Finite Group Databasebeta

← C2×#13080049 #15626706

Subgroups — C2×#13080049 #15626706

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×#10623264C211yesmaximal, characteristic
2C2×#10623114C211yesmaximal, characteristic, complemented
3#13080049C2116yesmaximal, direct product factor
4C2×#10622470C211yesmaximal, characteristic, complemented
5C2×#10622704C211yesmaximal, characteristic, complemented
6C2×#10622484C211yesmaximal, characteristic, complemented
7C2×#10622481C211yesmaximal, characteristic, complemented
8C2×#10622425C211yesmaximal, characteristic
9C2×#10622426C211yesmaximal, characteristic, complemented
10C2×#10622477C211yesmaximal, characteristic
11C2×#10622458C211yesmaximal, characteristic, complemented
12C2×#10622641C211yesmaximal, characteristic, complemented
13C2×#10622406C211yesmaximal, characteristic, complemented
14C2×#10622431C211yesmaximal, characteristic, complemented
15C2×#10622452C211yesmaximal, characteristic, complemented
16C2×C11×#475C211yesmaximal, characteristic, complemented
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#67000—21no—
20C2×#66999—21no—
21C2×#66999C2211yescharacteristic
22C2×#66997C2211yescharacteristic
23C22×#4326C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C22×Dic44C2211yescharacteristic
26C22×#4314C2211yescharacteristic
27C22×#4313C2211yescharacteristic
28C22×C8×D11C2211yescharacteristic
29#10623264—24no—
30#10623264C2218yes—
31#10623114—24no—
32#10623114C2218yescomplemented
33C2×#66951—21no—
34C2×#66951—21no—
35C2×#66950C2211yescharacteristic
36C2×#66950C2211yescharacteristic
37C2×#66948C2211yescharacteristic
38C2×#66947—21no—
39C2×#66946C2211yescharacteristic
40C2×#66943C2211yescharacteristic
41C2×#66942—21no—
42C2×#66940C2211yescharacteristic
43C2×#66929—21no—
44C2×#66928C2211yescharacteristic
45C2×#66925C2211yescharacteristic
46C2×#66923—21no—
47C2×C4×Dic22C2211yescharacteristic
48C11×#475C2218yescomplemented
49C2×C11×#106C2211yescharacteristic
50C2×C11×#106C2211yescharacteristic
51C2×C11×C4⋊C8C2211yescharacteristic
52C2×C11×#103C2211yescharacteristic
53C2×C11×#103C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×#66880C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58#10622704C2218yescomplemented
59#10622641C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66871C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622484C2218yescomplemented
68#10622481C2218yescomplemented
69#10622477C2218yes—
70#10622470C2218yescomplemented
71#10622458C2218yescomplemented
72#10622452C2218yescomplemented
73#10622431C2218yescomplemented
74#10622426C2218yescomplemented
75#10622425C2218yes—
76#10622406C2218yescomplemented
77C22×Q8×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D44—21no—
80C22×D44C2311yescharacteristic
81C22×C4×D11—21no—
82C22×C4×D11C2311yescharacteristic
83C22×Dic22C2311yescharacteristic
84C22×Dic22C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C11×C4⋊Q8—22no—
88C11×C4⋊Q8C2314yes—
89C4×Q8×C11—22no—
90C4×Q8×C11C2314yes—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98#67000—28no—
99#66999—22no—
100#66999—28no—
101#66999C2314yes—
102#66997—22no—
103#66997C2314yes—
104C2×#4326—42no—
105C2×#4326C2314yes—
106C2×#4325—42no—
107C2×#4325C2314yes—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4D411yescharacteristic
116C2×(C2×D11)⋊C4D411yescharacteristic
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11—21no—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4D411yescharacteristic
128C2×Dic11⋊C4D411yescharacteristic
129C2×C4×Dic11—21no—
130C2×C4×Dic11—21no—
131C2×C4×Dic11C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C2×Dic44—42no—
135C2×Dic44C2314yes—
136C2×#4314—42no—
137C2×#4314C2314yes—
138C2×#4313—42no—
139C2×#4313C2314yes—
140C2×C8×D11—42no—
141C2×C8×D11C2314yes—
142#66951—28no—
143#66951—28no—
144#66950—22no—
145#66950—22no—
146#66950C2314yes—
147#66950C2314yes—
148#66948—22no—
149#66948C2314yes—
150#66947—28no—
151#66946—22no—
152#66946C2314yes—
153#66943—22no—
154#66943C2314yes—
155#66942—28no—
156#66940—22no—
157#66940C2314yes—
158#66929—28no—
159#66928—22no—
160#66928C2314yes—
161#66925D414yes—
162#66925C2314yes—
163#66923—28no—
164C4×Dic22—22no—
165C4×Dic22C2314yes—
166C11×#106C2314yes—
167C11×#106C2314yes—
168C11×C4⋊C8C2314yes—
169C11×#103C2314yes—
170C11×#103C2314yes—
171#66885C2314yes—
172#66880C2314yes—
173Dic11⋊C8C2314yes—
174Dic11⋊C8C2314yes—
175#66874C2314yes—
176#66874C2314yes—
177#66874C2314yes—
178#66873C2314yes—
179#66871C2314yes—
180#66871C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3258—111nomaximal, Sylow
183C23×D11—21no—
184C23×D11C2×D411yescharacteristic
185C2×Q8×C11—21no—
186C2×Q8×C11—24no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11—82no—
190C2×Q8×C11C2412yes—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11C2×D411yescharacteristic
202C22×Dic11C2×D411yescharacteristic
203C22×Dic11C2×D411yescharacteristic
204C2×D44—24no—
205C2×D44—21no—
206C2×D44—22no—
207C2×D44—22no—
208C2×D44—82no—
209C2×D44C2412yes—
210C2×C4×D11—24no—
211C2×C4×D11—22no—
212C2×C4×D11—22no—
213C2×C4×D11—82no—
214C2×C4×D11C2×D412yes—
215C2×C4×D11C2412yes—
216C2×Dic22—21no—
217C2×Dic22—21no—
218C2×Dic22—22no—
219C2×Dic22—22no—
220C2×Dic22—22no—
221C2×Dic22—22no—
222C2×Dic22C2412yes—
223C2×Dic22C2412yes—
224C2×C8×C11—22no—
225C2×C8×C11—22no—
226C2×C8×C11C2412yes—
227C2×C8×C11C2412yes—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4C2412yes—
234C11×C4⋊C4C2412yes—
235C11×C4⋊C4C2412yes—
236C42×C11—24no—
237C42×C11C2×D412yes—
238C42×C11C2412yes—
239#4326—44no—
240#4325—44no—
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)⋊C4—24no—
248(C2×D11)⋊C4C2×D414yes—
249(C2×D11)⋊C4C2×D414yes—
250C4⋊Dic11—24no—
251C4⋊Dic11—24no—
252C4⋊Dic11—24no—
253C4⋊Dic11—21no—
254C4⋊Dic11C2412yes—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4C2×D414yes—
262Dic11⋊C4C2×D414yes—
263C4×Dic11—24no—
264C4×Dic11—24no—
265C4×Dic11C2×D412yes—
266C4×Dic11C2412yes—
267C2×C11⋊C8—22no—
268C2×C11⋊C8—22no—
269C2×C11⋊C8C2412yes—
270C2×C11⋊C8C2412yes—
271Dic44—44no—
272#4314—44no—
273#4313—44no—
274C8×D11—44no—
275C2×#542—111no—
276C2×#541—111no—
277#3258—1116no—
278C2×#479—111no—
279C2×#477—111no—
280C2×#475D1111yescharacteristic, complemented
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×#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—42no—
303Q8×C11—84no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D412yes—
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11H(5,𝔽2)12yes—
318C2×C4×C112−1+412yes—
319C2×C4×C11C2511yescharacteristic
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11C22×D412yes—
330C2×Dic11C22×D412yes—
331C2×Dic11C22×D412yes—
332D44—22no—
333D44—22no—
334D44—42no—
335D44—84no—
336C4×D11—24no—
337C4×D11—22no—
338C4×D11—22no—
339C4×D11—84no—
340Dic22—22no—
341Dic22—22no—
342Dic22—22no—
343Dic22—22no—
344Dic22—42no—
345Dic22—42no—
346C8×C11—22no—
347C8×C11—22no—
348C11⋊C8—22no—
349C11⋊C8—22no—
350C22×Q16—111no—
351C22×Q16—111no—
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#475C2×D1118yescomplemented
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×#106C2×D1111yescharacteristic
396C2×#106C2×D1111yescharacteristic
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—21no—
438C22×Q8—111no—
439C22×Q8—111no—
440C22×Q8C22×D1111yescharacteristic
441C22×D4—111no—
442C22×D4—221no—
443C23×C4—111no—
444C23×C4—221no—
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—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—222no—
471#125—228no—
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—228no—
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—111no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
510C2×C4⋊C4C22×D1111yescharacteristic
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#106C22×D1114yes—
529#106C22×D1114yes—
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—24no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—82no—
555C2×Q8—112no—
556C2×Q8—112no—
557C2×Q8—221no—
558C2×Q8—221no—
559C2×Q8—222no—
560C2×Q8—222no—
561C2×Q8—222no—
562C2×Q8—222no—
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—224no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—882no—
586C22×C4D4×D1111yescharacteristic
587C22×C4D4×D1111yescharacteristic
588C22×C4C23×D1111yescharacteristic
589Q16—444no—
590Q16—444no—
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—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—114no—
609C4⋊C4—114no—
610C4⋊C4—112no—
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—221no—
620C4⋊C4—224no—
621C4⋊C4C23×D1112yes—
622C4⋊C4C23×D1112yes—
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—42no—
653Q8—84no—
654Q8—222no—
655Q8—222no—
656Q8—222no—
657Q8—222no—
658Q8—442no—
659Q8—442no—
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#6704012yes—
694C2×C4#6704212yes—
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#1062316012yes—
709C22#1062329312yes—
710C22#1062331012yes—
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#1062316012yes—
725C4C2×#6704011yescharacteristic
726C4C2×#6704211yescharacteristic
727C2—442no—
728C2—882no—
729C2#1308004914yesdirect product factor
730C2C2×#1062316011yescharacteristic
731C2C2×#1062329311yescharacteristic
732C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenterC2×#475D11
hypocenterC11C2×#3258
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
2. C2×#10623114C2semidirect
3. #13080049C2direct (N × H)
4. C2×#10622470C2semidirect
5. C2×#10622704C2semidirect
6. C2×#10622484C2semidirect
7. C2×#10622481C2semidirect
9. C2×#10622426C2semidirect
11. C2×#10622458C2semidirect
12. C2×#10622641C2semidirect
13. C2×#10622406C2semidirect
14. C2×#10622431C2semidirect
15. C2×#10622452C2semidirect
16. C2×C11×#475C2semidirect
32. #10623114C22semidirect
48. C11×#475C22semidirect
58. #10622704C22semidirect
59. #10622641C22semidirect
67. #10622484C22semidirect
68. #10622481C22semidirect
70. #10622470C22semidirect
71. #10622458C22semidirect
72. #10622452C22semidirect
73. #10622431C22semidirect
74. #10622426C22semidirect
76. #10622406C22semidirect
280. C2×#475D11semidirect
384. #475C2×D11semidirect
542. C2×C11#3258semidirect
640. C11C2×#3258semidirect
729. C2#13080049direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232642
C2×#106231142
#130800492
C2×#106224702
C2×#106227042
C2×#106224842
C2×#106224812
C2×#106224252
C2×#106224262
C2×#106224772
C2×#106224582
C2×#106226412
C2×#106224062
C2×#106224312
C2×#106224522
C2×C11×#4752
C2×#325811