Finite Group Databasebeta

← C2×#13080040 #15626697

Subgroups — C2×#13080040 #15626697

Order 2816.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623113C211yesmaximal, characteristic
2C2×#10623262C211yesmaximal, characteristic, complemented
3#13080040C2116yesmaximal, direct product factor
4C2×#10622635C211yesmaximal, characteristic, complemented
5C2×#10622407C211yesmaximal, characteristic, complemented
6C2×#10622404C211yesmaximal, characteristic, complemented
7C2×#10622460C211yesmaximal, characteristic, complemented
8C2×#10622802C211yesmaximal, characteristic, complemented
9C2×#10622425C211yesmaximal, characteristic
10C2×#10622801C211yesmaximal, characteristic, complemented
11C2×#10622420C211yesmaximal, characteristic
12C2×#10622798C211yesmaximal, characteristic, complemented
13C2×#10622798C211yesmaximal, characteristic, complemented
14C2×#10622696C211yesmaximal, characteristic, complemented
15C2×#10622452C211yesmaximal, characteristic, complemented
16C2×C11×#462C211yesmaximal, characteristic, complemented
17C22×C11×Q16C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×#67000C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C2×#66999C2211yescharacteristic
24C2×#66999C2211yescharacteristic
25C2×Q8×Dic11C2211yescharacteristic
26C2×Q8×Dic11C2211yescharacteristic
27C22×#4325C2211yescharacteristic
28C22×#4325C2211yescharacteristic
29C22×#4313C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31#10623262—24no—
32#10623262C2218yescomplemented
33#10623113—24no—
34#10623113C2218yes—
35C2×#66951—21no—
36C2×#66951—21no—
37C2×#66949—21no—
38C2×#66948C2211yescharacteristic
39C2×#66947—21no—
40C2×#66942—21no—
41C2×#66942—21no—
42C2×#66941C2211yescharacteristic
43C2×#66929—21no—
44C2×#66928—21no—
45C2×C4×D44C2211yescharacteristic
46C2×#66925C2211yescharacteristic
47C2×#66923C2211yescharacteristic
48C11×#462C2218yescomplemented
49C2×C11×C4⋊C8C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#103C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×#66899C2211yescharacteristic
56#10622802C2218yescomplemented
57#10622801C2218yescomplemented
58#10622798C2218yescomplemented
59#10622798C2218yescomplemented
60C2×#66885C2211yescharacteristic
61C2×#66885C2211yescharacteristic
62C2×#66882C2211yescharacteristic
63C2×#66881C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65C2×Dic11⋊C8C2211yescharacteristic
66#10622696C2218yescomplemented
67#10622635C2218yescomplemented
68C2×#66872C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×C4⋊(C11⋊C8)C2211yescharacteristic
71#10622460C2218yescomplemented
72#10622452C2218yescomplemented
73#10622425C2218yes—
74#10622420C2218yes—
75#10622407C2218yescomplemented
76#10622404C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D44—21no—
81C22×D44C2311yescharacteristic
82C22×C4×D11—21no—
83C22×C4×D11C2311yescharacteristic
84C22×Dic22—21no—
85C2×C11×Q16—42no—
86C2×C11×Q16—42no—
87C2×C11×Q16C2314yes—
88C2×C11×Q16C2314yes—
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C11×C4⋊Q8—22no—
92C11×C4⋊Q8C2314yes—
93C4×Q8×C11—22no—
94C4×Q8×C11C2314yes—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101#67000—22no—
102#67000C2314yes—
103#66999—22no—
104#66999—22no—
105#66999—22no—
106#66999C2314yes—
107#66999C2314yes—
108#66999C2314yes—
109Q8×Dic11—22no—
110Q8×Dic11—22no—
111Q8×Dic11C2314yes—
112Q8×Dic11C2314yes—
113C2×#4325—42no—
114C2×#4325—42no—
115C2×#4325C2314yes—
116C2×#4325C2314yes—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4D411yescharacteristic
125C2×(C2×D11)⋊C4D411yescharacteristic
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4D411yescharacteristic
138C2×Dic11⋊C4D411yescharacteristic
139C2×C4×Dic11—21no—
140C2×C4×Dic11—21no—
141C2×C4×Dic11C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C2×#4313—42no—
145C2×#4313C2314yes—
146C2×C8×D11—42no—
147C2×C8×D11C2314yes—
148#66951—28no—
149#66951—28no—
150#66949—28no—
151#66948—22no—
152#66948C2314yes—
153#66947—28no—
154#66942—28no—
155#66942—28no—
156#66941—22no—
157#66941C2314yes—
158#66929—28no—
159#66928—28no—
160C4×D44—22no—
161C4×D44C2314yes—
162#66925D414yes—
163#66925C2314yes—
164#66923—22no—
165#66923C2314yes—
166C11×C4⋊C8C2314yes—
167C11×#103C2314yes—
168C11×#103C2314yes—
169#66899C2314yes—
170#66899C2314yes—
171#66899C2314yes—
172#66899C2314yes—
173#66885C2314yes—
174#66885C2314yes—
175#66882C2314yes—
176#66881C2314yes—
177Dic11⋊C8C2314yes—
178Dic11⋊C8C2314yes—
179#66872C2314yes—
180#66871C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3258—111nomaximal, Sylow
183C23×D11—21no—
184C23×D11C2×D411yescharacteristic
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—22no—
189C2×Q8×C11—22no—
190C2×Q8×C11—22no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11C2412yes—
195C2×Q8×C11C2412yes—
196C2×Q8×C11C2412yes—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2411yescharacteristic
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210C2×D44—24no—
211C2×D44—21no—
212C2×D44—22no—
213C2×D44—22no—
214C2×D44—82no—
215C2×D44C2412yes—
216C2×C4×D11—24no—
217C2×C4×D11—22no—
218C2×C4×D11—22no—
219C2×C4×D11—82no—
220C2×C4×D11C2×D412yes—
221C2×C4×D11C2412yes—
222C2×Dic22—24no—
223C2×Dic22—82no—
224C11×Q16—44no—
225C11×Q16—44no—
226C2×C8×C11—22no—
227C2×C8×C11—22no—
228C2×C8×C11C2412yes—
229C2×C8×C11C2412yes—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—24no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4C2412yes—
235C42×C11—24no—
236C42×C11C2×D412yes—
237C42×C11C2412yes—
238#4325—44no—
239#4325—44no—
240(C2×D11)⋊C4—24no—
241(C2×D11)⋊C4—24no—
242(C2×D11)⋊C4—24no—
243(C2×D11)⋊C4—24no—
244(C2×D11)⋊C4—24no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4C2×D414yes—
248(C2×D11)⋊C4C2×D414yes—
249C4⋊Dic11—24no—
250C4⋊Dic11—24no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
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⋊C4C2×D414yes—
264Dic11⋊C4C2×D414yes—
265C4×Dic11—24no—
266C4×Dic11—24no—
267C4×Dic11C2×D412yes—
268C4×Dic11C2412yes—
269C2×C11⋊C8—22no—
270C2×C11⋊C8—22no—
271C2×C11⋊C8C2412yes—
272C2×C11⋊C8C2412yes—
273#4313—44no—
274C8×D11—44no—
275C2×#542—111no—
276C2×#541—111no—
277#3258—1116no—
278C2×#479—111no—
279C2×#477—111no—
280C2×#475—111no—
281C2×#478—111no—
282C2×#470—111no—
283C2×#468—111no—
284C2×#467—111no—
285C2×#465—111no—
286C2×#464—111no—
287C2×#464—111no—
288C2×#462D1111yescharacteristic, complemented
289C2×#461—111no—
290C2×#424—111no—
291C23×C11C22×D411yescharacteristic
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—42no—
297C22×D11—42no—
298C22×D11—42no—
299C22×D11C22×D412yes—
300Q8×C11—22no—
301Q8×C11—22no—
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—22no—
306Q8×C11—42no—
307Q8×C11—42no—
308Q8×C11—42no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11C22×D412yes—
320C2×C4×C11C22×D412yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11H(5,𝔽2)12yes—
323C2×C4×C112−1+412yes—
324C2×C4×C11C2511yescharacteristic
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11C22×D412yes—
335C2×Dic11C22×D412yes—
336C2×Dic11C22×D412yes—
337D44—22no—
338D44—22no—
339D44—42no—
340D44—84no—
341C4×D11—24no—
342C4×D11—22no—
343C4×D11—22no—
344C4×D11—84no—
345Dic22—84no—
346C8×C11—22no—
347C8×C11—22no—
348C11⋊C8—22no—
349C11⋊C8—22no—
350C22×Q16C2×D1111yescharacteristic
351C22×Q16C2×D1111yescharacteristic
352C22×SD16—111no—
353C22×SD16—111no—
354C22×M16—111no—
355C23×C8—111no—
356#542—118no—
357#542—224no—
358#541—118no—
359#541—224no—
360C2×C4⋊Q8—111no—
361C2×C4⋊Q8C2×D1111yescharacteristic
362C2×#126—221no—
363C2×#126—221no—
364C2×#126—221no—
365C2×#125—111no—
366C2×#125—221no—
367C2×#125—221no—
368C2×#124—111no—
369C2×#124—221no—
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—111no—
378C2×C4×Q8C2×D1111yescharacteristic
379C2×C4×D4—111no—
380C2×#117—111no—
381#479—118no—
382#478—118no—
383#477—118no—
384#475—118no—
385#470—118no—
386#468—118no—
387#467—118no—
388#465—118no—
389#464—118no—
390#464—118no—
391#462C2×D1118yescomplemented
392#461—118no—
393C2×#107—111no—
394C2×#107—111no—
395C2×#106—111no—
396C2×#106—111no—
397#424—118no—
398C2×C4⋊C8—111no—
399C2×C4⋊C8—111no—
400C2×C4⋊C8—111no—
401C2×C4⋊C8C2×D1111yescharacteristic
402C2×#103—111no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103C2×D1111yescharacteristic
407C2×#103C2×D1111yescharacteristic
408C2×#102—111no—
409C2×#102—111no—
410C22×C11#53712yes—
411C22×C11#57712yes—
412C22×C11#57812yes—
413C22×C11C23×D411yescharacteristic
414C2×D11—22no—
415C2×D11—22no—
416C2×D11—22no—
417C2×D11—44no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—84no—
422C4×C11—22no—
423C4×C11—22no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11—42no—
427C4×C11—42no—
428C4×C11#53712yes—
429C4×C11C2×H(5,𝔽2)11yescharacteristic
430C4×C11C2×2−1+411yescharacteristic
431Dic11—22no—
432Dic11—22no—
433Dic11—22no—
434Dic11—42no—
435Dic11—42no—
436Dic11—42no—
437C22×Q8—221no—
438C22×Q8C22×D1111yescharacteristic
439C22×Q8C22×D1111yescharacteristic
440C22×Q8C22×D1111yescharacteristic
441C22×D4—111no—
442C22×D4—221no—
443C23×C4—111no—
444C23×C4—221no—
445C2×Q16—42no—
446C2×Q16—42no—
447C2×Q16C22×D1114yes—
448C2×Q16C22×D1114yes—
449C2×SD16—114no—
450C2×SD16—114no—
451C2×SD16—442no—
452C2×SD16—442no—
453C2×M16—114no—
454C2×M16—442no—
455C22×C8—111no—
456C22×C8—111no—
457C22×C8—114no—
458C22×C8—442no—
459C22×C8C22×D1111yescharacteristic
460C22×C8C22×D1111yescharacteristic
461C4⋊Q8—22no—
462C4⋊Q8—114no—
463C4⋊Q8—222no—
464C4⋊Q8C22×D1114yes—
465#126—228no—
466#126—228no—
467#126—228no—
468#125—114no—
469#125—228no—
470#125—228no—
471#125—222no—
472#124—114no—
473#124—228no—
474#124—222no—
475#123—228no—
476C22⋊Q8—114no—
477C22⋊Q8—114no—
478C22⋊Q8—114no—
479C22⋊Q8—228no—
480C22⋊Q8—222no—
481C22⋊Q8—222no—
482C22⋊Q8—222no—
483#121—114no—
484#121—222no—
485C4×Q8—22no—
486C4×Q8—114no—
487C4×Q8—114no—
488C4×Q8—222no—
489C4×Q8—222no—
490C4×Q8C22×D1114yes—
491C4×D4—114no—
492C4×D4—222no—
493#117—114no—
494#117—114no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
512C2×C22⋊C4—111no—
513C2×C22⋊C4—111no—
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—111no—
523C2×C42—221no—
524C2×C42—221no—
525C2×C42C22×D1111yescharacteristic
526#107—114no—
527#107—114no—
528#106—114no—
529#106—114no—
530C4⋊C8—114no—
531C4⋊C8—114no—
532C4⋊C8—114no—
533C4⋊C8C22×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—
542C2×C11#325814yescomplemented
543C2×C11C2×#53711yescharacteristic
544C2×C11C2×#57711yescharacteristic
545C2×C11C2×#57811yescharacteristic
546D11—42no—
547D11—82no—
548C24—111no—
549C24—221no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—224no—
560C2×Q8—882no—
561C2×Q8C23×D1112yes—
562C2×Q8C23×D1112yes—
563C2×Q8C23×D1112yes—
564C2×D4—112no—
565C2×D4—224no—
566C2×D4—221no—
567C2×D4—222no—
568C2×D4—222no—
569C2×D4—882no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—111no—
575C22×C4—111no—
576C22×C4—111no—
577C22×C4—112no—
578C22×C4—112no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—224no—
585C22×C4—882no—
586C22×C4D4×D1111yescharacteristic
587C22×C4D4×D1111yescharacteristic
588C22×C4C23×D1111yescharacteristic
589Q16—44no—
590Q16—44no—
591SD16—444no—
592SD16—444no—
593M16—444no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—112no—
597C2×C8—112no—
598C2×C8—222no—
599C2×C8—222no—
600C2×C8—444no—
601C2×C8C23×D1112yes—
602C2×C8C23×D1112yes—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—114no—
608C4⋊C4—114no—
609C4⋊C4—112no—
610C4⋊C4—112no—
611C4⋊C4—112no—
612C4⋊C4—224no—
613C4⋊C4—224no—
614C4⋊C4—224no—
615C4⋊C4—224no—
616C4⋊C4—224no—
617C4⋊C4—224no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4C23×D1112yes—
624C22⋊C4—114no—
625C22⋊C4—114no—
626C22⋊C4—224no—
627C22⋊C4—224no—
628C22⋊C4—224no—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C22⋊C4—224no—
633C42—24no—
634C42—112no—
635C42—112no—
636C42—224no—
637C42—224no—
638C42D4×D1112yes—
639C42C23×D1112yes—
640C11C2×#325811yescharacteristic, complemented, Sylow
641C23—112no—
642C23—222no—
643C23—222no—
644C23—222no—
645C23—222no—
646C23—442no—
647C23—442no—
648C23—442no—
649C23C2×D4×D1111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—884no—
660D4—222no—
661D4—222no—
662D4—442no—
663D4—884no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—112no—
675C2×C4—112no—
676C2×C4—112no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—224no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—442no—
687C2×C4—442no—
688C2×C4—442no—
689C2×C4—884no—
690C2×C4C2×D4×D1112yes—
691C2×C4C2×D4×D1112yes—
692C2×C4C2×D4×D1111yescharacteristic
693C2×C4#6703712yes—
694C2×C4#6704312yes—
695C2×C4C24×D1111yescharacteristic
696C8—22no—
697C8—22no—
698C8—222no—
699C8—222no—
700C22—222no—
701C22—222no—
702C22—222no—
703C22—444no—
704C22—442no—
705C22—442no—
706C22—442no—
707C22—884no—
708C22#1062313912yes—
709C22#1062329712yes—
710C22#1062330912yes—
711C22C22×D4×D1111yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—222no—
719C4—222no—
720C4—222no—
721C4—442no—
722C4—442no—
723C4—442no—
724C4#1062313912yes—
725C4C2×#6703711yescharacteristic
726C4C2×#6704311yescharacteristic
727C2—442no—
728C2—882no—
729C2#1308004014yesdirect product factor
730C2C2×#1062313911yescharacteristic
731C2C2×#1062330911yescharacteristic
732C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenterC2×#462D11
hypocenterC11C2×#3258
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
2. C2×#10623262C2semidirect
3. #13080040C2direct (N × H)
4. C2×#10622635C2semidirect
5. C2×#10622407C2semidirect
6. C2×#10622404C2semidirect
7. C2×#10622460C2semidirect
8. C2×#10622802C2semidirect
10. C2×#10622801C2semidirect
12. C2×#10622798C2semidirect
13. C2×#10622798C2semidirect
14. C2×#10622696C2semidirect
15. C2×#10622452C2semidirect
16. C2×C11×#462C2semidirect
32. #10623262C22semidirect
48. C11×#462C22semidirect
56. #10622802C22semidirect
57. #10622801C22semidirect
58. #10622798C22semidirect
59. #10622798C22semidirect
66. #10622696C22semidirect
67. #10622635C22semidirect
71. #10622460C22semidirect
72. #10622452C22semidirect
75. #10622407C22semidirect
76. #10622404C22semidirect
288. C2×#462D11semidirect
391. #462C2×D11semidirect
542. C2×C11#3258semidirect
640. C11C2×#3258semidirect
729. C2#13080040direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231132
C2×#106232622
#130800402
C2×#106226352
C2×#106224072
C2×#106224042
C2×#106224602
C2×#106228022
C2×#106224252
C2×#106228012
C2×#106224202
C2×#106227982
C2×#106226962
C2×#106224522
C2×C11×#4622
C2×#325811