Finite Group Databasebeta

← C2×#13080044 #15626701

Subgroups — C2×#13080044 #15626701

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×#10623065C211yesmaximal, characteristic
2C2×#10623049C211yesmaximal, characteristic, complemented
3#13080044C2116yesmaximal, direct product factor
4C2×#10622442C211yesmaximal, characteristic, complemented
5C2×#10622463C211yesmaximal, characteristic, complemented
6C2×#10622464C211yesmaximal, characteristic, complemented
7C2×#10622460C211yesmaximal, characteristic, complemented
8C2×#10622750C211yesmaximal, characteristic, complemented
9C2×#10622747C211yesmaximal, characteristic
10C2×#10622729C211yesmaximal, characteristic, complemented
11C2×#10622727C211yesmaximal, characteristic
12C2×#10622458C211yesmaximal, characteristic, complemented
13C2×#10622458C211yesmaximal, characteristic, complemented
14C2×#10622462C211yesmaximal, characteristic, complemented
15C2×#10622454C211yesmaximal, characteristic, complemented
16C2×C11×#424C211yesmaximal, characteristic, complemented
17C22×C11×M16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×#66983C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C22×Dic44C2211yescharacteristic
25C22×Dic44C2211yescharacteristic
26C22×#4314C2211yescharacteristic
27C22×#4314C2211yescharacteristic
28#10623065—24no—
29#10623065C2218yes—
30#10623049—24no—
31#10623049C2218yescomplemented
32C2×#66951—21no—
33C2×#66949—21no—
34C2×#66942—21no—
35C2×#66942—21no—
36C2×#66938—21no—
37C2×#66936—21no—
38C2×#66932—21no—
39C2×#66932—21no—
40C2×#66928C2211yescharacteristic
41C2×C4×D44C2211yescharacteristic
42C2×#66923C2211yescharacteristic
43C2×#66922C2211yescharacteristic
44C2×#66922C2211yescharacteristic
45C2×C4×Dic22C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic
48C11×#424C2218yescomplemented
49C2×C11×C4⋊C8C2211yescharacteristic
50C2×C11×C4⋊C8C2211yescharacteristic
51C2×C11×C4⋊C8C2211yescharacteristic
52C2×C11×C4⋊C8C2211yescharacteristic
53#10622750C2218yescomplemented
54#10622747C2218yes—
55#10622729C2218yescomplemented
56#10622727C2218yes—
57C2×#66885C2211yescharacteristic
58C2×#66885C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66881C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×#66880C2211yescharacteristic
65C2×#66880C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×#66880C2211yescharacteristic
69#10622464C2218yescomplemented
70#10622463C2218yescomplemented
71#10622462C2218yescomplemented
72#10622460C2218yescomplemented
73#10622458C2218yescomplemented
74#10622458C2218yescomplemented
75#10622454C2218yescomplemented
76#10622442C2218yescomplemented
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11—21no—
79C22×D44C2311yescharacteristic
80C22×C4×D11—21no—
81C22×Dic22—21no—
82C22×Dic22C2311yescharacteristic
83C22×Dic22C2311yescharacteristic
84C22×Dic22C2311yescharacteristic
85C2×C11×M16—42no—
86C2×C11×M16C2314yes—
87C22×C8×C11—42no—
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2314yes—
93C11×#117D414yes—
94C11×#117C2314yes—
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C11×C22⋊C4D411yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11—21no—
104#66983—22no—
105#66983C2314yes—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117#66977—22no—
118#66977—22no—
119#66977—22no—
120#66977C2314yes—
121#66977C2314yes—
122#66977C2314yes—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
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×C4×Dic11—21no—
132C2×C4×Dic11—21no—
133C2×C4×Dic11—21no—
134C2×Dic44—42no—
135C2×Dic44—42no—
136C2×Dic44C2314yes—
137C2×Dic44C2314yes—
138C2×#4314—42no—
139C2×#4314—42no—
140C2×#4314C2314yes—
141C2×#4314C2314yes—
142#66951—28no—
143#66949—28no—
144#66942—28no—
145#66942—28no—
146#66938—28no—
147#66936—28no—
148#66932—28no—
149#66932—28no—
150#66928—22no—
151#66928C2314yes—
152C4×D44—22no—
153C4×D44C2314yes—
154#66923—22no—
155#66923C2314yes—
156#66922—22no—
157#66922—22no—
158#66922C2314yes—
159#66922C2314yes—
160C4×Dic22—22no—
161C4×Dic22—22no—
162C4×Dic22—22no—
163C4×Dic22C2314yes—
164C4×Dic22C2314yes—
165C4×Dic22C2314yes—
166C11×C4⋊C8C2314yes—
167C11×C4⋊C8C2314yes—
168C11×C4⋊C8C2314yes—
169C11×C4⋊C8C2314yes—
170#66885C2314yes—
171#66885C2314yes—
172#66882C2314yes—
173#66882C2314yes—
174#66881C2314yes—
175#66881C2314yes—
176#66880C2314yes—
177#66880C2314yes—
178#66880C2314yes—
179#66880C2314yes—
180#66880C2314yes—
181#66880C2314yes—
182C2×#3258—111nomaximal, Sylow
183C24×C11C2×D411yescharacteristic
184C23×D11—21no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D412yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2411yescharacteristic
195C2×C22⋊D11—24no—
196C2×C22⋊D11—82no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
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—21no—
212C2×Dic22—21no—
213C2×Dic22—24no—
214C2×Dic22—22no—
215C2×Dic22—22no—
216C2×Dic22—22no—
217C2×Dic22—22no—
218C2×Dic22—22no—
219C2×Dic22—22no—
220C2×Dic22—82no—
221C2×Dic22C2412yes—
222C2×Dic22C2412yes—
223C2×Dic22C2412yes—
224C11×M16—44no—
225C2×C8×C11—22no—
226C2×C8×C11—22no—
227C2×C8×C11—22no—
228C2×C8×C11—22no—
229C2×C8×C11—44no—
230C2×C8×C11C2412yes—
231C2×C8×C11C2412yes—
232C2×C8×C11C2412yes—
233C2×C8×C11C2412yes—
234C11×C4⋊C4C2×D414yes—
235C11×C4⋊C4C2×D414yes—
236C11×C22⋊C4C2×D414yes—
237C11×C22⋊C4C2×D414yes—
238C42×C11C2×D412yes—
239C42×C11C2×D412yes—
240C42×C11C2412yes—
241C42×C11C2412yes—
242C22⋊Dic11—24no—
243C22⋊Dic11—24no—
244C22⋊Dic11—24no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11—24no—
254C4⋊Dic11—24no—
255C4⋊Dic11—24no—
256C4⋊Dic11C2412yes—
257C4⋊Dic11C2412yes—
258C4⋊Dic11C2412yes—
259C4⋊Dic11C2412yes—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268C4×Dic11—24no—
269C4×Dic11—24no—
270C4×Dic11—24no—
271Dic44—44no—
272Dic44—44no—
273#4314—44no—
274#4314—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×#462—111no—
289C2×#461—111no—
290C2×#424D1111yescharacteristic, complemented
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11C22×D412yes—
295C23×C11C22×D411yescharacteristic
296C22×D11—22no—
297C22×D11—42no—
298C22×D11—42no—
299C22×D11—42no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—24no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11C22×D412yes—
309C2×C4×C11C22×D412yes—
310C2×C4×C11C22×D412yes—
311C2×C4×C11C22×D412yes—
312C2×C4×C11C22×D412yes—
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11H(5,𝔽2)12yes—
315C2×C4×C112−1+412yes—
316C2×C4×C11C2511yescharacteristic
317C22⋊D11—84no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332D44—22no—
333D44—22no—
334D44—42no—
335C4×D11—84no—
336Dic22—22no—
337Dic22—22no—
338Dic22—22no—
339Dic22—22no—
340Dic22—22no—
341Dic22—22no—
342Dic22—42no—
343Dic22—42no—
344Dic22—42no—
345Dic22—84no—
346C8×C11—22no—
347C8×C11—22no—
348C8×C11—22no—
349C8×C11—22no—
350C22×Q16—111no—
351C22×Q16—111no—
352C22×SD16—111no—
353C22×SD16—111no—
354C22×M16C2×D1111yescharacteristic
355C23×C8C2×D1111yescharacteristic
356#542—118no—
357#542—224no—
358#541—118no—
359#541—224no—
360C2×C4⋊Q8—111no—
361C2×C4⋊Q8—111no—
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×Q8—111no—
379C2×C4×D4—111no—
380C2×#117C2×D1111yescharacteristic
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#462—118no—
392#461—118no—
393C2×#107—111no—
394C2×#107—111no—
395C2×#106—111no—
396C2×#106—111no—
397#424C2×D1118yescomplemented
398C2×C4⋊C8C2×D1111yescharacteristic
399C2×C4⋊C8C2×D1111yescharacteristic
400C2×C4⋊C8C2×D1111yescharacteristic
401C2×C4⋊C8C2×D1111yescharacteristic
402C2×#103—111no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#102—111no—
409C2×#102—111no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—44no—
414C22×C11#53712yes—
415C22×C11#57712yes—
416C22×C11#57812yes—
417C22×C11C23×D411yescharacteristic
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—84no—
422C4×C11—22no—
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—22no—
426C4×C11—22no—
427C4×C11#53712yes—
428C4×C11C2×H(5,𝔽2)11yescharacteristic
429C4×C11C2×2−1+411yescharacteristic
430Dic11—42no—
431Dic11—42no—
432Dic11—42no—
433Dic11—42no—
434Dic11—42no—
435Dic11—42no—
436Dic11—42no—
437C22×Q8—111no—
438C22×Q8—111no—
439C22×Q8—111no—
440C22×Q8—221no—
441C22×D4—111no—
442C22×D4—221no—
443C23×C4—221no—
444C23×C4C22×D1111yescharacteristic
445C2×Q16—114no—
446C2×Q16—114no—
447C2×Q16—442no—
448C2×Q16—442no—
449C2×SD16—114no—
450C2×SD16—114no—
451C2×SD16—442no—
452C2×SD16—442no—
453C2×M16—42no—
454C2×M16C22×D1114yes—
455C22×C8—42no—
456C22×C8C22×D1111yescharacteristic
457C22×C8C22×D1111yescharacteristic
458C22×C8C22×D1111yescharacteristic
459C22×C8C22×D1111yescharacteristic
460C22×C8C22×D1114yes—
461C4⋊Q8—114no—
462C4⋊Q8—114no—
463C4⋊Q8—222no—
464C4⋊Q8—222no—
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—222no—
480C22⋊Q8—222no—
481C22⋊Q8—222no—
482C22⋊Q8—228no—
483#121—114no—
484#121—222no—
485C4×Q8—114no—
486C4×Q8—114no—
487C4×Q8—114no—
488C4×Q8—222no—
489C4×Q8—222no—
490C4×Q8—222no—
491C4×D4—114no—
492C4×D4—222no—
493#117D4414yes—
494#117C22×D1114yes—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
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⋊C4D4411yescharacteristic
511C2×C4⋊C4D4411yescharacteristic
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4D4411yescharacteristic
520C2×C22⋊C4D4411yescharacteristic
521C2×C42—221no—
522C2×C42—221no—
523C2×C42—221no—
524C2×C42C22×D1111yescharacteristic
525C2×C42C22×D1111yescharacteristic
526#107—114no—
527#107—114no—
528#106—114no—
529#106—114no—
530C4⋊C8C22×D1114yes—
531C4⋊C8C22×D1114yes—
532C4⋊C8C22×D1114yes—
533C4⋊C8C22×D1114yes—
534#103—114no—
535#103—114no—
536#103—114no—
537#103—114no—
538#103—114no—
539#103—114no—
540#102—114no—
541#102—114no—
542C2×C11—42no—
543C2×C11#325814yescomplemented
544C2×C11C2×#53711yescharacteristic
545C2×C11C2×#57711yescharacteristic
546C2×C11C2×#57811yescharacteristic
547D11—82no—
548C24—221no—
549C24C2×D4411yescharacteristic
550C2×Q8—112no—
551C2×Q8—112no—
552C2×Q8—112no—
553C2×Q8—221no—
554C2×Q8—221no—
555C2×Q8—221no—
556C2×Q8—224no—
557C2×Q8—222no—
558C2×Q8—222no—
559C2×Q8—222no—
560C2×Q8—222no—
561C2×Q8—222no—
562C2×Q8—222no—
563C2×Q8—882no—
564C2×D4—112no—
565C2×D4—224no—
566C2×D4—221no—
567C2×D4—222no—
568C2×D4—222no—
569C2×D4—882no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—224no—
580C22×C4—882no—
581C22×C4C2×D4412yes—
582C22×C4C2×D4411yescharacteristic
583C22×C4C2×D4411yescharacteristic
584C22×C4C2×D4411yescharacteristic
585C22×C4C2×D4411yescharacteristic
586C22×C4C2×D4411yescharacteristic
587C22×C4C23×D1112yes—
588C22×C4C23×D1111yescharacteristic
589Q16—444no—
590Q16—444no—
591SD16—444no—
592SD16—444no—
593M16—44no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—44no—
599C2×C8C23×D1112yes—
600C2×C8C23×D1112yes—
601C2×C8C23×D1112yes—
602C2×C8C23×D1112yes—
603C4⋊C4—112no—
604C4⋊C4—112no—
605C4⋊C4—112no—
606C4⋊C4—112no—
607C4⋊C4—221no—
608C4⋊C4—221no—
609C4⋊C4—221no—
610C4⋊C4—221no—
611C4⋊C4—224no—
612C4⋊C4—224no—
613C4⋊C4—224no—
614C4⋊C4—224no—
615C4⋊C4—224no—
616C4⋊C4—224no—
617C4⋊C4—224no—
618C4⋊C4—224no—
619C4⋊C4—224no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4C2×D4414yes—
623C4⋊C4C2×D4414yes—
624C22⋊C4—224no—
625C22⋊C4—224no—
626C22⋊C4—224no—
627C22⋊C4—224no—
628C22⋊C4—224no—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C22⋊C4C2×D4414yes—
632C22⋊C4C2×D4414yes—
633C42—224no—
634C42—224no—
635C42—224no—
636C42C2×D4412yes—
637C42C2×D4412yes—
638C42C23×D1112yes—
639C42C23×D1112yes—
640C11C2×#325811yescharacteristic, complemented, Sylow
641C23—22no—
642C23—22no—
643C23—22no—
644C23—222no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23C22×D4412yes—
649C23C22×D4411yescharacteristic
650Q8—222no—
651Q8—222no—
652Q8—222no—
653Q8—222no—
654Q8—222no—
655Q8—222no—
656Q8—442no—
657Q8—442no—
658Q8—442no—
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—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—222no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—442no—
680C2×C4—442no—
681C2×C4—442no—
682C2×C4—442no—
683C2×C4—442no—
684C2×C4—442no—
685C2×C4—442no—
686C2×C4—884no—
687C2×C4C22×D4412yes—
688C2×C4C22×D4412yes—
689C2×C4C22×D4412yes—
690C2×C4C22×D4412yes—
691C2×C4C22×D4412yes—
692C2×C4C22×D4411yescharacteristic
693C2×C4#6703712yes—
694C2×C4#6704012yes—
695C2×C4C24×D1111yescharacteristic
696C8—22no—
697C8—22no—
698C8—22no—
699C8—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—442no—
705C22—442no—
706C22—442no—
707C22—884no—
708C22#1062304112yes—
709C22#1062328212yes—
710C22#1062328412yes—
711C22C23×D4411yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—442no—
718C4—442no—
719C4—442no—
720C4—442no—
721C4—442no—
722C4—442no—
723C4—442no—
724C4#1062304112yes—
725C4C2×#6703711yescharacteristic
726C4C2×#6704011yescharacteristic
727C2—42no—
728C2—882no—
729C2#1308004414yesdirect product factor
730C2C2×#1062304111yescharacteristic
731C2C2×#1062328211yescharacteristic
732C2C2×#1062328411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#424C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#424D11
hypocenterC11C2×#3258
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
2. C2×#10623049C2semidirect
3. #13080044C2direct (N × H)
4. C2×#10622442C2semidirect
5. C2×#10622463C2semidirect
6. C2×#10622464C2semidirect
7. C2×#10622460C2semidirect
8. C2×#10622750C2semidirect
10. C2×#10622729C2semidirect
12. C2×#10622458C2semidirect
13. C2×#10622458C2semidirect
14. C2×#10622462C2semidirect
15. C2×#10622454C2semidirect
16. C2×C11×#424C2semidirect
31. #10623049C22semidirect
48. C11×#424C22semidirect
53. #10622750C22semidirect
55. #10622729C22semidirect
69. #10622464C22semidirect
70. #10622463C22semidirect
71. #10622462C22semidirect
72. #10622460C22semidirect
73. #10622458C22semidirect
74. #10622458C22semidirect
75. #10622454C22semidirect
76. #10622442C22semidirect
290. C2×#424D11semidirect
397. #424C2×D11semidirect
543. C2×C11#3258semidirect
640. C11C2×#3258semidirect
729. C2#13080044direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230652
C2×#106230492
#130800442
C2×#106224422
C2×#106224632
C2×#106224642
C2×#106224602
C2×#106227502
C2×#106227472
C2×#106227292
C2×#106227272
C2×#106224582
C2×#106224622
C2×#106224542
C2×C11×#4242
C2×#325811