Finite Group Databasebeta

← C2×#13078870 #15622079

Subgroups — C2×#13078870 #15622079

Order 2816.

2210 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623228C211yesmaximal, characteristic, complemented
2C2×#10623076C211yesmaximal, characteristic
3#13078870C2116yesmaximal, direct product factor
4C2×#10622480C211yesmaximal, characteristic, complemented
5C2×#10622501C211yesmaximal, characteristic, complemented
6C2×#10622679C211yesmaximal, characteristic, complemented
7C2×#10622454C211yesmaximal, characteristic, complemented
8C2×#10622632C211yesmaximal, characteristic, complemented
9C2×#10622389C211yesmaximal, characteristic
10C2×#10622389C211yesmaximal, characteristic
11C2×#10622502C211yesmaximal, characteristic, complemented
12C2×#10622370C211yesmaximal, characteristic, complemented
13C2×#10622371C211yesmaximal, characteristic, complemented
14C2×#10622465C211yesmaximal, characteristic, complemented
15C2×#10622453C211yesmaximal, characteristic, complemented
16C2×C11×#478C211yesmaximal, characteristic, complemented
17C22×D4×D11C2211yescharacteristic
18C2×C11×#125C2211yescharacteristic, complemented
19C2×C4×D4×C11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C2×C4×C22⋊D11—21no—
24C22×(C2×D11)⋊C4—21no—
25C22×#4314C2211yescharacteristic
26C22×#4314C2211yescharacteristic
27#10623228—24no—
28#10623228C2218yescomplemented
29#10623076—24no—
30#10623076C2218yes—
31C2×#66951—21no—
32C2×#66951—21no—
33C2×#66950C2211yescharacteristic
34C2×#66950C2211yescharacteristic
35C2×#66946C2211yescharacteristic
36C2×#66945C2211yescharacteristic
37C2×#66943—21no—
38C2×#66943—21no—
39C2×#66940C2211yescharacteristic, complemented
40C2×#66940C2211yescharacteristic, complemented
41C2×(C22⋊D11)⋊C4—21no—
42C2×C22⋊C4×D11—21no—
43C2×C4×D44C2211yescharacteristic
44C2×#66925C2211yescharacteristic
45C2×#66922C2211yescharacteristic, complemented
46C11×#478C2218yescomplemented
47C2×C11×#107C2211yescharacteristic, complemented
48C2×C11×#106C2211yescharacteristic, complemented
49C2×C11×C4⋊C8C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×(C2×D11)⋊C8C2211yescharacteristic
53C2×(C2×D11)⋊C8C2211yescharacteristic
54C2×#66880C2211yescharacteristic, complemented
55C2×#66880C2211yescharacteristic, complemented
56C2×#66879C2211yescharacteristic, complemented
57C2×C8×Dic11C2211yescharacteristic, complemented
58#10622679C2218yescomplemented
59#10622632C2218yescomplemented
60C2×#66874C2211yescharacteristic, complemented
61C2×#66874C2211yescharacteristic, complemented
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66872C2211yescharacteristic, complemented
65C2×#66871C2211yescharacteristic, complemented
66C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
67#10622502C2218yescomplemented
68#10622501C2218yescomplemented
69#10622480C2218yescomplemented
70#10622465C2218yescomplemented
71#10622454C2218yescomplemented
72#10622453C2218yescomplemented
73#10622389C2218yes—
74#10622389C2218yes—
75#10622371C2218yescomplemented
76#10622370C2218yescomplemented
77C24×D11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C22×C22⋊D11—21no—
81C23×Dic11—21no—
82C2×D4×D11—24no—
83C2×D4×D11—24no—
84C2×D4×D11—22no—
85C2×D4×D11C2314yes—
86C22×D44C2311yescharacteristic
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×C4×D11C2311yescharacteristic
90C22×Dic22C2311yescharacteristic
91C22×Dic22C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C11×#125—22no—
95C11×#125C2314yescomplemented
96C4×D4×C11—22no—
97C4×D4×C11C2314yes—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C22⋊C4—21no—
104C2×C42×C11C2311yescharacteristic
105C2×C22⋊Dic11—21no—
106D4×Dic11—22no—
107D4×Dic11C2314yes—
108C2×#4324—24no—
109C2×#4324—24no—
110C2×#4324C2314yes—
111C2×#4324C2314yes—
112C4×C22⋊D11—28no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—28no—
119C2×(C2×D11)⋊C4D411yescharacteristic
120C2×(C2×D11)⋊C4D411yescharacteristic
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11C2311yescharacteristic
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4D411yescharacteristic
129C2×Dic11⋊C4D411yescharacteristic
130C2×C4×Dic11—21no—
131C2×C4×Dic11—21no—
132C2×C4×Dic11—21no—
133C2×C4×Dic11C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C2×#4314—24no—
137C2×#4314—24no—
138C2×#4314C2314yes—
139C2×#4314C2314yes—
140#66951—28no—
141#66951—28no—
142#66950—22no—
143#66950—22no—
144#66950C2314yes—
145#66950C2314yes—
146#66946—22no—
147#66946C2314yes—
148#66945—22no—
149#66945C2314yes—
150#66943—28no—
151#66943—28no—
152#66940—22no—
153#66940—22no—
154#66940C2314yescomplemented
155#66940C2314yescomplemented
156(C22⋊D11)⋊C4—28no—
157C22⋊C4×D11—28no—
158C4×D44—22no—
159C4×D44C2314yes—
160#66925D414yes—
161#66925C2314yes—
162#66922—22no—
163#66922C2314yescomplemented
164C11×#107C2314yescomplemented
165C11×#106C2314yescomplemented
166C11×C4⋊C8C2314yescomplemented
167C11×#102C2314yes—
168C11×#102C2314yes—
169(C2×D11)⋊C8C2314yes—
170(C2×D11)⋊C8C2314yes—
171#66880C2314yescomplemented
172#66880C2314yescomplemented
173#66879C2314yescomplemented
174C8×Dic11C2314yescomplemented
175#66874C2314yescomplemented
176#66874C2314yescomplemented
177#66873C2314yes—
178#66873C2314yes—
179#66872C2314yescomplemented
180#66871C2314yescomplemented
181C4⋊(C11⋊C8)C2314yescomplemented
182C2×#3123—111nomaximal, Sylow
183C24×C11—21no—
184C23×D11—21no—
185C23×D11—28no—
186C23×D11—24no—
187C23×D11—82no—
188C23×D11—82no—
189C23×D11C2×D411yescharacteristic
190C2×D4×C11—21no—
191C2×D4×C11—22no—
192C2×D4×C11#4114yes—
193C2×D4×C11C2412yes—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—24no—
198C22×C4×C11—82no—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—28no—
203C2×C22⋊D11—24no—
204C22×Dic11—24no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—82no—
209C22×Dic11C2×D411yescharacteristic
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212D4×D11—216no—
213D4×D11—28no—
214D4×D11—28no—
215C2×D44—21no—
216C2×D44—22no—
217C2×D44#4114yes—
218C2×D44C2412yes—
219C2×C4×D11—24no—
220C2×C4×D11—24no—
221C2×C4×D11—22no—
222C2×C4×D11—22no—
223C2×C4×D11—82no—
224C2×C4×D11—82no—
225C2×C4×D11C2×D412yes—
226C2×C4×D11C2412yes—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—22no—
230C2×Dic22—22no—
231C2×Dic22—22no—
232C2×Dic22—22no—
233C2×Dic22C2412yes—
234C2×Dic22C2412yes—
235C2×C8×C11—22no—
236C2×C8×C11—22no—
237C2×C8×C11C2412yes—
238C2×C8×C11C2412yes—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—24no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4C2412yes—
245C11×C4⋊C4C2412yes—
246C11×C4⋊C4C2412yes—
247C11×C22⋊C4—24no—
248C42×C11C2×D412yes—
249C42×C11C2412yes—
250C22⋊Dic11—24no—
251#4324—28no—
252#4324—28no—
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)⋊C4C2×D414yes—
259(C2×D11)⋊C4C2×D414yes—
260C4⋊Dic11—24no—
261C4⋊Dic11—24no—
262C4⋊Dic11—24no—
263C4⋊Dic11—24no—
264C4⋊Dic11—21no—
265C4⋊Dic11C2412yes—
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×Dic11C2412yes—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—22no—
277C2×C11⋊C8C2412yes—
278C2×C11⋊C8C2412yes—
279#4314—28no—
280#4314—28no—
281C2×#541—111no—
282C2×#518—111no—
283#3123—1116no—
284C2×#485—111no—
285C2×#485—111no—
286C2×#478—111no—
287C2×#478D1111yescharacteristic, complemented
288C2×#461—111no—
289C2×#461—111no—
290C2×#450—111no—
291C2×#450—111no—
292C2×#440—111no—
293C2×#440—111no—
294C2×C4×SD16—111no—
295C2×C4×SD16—111no—
296C2×#433—111no—
297C23×C11—24no—
298C23×C11—22no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11C22×D411yescharacteristic
302C22×D11—22no—
303C22×D11—24no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—216no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—84no—
311C22×D11—84no—
312C22×D11—816no—
313C22×D11C22×D412yes—
314D4×C11—24no—
315D4×C11—22no—
316D4×C11C2×#4114yes—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—84no—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4112yes—
330C2×C4×C11C2×#4112yes—
331C2×C4×C11C2511yescharacteristic
332C22⋊D11—216no—
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×Dic11—42no—
342C2×Dic11—84no—
343C2×Dic11C22×D412yes—
344C2×Dic11C22×D412yes—
345C2×Dic11C22×D412yes—
346D44—24no—
347D44—22no—
348D44C2×#4114yes—
349C4×D11—24no—
350C4×D11—22no—
351C4×D11—22no—
352C4×D11—84no—
353C4×D11—84no—
354Dic22—22no—
355Dic22—22no—
356Dic22—22no—
357Dic22—22no—
358Dic22—42no—
359Dic22—42no—
360C8×C11—22no—
361C8×C11—22no—
362C11⋊C8—22no—
363C11⋊C8—22no—
364C23×D4—111no—
365C22×SD16—111no—
366C22×SD16—111no—
367C22×SD16—111no—
368C22×SD16—111no—
369#541—118no—
370#541—224no—
371C2×C4⋊Q8—111no—
372C2×#126—221no—
373C2×#126—221no—
374C2×#125—221no—
375C2×#125—221no—
376C2×#125C2×D1111yescharacteristic, complemented
377C2×C22⋊Q8—111no—
378C2×C22⋊Q8—111no—
379#518—118no—
380#518—224no—
381C2×C4×Q8—111no—
382C2×C4×Q8—111no—
383C2×C4×D4—111no—
384C2×C4×D4—111no—
385C2×C4×D4—111no—
386C2×C4×D4—221no—
387C2×C4×D4—221no—
388C2×C4×D4C2×D1111yescharacteristic
389C2×#117—111no—
390C2×#117—111no—
391C22×C22⋊C4—221no—
392C22×C22⋊C4—221no—
393#485—118no—
394#485—118no—
395#478—118no—
396#478C2×D1118yescomplemented
397#461—118no—
398#461—118no—
399#450—118no—
400#450—118no—
401#440—118no—
402#440—118no—
403C4×SD16—118no—
404C4×SD16—118no—
405#433—118no—
406C2×#107—111no—
407C2×#107C2×D1111yescharacteristic, complemented
408C2×#106—111no—
409C2×#106C2×D1111yescharacteristic, complemented
410C2×C4⋊C8—111no—
411C2×C4⋊C8C2×D1111yescharacteristic, complemented
412C2×#103—111no—
413C2×#103—111no—
414C2×#103—111no—
415C2×#103—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102C2×D1111yescharacteristic
419C2×#102C2×D1111yescharacteristic
420C2×C22⋊C8—111no—
421C2×C22⋊C8—111no—
422C2×#97—111no—
423C2×C4×C8—111no—
424C22×C11—24no—
425C22×C11—48no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11#52512yes—
429C22×C11#57712yes—
430C22×C11#57712yes—
431C22×C11C23×D411yescharacteristic
432C2×D11—22no—
433C2×D11—24no—
434C2×D11—22no—
435C2×D11—22no—
436C2×D11—44no—
437C2×D11—48no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—816no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11#52512yes—
447C4×C11C22×#4111yescharacteristic
448C4×C11C22×#4111yescharacteristic
449Dic11—22no—
450Dic11—22no—
451Dic11—22no—
452Dic11—42no—
453Dic11—42no—
454Dic11—42no—
455C25—221no—
456C22×Q8—111no—
457C22×Q8—111no—
458C22×D4—114no—
459C22×D4—111no—
460C22×D4—222no—
461C22×D4—221no—
462C22×D4—224no—
463C22×D4—224no—
464C22×D4C22×D1111yescharacteristic
465C23×C4—21no—
466C23×C4—111no—
467C23×C4—221no—
468C23×C4—221no—
469C23×C4—221no—
470C2×SD16—114no—
471C2×SD16—114no—
472C2×SD16—114no—
473C2×SD16—114no—
474C2×SD16—224no—
475C2×SD16—224no—
476C2×SD16—224no—
477C2×SD16—224no—
478C22×C8—111no—
479C22×C8—111no—
480C22×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
482C4⋊Q8—114no—
483C4⋊Q8—222no—
484#126—228no—
485#126—228no—
486#125—22no—
487#125—228no—
488#125—228no—
489#125C22×D1114yescomplemented
490C22⋊Q8—114no—
491C22⋊Q8—114no—
492C22⋊Q8—222no—
493C22⋊Q8—222no—
494C4×Q8—114no—
495C4×Q8—114no—
496C4×Q8—222no—
497C4×Q8—222no—
498C4×D4—22no—
499C4×D4—114no—
500C4×D4—114no—
501C4×D4—114no—
502C4×D4—222no—
503C4×D4—222no—
504C4×D4—228no—
505C4×D4—228no—
506C4×D4—222no—
507C4×D4C22×D1114yes—
508#117—114no—
509#117—114no—
510#117—114no—
511#117—222no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C4⋊C4C22×D1111yescharacteristic
525C2×C4⋊C4C22×D1111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—111no—
528C2×C22⋊C4—111no—
529C2×C22⋊C4—228no—
530C2×C22⋊C4—228no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4—221no—
535C2×C22⋊C4—221no—
536C2×C22⋊C4—221no—
537C2×C42—111no—
538C2×C42—221no—
539C2×C42—221no—
540C2×C42—221no—
541C2×C42C22×D1111yescharacteristic
542#107—114no—
543#107C22×D1114yescomplemented
544#106—114no—
545#106C22×D1114yescomplemented
546C4⋊C8—114no—
547C4⋊C8C22×D1114yescomplemented
548#103—114no—
549#103—114no—
550#103—114no—
551#103—114no—
552#102—114no—
553#102—114no—
554#102C22×D1114yes—
555#102C22×D1114yes—
556C22⋊C8—114no—
557C22⋊C8—114no—
558#97—114no—
559C4×C8—114no—
560C2×C11—44no—
561C2×C11#312314yescomplemented
562C2×C11C2×#52511yescharacteristic
563C2×C11C2×#57711yescharacteristic
564C2×C11C2×#57711yescharacteristic
565D11—42no—
566D11—44no—
567C24—21no—
568C24—111no—
569C24—224no—
570C24—228no—
571C24—221no—
572C24—882no—
573C24—882no—
574C2×Q8—112no—
575C2×Q8—112no—
576C2×Q8—221no—
577C2×Q8—221no—
578C2×Q8—222no—
579C2×Q8—222no—
580C2×Q8—222no—
581C2×Q8—222no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—114no—
585C2×D4—112no—
586C2×D4—224no—
587C2×D4—228no—
588C2×D4—2216no—
589C2×D4—228no—
590C2×D4—228no—
591C2×D4—221no—
592C2×D4—222no—
593C2×D4#434314yes—
594C2×D4C23×D1112yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—82no—
600C22×C4—111no—
601C22×C4—111no—
602C22×C4—111no—
603C22×C4—112no—
604C22×C4—112no—
605C22×C4—224no—
606C22×C4—224no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—224no—
613C22×C4—882no—
614C22×C4—882no—
615C22×C4—882no—
616C22×C4D4×D1111yescharacteristic
617C22×C4D4×D1111yescharacteristic
618C22×C4C23×D1111yescharacteristic
619SD16—228no—
620SD16—228no—
621SD16—228no—
622SD16—228no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—112no—
626C2×C8—112no—
627C2×C8—222no—
628C2×C8—222no—
629C2×C8C23×D1112yes—
630C2×C8C23×D1112yes—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—114no—
637C4⋊C4—114no—
638C4⋊C4—112no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4—221no—
644C4⋊C4—224no—
645C4⋊C4—224no—
646C4⋊C4C23×D1112yes—
647C4⋊C4C23×D1112yes—
648C4⋊C4C23×D1112yes—
649C22⋊C4—24no—
650C22⋊C4—114no—
651C22⋊C4—114no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C22⋊C4—224no—
657C22⋊C4—224no—
658C42—112no—
659C42—112no—
660C42—224no—
661C42—224no—
662C42—224no—
663C42D4×D1112yes—
664C42C23×D1112yes—
665C11C2×#312311yescharacteristic, complemented, Sylow
666C23—24no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—112no—
671C23—2216no—
672C23—222no—
673C23—222no—
674C23—222no—
675C23—224no—
676C23—222no—
677C23—442no—
678C23—442no—
679C23—884no—
680C23—884no—
681C23—8816no—
682C23C2×D4×D1111yescharacteristic
683Q8—222no—
684Q8—222no—
685Q8—222no—
686Q8—222no—
687Q8—442no—
688Q8—442no—
689D4—24no—
690D4—22no—
691D4—114no—
692D4—2216no—
693D4—224no—
694D4—222no—
695D4C2×#434314yes—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—112no—
706C2×C4—112no—
707C2×C4—112no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—224no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—884no—
721C2×C4—884no—
722C2×C4—884no—
723C2×C4C2×D4×D1112yes—
724C2×C4C2×D4×D1112yes—
725C2×C4C2×D4×D1111yescharacteristic
726C2×C4C2×#434312yes—
727C2×C4#41×D1112yes—
728C2×C4C24×D1111yescharacteristic
729C8—22no—
730C8—22no—
731C8—222no—
732C8—222no—
733C22—24no—
734C22—48no—
735C22—42no—
736C22—42no—
737C22—222no—
738C22—224no—
739C22—222no—
740C22—222no—
741C22—444no—
742C22—448no—
743C22—442no—
744C22—442no—
745C22—8816no—
746C22#1062315812yes—
747C22#1062330112yes—
748C22#1062330612yes—
749C22C22×D4×D1111yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—222no—
756C4—222no—
757C4—222no—
758C4—442no—
759C4—442no—
760C4—442no—
761C4#1062315812yes—
762C4C22×#434311yescharacteristic
763C4C2×#41×D1111yescharacteristic
764C2—44no—
765C2—442no—
766C2—444no—
767C2#1307887014yesdirect product factor
768C2C2×#1062315811yescharacteristic
769C2C2×#1062330111yescharacteristic
770C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#478C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
hypercenterC2×#478D11
hypocenterC11C2×#3123
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#10623228C2semidirect
3. #13078870C2direct (N × H)
4. C2×#10622480C2semidirect
5. C2×#10622501C2semidirect
6. C2×#10622679C2semidirect
7. C2×#10622454C2semidirect
8. C2×#10622632C2semidirect
11. C2×#10622502C2semidirect
12. C2×#10622370C2semidirect
13. C2×#10622371C2semidirect
14. C2×#10622465C2semidirect
15. C2×#10622453C2semidirect
16. C2×C11×#478C2semidirect
18. C2×C11×#125C22semidirect
28. #10623228C22semidirect
39. C2×#66940C22semidirect
40. C2×#66940C22semidirect
45. C2×#66922C22semidirect
46. C11×#478C22semidirect
47. C2×C11×#107C22semidirect
48. C2×C11×#106C22semidirect
49. C2×C11×C4⋊C8C22semidirect
54. C2×#66880C22semidirect
55. C2×#66880C22semidirect
56. C2×#66879C22semidirect
57. C2×C8×Dic11C22semidirect
58. #10622679C22semidirect
59. #10622632C22semidirect
60. C2×#66874C22semidirect
61. C2×#66874C22semidirect
64. C2×#66872C22semidirect
65. C2×#66871C22semidirect
66. C2×C4⋊(C11⋊C8)C22semidirect
67. #10622502C22semidirect
68. #10622501C22semidirect
69. #10622480C22semidirect
70. #10622465C22semidirect
71. #10622454C22semidirect
72. #10622453C22semidirect
75. #10622371C22semidirect
76. #10622370C22semidirect
95. C11×#125C23semidirect
154. #66940C23semidirect
155. #66940C23semidirect
163. #66922C23semidirect
164. C11×#107C23semidirect
165. C11×#106C23semidirect
166. C11×C4⋊C8C23semidirect
171. #66880C23semidirect
172. #66880C23semidirect
173. #66879C23semidirect
174. C8×Dic11C23semidirect
175. #66874C23semidirect
176. #66874C23semidirect
179. #66872C23semidirect
180. #66871C23semidirect
181. C4⋊(C11⋊C8)C23semidirect
287. C2×#478D11semidirect
376. C2×#125C2×D11semidirect
396. #478C2×D11semidirect
407. C2×#107C2×D11semidirect
409. C2×#106C2×D11semidirect
411. C2×C4⋊C8C2×D11semidirect
489. #125C22×D11semidirect
543. #107C22×D11semidirect
545. #106C22×D11semidirect
547. C4⋊C8C22×D11semidirect
561. C2×C11#3123semidirect
665. C11C2×#3123semidirect
767. C2#13078870direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232282
C2×#106230762
#130788702
C2×#106224802
C2×#106225012
C2×#106226792
C2×#106224542
C2×#106226322
C2×#106223892
C2×#106225022
C2×#106223702
C2×#106223712
C2×#106224652
C2×#106224532
C2×C11×#4782
C2×#312311