Finite Group Databasebeta

← C2×#13081077 #15632326

Subgroups — C2×#13081077 #15632326

Order 2816.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623166C211yesmaximal, characteristic
2C2×#10623173C211yesmaximal, characteristic
3#13081077C2116yesmaximal, direct product factor
4C2×#10622489C211yesmaximal, characteristic, complemented
5C2×#10622657C211yesmaximal, characteristic, complemented
6C2×#10622428C211yesmaximal, characteristic, complemented
7C2×#10622418C211yesmaximal, characteristic, complemented
8C2×#10622656C211yesmaximal, characteristic, complemented
9C2×#10622412C211yesmaximal, characteristic, complemented
10C2×#10622404C211yesmaximal, characteristic, complemented
11C2×#10622802C211yesmaximal, characteristic, complemented
12C2×#10622797C211yesmaximal, characteristic, complemented
13C2×#10622724C211yesmaximal, characteristic
14C2×#10622494C211yesmaximal, characteristic, complemented
15C22×#66881C211yesmaximal, characteristic, complemented
16C2×C11×#467C211yesmaximal, characteristic, complemented
17C22×C11×Q16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C2×C4×C22⋊D11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×#4313C2211yescharacteristic
29#10623173—24no—
30#10623173C2218yes—
31#10623166—24no—
32#10623166C2218yes—
33C2×#66951—21no—
34C2×#66950—21no—
35C2×#66945C2211yescharacteristic
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×#66943—21no—
38C2×#66943C2211yescharacteristic
39C2×#66942—21no—
40C2×#66941C2211yescharacteristic
41C2×#66939—21no—
42C2×(C22⋊D11)⋊C4—21no—
43C2×#66931—21no—
44C2×#66930—21no—
45C11×#467C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×#66899C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622802C2218yescomplemented
55#10622797C2218yescomplemented
56#10622724C2218yes—
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66881C2211yescharacteristic
59C2×#66881C2211yescharacteristic
60C2×#66881C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66881C2218yescomplemented
63C2×#66879C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65#10622657C2218yescomplemented
66#10622656C2218yescomplemented
67C2×#66872C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622494C2218yescomplemented
72#10622489C2218yescomplemented
73#10622428C2218yescomplemented
74#10622418C2218yescomplemented
75#10622412C2218yescomplemented
76#10622404C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11D411yescharacteristic
81C23×Dic11—21no—
82C23×Dic11—21no—
83C22×C4×D11—21no—
84C22×C4×D11C2311yescharacteristic
85C22×Dic22—21no—
86C2×C11×Q16—24no—
87C2×C11×Q16C2314yes—
88C22×C8×C11—24no—
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2314yes—
91C22×C8×C11C2311yescharacteristic
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8C2314yes—
95C11×C22⋊Q8C2314yes—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C22⋊Dic11D411yescharacteristic
103#66999—22no—
104#66999—22no—
105#66999C2314yes—
106#66999C2314yes—
107Q8×Dic11—22no—
108Q8×Dic11—22no—
109Q8×Dic11C2314yes—
110Q8×Dic11C2314yes—
111C4×C22⋊D11D414yes—
112C4×C22⋊D11C2314yes—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4D411yescharacteristic
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11—21no—
119C2×C4⋊Dic11—22no—
120C2×C4⋊Dic11—22no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2314yes—
129C2×C4⋊Dic11C2314yes—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4D411yescharacteristic
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11—21no—
139C2×C4×Dic11C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C2×#4313—24no—
143C2×#4313C2314yes—
144#66951—28no—
145#66950—28no—
146#66945—22no—
147#66945C2314yes—
148C4⋊C4×D11—22no—
149C4⋊C4×D11C2314yes—
150#66943—28no—
151#66943—22no—
152#66943C2314yes—
153#66942—28no—
154#66941—22no—
155#66941C2314yes—
156#66939—28no—
157(C22⋊D11)⋊C4—28no—
158#66931—28no—
159#66930—28no—
160C11×#107C2314yes—
161C11×#103C2314yes—
162C11×#103C2314yes—
163#66899C2314yes—
164#66899C2314yes—
165#66899C2314yes—
166#66899C2314yes—
167C22⋊(C11⋊C8)C2314yes—
168(C2×D11)⋊C8C2314yes—
169#66881C2314yes—
170#66881C2314yes—
171#66881C2314yes—
172#66881C2314yes—
173#66879C2314yes—
174Dic11⋊C8C2314yes—
175#66872C2314yes—
176#66872C2314yes—
177#66871C2314yes—
178#66871C2314yes—
179C2×#3344—111nomaximal, Sylow
180C24×C11C2×D411yescharacteristic
181C23×D11C2×D411yescharacteristic
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11—22no—
187C2×Q8×C11—22no—
188C2×Q8×C11C2412yes—
189C2×Q8×C11C2412yes—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—24no—
201C2×C22⋊D11C2×D414yes—
202C22×Dic11—24no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—24no—
208C22×Dic11—44no—
209C22×Dic11—82no—
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212C22×Dic11C2×D411yescharacteristic
213C2×C4×D11—24no—
214C2×C4×D11—22no—
215C2×C4×D11—22no—
216C2×C4×D11—82no—
217C2×C4×D11C2×D412yes—
218C2×C4×D11C2412yes—
219C2×Dic22—24no—
220C2×Dic22—82no—
221C11×Q16—28no—
222C2×C8×C11—28no—
223C2×C8×C11—22no—
224C2×C8×C11#4114yes—
225C2×C8×C11C2412yes—
226C2×C8×C11C2412yes—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—24no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—24no—
231C11×C4⋊C4C2412yes—
232C11×C4⋊C4C2412yes—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C22⋊Dic11C2×D414yes—
236(C2×D11)⋊C4—24no—
237(C2×D11)⋊C4—24no—
238(C2×D11)⋊C4—24no—
239(C2×D11)⋊C4C2×D414yes—
240C4⋊Dic11—24no—
241C4⋊Dic11—24no—
242C4⋊Dic11—24no—
243C4⋊Dic11—21no—
244C4⋊Dic11—24no—
245C4⋊Dic11—24no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—21no—
249C4⋊Dic11C2412yes—
250C4⋊Dic11C2412yes—
251C4⋊Dic11C2412yes—
252C4⋊Dic11C2412yes—
253Dic11⋊C4—24no—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4C2×D414yes—
259C4×Dic11—24no—
260C4×Dic11—24no—
261C4×Dic11—24no—
262C4×Dic11C2×D412yes—
263C4×Dic11C2412yes—
264C2×C11⋊C8—22no—
265C2×C11⋊C8—22no—
266C2×C11⋊C8C2412yes—
267C2×C11⋊C8C2412yes—
268#4313—28no—
269C2×#554—111no—
270C2×#552—111no—
271#3344—1116no—
272C2×#501—111no—
273C2×#484—111no—
274C2×#485—111no—
275C2×#483—111no—
276C2×#483—111no—
277C2×#479—111no—
278C2×#475—111no—
279C2×#470—111no—
280C2×#467D1111yescharacteristic, complemented
281C2×#441—111no—
282C2×#435—111no—
283C2×#428—111no—
284C22×#106—111no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11#13714yes—
288C23×C11C22×D412yes—
289C23×C11C22×D411yescharacteristic
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11C22×D412yes—
294Q8×C11—22no—
295Q8×C11—22no—
296Q8×C11—22no—
297Q8×C11—22no—
298Q8×C11—42no—
299Q8×C11—42no—
300C2×C4×C11—22no—
301C2×C4×C11—24no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11C22×D412yes—
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C2×#4112yes—
315C2×C4×C112−1+412yes—
316C2×C4×C11C2511yescharacteristic
317C22⋊D11—28no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—48no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—84no—
331C2×Dic11C22×D412yes—
332C2×Dic11C22×D412yes—
333C2×Dic11C22×D412yes—
334C4×D11—24no—
335C4×D11—22no—
336C4×D11—22no—
337C4×D11—84no—
338Dic22—84no—
339C8×C11—22no—
340C8×C11C2×#4114yes—
341C11⋊C8—22no—
342C11⋊C8—22no—
343C22×Q16C2×D1111yescharacteristic
344C22×M16—111no—
345C23×C8C2×D1111yescharacteristic
346#554—118no—
347#554—224no—
348#552—118no—
349#552—224no—
350C2×C4⋊Q8—111no—
351C2×#126—221no—
352C2×#125—111no—
353C2×#125—221no—
354C2×#125—221no—
355C2×#123—221no—
356C2×C22⋊Q8—111no—
357C2×C22⋊Q8—111no—
358C2×C22⋊Q8—221no—
359C2×C22⋊Q8—221no—
360C2×C22⋊Q8C2×D1111yescharacteristic
361C2×C22⋊Q8C2×D1111yescharacteristic
362C2×C4×Q8—111no—
363C2×C4×Q8—111no—
364C2×C4×D4—111no—
365C2×C4×D4—221no—
366C2×#117—111no—
367C2×#117—221no—
368C22×C4⋊C4—111no—
369C22×C4⋊C4—111no—
370C22×C4⋊C4—111no—
371#501—118no—
372#485—118no—
373#484—118no—
374#483—118no—
375#483—118no—
376#479—118no—
377#475—118no—
378#470—118no—
379#467C2×D1118yescomplemented
380#441—118no—
381#435—118no—
382#428—118no—
383C2×#107—111no—
384C2×#107—111no—
385C2×#107C2×D1111yescharacteristic
386C2×#106—111no—
387C2×#106—111no—
388C2×#106—118no—
389C2×#106—111no—
390C2×#106—111no—
391C2×#106—111no—
392C2×#106—111no—
393C2×C4⋊C8—111no—
394C2×#103—111no—
395C2×#103—111no—
396C2×#103—111no—
397C2×#103—111no—
398C2×#103C2×D1111yescharacteristic
399C2×#103C2×D1111yescharacteristic
400C2×C22⋊C8—111no—
401C2×C22⋊C8—111no—
402C2×#97—111no—
403C22×C11—28no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11#54712yes—
407C22×C11C2×#13714yes—
408C22×C11C2×#13712yes—
409C22×C11#57712yes—
410C22×C11C23×D411yescharacteristic
411C2×D11—22no—
412C2×D11—22no—
413C2×D11—22no—
414C2×D11—44no—
415C4×C11—22no—
416C4×C11—42no—
417C4×C11—42no—
418C4×C11—42no—
419C4×C11—42no—
420C4×C11#54712yes—
421C4×C11C22×#4111yescharacteristic
422C4×C11C2×2−1+411yescharacteristic
423Dic11—22no—
424Dic11—22no—
425Dic11—22no—
426Dic11—42no—
427Dic11—42no—
428Dic11—42no—
429Dic11—42no—
430C22×Q8—221no—
431C22×Q8C22×D1111yescharacteristic
432C22×Q8C22×D1111yescharacteristic
433C22×D4—111no—
434C23×C4—111no—
435C23×C4—221no—
436C23×C4—221no—
437C23×C4—221no—
438C23×C4C22×D1111yescharacteristic
439C2×Q16—24no—
440C2×Q16C22×D1114yes—
441C2×M16—114no—
442C2×M16—224no—
443C22×C8—24no—
444C22×C8—111no—
445C22×C8—111no—
446C22×C8C22×D1111yescharacteristic
447C22×C8C22×D1114yes—
448C22×C8C22×D1111yescharacteristic
449C4⋊Q8—114no—
450C4⋊Q8—222no—
451#126—228no—
452#125—114no—
453#125—222no—
454#125—228no—
455#125—228no—
456#123—228no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—114no—
460C22⋊Q8—114no—
461C22⋊Q8—228no—
462C22⋊Q8—228no—
463C22⋊Q8—222no—
464C22⋊Q8—222no—
465C22⋊Q8C22×D1114yes—
466C22⋊Q8C22×D1114yes—
467C4×Q8—114no—
468C4×Q8—114no—
469C4×Q8—222no—
470C4×Q8—222no—
471C4×D4—114no—
472C4×D4—114no—
473C4×D4—228no—
474#117—114no—
475#117—228no—
476#117—222no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—114no—
485C2×C4⋊C4—114no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—222no—
488C2×C4⋊C4—221no—
489C2×C4⋊C4—221no—
490C2×C4⋊C4—221no—
491C2×C4⋊C4—221no—
492C2×C4⋊C4—221no—
493C2×C4⋊C4—221no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—222no—
499C2×C4⋊C4—222no—
500C2×C4⋊C4C22×D1111yescharacteristic
501C2×C4⋊C4C22×D1111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—111no—
505C2×C22⋊C4—111no—
506C2×C22⋊C4—221no—
507C2×C22⋊C4—221no—
508C2×C22⋊C4—221no—
509C2×C42—111no—
510C2×C42—221no—
511C2×C42—221no—
512C2×C42—221no—
513#107—114no—
514#107—114no—
515#107C22×D1114yes—
516#106—114no—
517#106—114no—
518#106—114no—
519#106—114no—
520#106—114no—
521#106—114no—
522C4⋊C8—114no—
523#103—114no—
524#103—114no—
525#103—114no—
526#103—114no—
527#103C22×D1114yes—
528#103C22×D1114yes—
529C22⋊C8—114no—
530C22⋊C8—114no—
531#97—114no—
532C2×C11—24no—
533C2×C11#334414yescomplemented
534C2×C11C2×#54711yescharacteristic
535C2×C11C22×#13711yescharacteristic
536C2×C11C2×#57711yescharacteristic
537D11—42no—
538C24—111no—
539C24D4×D1111yescharacteristic
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—224no—
547C2×Q8—882no—
548C2×Q8C23×D1112yes—
549C2×Q8C23×D1112yes—
550C2×D4—114no—
551C2×D4—224no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—111no—
559C22×C4—111no—
560C22×C4—111no—
561C22×C4—112no—
562C22×C4—112no—
563C22×C4—224no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—224no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—224no—
572C22×C4—444no—
573C22×C4—882no—
574C22×C4—882no—
575C22×C4D4×D1112yes—
576C22×C4D4×D1111yescharacteristic
577C22×C4C23×D1112yes—
578C22×C4C23×D1111yescharacteristic
579Q16—28no—
580M16—228no—
581C2×C8—22no—
582C2×C8—28no—
583C2×C8—112no—
584C2×C8—112no—
585C2×C8—222no—
586C2×C8—222no—
587C2×C8#434114yes—
588C2×C8C23×D1112yes—
589C2×C8C23×D1112yes—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—114no—
595C4⋊C4—112no—
596C4⋊C4—112no—
597C4⋊C4—112no—
598C4⋊C4—112no—
599C4⋊C4—224no—
600C4⋊C4—224no—
601C4⋊C4—224no—
602C4⋊C4—224no—
603C4⋊C4—224no—
604C4⋊C4—224no—
605C4⋊C4—224no—
606C4⋊C4—224no—
607C4⋊C4—221no—
608C4⋊C4—221no—
609C4⋊C4—224no—
610C4⋊C4—221no—
611C4⋊C4—221no—
612C4⋊C4—224no—
613C4⋊C4C23×D1112yes—
614C4⋊C4C23×D1112yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—114no—
618C22⋊C4—114no—
619C22⋊C4—224no—
620C22⋊C4—224no—
621C22⋊C4—224no—
622C42—112no—
623C42—112no—
624C42—224no—
625C42—224no—
626C42—224no—
627C11C2×#334411yescharacteristic, complemented, Sylow
628C23—22no—
629C23—22no—
630C23—112no—
631C23—222no—
632C23—222no—
633C23—222no—
634C23#6697114yes—
635C23C2×D4×D1112yes—
636C23C2×D4×D1111yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—22no—
641Q8—42no—
642Q8—42no—
643Q8—884no—
644D4—228no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—112no—
658C2×C4—112no—
659C2×C4—112no—
660C2×C4—222no—
661C2×C4—222no—
662C2×C4—222no—
663C2×C4—224no—
664C2×C4—222no—
665C2×C4—222no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—448no—
671C2×C4—442no—
672C2×C4—442no—
673C2×C4—442no—
674C2×C4—442no—
675C2×C4—884no—
676C2×C4—884no—
677C2×C4C2×D4×D1112yes—
678C2×C4C2×D4×D1111yescharacteristic
679C2×C4C2×#434112yes—
680C2×C4#6704312yes—
681C2×C4C24×D1111yescharacteristic
682C8—22no—
683C8—222no—
684C8—222no—
685C8C2×#434114yes—
686C22—22no—
687C22—22no—
688C22—28no—
689C22—222no—
690C22—222no—
691C22—222no—
692C22—444no—
693C22#1062314212yes—
694C22C2×#6697114yes—
695C22C2×#6697112yes—
696C22#1062330112yes—
697C22C22×D4×D1111yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—222no—
704C4—222no—
705C4—222no—
706C4—442no—
707C4—442no—
708C4—442no—
709C4—442no—
710C4#1062314212yes—
711C4C22×#434111yescharacteristic
712C4C2×#6704311yescharacteristic
713C2—24no—
714C2—442no—
715C2#1308107714yesdirect product factor
716C2C2×#1062314211yescharacteristic
717C2C22×#6697111yescharacteristic
718C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#467C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenterC2×#467D11
hypocenterC11C2×#3344
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
3. #13081077C2direct (N × H)
4. C2×#10622489C2semidirect
5. C2×#10622657C2semidirect
6. C2×#10622428C2semidirect
7. C2×#10622418C2semidirect
8. C2×#10622656C2semidirect
9. C2×#10622412C2semidirect
10. C2×#10622404C2semidirect
11. C2×#10622802C2semidirect
12. C2×#10622797C2semidirect
14. C2×#10622494C2semidirect
15. C22×#66881C2semidirect
16. C2×C11×#467C2semidirect
45. C11×#467C22semidirect
54. #10622802C22semidirect
55. #10622797C22semidirect
62. C2×#66881C22semidirect
65. #10622657C22semidirect
66. #10622656C22semidirect
71. #10622494C22semidirect
72. #10622489C22semidirect
73. #10622428C22semidirect
74. #10622418C22semidirect
75. #10622412C22semidirect
76. #10622404C22semidirect
280. C2×#467D11semidirect
379. #467C2×D11semidirect
533. C2×C11#3344semidirect
627. C11C2×#3344semidirect
715. C2#13081077direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231662
C2×#106231732
#130810772
C2×#106224892
C2×#106226572
C2×#106224282
C2×#106224182
C2×#106226562
C2×#106224122
C2×#106224042
C2×#106228022
C2×#106227972
C2×#106227242
C2×#106224942
C22×#668812
C2×C11×#4672
C2×#334411