Finite Group Databasebeta

← C2×#13078839 #15622046

Subgroups — C2×#13078839 #15622046

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×#10623047C211yesmaximal, characteristic, complemented
2#13078839C2116yesmaximal, direct product factor
3C2×#10622658C211yesmaximal, characteristic, complemented
4C2×#10622648C211yesmaximal, characteristic
5C2×#10622704C211yesmaximal, characteristic, complemented
6C2×#10622707C211yesmaximal, characteristic, complemented
7C2×#10622667C211yesmaximal, characteristic, complemented
8C2×#10622667C211yesmaximal, characteristic, complemented
9C2×#10622663C211yesmaximal, characteristic, complemented
10C2×#10622653C211yesmaximal, characteristic
11C2×#10622643C211yesmaximal, characteristic, complemented
12C2×#10622631C211yesmaximal, characteristic, complemented
13C2×C4×#4326C211yesmaximal, characteristic, complemented
14C2×C4×#4324C211yesmaximal, characteristic, complemented
15C2×#10622613C211yesmaximal, characteristic, complemented
16C2×C11×#542C211yesmaximal, characteristic
17C23×Dic22C2211yescharacteristic
18C11×#542—24no—
19C11×#542C2218yes—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#126—21no—
22C2×C11×#124—21no—
23C2×C11×#124C2211yescharacteristic
24C2×C11×#123—21no—
25C2×C11×C22⋊Q8—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C22×#4326C2211yescharacteristic
32C22×#4326C2211yescharacteristic
33C22×#4324C2211yescharacteristic
34C22×#4324C2211yescharacteristic
35C2×#66979C2211yescharacteristic
36#10623047—24no—
37#10623047C2218yescomplemented
38C2×#66940—21no—
39C2×#66940—21no—
40C2×#66930—21no—
41C2×#66930—21no—
42C2×C4×Dic22C2211yescharacteristic
43C2×C4×Dic22C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C2×C4×Dic22C2211yescharacteristic
46C2×#66899C2211yescharacteristic
47C2×#66899C2211yescharacteristic
48C2×#66896C2211yescharacteristic
49C2×#66896C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51C2×C22⋊(C11⋊C8)C2211yescharacteristic
52#10622707C2218yescomplemented
53#10622704C2218yescomplemented
54#10622667C2218yescomplemented
55#10622667C2218yescomplemented
56#10622663C2218yescomplemented
57#10622658C2218yescomplemented
58#10622653C2218yes—
59#10622648C2218yes—
60#10622643C2218yescomplemented
61C4×#4326C2218yescomplemented
62#10622631C2218yescomplemented
63C4×#4324C2218yescomplemented
64#10622613C2218yescomplemented
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66874C2211yescharacteristic
68C2×#66874C2211yescharacteristic
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—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11C2311yescharacteristic
83C23×Dic11—21no—
84C22×Dic22—21no—
85C22×Dic22—22no—
86C22×Dic22—24no—
87C22×Dic22—24no—
88C22×Dic22C2314yes—
89C22×Dic22C2311yescharacteristic
90C22×Dic22C2311yescharacteristic
91C11×C4⋊Q8—22no—
92C11×C4⋊Q8C2314yes—
93C11×#126—28no—
94C11×#124—28no—
95C11×#124—22no—
96C11×#124C2314yes—
97C11×#123—28no—
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8—28no—
100C11×C22⋊Q8C2314yes—
101C11×#121—22no—
102C11×#121C2314yes—
103C4×Q8×C11—22no—
104C4×Q8×C11C2314yes—
105C4×D4×C11—22no—
106C4×D4×C11C2314yes—
107C11×#117D414yes—
108C11×#117C2314yes—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4D411yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4D411yescharacteristic
122C2×C11×C22⋊C4D411yescharacteristic
123C2×C42×C11—21no—
124C2×C42×C11C2311yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C2×C22⋊Dic11—21no—
127C2×#4326—24no—
128C2×#4326—24no—
129C2×#4326C2314yes—
130C2×#4326C2314yes—
131C2×#4324—24no—
132C2×#4324—24no—
133C2×#4324C2314yes—
134C2×#4324C2314yes—
135#66979—22no—
136#66979C2314yes—
137C2×C4⋊Dic11C2311yescharacteristic
138C2×C4⋊Dic11C2311yescharacteristic
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×C4×Dic11—21no—
144C2×C4×Dic11—21no—
145C2×C4×Dic11—21no—
146C2×C4×Dic11—21no—
147C2×C4×Dic11—21no—
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152#66940—28no—
153#66940—28no—
154#66930—28no—
155#66930—28no—
156C4×Dic22—22no—
157C4×Dic22—22no—
158C4×Dic22—22no—
159C4×Dic22—22no—
160C4×Dic22C2314yes—
161C4×Dic22C2314yes—
162C4×Dic22C2314yes—
163C4×Dic22C2314yes—
164#66899C2314yes—
165#66899C2314yes—
166#66896C2314yes—
167#66896C2314yes—
168C22⋊(C11⋊C8)C2314yes—
169C22⋊(C11⋊C8)C2314yes—
170#66874C2314yes—
171#66874C2314yes—
172#66874C2314yes—
173#66874C2314yes—
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×C11—21no—
184C24×C11C2×D411yescharacteristic
185C2×Q8×C11—21no—
186C2×Q8×C11—24no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11—82no—
190C2×Q8×C11C2412yes—
191C2×D4×C11—24no—
192C2×D4×C11—21no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—82no—
196C2×D4×C11C2412yes—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—24no—
203C22×C4×C11—82no—
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2411yescharacteristic
212C22×Dic11—28no—
213C22×Dic11—24no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C2×Dic22—28no—
219C2×Dic22—216no—
220C2×Dic22—28no—
221C2×Dic22—28no—
222C2×Dic22—21no—
223C2×Dic22—21no—
224C2×Dic22—24no—
225C2×Dic22—22no—
226C2×Dic22—22no—
227C2×Dic22#4114yes—
228C2×Dic22#4114yes—
229C2×Dic22C2412yes—
230C2×Dic22C2412yes—
231C11×C4⋊C4—24no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4C2×D414yes—
237C11×C4⋊C4C2×D414yes—
238C11×C4⋊C4C2412yes—
239C11×C4⋊C4C2412yes—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—24no—
243C11×C22⋊C4—24no—
244C11×C22⋊C4—24no—
245C11×C22⋊C4C2×D414yes—
246C11×C22⋊C4C2×D414yes—
247C42×C11—24no—
248C42×C11C2×D412yes—
249C42×C11C2×D412yes—
250C42×C11C2412yes—
251C42×C11C2412yes—
252C22⋊Dic11—24no—
253#4326—28no—
254#4326—28no—
255#4324—28no—
256#4324—28no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11C2412yes—
260C4⋊Dic11C2412yes—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265C4×Dic11—24no—
266C4×Dic11—24no—
267C4×Dic11—24no—
268C4×Dic11—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×#542D1111yescharacteristic
279C2×#519—111no—
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×C11—22no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11C22×D412yes—
302C23×C11C22×D411yescharacteristic
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—42no—
306Q8×C11—84no—
307D4×C11—22no—
308D4×C11—22no—
309D4×C11—42no—
310D4×C11—84no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—24no—
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×D412yes—
329C2×C4×C11C22×D412yes—
330C2×C4×C11C22×D412yes—
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C2×#4112yes—
333C2×C4×C11C2×#4112yes—
334C2×C4×C11C2511yescharacteristic
335C2×Dic11—216no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344Dic22—216no—
345Dic22—24no—
346Dic22—24no—
347Dic22—22no—
348Dic22—22no—
349Dic22C2×#4114yes—
350Dic22C2×#4114yes—
351C11⋊C8—22no—
352C11⋊C8—22no—
353C11⋊C8—22no—
354C11⋊C8—22no—
355C23×Q8—111no—
356C22×Q16—111no—
357C22×Q16—111no—
358C22×SD16—111no—
359C22×SD16—111no—
360#542—24no—
361#542C2×D1118yes—
362C2×C4⋊Q8C2×D1111yescharacteristic
363C2×#126—21no—
364C2×#124—21no—
365C2×#124C2×D1111yescharacteristic
366C2×#123—21no—
367C2×C22⋊Q8—21no—
368C2×C22⋊Q8C2×D1111yescharacteristic
369C2×#121C2×D1111yescharacteristic
370#519—118no—
371#519—224no—
372C2×C4×Q8—111no—
373C2×C4×Q8—111no—
374C2×C4×Q8—111no—
375C2×C4×Q8—111no—
376C2×C4×Q8—221no—
377C2×C4×Q8—221no—
378C2×C4×Q8C2×D1111yescharacteristic
379C2×C4×D4C2×D1111yescharacteristic
380C2×#117—111no—
381C2×#117—221no—
382C2×#117—221no—
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—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—84no—
423C22×C11#52512yes—
424C22×C11#57712yes—
425C22×C11#57812yes—
426C22×C11C23×D411yescharacteristic
427C4×C11—22no—
428C4×C11—22no—
429C4×C11—22no—
430C4×C11—22no—
431C4×C11—22no—
432C4×C11—42no—
433C4×C11—42no—
434C4×C11—42no—
435C4×C11#52512yes—
436C4×C11C22×#4111yescharacteristic
437C4×C11C22×#4111yescharacteristic
438Dic11—24no—
439Dic11—24no—
440Dic11—42no—
441Dic11—42no—
442C22×Q8—21no—
443C22×Q8—111no—
444C22×Q8—111no—
445C22×Q8—114no—
446C22×Q8—224no—
447C22×Q8—224no—
448C22×Q8—221no—
449C22×Q8—222no—
450C22×Q8C22×D1111yescharacteristic
451C22×D4—21no—
452C22×D4C22×D1111yescharacteristic
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—22no—
469C4⋊Q8C22×D1114yes—
470#126—28no—
471#124—28no—
472#124—22no—
473#124C22×D1114yes—
474#123—28no—
475C22⋊Q8—22no—
476C22⋊Q8—28no—
477C22⋊Q8C22×D1114yes—
478#121—22no—
479#121C22×D1114yes—
480C4×Q8—22no—
481C4×Q8—114no—
482C4×Q8—114no—
483C4×Q8—114no—
484C4×Q8—114no—
485C4×Q8—228no—
486C4×Q8—228no—
487C4×Q8—222no—
488C4×Q8—222no—
489C4×Q8—222no—
490C4×Q8—222no—
491C4×Q8C22×D1114yes—
492C4×D4—22no—
493C4×D4C22×D1114yes—
494#117—114no—
495#117—222no—
496#117—228no—
497#117—228no—
498#117C22⋊D1114yes—
499#117C22×D1114yes—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
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×C4⋊C4C22×D1111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4C22⋊D1111yescharacteristic
520C2×C22⋊C4C22⋊D1111yescharacteristic
521C2×C42—21no—
522C2×C42—221no—
523C2×C42—221no—
524C2×C42—221no—
525C2×C42—221no—
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—82no—
549C2×C11#312114yescomplemented
550C2×C11C2×#52511yescharacteristic
551C2×C11C2×#57711yescharacteristic
552C2×C11C2×#57811yescharacteristic
553C24—21no—
554C24C2×C22⋊D1111yescharacteristic
555C2×Q8—21no—
556C2×Q8—24no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—82no—
560C2×Q8—114no—
561C2×Q8—114no—
562C2×Q8—112no—
563C2×Q8—112no—
564C2×Q8—228no—
565C2×Q8—228no—
566C2×Q8—228no—
567C2×Q8—2216no—
568C2×Q8—222no—
569C2×Q8—222no—
570C2×Q8—224no—
571C2×Q8—221no—
572C2×Q8—221no—
573C2×Q8C23×D1112yes—
574C2×D4—24no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—82no—
579C2×D4C23×D1112yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—82no—
587C22×C4—228no—
588C22×C4—224no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
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—21no—
617C4⋊C4—21no—
618C4⋊C4—112no—
619C4⋊C4—112no—
620C4⋊C4—221no—
621C4⋊C4—221no—
622C4⋊C4—224no—
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—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—224no—
636C22⋊C4C2×C22⋊D1114yes—
637C22⋊C4C2×C22⋊D1114yes—
638C42—24no—
639C42—224no—
640C42—224no—
641C42—224no—
642C42—224no—
643C42—224no—
644C42C2×C22⋊D1112yes—
645C42C2×C22⋊D1112yes—
646C42C23×D1112yes—
647C42C23×D1112yes—
648C11C2×#312111yescharacteristic, complemented, Sylow
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23C22×C22⋊D1112yes—
657C23C22×C22⋊D1111yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—84no—
662Q8—114no—
663Q8—114no—
664Q8—2216no—
665Q8—224no—
666Q8—224no—
667Q8—222no—
668Q8—222no—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—84no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—2216no—
689C2×C4—224no—
690C2×C4—224no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4#41×D1112yes—
698C2×C4#41×D1112yes—
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—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22#1062335912yes—
719C22#1062336712yes—
720C22#1062336912yes—
721C22C23×C22⋊D1111yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—224no—
731C4—224no—
732C4—442no—
733C4—442no—
734C4#1062335912yes—
735C4C2×#41×D1111yescharacteristic
736C4C2×#41×D1111yescharacteristic
737C2—42no—
738C2—82no—
739C2#1307883914yesdirect product factor
740C2C2×#1062335911yescharacteristic
741C2C2×#1062336711yescharacteristic
742C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#542C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC2×#542D11
hypocenterC11C2×#3121
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#10623047C2semidirect
2. #13078839C2direct (N × H)
3. C2×#10622658C2semidirect
5. C2×#10622704C2semidirect
6. C2×#10622707C2semidirect
7. C2×#10622667C2semidirect
8. C2×#10622667C2semidirect
9. C2×#10622663C2semidirect
11. C2×#10622643C2semidirect
12. C2×#10622631C2semidirect
13. C2×C4×#4326C2semidirect
14. C2×C4×#4324C2semidirect
15. C2×#10622613C2semidirect
37. #10623047C22semidirect
52. #10622707C22semidirect
53. #10622704C22semidirect
54. #10622667C22semidirect
55. #10622667C22semidirect
56. #10622663C22semidirect
57. #10622658C22semidirect
60. #10622643C22semidirect
61. C4×#4326C22semidirect
62. #10622631C22semidirect
63. C4×#4324C22semidirect
64. #10622613C22semidirect
549. C2×C11#3121semidirect
648. C11C2×#3121semidirect
739. C2#13078839direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230472
#130788392
C2×#106226582
C2×#106226482
C2×#106227042
C2×#106227072
C2×#106226672
C2×#106226632
C2×#106226532
C2×#106226432
C2×#106226312
C2×C4×#43262
C2×C4×#43242
C2×#106226132
C2×C11×#5422
C2×#312111