Finite Group Databasebeta

← C2×#13078848 #15622055

Subgroups — C2×#13078848 #15622055

Order 2816.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623174C211yesmaximal, characteristic
2C2×#10623047C211yesmaximal, characteristic, complemented
3#13078848C2116yesmaximal, direct product factor
4C2×#10622616C211yesmaximal, characteristic
5C2×#10622488C211yesmaximal, characteristic, complemented
6C2×#10622467C211yesmaximal, characteristic, complemented
7C2×#10622411C211yesmaximal, characteristic, complemented
8C2×#10622411C211yesmaximal, characteristic, complemented
9C2×#10622663C211yesmaximal, characteristic, complemented
10C2×#10622351C211yesmaximal, characteristic
11C2×#10622402C211yesmaximal, characteristic, complemented
12C2×#10622502C211yesmaximal, characteristic, complemented
13C2×#10622403C211yesmaximal, characteristic, complemented
14C2×#10622465C211yesmaximal, characteristic, complemented
15C2×#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#485C211yesmaximal, characteristic, complemented
17C23×Dic22C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×#67000C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C22×#4326C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×#66979C2211yescharacteristic
26C22×#4314C2211yescharacteristic
27C22×#4314C2211yescharacteristic
28#10623174—24no—
29#10623174C2218yes—
30#10623047—24no—
31#10623047C2218yescomplemented
32C2×#66951—21no—
33C2×#66950—21no—
34C2×#66946C2211yescharacteristic
35C2×#66941C2211yescharacteristic
36C2×#66940C2211yescharacteristic
37C2×#66940C2211yescharacteristic
38C2×#66940C2211yescharacteristic
39C2×#66940C2211yescharacteristic
40C2×#66938—21no—
41C2×#66936—21no—
42C2×#66930—21no—
43C2×#66930—21no—
44C2×C4×Dic22—21no—
45C2×C4×Dic22—21no—
46C11×#485C2218yescomplemented
47C2×C11×#107C2211yescharacteristic
48C2×C11×#106C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53C2×#66880C2211yescharacteristic
54C2×#66880C2211yescharacteristic
55C2×#66879C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×C8×Dic11C2211yescharacteristic
59#10622663C2218yescomplemented
60#10622616C2218yes—
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67#10622502C2218yescomplemented
68#10622488C2218yescomplemented
69#10622467C2218yescomplemented
70#10622465C2218yescomplemented
71#10622411C2218yescomplemented
72#10622411C2218yescomplemented
73#10622403C2218yescomplemented
74#10622402C2218yescomplemented
75#10622351C2218yes—
76#10622333C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11—21no—
80C23×Dic11—21no—
81C22×D44C2311yescharacteristic
82C22×C4×D11—21no—
83C22×Dic22—21no—
84C22×Dic22—22no—
85C22×Dic22—24no—
86C22×Dic22—24no—
87C22×Dic22—21no—
88C22×Dic22C2314yes—
89C22×Dic22C2311yescharacteristic
90C22×Dic22C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8C2314yes—
95C11×#117—22no—
96C11×#117C2314yes—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C42×C11—21no—
104C2×C22⋊Dic11D411yescharacteristic
105C2×C22⋊Dic11D411yescharacteristic
106#67000—22no—
107#67000C2314yes—
108Q8×Dic11—22no—
109Q8×Dic11C2314yes—
110C2×#4326—24no—
111C2×#4326—24no—
112C2×#4326C2314yes—
113C2×#4326C2314yes—
114#66983—22no—
115#66983C2314yes—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120#66979D414yes—
121#66979C2314yes—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11D411yescharacteristic
124C2×C4⋊Dic11D411yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×C4×Dic11—21no—
132C2×C4×Dic11—21no—
133C2×C4×Dic11—21no—
134C2×C4×Dic11—21no—
135C2×C4×Dic11—21no—
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C2×#4314—24no—
141C2×#4314—24no—
142C2×#4314C2314yes—
143C2×#4314C2314yes—
144#66951—28no—
145#66950—28no—
146#66946—22no—
147#66946C2314yes—
148#66941—22no—
149#66941C2314yes—
150#66940—22no—
151#66940—22no—
152#66940—22no—
153#66940—22no—
154#66940C2314yes—
155#66940C2314yes—
156#66940C2314yes—
157#66940C2314yes—
158#66938—28no—
159#66936—28no—
160#66930—28no—
161#66930—28no—
162C4×Dic22—28no—
163C4×Dic22—28no—
164C11×#107C2314yes—
165C11×#106C2314yes—
166C11×#103C2314yes—
167C11×#103C2314yes—
168C11×C22⋊C8C2314yes—
169C22⋊(C11⋊C8)C2314yes—
170#66880C2314yes—
171#66880C2314yes—
172#66879C2314yes—
173Dic11⋊C8C2314yes—
174Dic11⋊C8C2314yes—
175C8×Dic11C2314yes—
176#66874C2314yes—
177#66874C2314yes—
178#66873C2314yes—
179#66873C2314yes—
180#66872C2314yes—
181#66871C2314yes—
182C2×#3121—111nomaximal, Sylow
183C24×C11C2×D411yescharacteristic
184C23×D11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—22no—
187C2×Q8×C11—22no—
188C2×Q8×C11C2412yes—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—24no—
200C2×C22⋊D11—82no—
201C22×Dic11—28no—
202C22×Dic11—24no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11C2×D411yescharacteristic
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210C2×D44—21no—
211C2×D44—22no—
212C2×D44—22no—
213C2×D44C2412yes—
214C2×C4×D11—24no—
215C2×C4×D11—82no—
216C2×Dic22—28no—
217C2×Dic22—216no—
218C2×Dic22—28no—
219C2×Dic22—28no—
220C2×Dic22—24no—
221C2×Dic22—24no—
222C2×Dic22—21no—
223C2×Dic22—21no—
224C2×Dic22—22no—
225C2×Dic22—22no—
226C2×Dic22—82no—
227C2×Dic22#4114yes—
228C2×Dic22#4114yes—
229C2×Dic22C2412yes—
230C2×Dic22C2412yes—
231C2×C8×C11—22no—
232C2×C8×C11—22no—
233C2×C8×C11C2412yes—
234C2×C8×C11C2412yes—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4C2412yes—
240C11×C4⋊C4C2412yes—
241C11×C4⋊C4C2412yes—
242C11×C22⋊C4—24no—
243C11×C22⋊C4—24no—
244C42×C11—24no—
245C22⋊Dic11C2×D414yes—
246C22⋊Dic11C2×D414yes—
247#4326—28no—
248#4326—28no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11—21no—
255C4⋊Dic11C2×D414yes—
256C4⋊Dic11C2×D414yes—
257C4⋊Dic11C2412yes—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263C4×Dic11—24no—
264C4×Dic11—24no—
265C4×Dic11—24no—
266C4×Dic11—24no—
267C4×Dic11—24no—
268C4×Dic11C2×D412yes—
269C4×Dic11C2×D412yes—
270C4×Dic11C2412yes—
271C4×Dic11C2412yes—
272C2×C11⋊C8—22no—
273C2×C11⋊C8—22no—
274C2×C11⋊C8C2412yes—
275C2×C11⋊C8C2412yes—
276#4314—28no—
277#4314—28no—
278C2×#542—111no—
279C2×#519—111no—
280#3121—1116no—
281C2×#485D1111yescharacteristic, complemented
282C2×#482—111no—
283C2×#477—111no—
284C2×#475—111no—
285C2×#464—111no—
286C2×#464—111no—
287C2×#451—111no—
288C2×#448—111no—
289C2×#441—111no—
290C2×#440—111no—
291C2×C4×Q16—111no—
292C2×C4×SD16—111no—
293C2×#433—111no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11C22×D412yes—
298C23×C11C22×D411yescharacteristic
299C22×D11—22no—
300C22×D11—42no—
301C22×D11—42no—
302C22×D11—42no—
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—42no—
306C2×C4×C11—22no—
307C2×C4×C11—24no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11C22×D412yes—
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C2×#4112yes—
321C2×C4×C11C2×#4112yes—
322C2×C4×C11C2511yescharacteristic
323C22⋊D11—84no—
324C2×Dic11—216no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—42no—
335C2×Dic11C22×D412yes—
336C2×Dic11C22×D412yes—
337C2×Dic11C22×D412yes—
338C2×Dic11C22×D412yes—
339D44—22no—
340D44—22no—
341D44—42no—
342C4×D11—84no—
343Dic22—216no—
344Dic22—24no—
345Dic22—24no—
346Dic22—22no—
347Dic22—22no—
348Dic22—84no—
349Dic22C2×#4114yes—
350Dic22C2×#4114yes—
351C8×C11—22no—
352C8×C11—22no—
353C11⋊C8—22no—
354C11⋊C8—22no—
355C23×Q8—111no—
356C22×Q16—111no—
357C22×Q16—111no—
358C22×SD16—111no—
359C22×SD16—111no—
360#542—118no—
361#542—224no—
362C2×C4⋊Q8—111no—
363C2×#126—221no—
364C2×#124—111no—
365C2×#124—221no—
366C2×#123—221no—
367C2×C22⋊Q8—221no—
368C2×C22⋊Q8C2×D1111yescharacteristic
369C2×#121—111no—
370#519—118no—
371#519—224no—
372C2×C4×Q8—111no—
373C2×C4×Q8—111no—
374C2×C4×Q8—111no—
375C2×C4×Q8—111no—
376C2×C4×Q8—111no—
377C2×C4×Q8—221no—
378C2×C4×Q8—221no—
379C2×C4×D4—111no—
380C2×#117—111no—
381C2×#117—221no—
382C2×#117—221no—
383C2×#117C2×D1111yescharacteristic
384#485C2×D1118yescomplemented
385#482—118no—
386#477—118no—
387#475—118no—
388#464—118no—
389#464—118no—
390#451—118no—
391#448—118no—
392#441—118no—
393#440—118no—
394C4×Q16—118no—
395C4×SD16—118no—
396#433—118no—
397C2×#107—111no—
398C2×#107C2×D1111yescharacteristic
399C2×#106—111no—
400C2×#106C2×D1111yescharacteristic
401C2×C4⋊C8—111no—
402C2×C4⋊C8—111no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103C2×D1111yescharacteristic
408C2×#103C2×D1111yescharacteristic
409C2×#102—111no—
410C2×#102—111no—
411C2×C22⋊C8—111no—
412C2×C22⋊C8C2×D1111yescharacteristic
413C2×#97—111no—
414C2×C4×C8—111no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—44no—
419C22×C11#52512yes—
420C22×C11#57712yes—
421C22×C11#57812yes—
422C22×C11C23×D411yescharacteristic
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—84no—
427C4×C11—22no—
428C4×C11—42no—
429C4×C11—42no—
430C4×C11—42no—
431C4×C11—42no—
432C4×C11#52512yes—
433C4×C11C22×#4111yescharacteristic
434C4×C11C22×#4111yescharacteristic
435Dic11—24no—
436Dic11—24no—
437Dic11—22no—
438Dic11—22no—
439Dic11—22no—
440Dic11—22no—
441Dic11—42no—
442C22×Q8—111no—
443C22×Q8—111no—
444C22×Q8—114no—
445C22×Q8—221no—
446C22×Q8—224no—
447C22×Q8—224no—
448C22×Q8—221no—
449C22×Q8—222no—
450C22×Q8C22×D1111yescharacteristic
451C22×D4—111no—
452C22×D4—221no—
453C23×C4—221no—
454C23×C4—221no—
455C23×C4C22×D1111yescharacteristic
456C2×Q16—114no—
457C2×Q16—114no—
458C2×Q16—224no—
459C2×Q16—224no—
460C2×SD16—114no—
461C2×SD16—114no—
462C2×SD16—224no—
463C2×SD16—224no—
464C22×C8—111no—
465C22×C8—111no—
466C22×C8C22×D1111yescharacteristic
467C22×C8C22×D1111yescharacteristic
468C4⋊Q8—114no—
469C4⋊Q8—222no—
470#126—228no—
471#124—114no—
472#124—222no—
473#124—228no—
474#123—228no—
475C22⋊Q8—22no—
476C22⋊Q8—228no—
477C22⋊Q8C22×D1114yes—
478#121—114no—
479#121—222no—
480C4×Q8—114no—
481C4×Q8—114no—
482C4×Q8—114no—
483C4×Q8—114no—
484C4×Q8—114no—
485C4×Q8—228no—
486C4×Q8—228no—
487C4×Q8—222no—
488C4×Q8—222no—
489C4×Q8—222no—
490C4×Q8—222no—
491C4×Q8—222no—
492C4×D4—114no—
493C4×D4—222no—
494#117—22no—
495#117—114no—
496#117—114no—
497#117—228no—
498#117—228no—
499#117C22×D1114yes—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4C22×D1111yescharacteristic
511C2×C4⋊C4C22×D1111yescharacteristic
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—111no—
516C2×C22⋊C4—111no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C42—21no—
522C2×C42—111no—
523C2×C42—111no—
524C2×C42—221no—
525C2×C42—221no—
526C2×C42—221no—
527C2×C42—221no—
528C2×C42—221no—
529#107—114no—
530#107C22×D1114yes—
531#106—114no—
532#106C22×D1114yes—
533C4⋊C8—114no—
534C4⋊C8—114no—
535#103—114no—
536#103—114no—
537#103—114no—
538#103—114no—
539#103C22×D1114yes—
540#103C22×D1114yes—
541#102—114no—
542#102—114no—
543C22⋊C8—114no—
544C22⋊C8C22×D1114yes—
545#97—114no—
546C4×C8—114no—
547C2×C11—42no—
548C2×C11#312114yescomplemented
549C2×C11C2×#52511yescharacteristic
550C2×C11C2×#57711yescharacteristic
551C2×C11C2×#57811yescharacteristic
552D11—82no—
553C24—221no—
554C24D4×D1111yescharacteristic
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—114no—
559C2×Q8—114no—
560C2×Q8—112no—
561C2×Q8—112no—
562C2×Q8—224no—
563C2×Q8—228no—
564C2×Q8—228no—
565C2×Q8—228no—
566C2×Q8—2216no—
567C2×Q8—224no—
568C2×Q8—221no—
569C2×Q8—221no—
570C2×Q8—222no—
571C2×Q8—222no—
572C2×Q8—882no—
573C2×Q8C23×D1112yes—
574C2×D4—112no—
575C2×D4—224no—
576C2×D4—221no—
577C2×D4—222no—
578C2×D4—222no—
579C2×D4—882no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—111no—
587C22×C4—111no—
588C22×C4—111no—
589C22×C4—111no—
590C22×C4—224no—
591C22×C4—228no—
592C22×C4—224no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—882no—
597C22×C4D4×D1112yes—
598C22×C4D4×D1111yescharacteristic
599C22×C4C23×D1112yes—
600C22×C4C23×D1111yescharacteristic
601Q16—228no—
602Q16—228no—
603SD16—228no—
604SD16—228no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—112no—
608C2×C8—112no—
609C2×C8—222no—
610C2×C8—222no—
611C2×C8C23×D1112yes—
612C2×C8C23×D1112yes—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—114no—
618C4⋊C4—114no—
619C4⋊C4—112no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—224no—
626C4⋊C4—221no—
627C4⋊C4C23×D1112yes—
628C4⋊C4C23×D1112yes—
629C4⋊C4C23×D1112yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—114no—
633C22⋊C4—114no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C42—24no—
639C42—112no—
640C42—112no—
641C42—112no—
642C42—112no—
643C42—224no—
644C42—224no—
645C42—224no—
646C42—224no—
647C42—224no—
648C11C2×#312111yescharacteristic, complemented, Sylow
649C23—22no—
650C23—22no—
651C23—22no—
652C23—222no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23C2×D4×D1112yes—
657C23C2×D4×D1111yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—114no—
662Q8—114no—
663Q8—2216no—
664Q8—224no—
665Q8—224no—
666Q8—222no—
667Q8—222no—
668Q8—884no—
669D4—222no—
670D4—222no—
671D4—442no—
672D4—884no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—112no—
686C2×C4—112no—
687C2×C4—112no—
688C2×C4—112no—
689C2×C4—2216no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—224no—
695C2×C4—224no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—442no—
700C2×C4—884no—
701C2×C4C2×D4×D1112yes—
702C2×C4C2×D4×D1111yescharacteristic
703C2×C4#41×D1112yes—
704C2×C4#41×D1112yes—
705C2×C4C24×D1111yescharacteristic
706C8—22no—
707C8—22no—
708C8—222no—
709C8—222no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—442no—
715C22—442no—
716C22—442no—
717C22—884no—
718C22#1062318712yes—
719C22#1062330112yes—
720C22#1062331012yes—
721C22C22×D4×D1111yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—222no—
728C4—222no—
729C4—222no—
730C4—222no—
731C4—224no—
732C4—224no—
733C4—442no—
734C4#1062318712yes—
735C4C2×#41×D1111yescharacteristic
736C4C2×#41×D1111yescharacteristic
737C2—42no—
738C2—882no—
739C2#1307884814yesdirect product factor
740C2C2×#1062318711yescharacteristic
741C2C2×#1062330111yescharacteristic
742C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#485C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#485D11
hypocenterC11C2×#3121
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×#10623047C2semidirect
3. #13078848C2direct (N × H)
5. C2×#10622488C2semidirect
6. C2×#10622467C2semidirect
7. C2×#10622411C2semidirect
8. C2×#10622411C2semidirect
9. C2×#10622663C2semidirect
11. C2×#10622402C2semidirect
12. C2×#10622502C2semidirect
13. C2×#10622403C2semidirect
14. C2×#10622465C2semidirect
15. C2×#10622333C2semidirect
16. C2×C11×#485C2semidirect
31. #10623047C22semidirect
46. C11×#485C22semidirect
59. #10622663C22semidirect
67. #10622502C22semidirect
68. #10622488C22semidirect
69. #10622467C22semidirect
70. #10622465C22semidirect
71. #10622411C22semidirect
72. #10622411C22semidirect
73. #10622403C22semidirect
74. #10622402C22semidirect
76. #10622333C22semidirect
281. C2×#485D11semidirect
384. #485C2×D11semidirect
548. C2×C11#3121semidirect
648. C11C2×#3121semidirect
739. C2#13078848direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231742
C2×#106230472
#130788482
C2×#106226162
C2×#106224882
C2×#106224672
C2×#106224112
C2×#106226632
C2×#106223512
C2×#106224022
C2×#106225022
C2×#106224032
C2×#106224652
C2×#106223332
C2×C11×#4852
C2×#312111