Finite Group Databasebeta

← C2×#13081642 #15634736

Subgroups — C2×#13081642 #15634736

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623252C211yesmaximal, characteristic, complemented
2C2×#10623099C211yesmaximal, characteristic
3#13081642C2116yesmaximal, direct product factor
4C2×#10622803C211yesmaximal, characteristic
5C2×#10622699C211yesmaximal, characteristic
6C2×#10622794C211yesmaximal, characteristic, complemented
7C2×#10622798C211yesmaximal, characteristic
8C2×#10622458C211yesmaximal, characteristic
9C2×#10622406C211yesmaximal, characteristic, complemented
10C2×#10622795C211yesmaximal, characteristic, complemented
11C2×#10622431C211yesmaximal, characteristic
12C2×#10622441C211yesmaximal, characteristic, complemented
13C2×#10622643C211yesmaximal, characteristic, complemented
14C2×#10622402C211yesmaximal, characteristic, complemented
15C2×#10622401C211yesmaximal, characteristic
16C2×C11×#462C211yesmaximal, characteristic, complemented
17C22×C11×Q16C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×#67000C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C2×#66997C2211yescharacteristic
25C2×#66997C2211yescharacteristic
26C2×#66997C2211yescharacteristic
27C22×#4326C2211yescharacteristic
28C22×#4326C2211yescharacteristic
29C22×#4326C2211yescharacteristic
30C22×#4325C2211yescharacteristic
31C22×#4325C2211yescharacteristic
32C22×Dic44C2211yescharacteristic
33C22×#4314C2211yescharacteristic
34#10623252—24no—
35#10623252C2218yescomplemented
36#10623099—24no—
37#10623099C2218yes—
38C2×#66951—21no—
39C2×#66949—21no—
40C2×#66946C2211yescharacteristic
41C2×#66943—21no—
42C2×#66942—21no—
43C2×#66942—21no—
44C2×#66940—21no—
45C2×#66940C2211yescharacteristic
46C2×#66929—21no—
47C2×#66928C2211yescharacteristic
48C2×#66925—21no—
49C2×C4×Dic22C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic
51C11×#462C2218yescomplemented
52C2×C11×C4⋊C8C2211yescharacteristic
53C2×C11×#103C2211yescharacteristic
54C2×C11×#103C2211yescharacteristic
55C2×#66899C2211yescharacteristic
56#10622803C2218yes—
57#10622798C2218yes—
58#10622795C2218yescomplemented
59#10622794C2218yescomplemented
60C2×#66885C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×#66879C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65C2×C8×Dic11C2211yescharacteristic
66#10622699C2218yes—
67#10622643C2218yescomplemented
68C2×#66874C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66867C2211yescharacteristic
71#10622458C2218yes—
72#10622441C2218yescomplemented
73#10622431C2218yes—
74#10622406C2218yescomplemented
75#10622402C2218yescomplemented
76#10622401C2218yes—
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D44C2311yescharacteristic
81C22×C4×D11—21no—
82C22×Dic22D411yescharacteristic
83C22×Dic22C2311yescharacteristic
84C22×Dic22C2311yescharacteristic
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—
103Q8×Dic11—22no—
104Q8×Dic11—22no—
105Q8×Dic11C2314yes—
106Q8×Dic11C2314yes—
107#66997—22no—
108#66997—22no—
109#66997—22no—
110#66997C2314yes—
111#66997C2314yes—
112#66997C2314yes—
113C2×#4326—24no—
114C2×#4326—24no—
115C2×#4326—42no—
116C2×#4326C2314yes—
117C2×#4326C2314yes—
118C2×#4326C2314yes—
119C2×#4325—24no—
120C2×#4325—42no—
121C2×#4325C2314yes—
122C2×#4325C2314yes—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11D411yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4D411yescharacteristic
141C2×Dic11⋊C4D411yescharacteristic
142C2×C4×Dic11—21no—
143C2×C4×Dic11—21no—
144C2×C4×Dic11—21no—
145C2×C4×Dic11—21no—
146C2×C4×Dic11C2311yescharacteristic
147C2×C4×Dic11C2311yescharacteristic
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150C2×Dic44—42no—
151C2×Dic44C2314yes—
152C2×#4314—42no—
153C2×#4314C2314yes—
154#66951—28no—
155#66949—28no—
156#66946—22no—
157#66946C2314yes—
158#66943—28no—
159#66942—28no—
160#66942—28no—
161#66940—28no—
162#66940—22no—
163#66940C2314yes—
164#66929—28no—
165#66928—22no—
166#66928C2314yes—
167#66925—28no—
168C4×Dic22—22no—
169C4×Dic22D414yes—
170C4×Dic22C2314yes—
171C4×Dic22C2314yes—
172C11×C4⋊C8C2314yes—
173C11×#103C2314yes—
174C11×#103C2314yes—
175#66899C2314yes—
176#66885C2314yes—
177#66880C2314yes—
178#66879C2314yes—
179Dic11⋊C8C2314yes—
180Dic11⋊C8C2314yes—
181C8×Dic11C2314yes—
182#66874C2314yes—
183#66872C2314yes—
184#66867C2314yes—
185C2×#3398—111nomaximal, Sylow
186C23×D11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—22no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11—22no—
195C2×Q8×C11—22no—
196C2×Q8×C11C2412yes—
197C2×Q8×C11C2412yes—
198C2×Q8×C11C2412yes—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2411yescharacteristic
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11C2×D411yescharacteristic
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212C22×Dic11C2×D411yescharacteristic
213C2×D44—21no—
214C2×D44—22no—
215C2×D44—22no—
216C2×D44C2412yes—
217C2×C4×D11—24no—
218C2×C4×D11—44no—
219C2×Dic22—24no—
220C2×Dic22—21no—
221C2×Dic22—21no—
222C2×Dic22—22no—
223C2×Dic22—22no—
224C2×Dic22—22no—
225C2×Dic22—22no—
226C2×Dic22C2×D414yes—
227C2×Dic22C2412yes—
228C2×Dic22C2412yes—
229C11×Q16—44no—
230C11×Q16—44no—
231C2×C8×C11—22no—
232C2×C8×C11—22no—
233C2×C8×C11C2412yes—
234C2×C8×C11C2412yes—
235C11×C4⋊C4—24no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4C2412yes—
240C42×C11—24no—
241C42×C11C2×D412yes—
242C42×C11C2412yes—
243#4326—28no—
244#4326—28no—
245#4326—44no—
246#4325—28no—
247#4325—44no—
248(C2×D11)⋊C4—24no—
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—24no—
255C4⋊Dic11—21no—
256C4⋊Dic11C2×D414yes—
257C4⋊Dic11C2412yes—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4C2×D414yes—
267Dic11⋊C4C2×D414yes—
268C4×Dic11—24no—
269C4×Dic11—24no—
270C4×Dic11—24no—
271C4×Dic11—24no—
272C4×Dic11C2×D412yes—
273C4×Dic11C2×D412yes—
274C4×Dic11C2412yes—
275C4×Dic11C2412yes—
276C2×C11⋊C8—22no—
277C2×C11⋊C8#4114yes—
278C2×C11⋊C8C2412yes—
279C2×C11⋊C8C2412yes—
280Dic44—44no—
281#4314—44no—
282C2×#557—111no—
283C2×#556—111no—
284#3398—1116no—
285C2×#497—111no—
286C2×#497—111no—
287C2×#494—111no—
288C2×#464—111no—
289C2×#464—111no—
290C2×#462—111no—
291C2×#462—111no—
292C2×#462D1111yescharacteristic, complemented
293C2×#461—111no—
294C2×#446—111no—
295C2×#441—111no—
296C2×#441—111no—
297C2×C4×SD16—111no—
298C23×C11C22×D411yescharacteristic
299C22×D11—22no—
300C22×D11—42no—
301C22×D11—42no—
302C22×D11—42no—
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—42no—
310Q8×C11—42no—
311Q8×C11—42no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11C22×D412yes—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C2×#4112yes—
326C2×C4×C11H(5,𝔽2)12yes—
327C2×C4×C11C2511yescharacteristic
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11#13714yes—
338C2×Dic11C22×D412yes—
339C2×Dic11C22×D412yes—
340C2×Dic11C22×D412yes—
341C2×Dic11C22×D412yes—
342D44—22no—
343D44—22no—
344D44—42no—
345C4×D11—48no—
346Dic22—28no—
347Dic22—22no—
348Dic22—22no—
349Dic22—22no—
350Dic22—22no—
351Dic22—42no—
352Dic22—42no—
353C8×C11—22no—
354C8×C11—22no—
355C11⋊C8—22no—
356C11⋊C8C2×#4114yes—
357C22×Q16—111no—
358C22×Q16—111no—
359C22×Q16—111no—
360C22×Q16—111no—
361C22×Q16C2×D1111yescharacteristic
362C22×Q16C2×D1111yescharacteristic
363C22×SD16—111no—
364C22×SD16—111no—
365C22×SD16—111no—
366#557—118no—
367#557—224no—
368#556—118no—
369#556—224no—
370C2×C4⋊Q8—111no—
371C2×C4⋊Q8—111no—
372C2×C4⋊Q8—111no—
373C2×C4⋊Q8C2×D1111yescharacteristic
374C2×#126—221no—
375C2×#126—221no—
376C2×#125—221no—
377C2×#125—221no—
378C2×#125—221no—
379C2×#124—111no—
380C2×#124—111no—
381C2×C22⋊Q8—221no—
382C2×C4×Q8—111no—
383C2×C4×Q8—111no—
384C2×C4×Q8—111no—
385C2×C4×Q8—111no—
386C2×C4×Q8—111no—
387C2×C4×Q8—221no—
388C2×C4×Q8C2×D1111yescharacteristic
389C2×C4×D4—111no—
390C2×#117—221no—
391#497—118no—
392#497—118no—
393#494—118no—
394#464—118no—
395#464—118no—
396#462—118no—
397#462—118no—
398#462C2×D1118yescomplemented
399#461—118no—
400#446—118no—
401#441—118no—
402#441—118no—
403C4×SD16—118no—
404C2×#106—111no—
405C2×C4⋊C8—111no—
406C2×C4⋊C8—111no—
407C2×C4⋊C8C2×D1111yescharacteristic
408C2×#103—111no—
409C2×#103—111no—
410C2×#103—111no—
411C2×#103C2×D1111yescharacteristic
412C2×#103C2×D1111yescharacteristic
413C2×#102—111no—
414C2×#97—111no—
415C2×#97—111no—
416C2×C4×C8—111no—
417C22×C11#55012yes—
418C22×C11C2×#13712yes—
419C22×C11#57812yes—
420C22×C11C23×D411yescharacteristic
421C2×D11—42no—
422C2×D11—42no—
423C2×D11—42no—
424C2×D11—84no—
425C4×C11—22no—
426C4×C11—22no—
427C4×C11—42no—
428C4×C11—42no—
429C4×C11—42no—
430C4×C11—42no—
431C4×C11#55012yes—
432C4×C11C22×#4111yescharacteristic
433C4×C11C2×H(5,𝔽2)11yescharacteristic
434Dic11—22no—
435Dic11—22no—
436Dic11—22no—
437Dic11—42no—
438Dic11—42no—
439Dic11—42no—
440Dic11C2×#13714yes—
441C22×Q8—111no—
442C22×Q8—111no—
443C22×Q8—111no—
444C22×Q8C22×D1111yescharacteristic
445C22×Q8C22×D1111yescharacteristic
446C22×Q8C22×D1111yescharacteristic
447C22×D4—111no—
448C23×C4—221no—
449C2×Q16—42no—
450C2×Q16—42no—
451C2×Q16—114no—
452C2×Q16—114no—
453C2×Q16—114no—
454C2×Q16—114no—
455C2×Q16—224no—
456C2×Q16—224no—
457C2×Q16—442no—
458C2×Q16—442no—
459C2×Q16C22×D1114yes—
460C2×Q16C22×D1114yes—
461C2×SD16—114no—
462C2×SD16—114no—
463C2×SD16—114no—
464C2×SD16—224no—
465C2×SD16—442no—
466C2×SD16—442no—
467C22×C8—111no—
468C22×C8—111no—
469C22×C8C22×D1111yescharacteristic
470C22×C8C22×D1111yescharacteristic
471C4⋊Q8—22no—
472C4⋊Q8—114no—
473C4⋊Q8—114no—
474C4⋊Q8—114no—
475C4⋊Q8—222no—
476C4⋊Q8—222no—
477C4⋊Q8—222no—
478C4⋊Q8C22×D1114yes—
479#126—228no—
480#126—228no—
481#125—228no—
482#125—228no—
483#125—228no—
484#124—114no—
485#124—114no—
486#124—222no—
487#124—222no—
488C22⋊Q8—228no—
489C4×Q8—22no—
490C4×Q8—114no—
491C4×Q8—114no—
492C4×Q8—114no—
493C4×Q8—114no—
494C4×Q8—114no—
495C4×Q8—114no—
496C4×Q8—222no—
497C4×Q8—222no—
498C4×Q8—222no—
499C4×Q8—228no—
500C4×Q8—222no—
501C4×Q8C22×D1114yes—
502C4×D4—114no—
503C4×D4—222no—
504#117—228no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4C22×D1111yescharacteristic
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C42—21no—
529C2×C42—111no—
530C2×C42—111no—
531C2×C42—221no—
532C2×C42—221no—
533C2×C42—221no—
534C2×C42—221no—
535C2×C42C22×D1111yescharacteristic
536#106—114no—
537C4⋊C8—114no—
538C4⋊C8—114no—
539C4⋊C8C22×D1114yes—
540#103—114no—
541#103—114no—
542#103—114no—
543#103C22×D1114yes—
544#103C22×D1114yes—
545#102—114no—
546#97—114no—
547#97—114no—
548C4×C8—114no—
549C2×C11#339814yescomplemented
550C2×C11C2×#55011yescharacteristic
551C2×C11C22×#13711yescharacteristic
552C2×C11C2×#57811yescharacteristic
553D11—82no—
554C24—221no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—114no—
565C2×Q8—112no—
566C2×Q8—112no—
567C2×Q8—224no—
568C2×Q8—221no—
569C2×Q8—221no—
570C2×Q8—222no—
571C2×Q8—222no—
572C2×Q8—222no—
573C2×Q8—222no—
574C2×Q8C23×D1112yes—
575C2×Q8C23×D1112yes—
576C2×Q8C23×D1112yes—
577C2×D4—112no—
578C2×D4—221no—
579C2×D4—222no—
580C2×D4—222no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—111no—
586C22×C4—111no—
587C22×C4—111no—
588C22×C4—111no—
589C22×C4—224no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—444no—
594C22×C4D4×D1111yescharacteristic
595C22×C4D4×D1111yescharacteristic
596C22×C4C23×D1111yescharacteristic
597Q16—44no—
598Q16—44no—
599Q16—228no—
600Q16—228no—
601Q16—444no—
602Q16—444no—
603SD16—228no—
604SD16—444no—
605SD16—444no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—114no—
609C2×C8—112no—
610C2×C8—112no—
611C2×C8—222no—
612C2×C8C23×D1112yes—
613C2×C8C23×D1112yes—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—114no—
619C4⋊C4—114no—
620C4⋊C4—114no—
621C4⋊C4—112no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—224no—
626C4⋊C4—224no—
627C4⋊C4—224no—
628C4⋊C4—224no—
629C4⋊C4—224no—
630C4⋊C4—224no—
631C4⋊C4—221no—
632C4⋊C4—224no—
633C4⋊C4C23×D1112yes—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C22⋊C4—224no—
639C42—24no—
640C42—112no—
641C42—112no—
642C42—112no—
643C42—112no—
644C42—224no—
645C42—224no—
646C42—224no—
647C42—224no—
648C42D4×D1112yes—
649C42C23×D1112yes—
650C11C2×#339811yescharacteristic, complemented, Sylow
651C23—222no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23C2×D4×D1111yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—228no—
666Q8—222no—
667Q8—222no—
668Q8—222no—
669Q8—222no—
670Q8—442no—
671Q8—442no—
672D4—222no—
673D4—222no—
674D4—442no—
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—114no—
686C2×C4—112no—
687C2×C4—112no—
688C2×C4—112no—
689C2×C4—112no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—448no—
697C2×C4—442no—
698C2×C4—442no—
699C2×C4—442no—
700C2×C4C2×D4×D1112yes—
701C2×C4C2×D4×D1112yes—
702C2×C4C2×D4×D1111yescharacteristic
703C2×C4#6703712yes—
704C2×C4#41×D1112yes—
705C2×C4C24×D1111yescharacteristic
706C8—22no—
707C8—22no—
708C8—114no—
709C8—222no—
710C22—442no—
711C22—442no—
712C22—442no—
713C22—884no—
714C22#1062313012yes—
715C22#1062329712yes—
716C22D11×#13712yes—
717C22C22×D4×D1111yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—114no—
725C4—222no—
726C4—222no—
727C4—222no—
728C4—442no—
729C4—442no—
730C4—442no—
731C4#1062313012yes—
732C4C2×#6703711yescharacteristic
733C4C2×#41×D1111yescharacteristic
734C2—882no—
735C2#1308164214yesdirect product factor
736C2C2×#1062313011yescharacteristic
737C2C2×D11×#13711yescharacteristic
738C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#462D11
hypocenterC11C2×#3398
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
1. C2×#10623252C2semidirect
3. #13081642C2direct (N × H)
6. C2×#10622794C2semidirect
9. C2×#10622406C2semidirect
10. C2×#10622795C2semidirect
12. C2×#10622441C2semidirect
13. C2×#10622643C2semidirect
14. C2×#10622402C2semidirect
16. C2×C11×#462C2semidirect
35. #10623252C22semidirect
51. C11×#462C22semidirect
58. #10622795C22semidirect
59. #10622794C22semidirect
67. #10622643C22semidirect
72. #10622441C22semidirect
74. #10622406C22semidirect
75. #10622402C22semidirect
292. C2×#462D11semidirect
398. #462C2×D11semidirect
549. C2×C11#3398semidirect
650. C11C2×#3398semidirect
735. C2#13081642direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232522
C2×#106230992
#130816422
C2×#106228032
C2×#106226992
C2×#106227942
C2×#106227982
C2×#106224582
C2×#106224062
C2×#106227952
C2×#106224312
C2×#106224412
C2×#106226432
C2×#106224022
C2×#106224012
C2×C11×#4622
C2×#339811