Finite Group Databasebeta

← C2×#13079323 #15623694

Subgroups — C2×#13079323 #15623694

Order 2816.

1998 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic, complemented
2C2×#10623111C211yesmaximal, characteristic
3#13079323C2116yesmaximal, direct product factor
4C2×#10622469C211yesmaximal, characteristic, complemented
5C2×#10622803C211yesmaximal, characteristic, complemented
6C2×#10622410C211yesmaximal, characteristic, complemented
7C2×#10622408C211yesmaximal, characteristic, complemented
8C2×#10622426C211yesmaximal, characteristic, complemented
9C2×#10622801C211yesmaximal, characteristic, complemented
10C2×#10622420C211yesmaximal, characteristic
11C2×#10622477C211yesmaximal, characteristic
12C2×#10622643C211yesmaximal, characteristic, complemented
13C2×#10622323C211yesmaximal, characteristic, complemented
14C2×#10622639C211yesmaximal, characteristic, complemented
15C2×D11×#97C211yesmaximal, characteristic, complemented
16C2×C11×#441C211yesmaximal, characteristic, complemented
17C22×C11×Q16C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×#67000C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C2×#66997C2211yescharacteristic
24C22×#4326C2211yescharacteristic
25C22×#4325C2211yescharacteristic
26C22×#4314C2211yescharacteristic
27C22×C8×D11C2211yescharacteristic
28C22×C8×D11C2211yescharacteristic
29#10623111—24no—
30#10623111C2218yes—
31#10623109—24no—
32#10623109C2218yescomplemented
33C2×#66951—21no—
34C2×#66950C2211yescharacteristic
35C2×#66949—21no—
36C2×#66948C2211yescharacteristic
37C2×#66947—21no—
38C2×#66943C2211yescharacteristic
39C2×#66942—21no—
40C2×#66941C2211yescharacteristic
41C2×C4×D44—21no—
42C2×C4×D44C2211yescharacteristic
43C2×#66925—21no—
44C2×#66925—21no—
45C2×C42×D11C2211yescharacteristic
46C2×C4×Dic22—21no—
47C2×C4×Dic22C2211yescharacteristic
48C11×#441C2218yescomplemented
49C2×C11×#106C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#103C2211yescharacteristic
52C2×C11×#97C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55#10622803C2218yescomplemented
56#10622801C2218yescomplemented
57C2×#66885C2211yescharacteristic
58C2×#66882C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60C2×#66879C2211yescharacteristic
61C2×#66879C2211yescharacteristic
62#10622643C2218yescomplemented
63#10622639C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×#66867C2211yescharacteristic
69#10622477C2218yes—
70#10622469C2218yescomplemented
71#10622426C2218yescomplemented
72#10622420C2218yes—
73#10622410C2218yescomplemented
74#10622408C2218yescomplemented
75#10622323C2218yescomplemented
76D11×#97C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D44—21no—
80C22×D44C2311yescharacteristic
81C22×C4×D11—21no—
82C22×C4×D11D411yescharacteristic
83C22×C4×D11D411yescharacteristic
84C22×C4×D11C2311yescharacteristic
85C22×Dic22—21no—
86C22×Dic22C2311yescharacteristic
87C2×C11×Q16—24no—
88C2×C11×Q16C2314yes—
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C4×Q8×C11—22no—
92C4×Q8×C11—22no—
93C4×Q8×C11C2314yes—
94C4×Q8×C11C2314yes—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C42×C11—21no—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102#67000—22no—
103#67000C2314yes—
104#66999—22no—
105#66999—22no—
106#66999C2314yes—
107#66999C2314yes—
108#66997—22no—
109#66997C2314yes—
110C2×#4326—24no—
111C2×#4326C2314yes—
112C2×#4325—24no—
113C2×#4325C2314yes—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×C4×Dic11—21no—
133C2×C4×Dic11D411yescharacteristic
134C2×C4×Dic11D411yescharacteristic
135C2×C4×Dic11C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C2×#4314—24no—
139C2×#4314C2314yes—
140C2×C8×D11—24no—
141C2×C8×D11—24no—
142C2×C8×D11C2314yes—
143C2×C8×D11C2314yes—
144#66951—28no—
145#66950—22no—
146#66950C2314yes—
147#66949—28no—
148#66948—22no—
149#66948C2314yes—
150#66947—28no—
151#66943—22no—
152#66943C2314yes—
153#66942—28no—
154#66941—22no—
155#66941C2314yes—
156C4×D44—28no—
157C4×D44—22no—
158C4×D44C2314yes—
159#66925—28no—
160#66925—28no—
161C42×D11D414yes—
162C42×D11C2314yes—
163C4×Dic22—22no—
164C4×Dic22—28no—
165C4×Dic22C2314yes—
166C11×#106C2314yes—
167C11×#103C2314yes—
168C11×#103C2314yes—
169C11×#97C2314yes—
170#66899C2314yes—
171#66899C2314yes—
172#66885C2314yes—
173#66882C2314yes—
174#66880C2314yes—
175#66879C2314yes—
176#66879C2314yes—
177#66874C2314yes—
178#66873C2314yes—
179#66872C2314yes—
180#66871C2314yes—
181#66867C2314yes—
182C2×#3181—111nomaximal, Sylow
183C23×D11—21no—
184C23×D11C2×D411yescharacteristic
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11—22no—
190C2×Q8×C11—22no—
191C2×Q8×C11C2412yes—
192C2×Q8×C11C2412yes—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11C2×D411yescharacteristic
204C22×Dic11C2×D411yescharacteristic
205C22×Dic11C2×D411yescharacteristic
206C2×D44—24no—
207C2×D44—21no—
208C2×D44—22no—
209C2×D44—22no—
210C2×D44—44no—
211C2×D44C2412yes—
212C2×C4×D11—24no—
213C2×C4×D11—24no—
214C2×C4×D11—22no—
215C2×C4×D11—22no—
216C2×C4×D11—42no—
217C2×C4×D11—44no—
218C2×C4×D11C2×D412yes—
219C2×C4×D11C2×D414yes—
220C2×C4×D11C2×D414yes—
221C2×C4×D11C2412yes—
222C2×Dic22—24no—
223C2×Dic22—21no—
224C2×Dic22—22no—
225C2×Dic22—22no—
226C2×Dic22—44no—
227C2×Dic22C2412yes—
228C11×Q16—28no—
229C2×C8×C11—22no—
230C2×C8×C11#4114yes—
231C2×C8×C11C2412yes—
232C2×C8×C11C2412yes—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—24no—
237C11×C4⋊C4C2412yes—
238C11×C4⋊C4C2412yes—
239C42×C11—24no—
240C42×C11—24no—
241C42×C11C2×D412yes—
242C42×C11C2412yes—
243#4326—28no—
244#4325—28no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252C4⋊Dic11—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11C2412yes—
257C4⋊Dic11C2412yes—
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×Dic11C2×D414yes—
267C4×Dic11C2×D412yes—
268C4×Dic11C2×D414yes—
269C4×Dic11C2412yes—
270C2×C11⋊C8—22no—
271C2×C11⋊C8#4114yes—
272C2×C11⋊C8C2412yes—
273C2×C11⋊C8C2412yes—
274#4314—28no—
275C8×D11—28no—
276C8×D11—28no—
277C2×#533—111no—
278C2×#529—111no—
279#3181—1116no—
280C2×#501—111no—
281C2×#497—111no—
282C2×#491—111no—
283C2×#489—111no—
284C2×#467—111no—
285C2×#467—111no—
286C2×#465—111no—
287C2×#465—111no—
288C2×#441—111no—
289C2×#441D1111yescharacteristic, complemented
290C2×#440—111no—
291C2×#440—111no—
292C22×#97—111no—
293C23×C11C22×D411yescharacteristic
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—42no—
298C22×D11—42no—
299C22×D11—42no—
300C22×D11#13714yes—
301C22×D11C22×D412yes—
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—22no—
306Q8×C11—42no—
307Q8×C11—42no—
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×D412yes—
320C2×C4×C11C22×D411yescharacteristic
321C2×C4×C11C2×#4112yes—
322C2×C4×C11C2×#4112yes—
323C2×C4×C11C2511yescharacteristic
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11C22×D412yes—
334C2×Dic11C22×D412yes—
335C2×Dic11C22×D412yes—
336D44—22no—
337D44—22no—
338D44—48no—
339D44—42no—
340C4×D11—28no—
341C4×D11—24no—
342C4×D11—22no—
343C4×D11—22no—
344C4×D11—44no—
345C4×D11—48no—
346Dic22—22no—
347Dic22—22no—
348Dic22—48no—
349Dic22—42no—
350C8×C11—22no—
351C8×C11C2×#4114yes—
352C11⋊C8—22no—
353C11⋊C8C2×#4114yes—
354C22×Q16—111no—
355C22×Q16C2×D1111yescharacteristic
356C22×SD16—111no—
357C22×SD16—111no—
358C23×C8—111no—
359C23×C8—111no—
360#533—118no—
361#533—224no—
362C2×C4⋊Q8—111no—
363C2×C4⋊Q8—111no—
364#529—118no—
365#529—224no—
366C2×#126—221no—
367C2×#125—111no—
368C2×#125—221no—
369C2×#124—111no—
370C2×#123—221no—
371C2×C22⋊Q8—111no—
372C2×C22⋊Q8—111no—
373C2×C22⋊Q8—111no—
374C2×C22⋊Q8—221no—
375C2×#121—111no—
376C2×C4×Q8—111no—
377C2×C4×Q8—221no—
378C2×C4×Q8C2×D1111yescharacteristic
379C2×C4×Q8C2×D1111yescharacteristic
380C2×C4×D4—111no—
381C2×C4×D4—221no—
382C2×#117—221no—
383C2×#117—221no—
384C22×C42—111no—
385#501—118no—
386#497—118no—
387#491—118no—
388#489—118no—
389#467—118no—
390#467—118no—
391#465—118no—
392#465—118no—
393#441—118no—
394#441C2×D1118yescomplemented
395#440—118no—
396#440—118no—
397C2×#107—111no—
398C2×#107—111no—
399C2×#106—111no—
400C2×#106C2×D1111yescharacteristic
401C2×#103—111no—
402C2×#103—111no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103C2×D1111yescharacteristic
406C2×#103C2×D1111yescharacteristic
407C2×#102—111no—
408C2×#102—111no—
409C2×#97—111no—
410C2×#97—111no—
411C2×#97—111no—
412C2×#97—118no—
413C2×#97C2×D1111yescharacteristic
414C22×C11#53212yes—
415C22×C11C2×#13712yes—
416C22×C11#57512yes—
417C22×C11C23×D411yescharacteristic
418C2×D11—28no—
419C2×D11—22no—
420C2×D11—22no—
421C2×D11—42no—
422C2×D11—42no—
423C2×D11—42no—
424C2×D11—84no—
425C2×D11C2×#13714yes—
426C4×C11—22no—
427C4×C11—22no—
428C4×C11—42no—
429C4×C11—42no—
430C4×C11—42no—
431C4×C11—42no—
432C4×C11#53212yes—
433C4×C11C22×#4111yescharacteristic
434C4×C11C22×#4111yescharacteristic
435Dic11—22no—
436Dic11—22no—
437Dic11—22no—
438Dic11—42no—
439Dic11—42no—
440Dic11—42no—
441C22×Q8—111no—
442C22×Q8—221no—
443C22×Q8C22×D1111yescharacteristic
444C22×Q8C22×D1111yescharacteristic
445C22×D4—111no—
446C22×D4—221no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—221no—
451C2×Q16—24no—
452C2×Q16—114no—
453C2×Q16—224no—
454C2×Q16C22×D1114yes—
455C2×SD16—114no—
456C2×SD16—114no—
457C2×SD16—224no—
458C2×SD16—224no—
459C22×C8—111no—
460C22×C8—111no—
461C22×C8—114no—
462C22×C8—114no—
463C22×C8—224no—
464C22×C8—224no—
465C22×C8C22×D1111yescharacteristic
466C22×C8C22×D1111yescharacteristic
467C4⋊Q8—114no—
468C4⋊Q8—114no—
469C4⋊Q8—222no—
470C4⋊Q8—222no—
471#126—228no—
472#125—114no—
473#125—222no—
474#125—228no—
475#124—114no—
476#124—222no—
477#123—228no—
478C22⋊Q8—114no—
479C22⋊Q8—114no—
480C22⋊Q8—114no—
481C22⋊Q8—222no—
482C22⋊Q8—228no—
483C22⋊Q8—222no—
484C22⋊Q8—222no—
485#121—114no—
486#121—222no—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—114no—
490C4×Q8—228no—
491C4×Q8—222no—
492C4×Q8C22×D1114yes—
493C4×Q8C22×D1114yes—
494C4×D4—114no—
495C4×D4—228no—
496C4×D4—222no—
497#117—228no—
498#117—228no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—221no—
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⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C4⋊C4C22×D1111yescharacteristic
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C42—21no—
522C2×C42—21no—
523C2×C42—111no—
524C2×C42—111no—
525C2×C42—111no—
526C2×C42—114no—
527C2×C42—114no—
528C2×C42—221no—
529C2×C42C22×D1111yescharacteristic
530#107—114no—
531#107—114no—
532#106—114no—
533#106C22×D1114yes—
534#103—114no—
535#103—114no—
536#103—114no—
537#103—114no—
538#103C22×D1114yes—
539#103C22×D1114yes—
540#102—114no—
541#102—114no—
542#97—114no—
543#97—114no—
544#97—114no—
545#97C22×D1114yes—
546C2×C11#318114yescomplemented
547C2×C11C2×#53211yescharacteristic
548C2×C11C22×#13711yescharacteristic
549C2×C11C2×#57511yescharacteristic
550D11—24no—
551D11—82no—
552C24—111no—
553C24—221no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—112no—
561C2×Q8—224no—
562C2×Q8—221no—
563C2×Q8—222no—
564C2×Q8—222no—
565C2×Q8—444no—
566C2×Q8C23×D1112yes—
567C2×Q8C23×D1112yes—
568C2×D4—112no—
569C2×D4—224no—
570C2×D4—222no—
571C2×D4—221no—
572C2×D4—222no—
573C2×D4—444no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—111no—
579C22×C4—111no—
580C22×C4—111no—
581C22×C4—114no—
582C22×C4—112no—
583C22×C4—112no—
584C22×C4—114no—
585C22×C4—224no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—224no—
592C22×C4—442no—
593C22×C4—444no—
594C22×C4D4×D1111yescharacteristic
595C22×C4D4×D1111yescharacteristic
596C22×C4C23×D1111yescharacteristic
597Q16—28no—
598Q16—228no—
599SD16—228no—
600SD16—228no—
601C2×C8—22no—
602C2×C8—114no—
603C2×C8—112no—
604C2×C8—112no—
605C2×C8—228no—
606C2×C8—222no—
607C2×C8—228no—
608C2×C8#433914yes—
609C2×C8C23×D1112yes—
610C2×C8C23×D1112yes—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—112no—
616C4⋊C4—112no—
617C4⋊C4—224no—
618C4⋊C4—224no—
619C4⋊C4—224no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—221no—
626C4⋊C4—221no—
627C4⋊C4—224no—
628C4⋊C4C23×D1112yes—
629C4⋊C4C23×D1112yes—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C42—24no—
638C42—24no—
639C42—114no—
640C42—114no—
641C42—112no—
642C42—112no—
643C42—224no—
644C42D4×D1112yes—
645C42C23×D1112yes—
646C11C2×#318111yescharacteristic, complemented, Sylow
647C23—114no—
648C23—112no—
649C23—222no—
650C23—222no—
651C23—222no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23C2×D4×D1111yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—222no—
663Q8—222no—
664Q8—448no—
665Q8—442no—
666D4—222no—
667D4—222no—
668D4—448no—
669D4—442no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—112no—
681C2×C4—112no—
682C2×C4—112no—
683C2×C4—228no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—224no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—444no—
694C2×C4—448no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4C2×#433912yes—
699C2×C4C2×D4×D1112yes—
700C2×C4C2×D4×D1112yes—
701C2×C4C2×D4×D1111yescharacteristic
702C2×C4#41×D1112yes—
703C2×C4C24×D1111yescharacteristic
704C8—22no—
705C8—114no—
706C8—222no—
707C8C2×#433914yes—
708C22—114no—
709C22—228no—
710C22—222no—
711C22—222no—
712C22—442no—
713C22—442no—
714C22—442no—
715C22—884no—
716C22#1062307912yes—
717C22D11×#13712yes—
718C22#1062330812yes—
719C22C22×D4×D1111yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—222no—
727C4—222no—
728C4—222no—
729C4—442no—
730C4—442no—
731C4—442no—
732C4#1062307912yes—
733C4C22×#433911yescharacteristic
734C4C2×#41×D1111yescharacteristic
735C2—224no—
736C2—882no—
737C2#1307932314yesdirect product factor
738C2C2×#1062307911yescharacteristic
739C2C2×D11×#13711yescharacteristic
740C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#441C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenterC2×#441D11
hypocenterC11C2×#3181
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C2×#10623109C2semidirect
3. #13079323C2direct (N × H)
4. C2×#10622469C2semidirect
5. C2×#10622803C2semidirect
6. C2×#10622410C2semidirect
7. C2×#10622408C2semidirect
8. C2×#10622426C2semidirect
9. C2×#10622801C2semidirect
12. C2×#10622643C2semidirect
13. C2×#10622323C2semidirect
14. C2×#10622639C2semidirect
15. C2×D11×#97C2semidirect
16. C2×C11×#441C2semidirect
32. #10623109C22semidirect
48. C11×#441C22semidirect
55. #10622803C22semidirect
56. #10622801C22semidirect
62. #10622643C22semidirect
63. #10622639C22semidirect
70. #10622469C22semidirect
71. #10622426C22semidirect
73. #10622410C22semidirect
74. #10622408C22semidirect
75. #10622323C22semidirect
76. D11×#97C22semidirect
289. C2×#441D11semidirect
394. #441C2×D11semidirect
546. C2×C11#3181semidirect
646. C11C2×#3181semidirect
737. C2#13079323direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231092
C2×#106231112
#130793232
C2×#106224692
C2×#106228032
C2×#106224102
C2×#106224082
C2×#106224262
C2×#106228012
C2×#106224202
C2×#106224772
C2×#106226432
C2×#106223232
C2×#106226392
C2×D11×#972
C2×C11×#4412
C2×#318111