127C2×#4326C2314yes—
128#66989—22no—
129#66989—22no—
130#66989C2314yes—
131#66989C2314yes—
132#66988—28no—
133#66988—28no—
134C2×#4324—42no—
135C2×#4324C2314yes—
136#66979D414yes—
137#66979C2314yes—
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11D411yescharacteristic
141C2×C4⋊Dic11D411yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143#66977—22no—
144#66977—28no—
145#66977—28no—
146#66977C2314yes—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4—21no—
154C2×Dic11⋊C4—21no—
155C2×Dic11⋊C4—21no—
156C2×C4×Dic11—21no—
157C2×C4×Dic11—21no—
158C2×C4×Dic11C2311yescharacteristic
159C2×C4×Dic11C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2311yescharacteristic
162C2×Dic44—42no—
163C2×Dic44—42no—
164C2×Dic44C2314yes—
165C2×Dic44C2314yes—
166#66943—28no—
167#66943—22no—
168#66943C2314yes—
169#66942—28no—
170#66940—22no—
171#66940C2314yes—
172#66932—28no—
173#66932—28no—
174C11×#103C2314yes—
175C11×#102C2314yes—
176C11×C22⋊C8C2314yes—
177#66899C2314yes—
178#66896C2314yes—
179C22⋊(C11⋊C8)C2314yes—
180#66880C2314yes—
181#66880C2314yes—
182#66879C2314yes—
183Dic11⋊C8C2314yes—
184Dic11⋊C8C2314yes—
185C8×Dic11C2314yes—
186#66874C2314yes—
187#66874C2314yes—
188C2×#3223—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11C2×D411yescharacteristic
191C11×#41—44no—
192C11×#41—44no—
193C11×#41—48no—
194C2×Q8×C11—21no—
195C2×Q8×C11—21no—
196C2×Q8×C11—22no—
197C2×Q8×C11—22no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×Q8×C11C2412yes—
201C2×Q8×C11C2412yes—
202C2×D4×C11—24no—
203C2×D4×C11—21no—
204C2×D4×C11—22no—
205C2×D4×C11—22no—
206C2×D4×C11—44no—
207C2×D4×C11C2412yes—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—24no—
214C22×C4×C11—44no—
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2411yescharacteristic
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—24no—
224C22×Dic11—44no—
225C22×Dic11C2×D411yescharacteristic
226C22×Dic11C2×D411yescharacteristic
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229C2×Dic22—21no—
230C2×Dic22—24no—
231C2×Dic22—21no—
232C2×Dic22—21no—
233C2×Dic22—22no—
234C2×Dic22—22no—
235C2×Dic22—22no—
236C2×Dic22—22no—
237C2×Dic22—22no—
238C2×Dic22—22no—
239C2×Dic22—44no—
240C2×Dic22—44no—
241C2×Dic22—44no—
242C2×Dic22—48no—
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—21no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4C2412yes—
255C11×C22⋊C4—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—24no—
258C22⋊Dic11—24no—
259C22⋊Dic11—24no—
260C22⋊Dic11—24no—
261C22⋊Dic11C2×D414yes—
262C22⋊Dic11C2×D414yes—
263#4326—44no—
264#4326—44no—
265#4326—44no—
266#4324—44no—
267C4⋊Dic11—24no—
268C4⋊Dic11—24no—
269C4⋊Dic11—21no—
270C4⋊Dic11C2×D414yes—
271C4⋊Dic11C2×D414yes—
272C4⋊Dic11C2412yes—
273Dic11⋊C4—24no—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282C4×Dic11—24no—
283C4×Dic11—24no—
284C4×Dic11C2×D412yes—
285C4×Dic11C2×D412yes—
286C4×Dic11C2412yes—
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×#464—111no—
303C2×#462—111no—
304C2×#462—111no—
305C2×#452—111no—
306C2×#452D1111yescharacteristic
307C2×#451—111no—
308C2×#451—111no—
309C2×#433—111no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11C22×D412yes—
318C23×C11C22×D411yescharacteristic
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—48no—
328D4×C11—42no—
329C2×C4×C11—22no—
330C2×C4×C11—24no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—48no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11H(5,𝔽2)12yes—
343C2×C4×C11H(5,𝔽2)12yes—
344C2×C4×C11C2511yescharacteristic
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
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×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11C22×D412yes—
359C2×Dic11C22×D412yes—
360C2×Dic11C22×D412yes—
361C2×Dic11C22×D412yes—
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×#41C2×D1111yescharacteristic
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×#124—111no—
400C2×#123—221no—
401C2×#123—221no—
402C2×C22⋊Q8—111no—
403C2×C22⋊Q8—221no—
404C2×C22⋊Q8—221no—
405C2×C22⋊Q8C2×D1111yescharacteristic
406C2×C4×Q8—111no—
407C2×C4×Q8—111no—
408C2×#117—111no—
409#497—118no—
410#494—118no—
411#491—118no—
412#488—118no—
413#464—118no—
414#464—118no—
415#462—118no—
416#462—118no—
417#452—118no—
418#452C2×D1118yes—
419#451—118no—
420#451—118no—
421#433—118no—
422C2×C4⋊C8—111no—
423C2×C4⋊C8—111no—
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⋊C8C2×D1111yescharacteristic
434C2×#97—111no—
435C2×C4×C8—111no—
436C22×C11—22no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—44no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—84no—
444C22×C11#53512yes—
445C22×C11#57812yes—
446C22×C11#57812yes—
447C22×C11C23×D411yescharacteristic
448C4×C11—22no—
449C4×C11—42no—
450C4×C11—42no—
451C4×C11—42no—
452C4×C11#53512yes—
453C4×C11C2×H(5,𝔽2)11yescharacteristic
454C4×C11C2×H(5,𝔽2)11yescharacteristic
455Dic11—22no—
456Dic11—22no—
457Dic11—22no—
458Dic11—22no—
459Dic11—42no—
460Dic11—42no—
461Dic11—42no—
462Dic11—42no—
463C2×#41—22no—
464C2×#41—42no—
465C2×#41—42no—
466C2×#41C22×D1114yes—
467C22×Q8—111no—
468C22×Q8—111no—
469C22×Q8—111no—
470C22×Q8—114no—
471C22×Q8—221no—
472C22×Q8—222no—
473C22×Q8—442no—
474C22×Q8—442no—
475C22×Q8C22×D1111yescharacteristic
476C22×Q8C22×D1111yescharacteristic
477C22×D4—21no—
478C22×D4C22×D1111yescharacteristic
479C23×C4—21no—
480C23×C4—221no—
481C23×C4C22×D1111yescharacteristic
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—222no—
512#125—228no—
513#125—228no—
514#124—114no—
515#124—114no—
516#124—222no—
517#124—222no—
518#123—228no—
519#123—228no—
520C22⋊Q8—22no—
521C22⋊Q8—114no—
522C22⋊Q8—228no—
523C22⋊Q8—228no—
524C22⋊Q8—222no—
525C22⋊Q8C22×D1114yes—
526C4×Q8—114no—
527C4×Q8—114no—
528C4×Q8—222no—
529C4×Q8—222no—
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—111no—
550C2×C22⋊C4—111no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C42—111no—
557C2×C42—111no—
558C2×C42—221no—
559C2×C42—221no—
560C4⋊C8—114no—
561C4⋊C8—114no—
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⋊C8C22×D1114yes—
572#97—114no—
573C4×C8—114no—
574C2×C11—42no—
575C2×C11—82no—
576C2×C11#322314yescomplemented
577C2×C11C2×#53511yescharacteristic
578C2×C11C2×#57811yescharacteristic
579C2×C11C2×#57811yescharacteristic
580C24—21no—
581C24D4×D1111yescharacteristic
582#41—44no—
583#41—44no—
584#41—48no—
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—221no—
595C2×Q8—224no—
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—24no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—44no—
615C2×D4C23×D1112yes—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—24no—
622C22×C4—44no—
623C22×C4—111no—
624C22×C4—111no—
625C22×C4—111no—
626C22×C4—111no—
627C22×C4—224no—
628C22×C4—221no—
629C22×C4—221no—
630C22×C4—221no—
631C22×C4—221no—
632C22×C4—444no—
633C22×C4D4×D1112yes—
634C22×C4D4×D1111yescharacteristic
635C22×C4C23×D1112yes—
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—224no—
667C4⋊C4—224no—
668C4⋊C4—221no—
669C4⋊C4—224no—
670C4⋊C4C23×D1112yes—
671C22⋊C4—24no—
672C22⋊C4—114no—
673C22⋊C4—114no—
674C22⋊C4—224no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C42—112no—
680C42—112no—
681C42—112no—
682C42—112no—
683C42—224no—
684C42—224no—
685C11C2×#322311yescharacteristic, complemented, Sylow
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23C2×D4×D1112yes—
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—48no—
714D4—42no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—48no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—112no—
727C2×C4—112no—
728C2×C4—112no—
729C2×C4—112no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—448no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4C2×D4×D1112yes—
744C2×C4C2×D4×D1111yescharacteristic
745C2×C4#6703712yes—
746C2×C4#6703712yes—
747C2×C4C24×D1111yescharacteristic
748C8—22no—
749C8—22no—
750C8—222no—
751C8—222no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—44no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—84no—
760C22#1062312312yes—
761C22#1062330212yes—
762C22#1062331012yes—
763C22C22×D4×D1111yescharacteristic
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—222no—
769C4—222no—
770C4—222no—
771C4—222no—
772C4—442no—
773C4—442no—
774C4—442no—
775C4—442no—
776C4#1062312312yes—
777C4C2×#6703711yescharacteristic
778C4C2×#6703711yescharacteristic
779C2—42no—
780C2—82no—
781C2#1307969714yesdirect product factor
782C2C2×#1062312311yescharacteristic
783C2C2×#1062330211yescharacteristic
784C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#452C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC2×#452D11
hypocenterC11C2×#3223
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×#10623156C2semidirect
3. #13079697C2direct (N × H)
4. C2×#10622780C2semidirect
5. C2×#10622794C2semidirect
6. C2×#10622410C2semidirect
7. C2×#10622381C2semidirect
8. C2×#10622380C2semidirect
9. C2×#10622779C2semidirect
10. C2×#10622406C2semidirect
11. C2×#10622795C2semidirect
13. C2×#10622352C2semidirect
14. C2×#10622663C2semidirect
15. C2×#10622333C2semidirect
43. #10623156C22semidirect
58. #10622795C22semidirect
59. #10622794C22semidirect
60. #10622780C22semidirect
61. #10622779C22semidirect
68. #10622663C22semidirect
71. #10622410C22semidirect
72. #10622406C22semidirect
73. #10622381C22semidirect
74. #10622380C22semidirect
75. #10622352C22semidirect
76. #10622333C22semidirect
576. C2×C11#3223semidirect
685. C11C2×#3223semidirect
781. C2#13079697direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231562
C2×#106233562
#130796972
C2×#106227802
C2×#106227942
C2×#106224102
C2×#106223812
C2×#106223802
C2×#106227792
C2×#106224062
C2×#106227952
C2×#106228522
C2×#106223522
C2×#106226632
C2×#106223332
C2×C11×#4522
C2×#322311