Finite Group Databasebeta

← C2×#13081690 #15634788

Subgroups — C2×#13081690 #15634788

Order 2816.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623263C211yesmaximal, characteristic, complemented
2C2×#10623099C211yesmaximal, characteristic, complemented
3#13081690C2116yesmaximal, direct product factor
4C2×#10622803C211yesmaximal, characteristic, complemented
5C2×#10622699C211yesmaximal, characteristic, complemented
6C2×#10622804C211yesmaximal, characteristic
7C2×#10622411C211yesmaximal, characteristic, complemented
8C2×#10622798C211yesmaximal, characteristic, complemented
9C2×#10622795C211yesmaximal, characteristic, complemented
10C2×#10622432C211yesmaximal, characteristic
11C2×#10622457C211yesmaximal, characteristic
12C2×#10622441C211yesmaximal, characteristic, complemented
13C2×#10622430C211yesmaximal, characteristic, complemented
14C2×#10622639C211yesmaximal, characteristic, complemented
15C2×#10622403C211yesmaximal, characteristic, complemented
16C2×C11×#462C211yesmaximal, characteristic, complemented
17C22×C11×Q16C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×#67000C2211yescharacteristic
22C2×#67000C2211yescharacteristic
23C2×#67000C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C2×Q8×Dic11C2211yescharacteristic
26C2×#66997C2211yescharacteristic
27C22×#4326C2211yescharacteristic
28C22×#4326C2211yescharacteristic
29C22×#4325C2211yescharacteristic
30C22×#4325C2211yescharacteristic
31C22×#4325C2211yescharacteristic
32C22×D88C2211yescharacteristic
33C22×#4314C2211yescharacteristic
34#10623263—24no—
35#10623263C2218yescomplemented
36#10623099—24no—
37#10623099C2218yescomplemented
38C2×#66951—21no—
39C2×#66951—21no—
40C2×#66951—21no—
41C2×#66950—21no—
42C2×#66949—21no—
43C2×#66946C2211yescharacteristic
44C2×#66945—21no—
45C2×#66940C2211yescharacteristic
46C2×#66929—21no—
47C2×#66928C2211yescharacteristic
48C2×C4×D44C2211yescharacteristic
49C2×#66925—21no—
50C2×C4×Dic22C2211yescharacteristic
51C11×#462C2218yescomplemented
52C2×C11×C4⋊C8C2211yescharacteristic
53C2×C11×#103C2211yescharacteristic
54C2×C11×#103C2211yescharacteristic
55C2×#66899C2211yescharacteristic
56#10622804C2218yes—
57#10622803C2218yescomplemented
58#10622798C2218yescomplemented
59#10622795C2218yescomplemented
60C2×#66885C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×#66879C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65C2×C8×Dic11C2211yescharacteristic
66#10622699C2218yescomplemented
67#10622639C2218yescomplemented
68C2×#66873C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66867C2211yescharacteristic
71#10622457C2218yes—
72#10622441C2218yescomplemented
73#10622432C2218yes—
74#10622430C2218yescomplemented
75#10622411C2218yescomplemented
76#10622403C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D44C2311yescharacteristic
81C22×D44C2311yescharacteristic
82C22×C4×D11—21no—
83C22×C4×D11—21no—
84C22×Dic22D411yescharacteristic
85C22×Dic22C2311yescharacteristic
86C2×C11×Q16—42no—
87C2×C11×Q16—42no—
88C2×C11×Q16C2314yes—
89C2×C11×Q16C2314yes—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C11×C4⋊Q8—22no—
93C11×C4⋊Q8C2314yes—
94C4×Q8×C11—22no—
95C4×Q8×C11C2314yes—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102#67000—22no—
103#67000—22no—
104#67000—22no—
105#67000C2314yes—
106#67000C2314yes—
107#67000C2314yes—
108Q8×Dic11—22no—
109Q8×Dic11—22no—
110Q8×Dic11C2314yes—
111Q8×Dic11C2314yes—
112#66997—22no—
113#66997C2314yes—
114C2×#4326—24no—
115C2×#4326—42no—
116C2×#4326C2314yes—
117C2×#4326C2314yes—
118C2×#4325—24no—
119C2×#4325—24no—
120C2×#4325—42no—
121C2×#4325C2314yes—
122C2×#4325C2314yes—
123C2×#4325C2314yes—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×C4⋊Dic11—21no—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11D411yescharacteristic
137C2×C4⋊Dic11C2311yescharacteristic
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4D411yescharacteristic
142C2×Dic11⋊C4D411yescharacteristic
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×D88—42no—
151C2×D88C2314yes—
152C2×#4314—42no—
153C2×#4314C2314yes—
154#66951—28no—
155#66951—28no—
156#66951—28no—
157#66950—28no—
158#66949—28no—
159#66946—22no—
160#66946C2314yes—
161#66945—28no—
162#66940—22no—
163#66940C2314yes—
164#66929—28no—
165#66928—22no—
166#66928C2314yes—
167C4×D44—22no—
168C4×D44C2314yes—
169#66925—28no—
170C4×Dic22D414yes—
171C4×Dic22C2314yes—
172C11×C4⋊C8C2314yes—
173C11×#103C2314yes—
174C11×#103C2314yes—
175#66899C2314yes—
176#66885C2314yes—
177#66880C2314yes—
178#66879C2314yes—
179Dic11⋊C8C2314yes—
180Dic11⋊C8C2314yes—
181C8×Dic11C2314yes—
182#66873C2314yes—
183#66871C2314yes—
184#66867C2314yes—
185C2×#3402—111nomaximal, Sylow
186C23×D11—21no—
187C23×D11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11—22no—
195C2×Q8×C11—22no—
196C2×Q8×C11—22no—
197C2×Q8×C11C2412yes—
198C2×Q8×C11C2412yes—
199C2×Q8×C11C2412yes—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2411yescharacteristic
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11C2×D411yescharacteristic
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212C22×Dic11C2×D411yescharacteristic
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—22no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44—22no—
219C2×D44C2412yes—
220C2×D44C2412yes—
221C2×C4×D11—24no—
222C2×C4×D11—24no—
223C2×C4×D11—44no—
224C2×C4×D11—44no—
225C2×Dic22—21no—
226C2×Dic22—22no—
227C2×Dic22—22no—
228C2×Dic22—42no—
229C2×Dic22C2×D414yes—
230C2×Dic22C2412yes—
231C11×Q16—44no—
232C11×Q16—44no—
233C2×C8×C11—22no—
234C2×C8×C11—22no—
235C2×C8×C11C2412yes—
236C2×C8×C11C2412yes—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4—24no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4C2412yes—
242C42×C11—24no—
243C42×C11C2×D412yes—
244C42×C11C2412yes—
245#4326—28no—
246#4326—44no—
247#4325—28no—
248#4325—28no—
249#4325—44no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260C4⋊Dic11—24no—
261C4⋊Dic11—24no—
262C4⋊Dic11—21no—
263C4⋊Dic11C2×D414yes—
264C4⋊Dic11C2412yes—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4C2×D414yes—
269Dic11⋊C4C2×D414yes—
270C4×Dic11—24no—
271C4×Dic11—24no—
272C4×Dic11—24no—
273C4×Dic11C2×D412yes—
274C4×Dic11C2×D412yes—
275C4×Dic11C2412yes—
276C4×Dic11C2412yes—
277C2×C11⋊C8—22no—
278C2×C11⋊C8#4114yes—
279C2×C11⋊C8C2412yes—
280C2×C11⋊C8C2412yes—
281D88—44no—
282#4314—44no—
283C2×#556—111no—
284C2×#556—111no—
285#3402—1116no—
286C2×#497—111no—
287C2×#497—111no—
288C2×#495—111no—
289C2×#464—111no—
290C2×#464—111no—
291C2×#462—111no—
292C2×#462D1111yescharacteristic, complemented
293C2×#463—111no—
294C2×#463—111no—
295C2×#446—111no—
296C2×#440—111no—
297C2×#440—111no—
298C2×C4×Q16—111no—
299C23×C11C22×D411yescharacteristic
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—42no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—42no—
308Q8×C11—22no—
309Q8×C11—22no—
310Q8×C11—22no—
311Q8×C11—22no—
312Q8×C11—22no—
313Q8×C11—22no—
314Q8×C11—42no—
315Q8×C11—42no—
316Q8×C11—42no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D412yes—
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C2×#4112yes—
331C2×C4×C11H(5,𝔽2)12yes—
332C2×C4×C11C2511yescharacteristic
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11C22×D412yes—
342C2×Dic11C22×D412yes—
343C2×Dic11C22×D412yes—
344C2×Dic11C22×D412yes—
345D44—22no—
346D44—22no—
347D44—22no—
348D44—22no—
349D44—42no—
350D44—42no—
351C4×D11—48no—
352C4×D11—48no—
353Dic22—22no—
354Dic22—22no—
355Dic22—44no—
356Dic22—42no—
357C8×C11—22no—
358C8×C11—22no—
359C11⋊C8—22no—
360C11⋊C8C2×#4114yes—
361C22×Q16—111no—
362C22×Q16—111no—
363C22×Q16C2×D1111yescharacteristic
364C22×Q16C2×D1111yescharacteristic
365C22×SD16—111no—
366C22×SD16—111no—
367C22×SD16—111no—
368C22×SD16—111no—
369C22×D8—111no—
370#556—118no—
371#556—118no—
372#556—224no—
373#556—224no—
374C2×C4⋊Q8—111no—
375C2×C4⋊Q8C2×D1111yescharacteristic
376C2×#126—221no—
377C2×#126—221no—
378C2×#126—221no—
379C2×#126—221no—
380C2×#124—111no—
381C2×#124—111no—
382C2×#124—111no—
383C2×#124—111no—
384C2×C22⋊Q8—221no—
385C2×C22⋊Q8—221no—
386C2×C4×Q8—111no—
387C2×C4×Q8—111no—
388C2×C4×Q8—111no—
389C2×C4×Q8—111no—
390C2×C4×Q8C2×D1111yescharacteristic
391C2×C4×D4—111no—
392C2×C4×D4—111no—
393C2×#117—221no—
394C2×#117—221no—
395#497—118no—
396#497—118no—
397#495—118no—
398#464—118no—
399#464—118no—
400#463—118no—
401#463—118no—
402#462—118no—
403#462C2×D1118yescomplemented
404#446—118no—
405#440—118no—
406#440—118no—
407C4×Q16—118no—
408C2×#107—111no—
409C2×C4⋊C8—111no—
410C2×C4⋊C8—111no—
411C2×C4⋊C8C2×D1111yescharacteristic
412C2×#103—111no—
413C2×#103—111no—
414C2×#103C2×D1111yescharacteristic
415C2×#103C2×D1111yescharacteristic
416C2×#102—111no—
417C2×#102—111no—
418C2×#97—111no—
419C2×#97—111no—
420C2×C4×C8—111no—
421C22×C11#55012yes—
422C22×C11#57512yes—
423C22×C11#57812yes—
424C22×C11C23×D411yescharacteristic
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—42no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—84no—
432C2×D11—84no—
433C4×C11—22no—
434C4×C11—22no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11—42no—
439C4×C11#55012yes—
440C4×C11C22×#4111yescharacteristic
441C4×C11C2×H(5,𝔽2)11yescharacteristic
442Dic11—22no—
443Dic11—22no—
444Dic11—22no—
445Dic11—22no—
446Dic11—42no—
447Dic11—42no—
448C22×Q8—111no—
449C22×Q8—111no—
450C22×Q8C22×D1111yescharacteristic
451C22×Q8C22×D1111yescharacteristic
452C22×Q8C22×D1111yescharacteristic
453C22×D4—111no—
454C22×D4—111no—
455C23×C4—221no—
456C23×C4—221no—
457C2×Q16—42no—
458C2×Q16—42no—
459C2×Q16—114no—
460C2×Q16—114no—
461C2×Q16—224no—
462C2×Q16—442no—
463C2×Q16C22×D1114yes—
464C2×Q16C22×D1114yes—
465C2×SD16—114no—
466C2×SD16—114no—
467C2×SD16—114no—
468C2×SD16—114no—
469C2×SD16—224no—
470C2×SD16—224no—
471C2×SD16—442no—
472C2×SD16—442no—
473C2×D8—114no—
474C2×D8—442no—
475C22×C8—111no—
476C22×C8—111no—
477C22×C8C22×D1111yescharacteristic
478C22×C8C22×D1111yescharacteristic
479C4⋊Q8—22no—
480C4⋊Q8—114no—
481C4⋊Q8—222no—
482C4⋊Q8C22×D1114yes—
483#126—228no—
484#126—228no—
485#126—228no—
486#126—228no—
487#124—114no—
488#124—114no—
489#124—114no—
490#124—114no—
491#124—222no—
492#124—222no—
493#124—222no—
494#124—222no—
495C22⋊Q8—228no—
496C22⋊Q8—228no—
497C4×Q8—22no—
498C4×Q8—114no—
499C4×Q8—114no—
500C4×Q8—114no—
501C4×Q8—114no—
502C4×Q8—114no—
503C4×Q8—222no—
504C4×Q8—222no—
505C4×Q8—222no—
506C4×Q8C22×D1114yes—
507C4×D4—114no—
508C4×D4—114no—
509C4×D4—222no—
510C4×D4—222no—
511#117—228no—
512#117—228no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—111no—
518C2×C4⋊C4—111no—
519C2×C4⋊C4—111no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4—221no—
524C2×C4⋊C4—221no—
525C2×C4⋊C4C22×D1111yescharacteristic
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4—221no—
535C2×C22⋊C4—221no—
536C2×C42—21no—
537C2×C42—111no—
538C2×C42—111no—
539C2×C42—221no—
540C2×C42—221no—
541C2×C42—221no—
542C2×C42C22×D1111yescharacteristic
543#107—114no—
544C4⋊C8—114no—
545C4⋊C8—114no—
546C4⋊C8C22×D1114yes—
547#103—114no—
548#103—114no—
549#103C22×D1114yes—
550#103C22×D1114yes—
551#102—114no—
552#102—114no—
553#97—114no—
554#97—114no—
555C4×C8—114no—
556C2×C11#340214yescomplemented
557C2×C11C2×#55011yescharacteristic
558C2×C11C2×#57511yescharacteristic
559C2×C11C2×#57811yescharacteristic
560D11—82no—
561D11—82no—
562C24—221no—
563C24—221no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—114no—
574C2×Q8—112no—
575C2×Q8—221no—
576C2×Q8—222no—
577C2×Q8—222no—
578C2×Q8—442no—
579C2×Q8C23×D1112yes—
580C2×Q8C23×D1112yes—
581C2×Q8C23×D1112yes—
582C2×D4—112no—
583C2×D4—112no—
584C2×D4—221no—
585C2×D4—221no—
586C2×D4—222no—
587C2×D4—222no—
588C2×D4—222no—
589C2×D4—222no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—111no—
595C22×C4—111no—
596C22×C4—111no—
597C22×C4—111no—
598C22×C4—224no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—224no—
602C22×C4—444no—
603C22×C4—444no—
604C22×C4D4×D1111yescharacteristic
605C22×C4D4×D1111yescharacteristic
606C22×C4C23×D1111yescharacteristic
607Q16—44no—
608Q16—44no—
609Q16—228no—
610Q16—444no—
611SD16—228no—
612SD16—228no—
613SD16—444no—
614SD16—444no—
615D8—444no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—114no—
619C2×C8—112no—
620C2×C8—112no—
621C2×C8—222no—
622C2×C8C23×D1112yes—
623C2×C8C23×D1112yes—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—21no—
628C4⋊C4—114no—
629C4⋊C4—114no—
630C4⋊C4—114no—
631C4⋊C4—112no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C4⋊C4—224no—
635C4⋊C4—224no—
636C4⋊C4—224no—
637C4⋊C4—221no—
638C4⋊C4C23×D1112yes—
639C22⋊C4—224no—
640C22⋊C4—224no—
641C22⋊C4—224no—
642C22⋊C4—224no—
643C22⋊C4—224no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C22⋊C4—224no—
648C22⋊C4—224no—
649C42—24no—
650C42—112no—
651C42—112no—
652C42—112no—
653C42—112no—
654C42—224no—
655C42—224no—
656C42—224no—
657C42D4×D1112yes—
658C42C23×D1112yes—
659C11C2×#340211yescharacteristic, complemented, Sylow
660C23—222no—
661C23—222no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23C2×D4×D1111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—22no—
674Q8—22no—
675Q8—42no—
676Q8—42no—
677Q8—42no—
678Q8—222no—
679Q8—222no—
680Q8—444no—
681Q8—442no—
682D4—222no—
683D4—222no—
684D4—222no—
685D4—222no—
686D4—442no—
687D4—442no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—112no—
699C2×C4—112no—
700C2×C4—112no—
701C2×C4—112no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—448no—
709C2×C4—448no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4C2×D4×D1112yes—
713C2×C4C2×D4×D1112yes—
714C2×C4C2×D4×D1111yescharacteristic
715C2×C4#6703712yes—
716C2×C4#41×D1112yes—
717C2×C4C24×D1111yescharacteristic
718C8—22no—
719C8—22no—
720C8—114no—
721C8—222no—
722C22—442no—
723C22—442no—
724C22—442no—
725C22—442no—
726C22—442no—
727C22—442no—
728C22—884no—
729C22—884no—
730C22#1062313012yes—
731C22#1062329712yes—
732C22#1062330812yes—
733C22C22×D4×D1111yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—222no—
741C4—222no—
742C4—222no—
743C4—222no—
744C4—442no—
745C4—442no—
746C4#1062313012yes—
747C4C2×#6703711yescharacteristic
748C4C2×#41×D1111yescharacteristic
749C2—882no—
750C2—882no—
751C2#1308169014yesdirect product factor
752C2C2×#1062313011yescharacteristic
753C2C2×#1062330811yescharacteristic
754C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
prime radicalC22×D88C22
hypercenterC2×#462D11
hypocenterC11C2×#3402
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×#10623263C2semidirect
2. C2×#10623099C2semidirect
3. #13081690C2direct (N × H)
4. C2×#10622803C2semidirect
5. C2×#10622699C2semidirect
7. C2×#10622411C2semidirect
8. C2×#10622798C2semidirect
9. C2×#10622795C2semidirect
12. C2×#10622441C2semidirect
13. C2×#10622430C2semidirect
14. C2×#10622639C2semidirect
15. C2×#10622403C2semidirect
16. C2×C11×#462C2semidirect
35. #10623263C22semidirect
37. #10623099C22semidirect
51. C11×#462C22semidirect
57. #10622803C22semidirect
58. #10622798C22semidirect
59. #10622795C22semidirect
66. #10622699C22semidirect
67. #10622639C22semidirect
72. #10622441C22semidirect
74. #10622430C22semidirect
75. #10622411C22semidirect
76. #10622403C22semidirect
292. C2×#462D11semidirect
403. #462C2×D11semidirect
556. C2×C11#3402semidirect
659. C11C2×#3402semidirect
751. C2#13081690direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×#106230992
#130816902
C2×#106228032
C2×#106226992
C2×#106228042
C2×#106224112
C2×#106227982
C2×#106227952
C2×#106224322
C2×#106224572
C2×#106224412
C2×#106224302
C2×#106226392
C2×#106224032
C2×C11×#4622
C2×#340211