Finite Group Databasebeta

← C2×#13081073 #15632322

Subgroups — C2×#13081073 #15632322

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×#10623074C211yesmaximal, characteristic
2C2×#10623072C211yesmaximal, characteristic
3#13081073C2116yesmaximal, direct product factor
4C2×#10622315C211yesmaximal, characteristic, complemented
5C2×#10622335C211yesmaximal, characteristic, complemented
6C2×#10622336C211yesmaximal, characteristic, complemented
7C2×#10622334C211yesmaximal, characteristic, complemented
8C2×#10622334C211yesmaximal, characteristic, complemented
9C2×#10622442C211yesmaximal, characteristic, complemented
10C2×#10622464C211yesmaximal, characteristic, complemented
11C2×#10622750C211yesmaximal, characteristic, complemented
12C2×#10622729C211yesmaximal, characteristic, complemented
13C2×#10622329C211yesmaximal, characteristic, complemented
14C2×#10622734C211yesmaximal, characteristic, complemented
15C22×#66881C211yesmaximal, characteristic, complemented
16C2×C11×#435C211yesmaximal, characteristic
17C22×C11×M16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66988—21no—
21C2×D4×Dic11—21no—
22C2×#66979C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C2×#66977C2211yescharacteristic
27C2×#66977C2211yescharacteristic
28C2×#66977C2211yescharacteristic
29C2×#66977C2211yescharacteristic
30C22×Dic44C2211yescharacteristic
31#10623074—24no—
32#10623074C2218yes—
33#10623072—24no—
34#10623072C2218yes—
35C2×#66943—21no—
36C2×#66942—21no—
37C2×#66932—21no—
38C2×#66931—21no—
39C2×#66931—21no—
40C2×#66930—21no—
41C2×#66923C2211yescharacteristic
42C2×#66922C2211yescharacteristic
43C2×C4×Dic22C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C11×#435C2218yes—
46C2×C11×C4⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C2×C11×#97C2211yescharacteristic
50#10622750C2218yescomplemented
51#10622734C2218yescomplemented
52#10622729C2218yescomplemented
53C2×#66882C2211yescharacteristic
54C2×#66882C2211yescharacteristic
55C2×#66882C2211yescharacteristic
56C2×#66881C2211yescharacteristic
57C2×#66881C2211yescharacteristic
58C2×#66881C2211yescharacteristic
59C2×#66881C2211yescharacteristic
60C2×#66881C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66881C2218yescomplemented
63C2×#66880C2211yescharacteristic
64C2×#66880C2211yescharacteristic
65C2×#66880C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×#66880C2211yescharacteristic
69#10622464C2218yescomplemented
70#10622442C2218yescomplemented
71#10622336C2218yescomplemented
72#10622335C2218yescomplemented
73#10622334C2218yescomplemented
74#10622334C2218yescomplemented
75#10622329C2218yescomplemented
76#10622315C2218yescomplemented
77C22×D4×C11D411yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×Dic11—21no—
81C23×Dic11—21no—
82C23×Dic11—21no—
83C22×Dic22—21no—
84C22×Dic22C2311yescharacteristic
85C22×Dic22C2311yescharacteristic
86C2×C11×M16—24no—
87C2×C11×M16C2314yes—
88C22×C8×C11—24no—
89C22×C8×C11C2314yes—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C4×D4×C11D414yes—
95C4×D4×C11C2314yes—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C11×C22⋊C4D411yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105#66988—28no—
106D4×Dic11—28no—
107#66979—22no—
108#66979C2314yes—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11—22no—
114C2×C4⋊Dic11—22no—
115C2×C4⋊Dic11—22no—
116C2×C4⋊Dic11C2314yes—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2314yes—
124C2×C4⋊Dic11C2314yes—
125#66977—22no—
126#66977—22no—
127#66977—22no—
128#66977—22no—
129#66977C2314yes—
130#66977C2314yes—
131#66977C2314yes—
132#66977C2314yes—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×C4×Dic11—21no—
142C2×C4×Dic11—21no—
143C2×C4×Dic11—21no—
144C2×Dic44—24no—
145C2×Dic44C2314yes—
146#66943—28no—
147#66942—28no—
148#66932—28no—
149#66931—28no—
150#66931—28no—
151#66930—28no—
152#66923—22no—
153#66923C2314yes—
154#66922—22no—
155#66922C2314yes—
156C4×Dic22—22no—
157C4×Dic22—22no—
158C4×Dic22C2314yes—
159C4×Dic22C2314yes—
160C11×C4⋊C8C2314yes—
161C11×C22⋊C8C2314yes—
162C11×C22⋊C8C2314yes—
163C11×#97C2314yes—
164#66882C2314yes—
165#66882C2314yes—
166#66882C2314yes—
167#66881C2314yes—
168#66881C2314yes—
169#66881C2314yes—
170#66881C2314yes—
171#66881C2314yes—
172#66881C2314yes—
173#66880C2314yes—
174#66880C2314yes—
175#66880C2314yes—
176#66880C2314yes—
177#66880C2314yes—
178#66880C2314yes—
179C2×#3344—111nomaximal, Sylow
180C24×C11C2×D411yescharacteristic
181C24×C11C2×D411yescharacteristic
182C2×D4×C11—24no—
183C2×D4×C11C2×D414yes—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D412yes—
193C22×C4×C11C2×D412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2411yescharacteristic
197C22×Dic11—24no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—24no—
207C22×Dic11—24no—
208C22×Dic11—44no—
209C22×Dic11—82no—
210C22×Dic11—82no—
211C2×Dic22—21no—
212C2×Dic22—21no—
213C2×Dic22—24no—
214C2×Dic22—22no—
215C2×Dic22—22no—
216C2×Dic22—22no—
217C2×Dic22—22no—
218C2×Dic22—82no—
219C2×Dic22C2412yes—
220C2×Dic22C2412yes—
221C11×M16—28no—
222C2×C8×C11—28no—
223C2×C8×C11—22no—
224C2×C8×C11—22no—
225C2×C8×C11—22no—
226C2×C8×C11#4114yes—
227C2×C8×C11C2412yes—
228C2×C8×C11C2412yes—
229C2×C8×C11C2412yes—
230C2×C8×C11C2412yes—
231C11×C4⋊C4C2×D414yes—
232C11×C22⋊C4C2×D414yes—
233C11×C22⋊C4C2×D414yes—
234C42×C11C2×D412yes—
235C42×C11C2412yes—
236C22⋊Dic11—24no—
237C22⋊Dic11—24no—
238C22⋊Dic11—24no—
239C22⋊Dic11—24no—
240C22⋊Dic11—24no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—24no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—24no—
249C4⋊Dic11—24no—
250C4⋊Dic11—24no—
251C4⋊Dic11C2412yes—
252C4⋊Dic11C2412yes—
253C4⋊Dic11C2412yes—
254C4⋊Dic11C2412yes—
255C4⋊Dic11C2412yes—
256C4⋊Dic11C2412yes—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265C4×Dic11—24no—
266C4×Dic11—24no—
267C4×Dic11—24no—
268Dic44—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×#467—111no—
281C2×#441—111no—
282C2×#435D1111yescharacteristic
283C2×#428—111no—
284C22×#106—111no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11#13714yes—
291C23×C11C22×D412yes—
292C23×C11C22×D412yes—
293C23×C11C22×D411yescharacteristic
294D4×C11—28no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11C22×D412yes—
306C2×C4×C11C22×D412yes—
307C2×C4×C11C22×D412yes—
308C2×C4×C11C22×D412yes—
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C2×#4112yes—
311C2×C4×C112−1+412yes—
312C2×C4×C11C2511yescharacteristic
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—42no—
322C2×Dic11—42no—
323C2×Dic11—48no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—84no—
331C2×Dic11—84no—
332Dic22—22no—
333Dic22—22no—
334Dic22—22no—
335Dic22—22no—
336Dic22—42no—
337Dic22—42no—
338Dic22—84no—
339C8×C11—22no—
340C8×C11—22no—
341C8×C11—22no—
342C8×C11C2×#4114yes—
343C22×Q16—111no—
344C22×M16C2×D1111yescharacteristic
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—111no—
359C2×C22⋊Q8—111no—
360C2×C22⋊Q8—221no—
361C2×C22⋊Q8—221no—
362C2×C4×Q8—111no—
363C2×C4×Q8—111no—
364C2×C4×D4—221no—
365C2×C4×D4C2×D1111yescharacteristic
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#467—118no—
380#441—118no—
381#435C2×D1118yes—
382#428—118no—
383C2×#107—111no—
384C2×#107—111no—
385C2×#107—111no—
386C2×#106—111no—
387C2×#106—111no—
388C2×#106—111no—
389C2×#106—111no—
390C2×#106—118no—
391C2×#106—111no—
392C2×#106—111no—
393C2×C4⋊C8C2×D1111yescharacteristic
394C2×#103—111no—
395C2×#103—111no—
396C2×#103—111no—
397C2×#103—111no—
398C2×#103—111no—
399C2×#103—111no—
400C2×C22⋊C8C2×D1111yescharacteristic
401C2×C22⋊C8C2×D1111yescharacteristic
402C2×#97C2×D1111yescharacteristic
403C22×C11—28no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—44no—
410C22×C11#54712yes—
411C22×C11C2×#13714yes—
412C22×C11C2×#13712yes—
413C22×C11#57712yes—
414C22×C11C23×D411yescharacteristic
415C4×C11—22no—
416C4×C11—22no—
417C4×C11—22no—
418C4×C11—22no—
419C4×C11#54712yes—
420C4×C11C22×#4111yescharacteristic
421C4×C11C2×2−1+411yescharacteristic
422Dic11—42no—
423Dic11—42no—
424Dic11—42no—
425Dic11—42no—
426Dic11—42no—
427Dic11—42no—
428Dic11—42no—
429Dic11—42no—
430C22×Q8—111no—
431C22×Q8—111no—
432C22×Q8—221no—
433C22×D4D4411yescharacteristic
434C23×C4—221no—
435C23×C4—221no—
436C23×C4—221no—
437C23×C4C22×D1111yescharacteristic
438C23×C4C22×D1111yescharacteristic
439C2×Q16—114no—
440C2×Q16—224no—
441C2×M16—24no—
442C2×M16C22×D1114yes—
443C22×C8—24no—
444C22×C8C22×D1111yescharacteristic
445C22×C8C22×D1114yes—
446C22×C8C22×D1111yescharacteristic
447C22×C8C22×D1111yescharacteristic
448C22×C8C22×D1111yescharacteristic
449C4⋊Q8—114no—
450C4⋊Q8—222no—
451#126—228no—
452#125—114no—
453#125—228no—
454#125—228no—
455#125—222no—
456#123—228no—
457C22⋊Q8—114no—
458C22⋊Q8—114no—
459C22⋊Q8—114no—
460C22⋊Q8—114no—
461C22⋊Q8—222no—
462C22⋊Q8—222no—
463C22⋊Q8—222no—
464C22⋊Q8—222no—
465C22⋊Q8—228no—
466C22⋊Q8—228no—
467C4×Q8—114no—
468C4×Q8—114no—
469C4×Q8—222no—
470C4×Q8—222no—
471C4×D4—228no—
472C4×D4D4414yes—
473C4×D4C22×D1114yes—
474#117—114no—
475#117—222no—
476#117—228no—
477C2×C4⋊C4—111no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4—114no—
483C2×C4⋊C4—114no—
484C2×C4⋊C4—114no—
485C2×C4⋊C4—111no—
486C2×C4⋊C4—221no—
487C2×C4⋊C4—221no—
488C2×C4⋊C4—221no—
489C2×C4⋊C4—222no—
490C2×C4⋊C4—222no—
491C2×C4⋊C4—222no—
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—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4D4411yescharacteristic
502C2×C22⋊C4—221no—
503C2×C22⋊C4—221no—
504C2×C22⋊C4—221no—
505C2×C22⋊C4—221no—
506C2×C22⋊C4—221no—
507C2×C22⋊C4D4411yescharacteristic
508C2×C22⋊C4D4411yescharacteristic
509C2×C42—221no—
510C2×C42—221no—
511C2×C42—221no—
512C2×C42C22×D1111yescharacteristic
513#107—114no—
514#107—114no—
515#107—114no—
516#106—114no—
517#106—114no—
518#106—114no—
519#106—114no—
520#106—114no—
521#106—114no—
522C4⋊C8C22×D1114yes—
523#103—114no—
524#103—114no—
525#103—114no—
526#103—114no—
527#103—114no—
528#103—114no—
529C22⋊C8C22×D1114yes—
530C22⋊C8C22×D1114yes—
531#97C22×D1114yes—
532C2×C11—24no—
533C2×C11—42no—
534C2×C11#334414yescomplemented
535C2×C11C2×#54711yescharacteristic
536C2×C11C22×#13711yescharacteristic
537C2×C11C2×#57711yescharacteristic
538C24C2×D4411yescharacteristic
539C24C2×D4411yescharacteristic
540C2×Q8—112no—
541C2×Q8—112no—
542C2×Q8—221no—
543C2×Q8—221no—
544C2×Q8—224no—
545C2×Q8—222no—
546C2×Q8—222no—
547C2×Q8—222no—
548C2×Q8—222no—
549C2×Q8—882no—
550C2×D4—24no—
551C2×D4C2×D4414yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—224no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—224no—
566C22×C4—224no—
567C22×C4—444no—
568C22×C4—882no—
569C22×C4—882no—
570C22×C4C2×D4412yes—
571C22×C4C2×D4412yes—
572C22×C4C2×D4411yescharacteristic
573C22×C4C2×D4411yescharacteristic
574C22×C4C2×D4411yescharacteristic
575C22×C4C2×D4411yescharacteristic
576C22×C4C23×D1112yes—
577C22×C4C23×D1112yes—
578C22×C4C23×D1111yescharacteristic
579Q16—228no—
580M16—28no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—28no—
585C2×C8#434114yes—
586C2×C8C23×D1112yes—
587C2×C8C23×D1112yes—
588C2×C8C23×D1112yes—
589C2×C8C23×D1112yes—
590C4⋊C4—112no—
591C4⋊C4—112no—
592C4⋊C4—112no—
593C4⋊C4—112no—
594C4⋊C4—112no—
595C4⋊C4—112no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—224no—
599C4⋊C4—224no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4—224no—
604C4⋊C4—221no—
605C4⋊C4—224no—
606C4⋊C4—224no—
607C4⋊C4—224no—
608C4⋊C4—224no—
609C4⋊C4—224no—
610C4⋊C4—224no—
611C4⋊C4—224no—
612C4⋊C4—224no—
613C4⋊C4—224no—
614C4⋊C4C2×D4414yes—
615C22⋊C4—224no—
616C22⋊C4—224no—
617C22⋊C4—224no—
618C22⋊C4—224no—
619C22⋊C4—224no—
620C22⋊C4C2×D4414yes—
621C22⋊C4C2×D4414yes—
622C42—224no—
623C42—224no—
624C42—224no—
625C42C2×D4412yes—
626C42C23×D1112yes—
627C11C2×#334411yescharacteristic, complemented, Sylow
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#6696214yes—
634C23C22×D4412yes—
635C23C22×D4412yes—
636C23C22×D4411yescharacteristic
637Q8—222no—
638Q8—222no—
639Q8—222no—
640Q8—222no—
641Q8—442no—
642Q8—442no—
643Q8—884no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—222no—
656C2×C4—222no—
657C2×C4—222no—
658C2×C4—222no—
659C2×C4—222no—
660C2×C4—222no—
661C2×C4—222no—
662C2×C4—222no—
663C2×C4—448no—
664C2×C4—442no—
665C2×C4—442no—
666C2×C4—442no—
667C2×C4—442no—
668C2×C4—442no—
669C2×C4—442no—
670C2×C4—442no—
671C2×C4—442no—
672C2×C4—884no—
673C2×C4—884no—
674C2×C4C22×D4412yes—
675C2×C4C22×D4412yes—
676C2×C4C22×D4412yes—
677C2×C4C22×D4412yes—
678C2×C4C22×D4411yescharacteristic
679C2×C4C2×#434112yes—
680C2×C4#6704312yes—
681C2×C4C24×D1111yescharacteristic
682C8—22no—
683C8—22no—
684C8—22no—
685C8C2×#434114yes—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#1062308612yes—
694C22C2×#6696214yes—
695C22C2×#6696212yes—
696C22#1062328212yes—
697C22C23×D4411yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—442no—
703C4—442no—
704C4—442no—
705C4—442no—
706C4—442no—
707C4—442no—
708C4—442no—
709C4—442no—
710C4#1062308612yes—
711C4C22×#434111yescharacteristic
712C4C2×#6704311yescharacteristic
713C2—24no—
714C2—42no—
715C2#1308107314yesdirect product factor
716C2C2×#1062308611yescharacteristic
717C2C22×#6696211yescharacteristic
718C2C2×#1062328211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenterC2×#435D11
hypocenterC11C2×#3344
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #13081073C2direct (N × H)
4. C2×#10622315C2semidirect
5. C2×#10622335C2semidirect
6. C2×#10622336C2semidirect
7. C2×#10622334C2semidirect
8. C2×#10622334C2semidirect
9. C2×#10622442C2semidirect
10. C2×#10622464C2semidirect
11. C2×#10622750C2semidirect
12. C2×#10622729C2semidirect
13. C2×#10622329C2semidirect
14. C2×#10622734C2semidirect
15. C22×#66881C2semidirect
50. #10622750C22semidirect
51. #10622734C22semidirect
52. #10622729C22semidirect
62. C2×#66881C22semidirect
69. #10622464C22semidirect
70. #10622442C22semidirect
71. #10622336C22semidirect
72. #10622335C22semidirect
73. #10622334C22semidirect
74. #10622334C22semidirect
75. #10622329C22semidirect
76. #10622315C22semidirect
534. C2×C11#3344semidirect
627. C11C2×#3344semidirect
715. C2#13081073direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×#106230722
#130810732
C2×#106223152
C2×#106223352
C2×#106223362
C2×#106223342
C2×#106224422
C2×#106224642
C2×#106227502
C2×#106227292
C2×#106223292
C2×#106227342
C22×#668812
C2×C11×#4352
C2×#334411