Finite Group Databasebeta

← C2×#13078845 #15622052

Subgroups — C2×#13078845 #15622052

Order 2816.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623065C211yesmaximal, characteristic
2#13078845C2116yesmaximal, direct product factor
3C2×#10622609C211yesmaximal, characteristic, complemented
4C2×#10622616C211yesmaximal, characteristic
5C2×#10622634C211yesmaximal, characteristic, complemented
6C2×#10622633C211yesmaximal, characteristic, complemented
7C2×#10622641C211yesmaximal, characteristic, complemented
8C2×#10622641C211yesmaximal, characteristic, complemented
9C2×#10622841C211yesmaximal, characteristic, complemented
10C2×#10622840C211yesmaximal, characteristic
11C2×#10622643C211yesmaximal, characteristic, complemented
12C2×#10622639C211yesmaximal, characteristic, complemented
13C2×C4×#4326C211yesmaximal, characteristic, complemented
14C2×C4×#4325C211yesmaximal, characteristic, complemented
15C2×#10622613C211yesmaximal, characteristic, complemented
16C2×C11×#519C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C11×#519—24no—
19C11×#519C2218yescomplemented
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11—21no—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C11×#117—21no—
27C2×C11×#117—21no—
28C2×C11×#117C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C22×#4326C2211yescharacteristic
32C22×#4325C2211yescharacteristic
33C22×#4325C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36#10623065—24no—
37#10623065C2218yes—
38C2×#66951—21no—
39C2×#66949—21no—
40C2×#66938—21no—
41C2×#66936—21no—
42C2×#66928C2211yescharacteristic
43C2×C4×D44C2211yescharacteristic
44C2×#66922C2211yescharacteristic
45C2×C4×Dic22C2211yescharacteristic
46#10622841C2218yescomplemented
47#10622840C2218yes—
48C2×#66899C2211yescharacteristic
49C2×#66899C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622643C2218yescomplemented
55C4×#4326C2218yescomplemented
56#10622641C2218yescomplemented
57#10622641C2218yescomplemented
58#10622639C2218yescomplemented
59C4×#4325C2218yescomplemented
60#10622634C2218yescomplemented
61#10622633C2218yescomplemented
62#10622616C2218yes—
63#10622613C2218yescomplemented
64#10622609C2218yescomplemented
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75C2×#66867C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×Q8×C11—24no—
78C22×Q8×C11—24no—
79C22×Q8×C11—21no—
80C22×Q8×C11—22no—
81C22×Q8×C11C2314yes—
82C22×Q8×C11C2311yescharacteristic
83C22×Q8×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—21no—
87C22×D44C2311yescharacteristic
88C22×C4×D11—21no—
89C22×Dic22—21no—
90C22×Dic22C2311yescharacteristic
91C4×Q8×C11—28no—
92C4×Q8×C11—28no—
93C4×Q8×C11—22no—
94C4×Q8×C11—22no—
95C4×Q8×C11—22no—
96C4×Q8×C11—22no—
97C4×Q8×C11C2314yes—
98C4×Q8×C11C2314yes—
99C4×Q8×C11C2314yes—
100C4×Q8×C11C2314yes—
101C11×#117—22no—
102C11×#117—28no—
103C11×#117—28no—
104C11×#117D414yes—
105C11×#117C2314yes—
106C11×#117C2314yes—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4D411yescharacteristic
117C2×C11×C22⋊C4D411yescharacteristic
118C2×C42×C11—21no—
119C2×C42×C11—21no—
120C2×C42×C11—21no—
121C2×C42×C11—21no—
122C2×C42×C11—21no—
123C2×C42×C11C2311yescharacteristic
124C2×C42×C11C2311yescharacteristic
125C2×C22⋊Dic11—21no—
126C2×#4326—24no—
127C2×#4326—24no—
128C2×#4326C2314yes—
129C2×#4326C2314yes—
130C2×#4325—24no—
131C2×#4325—24no—
132C2×#4325C2314yes—
133C2×#4325C2314yes—
134#66983—22no—
135#66983C2314yes—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×C4⋊Dic11—21no—
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143#66977—22no—
144#66977C2314yes—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×C4×Dic11—21no—
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152#66951—28no—
153#66949—28no—
154#66938—28no—
155#66936—28no—
156#66928—22no—
157#66928C2314yes—
158C4×D44—22no—
159C4×D44C2314yes—
160#66922—22no—
161#66922C2314yes—
162C4×Dic22—22no—
163C4×Dic22C2314yes—
164#66899C2314yes—
165#66899C2314yes—
166#66899C2314yes—
167#66899C2314yes—
168C22⋊(C11⋊C8)C2314yes—
169C22⋊(C11⋊C8)C2314yes—
170#66874C2314yes—
171#66874C2314yes—
172#66873C2314yes—
173#66873C2314yes—
174#66872C2314yes—
175#66872C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178C4⋊(C11⋊C8)C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180#66867C2314yes—
181C4×C11⋊C8C2314yes—
182C2×#3121—111nomaximal, Sylow
183C24×C11C2×D411yescharacteristic
184C23×D11—21no—
185C2×Q8×C11—216no—
186C2×Q8×C11—28no—
187C2×Q8×C11—28no—
188C2×Q8×C11—28no—
189C2×Q8×C11—24no—
190C2×Q8×C11—21no—
191C2×Q8×C11—21no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11#4114yes—
195C2×Q8×C11#4114yes—
196C2×Q8×C11C2412yes—
197C2×Q8×C11C2412yes—
198C22×C4×C11—28no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—24no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2412yes—
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—24no—
215C2×C22⋊D11—82no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C2×D44—21no—
220C2×D44—22no—
221C2×D44—22no—
222C2×D44C2412yes—
223C2×C4×D11—24no—
224C2×C4×D11—82no—
225C2×Dic22—21no—
226C2×Dic22—24no—
227C2×Dic22—22no—
228C2×Dic22—22no—
229C2×Dic22—82no—
230C2×Dic22C2412yes—
231C11×C4⋊C4—24no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4C2×D414yes—
238C11×C4⋊C4C2×D414yes—
239C11×C4⋊C4C2412yes—
240C11×C4⋊C4C2412yes—
241C11×C22⋊C4—24no—
242C11×C22⋊C4C2×D414yes—
243C11×C22⋊C4C2×D414yes—
244C42×C11—24no—
245C42×C11—24no—
246C42×C11—24no—
247C42×C11—24no—
248C42×C11—24no—
249C42×C11C2×D412yes—
250C42×C11C2×D412yes—
251C42×C11C2412yes—
252C42×C11C2412yes—
253C22⋊Dic11—24no—
254#4326—28no—
255#4326—28no—
256#4325—28no—
257#4325—28no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—24no—
265C4⋊Dic11C2412yes—
266C4⋊Dic11C2412yes—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269C4×Dic11—24no—
270C2×C11⋊C8—22no—
271C2×C11⋊C8—22no—
272C2×C11⋊C8—22no—
273C2×C11⋊C8—22no—
274C2×C11⋊C8C2412yes—
275C2×C11⋊C8C2412yes—
276C2×C11⋊C8C2412yes—
277C2×C11⋊C8C2412yes—
278C2×#542—111no—
279C2×#519D1111yescharacteristic, complemented
280#3121—1116no—
281C2×#485—111no—
282C2×#482—111no—
283C2×#477—111no—
284C2×#475—111no—
285C2×#464—111no—
286C2×#464—111no—
287C2×#451—111no—
288C2×#448—111no—
289C2×#441—111no—
290C2×#440—111no—
291C2×C4×Q16—111no—
292C2×C4×SD16—111no—
293C2×#433—111no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11C22×D412yes—
298C23×C11C22×D411yescharacteristic
299C22×D11—22no—
300C22×D11—42no—
301C22×D11—42no—
302C22×D11—42no—
303Q8×C11—216no—
304Q8×C11—24no—
305Q8×C11—24no—
306Q8×C11—22no—
307Q8×C11—22no—
308Q8×C11C2×#4114yes—
309Q8×C11C2×#4114yes—
310C2×C4×C11—216no—
311C2×C4×C11—24no—
312C2×C4×C11—24no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—24no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D412yes—
329C2×C4×C11C22×D412yes—
330C2×C4×C11C22×D412yes—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C2×#4112yes—
334C2×C4×C11C2×#4112yes—
335C2×C4×C11C2511yescharacteristic
336C22⋊D11—84no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343D44—22no—
344D44—22no—
345D44—42no—
346C4×D11—84no—
347Dic22—22no—
348Dic22—22no—
349Dic22—42no—
350Dic22—84no—
351C11⋊C8—22no—
352C11⋊C8—22no—
353C11⋊C8—22no—
354C11⋊C8—22no—
355C23×Q8C2×D1111yescharacteristic
356C22×Q16—111no—
357C22×Q16—111no—
358C22×SD16—111no—
359C22×SD16—111no—
360#542—118no—
361#542—224no—
362C2×C4⋊Q8—111no—
363C2×#126—221no—
364C2×#124—111no—
365C2×#124—221no—
366C2×#123—221no—
367C2×C22⋊Q8—111no—
368C2×C22⋊Q8—221no—
369C2×#121—111no—
370#519—24no—
371#519C2×D1118yescomplemented
372C2×C4×Q8—21no—
373C2×C4×Q8—21no—
374C2×C4×Q8—111no—
375C2×C4×Q8C2×D1111yescharacteristic
376C2×C4×Q8C2×D1111yescharacteristic
377C2×C4×Q8C2×D1111yescharacteristic
378C2×C4×Q8C2×D1111yescharacteristic
379C2×C4×D4—111no—
380C2×#117—21no—
381C2×#117—21no—
382C2×#117C2×D1111yescharacteristic
383C2×#117C2×D1111yescharacteristic
384#485—118no—
385#482—118no—
386#477—118no—
387#475—118no—
388#464—118no—
389#464—118no—
390#451—118no—
391#448—118no—
392#441—118no—
393#440—118no—
394C4×Q16—118no—
395C4×SD16—118no—
396#433—118no—
397C2×#107—111no—
398C2×#107—111no—
399C2×#106—111no—
400C2×#106—111no—
401C2×C4⋊C8—111no—
402C2×C4⋊C8—111no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#103—111no—
409C2×#102—111no—
410C2×#102—111no—
411C2×C22⋊C8—111no—
412C2×C22⋊C8—111no—
413C2×#97—111no—
414C2×C4×C8—111no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—44no—
419C22×C11#52512yes—
420C22×C11#57712yes—
421C22×C11#57812yes—
422C22×C11C23×D411yescharacteristic
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—84no—
427C4×C11—24no—
428C4×C11—24no—
429C4×C11—22no—
430C4×C11—22no—
431C4×C11—22no—
432C4×C11—22no—
433C4×C11—22no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11#52512yes—
437C4×C11C22×#4111yescharacteristic
438C4×C11C22×#4111yescharacteristic
439Dic11—42no—
440Dic11—42no—
441Dic11—42no—
442C22×Q8—24no—
443C22×Q8—24no—
444C22×Q8—21no—
445C22×Q8—22no—
446C22×Q8—111no—
447C22×Q8—221no—
448C22×Q8C22×D1114yes—
449C22×Q8C22×D1111yescharacteristic
450C22×Q8C22×D1111yescharacteristic
451C22×D4—111no—
452C22×D4—221no—
453C23×C4—21no—
454C23×C4—221no—
455C23×C4C22×D1111yescharacteristic
456C2×Q16—114no—
457C2×Q16—114no—
458C2×Q16—224no—
459C2×Q16—224no—
460C2×SD16—114no—
461C2×SD16—114no—
462C2×SD16—224no—
463C2×SD16—224no—
464C22×C8—111no—
465C22×C8—111no—
466C22×C8—111no—
467C22×C8—111no—
468C4⋊Q8—114no—
469C4⋊Q8—222no—
470#126—228no—
471#124—114no—
472#124—228no—
473#124—222no—
474#123—228no—
475C22⋊Q8—114no—
476C22⋊Q8—222no—
477C22⋊Q8—228no—
478#121—114no—
479#121—222no—
480C4×Q8—28no—
481C4×Q8—28no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—22no—
485C4×Q8—22no—
486C4×Q8—114no—
487C4×Q8—222no—
488C4×Q8C22×D1114yes—
489C4×Q8C22×D1114yes—
490C4×Q8C22×D1114yes—
491C4×Q8C22×D1114yes—
492C4×D4—114no—
493C4×D4—222no—
494#117—22no—
495#117—28no—
496#117—28no—
497#117C22⋊D1114yes—
498#117C22×D1114yes—
499#117C22×D1114yes—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—111no—
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×C4⋊C4C22×D1111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4C22⋊D1111yescharacteristic
520C2×C22⋊C4C22⋊D1111yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42—21no—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42—221no—
527C2×C42C22×D1111yescharacteristic
528C2×C42C22×D1111yescharacteristic
529#107—114no—
530#107—114no—
531#106—114no—
532#106—114no—
533C4⋊C8—114no—
534C4⋊C8—114no—
535#103—114no—
536#103—114no—
537#103—114no—
538#103—114no—
539#103—114no—
540#103—114no—
541#102—114no—
542#102—114no—
543C22⋊C8—114no—
544C22⋊C8—114no—
545#97—114no—
546C4×C8—114no—
547C2×C11—42no—
548C2×C11#312114yescomplemented
549C2×C11C2×#52511yescharacteristic
550C2×C11C2×#57711yescharacteristic
551C2×C11C2×#57811yescharacteristic
552D11—82no—
553C24—221no—
554C24C2×C22⋊D1111yescharacteristic
555C2×Q8—216no—
556C2×Q8—28no—
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—24no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—112no—
565C2×Q8—221no—
566C2×Q8—224no—
567C2×Q8—222no—
568C2×Q8—222no—
569C2×Q8—882no—
570C2×Q8#433914yes—
571C2×Q8#433914yes—
572C2×Q8C23×D1112yes—
573C2×Q8C23×D1112yes—
574C2×D4—112no—
575C2×D4—224no—
576C2×D4—222no—
577C2×D4—222no—
578C2×D4—221no—
579C2×D4—882no—
580C22×C4—28no—
581C22×C4—24no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—224no—
592C22×C4—882no—
593C22×C4C2×C22⋊D1112yes—
594C22×C4C2×C22⋊D1111yescharacteristic
595C22×C4C2×C22⋊D1111yescharacteristic
596C22×C4C2×C22⋊D1111yescharacteristic
597C22×C4C2×C22⋊D1111yescharacteristic
598C22×C4C2×C22⋊D1111yescharacteristic
599C22×C4C23×D1112yes—
600C22×C4C23×D1111yescharacteristic
601Q16—228no—
602Q16—228no—
603SD16—228no—
604SD16—228no—
605C2×C8—112no—
606C2×C8—112no—
607C2×C8—112no—
608C2×C8—112no—
609C2×C8—222no—
610C2×C8—222no—
611C2×C8—222no—
612C2×C8—222no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—112no—
620C4⋊C4—112no—
621C4⋊C4—221no—
622C4⋊C4—221no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—224no—
626C4⋊C4C2×C22⋊D1114yes—
627C4⋊C4C2×C22⋊D1114yes—
628C4⋊C4C23×D1112yes—
629C4⋊C4C23×D1112yes—
630C22⋊C4—24no—
631C22⋊C4—224no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4C2×C22⋊D1114yes—
637C22⋊C4C2×C22⋊D1114yes—
638C42—24no—
639C42—24no—
640C42—24no—
641C42—24no—
642C42—24no—
643C42—224no—
644C42C2×C22⋊D1112yes—
645C42C2×C22⋊D1112yes—
646C42C23×D1112yes—
647C42C23×D1112yes—
648C11C2×#312111yescharacteristic, complemented, Sylow
649C23—22no—
650C23—22no—
651C23—22no—
652C23—222no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23C22×C22⋊D1112yes—
657C23C22×C22⋊D1111yescharacteristic
658Q8—216no—
659Q8—24no—
660Q8—24no—
661Q8—22no—
662Q8—22no—
663Q8—222no—
664Q8—222no—
665Q8—442no—
666Q8—884no—
667Q8C2×#433914yes—
668Q8C2×#433914yes—
669D4—222no—
670D4—222no—
671D4—442no—
672D4—884no—
673C2×C4—216no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—442no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4—884no—
697C2×C4C2×#433912yes—
698C2×C4C2×#433912yes—
699C2×C4C22×C22⋊D1112yes—
700C2×C4C22×C22⋊D1112yes—
701C2×C4C22×C22⋊D1112yes—
702C2×C4C22×C22⋊D1112yes—
703C2×C4C22×C22⋊D1112yes—
704C2×C4C22×C22⋊D1111yescharacteristic
705C2×C4C24×D1111yescharacteristic
706C8—222no—
707C8—222no—
708C8—222no—
709C8—222no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—442no—
715C22—442no—
716C22—442no—
717C22—884no—
718C22#1062332212yes—
719C22#1062336812yes—
720C22#1062336912yes—
721C22C23×C22⋊D1111yescharacteristic
722C4—24no—
723C4—24no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—22no—
729C4—42no—
730C4—42no—
731C4—442no—
732C4—442no—
733C4—442no—
734C4#1062332212yes—
735C4C22×#433911yescharacteristic
736C4C22×#433911yescharacteristic
737C2—42no—
738C2—882no—
739C2#1307884514yesdirect product factor
740C2C2×#1062332211yescharacteristic
741C2C2×#1062336811yescharacteristic
742C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#519C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#519D11
hypocenterC11C2×#3121
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. #13078845C2direct (N × H)
3. C2×#10622609C2semidirect
5. C2×#10622634C2semidirect
6. C2×#10622633C2semidirect
7. C2×#10622641C2semidirect
8. C2×#10622641C2semidirect
9. C2×#10622841C2semidirect
11. C2×#10622643C2semidirect
12. C2×#10622639C2semidirect
13. C2×C4×#4326C2semidirect
14. C2×C4×#4325C2semidirect
15. C2×#10622613C2semidirect
16. C2×C11×#519C2semidirect
19. C11×#519C22semidirect
46. #10622841C22semidirect
54. #10622643C22semidirect
55. C4×#4326C22semidirect
56. #10622641C22semidirect
57. #10622641C22semidirect
58. #10622639C22semidirect
59. C4×#4325C22semidirect
60. #10622634C22semidirect
61. #10622633C22semidirect
63. #10622613C22semidirect
64. #10622609C22semidirect
279. C2×#519D11semidirect
371. #519C2×D11semidirect
548. C2×C11#3121semidirect
648. C11C2×#3121semidirect
739. C2#13078845direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230652
#130788452
C2×#106226092
C2×#106226162
C2×#106226342
C2×#106226332
C2×#106226412
C2×#106228412
C2×#106228402
C2×#106226432
C2×#106226392
C2×C4×#43262
C2×C4×#43252
C2×#106226132
C2×C11×#5192
C2×#312111