Finite Group Databasebeta

← C2×#13079914 #15626010

Subgroups — C2×#13079914 #15626010

Order 2816.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623065C211yesmaximal, characteristic
2#13079914C2116yesmaximal, direct product factor
3C2×#10622678C211yesmaximal, characteristic, complemented
4C2×#10622692C211yesmaximal, characteristic, complemented
5C2×#10622702C211yesmaximal, characteristic, complemented
6C2×#10622681C211yesmaximal, characteristic, complemented
7C2×#10622581C211yesmaximal, characteristic
8C2×#10622609C211yesmaximal, characteristic, complemented
9C2×#10622616C211yesmaximal, characteristic
10C2×#10622584C211yesmaximal, characteristic, complemented
11C2×#10622676C211yesmaximal, characteristic, complemented
12C2×#10622707C211yesmaximal, characteristic, complemented
13C2×#10622679C211yesmaximal, characteristic, complemented
14C2×#10622697C211yesmaximal, characteristic, complemented
15C2×#10622613C211yesmaximal, characteristic, complemented
16C2×C11×#544C211yesmaximal, characteristic, complemented
17C11×#544—24no—
18C11×#544C2218yescomplemented
19C2×C11×C4⋊Q8—21no—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C11×#125—21no—
23C2×C11×#125C2211yescharacteristic
24C2×C11×#125C2211yescharacteristic
25C2×C11×C22⋊Q8—21no—
26C2×C11×C22⋊Q8—21no—
27C2×C11×#117C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C2×#66983C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32#10623065—24no—
33#10623065C2218yes—
34C2×#66951—21no—
35C2×#66949—21no—
36C2×#66938—21no—
37C2×#66936—21no—
38C2×#66928C2211yescharacteristic
39C2×C4×D44C2211yescharacteristic
40C2×#66922C2211yescharacteristic
41C2×C4×Dic22C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44#10622707C2218yescomplemented
45#10622702C2218yescomplemented
46#10622697C2218yescomplemented
47#10622692C2218yescomplemented
48#10622681C2218yescomplemented
49#10622679C2218yescomplemented
50#10622678C2218yescomplemented
51#10622676C2218yescomplemented
52#10622616C2218yes—
53#10622613C2218yescomplemented
54#10622609C2218yescomplemented
55#10622584C2218yescomplemented
56C2×#66874C2211yescharacteristic
57C2×#66874C2211yescharacteristic
58C2×#66874C2211yescharacteristic
59C2×#66874C2211yescharacteristic
60#10622581C2218yes—
61C2×#66873C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75C2×#66867C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×Q8×C11—21no—
78C22×Q8×C11—21no—
79C23×C4×C11—21no—
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×Dic22—21no—
85C22×Dic22C2311yescharacteristic
86C11×C4⋊Q8—28no—
87C11×C4⋊Q8—22no—
88C11×C4⋊Q8—22no—
89C11×C4⋊Q8C2314yes—
90C11×C4⋊Q8C2314yes—
91C11×#125—28no—
92C11×#125—22no—
93C11×#125—22no—
94C11×#125C2314yes—
95C11×#125C2314yes—
96C11×C22⋊Q8—28no—
97C11×C22⋊Q8—28no—
98C11×#117—22no—
99C11×#117D414yes—
100C11×#117C2314yes—
101C11×#117C2314yes—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—22no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4D411yescharacteristic
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2314yes—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4D411yescharacteristic
119C2×C11×C22⋊C4D411yescharacteristic
120C2×C42×C11—21no—
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C2×C22⋊Dic11—21no—
124#66983—22no—
125#66983C2314yes—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×C4⋊Dic11—21no—
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133#66977—22no—
134#66977C2314yes—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×C4×Dic11—21no—
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142#66951—28no—
143#66949—28no—
144#66938—28no—
145#66936—28no—
146#66928—22no—
147#66928C2314yes—
148C4×D44—22no—
149C4×D44C2314yes—
150#66922—22no—
151#66922C2314yes—
152C4×Dic22—22no—
153C4×Dic22C2314yes—
154C22⋊(C11⋊C8)C2314yes—
155C22⋊(C11⋊C8)C2314yes—
156#66874C2314yes—
157#66874C2314yes—
158#66874C2314yes—
159#66874C2314yes—
160#66873C2314yes—
161#66873C2314yes—
162#66873C2314yes—
163#66873C2314yes—
164#66872C2314yes—
165#66872C2314yes—
166#66872C2314yes—
167#66872C2314yes—
168#66872C2314yes—
169#66872C2314yes—
170#66871C2314yes—
171#66871C2314yes—
172C4⋊(C11⋊C8)C2314yes—
173C4⋊(C11⋊C8)C2314yes—
174#66867C2314yes—
175C4×C11⋊C8C2314yes—
176C2×#3244—111nomaximal, Sylow
177C24×C11C2×D411yescharacteristic
178C23×D11—21no—
179C2×Q8×C11—24no—
180C2×Q8×C11—24no—
181C2×Q8×C11—82no—
182C2×Q8×C11—82no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—24no—
190C22×C4×C11—82no—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2412yes—
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—24no—
200C2×C22⋊D11—82no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C2×D44—21no—
205C2×D44—22no—
206C2×D44—22no—
207C2×D44C2412yes—
208C2×C4×D11—24no—
209C2×C4×D11—82no—
210C2×Dic22—21no—
211C2×Dic22—24no—
212C2×Dic22—22no—
213C2×Dic22—22no—
214C2×Dic22—82no—
215C2×Dic22C2412yes—
216C11×C4⋊C4—24no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—24no—
220C11×C4⋊C4—24no—
221C11×C4⋊C4—24no—
222C11×C4⋊C4—24no—
223C11×C4⋊C4—24no—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4C2×D414yes—
228C11×C4⋊C4C2×D414yes—
229C11×C4⋊C4C2412yes—
230C11×C4⋊C4C2412yes—
231C11×C4⋊C4C2412yes—
232C11×C4⋊C4C2412yes—
233C11×C22⋊C4—24no—
234C11×C22⋊C4C2×D414yes—
235C11×C22⋊C4C2×D414yes—
236C42×C11—24no—
237C42×C11C2×D412yes—
238C42×C11C2×D412yes—
239C42×C11C2412yes—
240C42×C11C2412yes—
241C22⋊Dic11—24no—
242(C2×D11)⋊C4—24no—
243(C2×D11)⋊C4—24no—
244(C2×D11)⋊C4—24no—
245(C2×D11)⋊C4—24no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—24no—
249C4⋊Dic11C2412yes—
250C4⋊Dic11C2412yes—
251Dic11⋊C4—24no—
252Dic11⋊C4—24no—
253C4×Dic11—24no—
254C2×C11⋊C8—22no—
255C2×C11⋊C8—22no—
256C2×C11⋊C8—22no—
257C2×C11⋊C8—22no—
258C2×C11⋊C8C2412yes—
259C2×C11⋊C8C2412yes—
260C2×C11⋊C8C2412yes—
261C2×C11⋊C8C2412yes—
262C2×#544D1111yescharacteristic, complemented
263C2×#542—111no—
264#3244—1116no—
265C2×#501—111no—
266C2×#498—111no—
267C2×#489—111no—
268C2×#488—111no—
269C2×#481—111no—
270C2×#485—111no—
271C2×#482—111no—
272C2×#483—111no—
273C2×#479—111no—
274C2×#475—111no—
275C2×#478—111no—
276C2×#476—111no—
277C2×#433—111no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11C22×D412yes—
282C23×C11C22×D411yescharacteristic
283C22×D11—22no—
284C22×D11—42no—
285C22×D11—42no—
286C22×D11—42no—
287Q8×C11—84no—
288Q8×C11—84no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—24no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—84no—
306C2×C4×C11C22×D412yes—
307C2×C4×C11C22×D412yes—
308C2×C4×C11C22×D412yes—
309C2×C4×C11C22×D412yes—
310C2×C4×C11C22×D412yes—
311C2×C4×C11C22×D411yescharacteristic
312C2×C4×C112−1+412yes—
313C2×C4×C112−1+412yes—
314C2×C4×C11C2511yescharacteristic
315C22⋊D11—84no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—42no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322D44—22no—
323D44—22no—
324D44—42no—
325C4×D11—84no—
326Dic22—22no—
327Dic22—22no—
328Dic22—42no—
329Dic22—84no—
330C11⋊C8—22no—
331C11⋊C8—22no—
332C11⋊C8—22no—
333C11⋊C8—22no—
334#544—24no—
335#544C2×D1118yescomplemented
336#542—118no—
337#542—224no—
338C2×C4⋊Q8—21no—
339C2×C4⋊Q8—111no—
340C2×C4⋊Q8C2×D1111yescharacteristic
341C2×C4⋊Q8C2×D1111yescharacteristic
342C2×#126—221no—
343C2×#125—21no—
344C2×#125C2×D1111yescharacteristic
345C2×#125C2×D1111yescharacteristic
346C2×#124—111no—
347C2×#124—221no—
348C2×#123—221no—
349C2×C22⋊Q8—21no—
350C2×C22⋊Q8—21no—
351C2×C22⋊Q8—111no—
352C2×C22⋊Q8—221no—
353C2×#121—111no—
354C2×C4×Q8—111no—
355C2×C4×D4—111no—
356C2×#117C2×D1111yescharacteristic
357C2×#117C2×D1111yescharacteristic
358C22×C4⋊C4C2×D1111yescharacteristic
359#501—118no—
360#498—118no—
361#489—118no—
362#488—118no—
363#485—118no—
364#483—118no—
365#482—118no—
366#481—118no—
367#479—118no—
368#478—118no—
369#476—118no—
370#475—118no—
371#433—118no—
372C2×#107—111no—
373C2×#107—111no—
374C2×#106—111no—
375C2×#106—111no—
376C2×#106—111no—
377C2×#106—111no—
378C2×#106—111no—
379C2×#106—111no—
380C2×C4⋊C8—111no—
381C2×C4⋊C8—111no—
382C2×#103—111no—
383C2×#103—111no—
384C2×#103—111no—
385C2×#103—111no—
386C2×#102—111no—
387C2×#102—111no—
388C2×#102—111no—
389C2×#102—111no—
390C2×C22⋊C8—111no—
391C2×C22⋊C8—111no—
392C2×#97—111no—
393C2×C4×C8—111no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—44no—
398C22×C11#53612yes—
399C22×C11#57712yes—
400C22×C11#57712yes—
401C22×C11C23×D411yescharacteristic
402C2×D11—42no—
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—84no—
406C4×C11—22no—
407C4×C11—22no—
408C4×C11—22no—
409C4×C11—22no—
410C4×C11—22no—
411C4×C11—42no—
412C4×C11—42no—
413C4×C11—42no—
414C4×C11—42no—
415C4×C11#53612yes—
416C4×C11C2×2−1+411yescharacteristic
417C4×C11C2×2−1+411yescharacteristic
418Dic11—42no—
419Dic11—42no—
420Dic11—42no—
421C22×Q8—21no—
422C22×Q8—21no—
423C22×Q8—111no—
424C22×Q8—221no—
425C22×D4—111no—
426C22×D4—221no—
427C23×C4—21no—
428C23×C4—221no—
429C23×C4C22×D1111yescharacteristic
430C22×C8—111no—
431C22×C8—111no—
432C22×C8—111no—
433C22×C8—111no—
434C4⋊Q8—28no—
435C4⋊Q8—22no—
436C4⋊Q8—22no—
437C4⋊Q8—114no—
438C4⋊Q8—222no—
439C4⋊Q8C22×D1114yes—
440C4⋊Q8C22×D1114yes—
441#126—228no—
442#125—28no—
443#125—22no—
444#125—22no—
445#125C22×D1114yes—
446#125C22×D1114yes—
447#124—114no—
448#124—228no—
449#124—222no—
450#123—228no—
451C22⋊Q8—28no—
452C22⋊Q8—28no—
453C22⋊Q8—114no—
454C22⋊Q8—222no—
455C22⋊Q8—228no—
456#121—114no—
457#121—222no—
458C4×Q8—114no—
459C4×Q8—222no—
460C4×D4—114no—
461C4×D4—222no—
462#117—22no—
463#117C22⋊D1114yes—
464#117C22×D1114yes—
465#117C22×D1114yes—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4C22⋊D1111yescharacteristic
480C2×C4⋊C4C22⋊D1111yescharacteristic
481C2×C4⋊C4C22×D1111yescharacteristic
482C2×C4⋊C4C22×D1111yescharacteristic
483C2×C4⋊C4C22×D1114yes—
484C2×C4⋊C4C22×D1111yescharacteristic
485C2×C4⋊C4C22×D1111yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4—221no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4—221no—
492C2×C22⋊C4C22⋊D1111yescharacteristic
493C2×C22⋊C4C22⋊D1111yescharacteristic
494C2×C42—21no—
495C2×C42—221no—
496C2×C42C22×D1111yescharacteristic
497C2×C42C22×D1111yescharacteristic
498#107—114no—
499#107—114no—
500#106—114no—
501#106—114no—
502#106—114no—
503#106—114no—
504#106—114no—
505#106—114no—
506C4⋊C8—114no—
507C4⋊C8—114no—
508#103—114no—
509#103—114no—
510#103—114no—
511#103—114no—
512#102—114no—
513#102—114no—
514#102—114no—
515#102—114no—
516C22⋊C8—114no—
517C22⋊C8—114no—
518#97—114no—
519C4×C8—114no—
520C2×C11—42no—
521C2×C11#324414yescomplemented
522C2×C11C2×#53611yescharacteristic
523C2×C11C2×#57711yescharacteristic
524C2×C11C2×#57711yescharacteristic
525D11—82no—
526C24—221no—
527C24C2×C22⋊D1111yescharacteristic
528C2×Q8—24no—
529C2×Q8—24no—
530C2×Q8—82no—
531C2×Q8—82no—
532C2×Q8—112no—
533C2×Q8—221no—
534C2×Q8—224no—
535C2×Q8—222no—
536C2×Q8—222no—
537C2×Q8—882no—
538C2×D4—112no—
539C2×D4—224no—
540C2×D4—222no—
541C2×D4—222no—
542C2×D4—221no—
543C2×D4—882no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—82no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—224no—
556C22×C4—882no—
557C22×C4C2×C22⋊D1112yes—
558C22×C4C2×C22⋊D1111yescharacteristic
559C22×C4C2×C22⋊D1111yescharacteristic
560C22×C4C2×C22⋊D1111yescharacteristic
561C22×C4C2×C22⋊D1111yescharacteristic
562C22×C4C2×C22⋊D1111yescharacteristic
563C22×C4C23×D1112yes—
564C22×C4C23×D1111yescharacteristic
565C2×C8—112no—
566C2×C8—112no—
567C2×C8—112no—
568C2×C8—112no—
569C2×C8—222no—
570C2×C8—222no—
571C2×C8—222no—
572C2×C8—222no—
573C4⋊C4—24no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—112no—
585C4⋊C4—112no—
586C4⋊C4—221no—
587C4⋊C4—221no—
588C4⋊C4—224no—
589C4⋊C4—224no—
590C4⋊C4—224no—
591C4⋊C4C2×C22⋊D1114yes—
592C4⋊C4C2×C22⋊D1114yes—
593C4⋊C4C23×D1112yes—
594C4⋊C4C23×D1112yes—
595C4⋊C4C23×D1112yes—
596C4⋊C4C23×D1112yes—
597C22⋊C4—24no—
598C22⋊C4—224no—
599C22⋊C4—224no—
600C22⋊C4—224no—
601C22⋊C4—224no—
602C22⋊C4—224no—
603C22⋊C4C2×C22⋊D1114yes—
604C22⋊C4C2×C22⋊D1114yes—
605C42—24no—
606C42—224no—
607C42C2×C22⋊D1112yes—
608C42C2×C22⋊D1112yes—
609C42C23×D1112yes—
610C42C23×D1112yes—
611C11C2×#324411yescharacteristic, complemented, Sylow
612C23—22no—
613C23—22no—
614C23—22no—
615C23—222no—
616C23—442no—
617C23—442no—
618C23—442no—
619C23C22×C22⋊D1112yes—
620C23C22×C22⋊D1111yescharacteristic
621Q8—84no—
622Q8—84no—
623Q8—222no—
624Q8—222no—
625Q8—442no—
626Q8—884no—
627D4—222no—
628D4—222no—
629D4—442no—
630D4—884no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—84no—
648C2×C4—222no—
649C2×C4—222no—
650C2×C4—222no—
651C2×C4—442no—
652C2×C4—442no—
653C2×C4—442no—
654C2×C4—884no—
655C2×C4#6704012yes—
656C2×C4#6704012yes—
657C2×C4C22×C22⋊D1112yes—
658C2×C4C22×C22⋊D1112yes—
659C2×C4C22×C22⋊D1112yes—
660C2×C4C22×C22⋊D1112yes—
661C2×C4C22×C22⋊D1112yes—
662C2×C4C22×C22⋊D1111yescharacteristic
663C2×C4C24×D1111yescharacteristic
664C8—222no—
665C8—222no—
666C8—222no—
667C8—222no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—442no—
673C22—442no—
674C22—442no—
675C22—884no—
676C22#1062334712yes—
677C22#1062336712yes—
678C22#1062336812yes—
679C22C23×C22⋊D1111yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—442no—
690C4—442no—
691C4—442no—
692C4#1062334712yes—
693C4C2×#6704011yescharacteristic
694C4C2×#6704011yescharacteristic
695C2—42no—
696C2—882no—
697C2#1307991414yesdirect product factor
698C2C2×#1062334711yescharacteristic
699C2C2×#1062336811yescharacteristic
700C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#544C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#544D11
hypocenterC11C2×#3244
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #13079914C2direct (N × H)
3. C2×#10622678C2semidirect
4. C2×#10622692C2semidirect
5. C2×#10622702C2semidirect
6. C2×#10622681C2semidirect
8. C2×#10622609C2semidirect
10. C2×#10622584C2semidirect
11. C2×#10622676C2semidirect
12. C2×#10622707C2semidirect
13. C2×#10622679C2semidirect
14. C2×#10622697C2semidirect
15. C2×#10622613C2semidirect
16. C2×C11×#544C2semidirect
18. C11×#544C22semidirect
44. #10622707C22semidirect
45. #10622702C22semidirect
46. #10622697C22semidirect
47. #10622692C22semidirect
48. #10622681C22semidirect
49. #10622679C22semidirect
50. #10622678C22semidirect
51. #10622676C22semidirect
53. #10622613C22semidirect
54. #10622609C22semidirect
55. #10622584C22semidirect
262. C2×#544D11semidirect
335. #544C2×D11semidirect
521. C2×C11#3244semidirect
611. C11C2×#3244semidirect
697. C2#13079914direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230652
#130799142
C2×#106226782
C2×#106226922
C2×#106227022
C2×#106226812
C2×#106225812
C2×#106226092
C2×#106226162
C2×#106225842
C2×#106226762
C2×#106227072
C2×#106226792
C2×#106226972
C2×#106226132
C2×C11×#5442
C2×#324411