Finite Group Databasebeta

← C2×#13079725 #15625168

Subgroups — C2×#13079725 #15625168

Order 2816.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623065C211yesmaximal, characteristic, complemented
2#13079725C2116yesmaximal, direct product factor
3C2×#10622699C211yesmaximal, characteristic, complemented
4C2×#10622672C211yesmaximal, characteristic, complemented
5C2×#10622668C211yesmaximal, characteristic, complemented
6C2×#10622694C211yesmaximal, characteristic, complemented
7C2×#10622667C211yesmaximal, characteristic, complemented
8C2×#10622703C211yesmaximal, characteristic, complemented
9C2×#10622670C211yesmaximal, characteristic, complemented
10C2×#10622696C211yesmaximal, characteristic, complemented
11C2×#10622852C211yesmaximal, characteristic, complemented
12C2×#10622851C211yesmaximal, characteristic
13C2×#10622841C211yesmaximal, characteristic, complemented
14C2×#10622840C211yesmaximal, characteristic, complemented
15C2×#10622613C211yesmaximal, characteristic, complemented
16C2×C11×#536C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic
19C11×#536—24no—
20C11×#536C2218yescomplemented
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C11×C4⋊Q8C2211yescharacteristic
23C2×C11×#124C2211yescharacteristic
24C2×C11×#124C2211yescharacteristic
25C2×C11×#123—21no—
26C2×C11×#123—21no—
27C2×C11×C22⋊Q8—21no—
28C2×C11×C22⋊Q8—21no—
29C2×C11×#117C2211yescharacteristic
30C22×#4326C2211yescharacteristic
31C22×#4326C2211yescharacteristic
32C22×#4326C2211yescharacteristic
33C22×#4325C2211yescharacteristic
34C22×#4325C2211yescharacteristic
35C22×#4325C2211yescharacteristic
36C22×#4324C2211yescharacteristic
37C22×#4323C2211yescharacteristic
38C2×#66983C2211yescharacteristic
39C2×#66977C2211yescharacteristic
40#10623065—24no—
41#10623065C2218yescomplemented
42C2×#66951—21no—
43C2×#66949—21no—
44C2×#66938—21no—
45C2×#66936—21no—
46C2×#66928C2211yescharacteristic
47C2×C4×D44C2211yescharacteristic
48C2×#66922C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic
50#10622852C2218yescomplemented
51#10622851C2218yes—
52#10622841C2218yescomplemented
53#10622840C2218yescomplemented
54C2×#66899C2211yescharacteristic
55C2×#66899C2211yescharacteristic
56C2×#66899C2211yescharacteristic
57C2×#66899C2211yescharacteristic
58C2×#66899C2211yescharacteristic
59C2×#66899C2211yescharacteristic
60C2×#66896C2211yescharacteristic
61C2×#66896C2211yescharacteristic
62C2×C22⋊(C11⋊C8)C2211yescharacteristic
63C2×C22⋊(C11⋊C8)C2211yescharacteristic
64#10622703C2218yescomplemented
65#10622699C2218yescomplemented
66#10622696C2218yescomplemented
67#10622694C2218yescomplemented
68#10622672C2218yescomplemented
69#10622670C2218yescomplemented
70#10622668C2218yescomplemented
71#10622667C2218yescomplemented
72#10622613C2218yescomplemented
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75C2×#66867C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C2×C11×#41—22no—
78C2×C11×#41—42no—
79C2×C11×#41—42no—
80C2×C11×#41C2314yes—
81C22×Q8×C11—21no—
82C22×Q8×C11—22no—
83C22×Q8×C11—42no—
84C22×Q8×C11—42no—
85C22×Q8×C11C2311yescharacteristic
86C22×Q8×C11C2311yescharacteristic
87C22×Q8×C11C2311yescharacteristic
88C22×Q8×C11C2314yes—
89C22×D4×C11—21no—
90C22×D4×C11C2311yescharacteristic
91C23×C4×C11—21no—
92C23×C4×C11—21no—
93C23×C4×C11C2311yescharacteristic
94C22×C22⋊D11—21no—
95C22×D44C2311yescharacteristic
96C22×C4×D11—21no—
97C22×Dic22—21no—
98C22×Dic22C2311yescharacteristic
99C11×C4⋊Q8—22no—
100C11×C4⋊Q8—22no—
101C11×C4⋊Q8C2314yes—
102C11×C4⋊Q8C2314yes—
103C11×#124—22no—
104C11×#124—22no—
105C11×#124C2314yes—
106C11×#124C2314yes—
107C11×#123—28no—
108C11×#123—28no—
109C11×C22⋊Q8—28no—
110C11×C22⋊Q8—28no—
111C11×#117D414yes—
112C11×#117C2314yes—
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4D411yescharacteristic
118C2×C11×C4⋊C4D411yescharacteristic
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4D411yescharacteristic
124C2×C11×C22⋊C4D411yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C22⋊Dic11—21no—
128C2×#4326—42no—
129C2×#4326—42no—
130C2×#4326—42no—
131C2×#4326C2314yes—
132C2×#4326C2314yes—
133C2×#4326C2314yes—
134C2×#4325—42no—
135C2×#4325—42no—
136C2×#4325—42no—
137C2×#4325C2314yes—
138C2×#4325C2314yes—
139C2×#4325C2314yes—
140C2×#4324—42no—
141C2×#4324C2314yes—
142C2×#4323—42no—
143C2×#4323C2314yes—
144#66983—22no—
145#66983C2314yes—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—21no—
149C2×(C2×D11)⋊C4—21no—
150C2×C4⋊Dic11—21no—
151C2×C4⋊Dic11C2311yescharacteristic
152C2×C4⋊Dic11C2311yescharacteristic
153#66977—22no—
154#66977C2314yes—
155C2×Dic11⋊C4—21no—
156C2×Dic11⋊C4—21no—
157C2×C4×Dic11—21no—
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2311yescharacteristic
162#66951—28no—
163#66949—28no—
164#66938—28no—
165#66936—28no—
166#66928—22no—
167#66928C2314yes—
168C4×D44—22no—
169C4×D44C2314yes—
170#66922—22no—
171#66922C2314yes—
172C4×Dic22—22no—
173C4×Dic22C2314yes—
174#66899C2314yes—
175#66899C2314yes—
176#66899C2314yes—
177#66899C2314yes—
178#66899C2314yes—
179#66899C2314yes—
180#66896C2314yes—
181#66896C2314yes—
182C22⋊(C11⋊C8)C2314yes—
183C22⋊(C11⋊C8)C2314yes—
184C4⋊(C11⋊C8)C2314yes—
185C4⋊(C11⋊C8)C2314yes—
186#66867C2314yes—
187C4×C11⋊C8C2314yes—
188C2×#3225—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11C2×D411yescharacteristic
191C23×D11—21no—
192C11×#41—44no—
193C11×#41—44no—
194C11×#41—48no—
195C2×Q8×C11—24no—
196C2×Q8×C11—21no—
197C2×Q8×C11—21no—
198C2×Q8×C11—21no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11—22no—
203C2×Q8×C11—22no—
204C2×Q8×C11—22no—
205C2×Q8×C11—44no—
206C2×Q8×C11—44no—
207C2×Q8×C11—44no—
208C2×Q8×C11—48no—
209C2×Q8×C11C2412yes—
210C2×Q8×C11C2412yes—
211C2×Q8×C11C2412yes—
212C2×D4×C11—24no—
213C2×D4×C11—21no—
214C2×D4×C11—22no—
215C2×D4×C11—22no—
216C2×D4×C11—44no—
217C2×D4×C11C2412yes—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—24no—
224C22×C4×C11—24no—
225C22×C4×C11—44no—
226C22×C4×C11—44no—
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D412yes—
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2412yes—
234C22×C4×C11C2411yescharacteristic
235C2×C22⋊D11—24no—
236C2×C22⋊D11—82no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C2×D44—21no—
241C2×D44—22no—
242C2×D44—22no—
243C2×D44C2412yes—
244C2×C4×D11—24no—
245C2×C4×D11—82no—
246C2×Dic22—21no—
247C2×Dic22—24no—
248C2×Dic22—22no—
249C2×Dic22—22no—
250C2×Dic22—82no—
251C2×Dic22C2412yes—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—24no—
255C11×C4⋊C4—24no—
256C11×C4⋊C4C2×D414yes—
257C11×C4⋊C4C2×D414yes—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—24no—
262C11×C22⋊C4C2×D414yes—
263C11×C22⋊C4C2×D414yes—
264C42×C11C2×D412yes—
265C42×C11C2×D412yes—
266C42×C11C2412yes—
267C42×C11C2412yes—
268C22⋊Dic11—24no—
269#4326—44no—
270#4326—44no—
271#4326—44no—
272#4325—44no—
273#4325—44no—
274#4325—44no—
275#4324—44no—
276#4323—44no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281C4⋊Dic11—21no—
282C4⋊Dic11—21no—
283C4⋊Dic11—24no—
284C4⋊Dic11C2412yes—
285C4⋊Dic11C2412yes—
286Dic11⋊C4—24no—
287Dic11⋊C4—24no—
288C4×Dic11—24no—
289C2×C11⋊C8—22no—
290C2×C11⋊C8—22no—
291C2×C11⋊C8—22no—
292C2×C11⋊C8—22no—
293C2×C11⋊C8C2412yes—
294C2×C11⋊C8C2412yes—
295C2×C11⋊C8C2412yes—
296C2×C11⋊C8C2412yes—
297C2×#542—111no—
298C2×#536D1111yescharacteristic, complemented
299#3225—1116no—
300C2×#497—111no—
301C2×#495—111no—
302C2×#489—111no—
303C2×#487—111no—
304C2×#464—111no—
305C2×#462—111no—
306C2×#463—111no—
307C2×#461—111no—
308C2×#452—111no—
309C2×#449—111no—
310C2×#451—111no—
311C2×#448—111no—
312C2×#433—111no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11C22×D412yes—
321C23×C11C22×D411yescharacteristic
322C22×D11—22no—
323C22×D11—42no—
324C22×D11—42no—
325C22×D11—42no—
326Q8×C11—22no—
327Q8×C11—22no—
328Q8×C11—22no—
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—22no—
332Q8×C11—48no—
333Q8×C11—42no—
334Q8×C11—42no—
335Q8×C11—42no—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11—48no—
339D4×C11—42no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—24no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—48no—
352C2×C4×C11—48no—
353C2×C4×C11—42no—
354C2×C4×C11—42no—
355C2×C4×C11—42no—
356C2×C4×C11C22×D412yes—
357C2×C4×C11C22×D412yes—
358C2×C4×C11C22×D412yes—
359C2×C4×C11C22×D412yes—
360C2×C4×C11C22×D412yes—
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11H(5,𝔽2)12yes—
363C2×C4×C11H(5,𝔽2)12yes—
364C2×C4×C11C2511yescharacteristic
365C22⋊D11—84no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—42no—
370C2×Dic11—42no—
371C2×Dic11—42no—
372D44—22no—
373D44—22no—
374D44—42no—
375C4×D11—84no—
376Dic22—22no—
377Dic22—22no—
378Dic22—42no—
379Dic22—84no—
380C11⋊C8—22no—
381C11⋊C8—22no—
382C11⋊C8—22no—
383C11⋊C8—22no—
384C22×#41C2×D1111yescharacteristic
385C23×Q8C2×D1111yescharacteristic
386C22×Q16—111no—
387C22×Q16—111no—
388C22×Q16—111no—
389C22×SD16—111no—
390C22×SD16—111no—
391C22×SD16—111no—
392C22×SD16—111no—
393C22×D8—111no—
394#542—118no—
395#542—224no—
396#536—24no—
397#536C2×D1118yescomplemented
398C2×C4⋊Q8—111no—
399C2×C4⋊Q8C2×D1111yescharacteristic
400C2×C4⋊Q8C2×D1111yescharacteristic
401C2×#126—221no—
402C2×#124—111no—
403C2×#124—221no—
404C2×#124C2×D1111yescharacteristic
405C2×#124C2×D1111yescharacteristic
406C2×#123—21no—
407C2×#123—21no—
408C2×#123—221no—
409C2×C22⋊Q8—21no—
410C2×C22⋊Q8—21no—
411C2×C22⋊Q8—111no—
412C2×C22⋊Q8—221no—
413C2×#121—111no—
414C2×C4×Q8—111no—
415C2×C4×D4—111no—
416C2×#117C2×D1111yescharacteristic
417#497—118no—
418#495—118no—
419#489—118no—
420#487—118no—
421#464—118no—
422#463—118no—
423#462—118no—
424#461—118no—
425#452—118no—
426#451—118no—
427#449—118no—
428#448—118no—
429#433—118no—
430C2×C4⋊C8—111no—
431C2×C4⋊C8—111no—
432C2×#103—111no—
433C2×#103—111no—
434C2×#103—111no—
435C2×#103—111no—
436C2×#103—111no—
437C2×#103—111no—
438C2×#102—111no—
439C2×#102—111no—
440C2×C22⋊C8—111no—
441C2×C22⋊C8—111no—
442C2×#97—111no—
443C2×C4×C8—111no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—44no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—84no—
452C22×C11#53512yes—
453C22×C11#57712yes—
454C22×C11#57812yes—
455C22×C11C23×D411yescharacteristic
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—84no—
460C4×C11—22no—
461C4×C11—22no—
462C4×C11—22no—
463C4×C11—22no—
464C4×C11—22no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11#53512yes—
469C4×C11C2×H(5,𝔽2)11yescharacteristic
470C4×C11C2×H(5,𝔽2)11yescharacteristic
471Dic11—42no—
472Dic11—42no—
473Dic11—42no—
474C2×#41—22no—
475C2×#41—42no—
476C2×#41—42no—
477C2×#41C22×D1114yes—
478C22×Q8—21no—
479C22×Q8—22no—
480C22×Q8—42no—
481C22×Q8—42no—
482C22×Q8—111no—
483C22×Q8—221no—
484C22×Q8C22×D1111yescharacteristic
485C22×Q8C22×D1111yescharacteristic
486C22×Q8C22×D1111yescharacteristic
487C22×Q8C22×D1114yes—
488C22×D4—21no—
489C22×D4—111no—
490C22×D4—221no—
491C22×D4C22×D1111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—221no—
495C23×C4C22×D1111yescharacteristic
496C2×Q16—114no—
497C2×Q16—114no—
498C2×Q16—114no—
499C2×Q16—442no—
500C2×Q16—442no—
501C2×Q16—442no—
502C2×SD16—114no—
503C2×SD16—114no—
504C2×SD16—114no—
505C2×SD16—114no—
506C2×SD16—442no—
507C2×SD16—442no—
508C2×SD16—442no—
509C2×SD16—442no—
510C2×D8—114no—
511C2×D8—442no—
512C22×C8—111no—
513C22×C8—111no—
514C22×C8—111no—
515C22×C8—111no—
516C4⋊Q8—22no—
517C4⋊Q8—22no—
518C4⋊Q8—114no—
519C4⋊Q8—222no—
520C4⋊Q8C22×D1114yes—
521C4⋊Q8C22×D1114yes—
522#126—228no—
523#124—22no—
524#124—22no—
525#124—114no—
526#124—228no—
527#124—222no—
528#124C22×D1114yes—
529#124C22×D1114yes—
530#123—28no—
531#123—28no—
532#123—228no—
533C22⋊Q8—28no—
534C22⋊Q8—28no—
535C22⋊Q8—114no—
536C22⋊Q8—222no—
537C22⋊Q8—228no—
538#121—114no—
539#121—222no—
540C4×Q8—114no—
541C4×Q8—222no—
542C4×D4—114no—
543C4×D4—222no—
544#117C22⋊D1114yes—
545#117C22×D1114yes—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4C22⋊D1111yescharacteristic
556C2×C4⋊C4C22⋊D1111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4C22⋊D1111yescharacteristic
567C2×C22⋊C4C22⋊D1111yescharacteristic
568C2×C42—221no—
569C2×C42C22×D1111yescharacteristic
570C2×C42C22×D1111yescharacteristic
571C4⋊C8—114no—
572C4⋊C8—114no—
573#103—114no—
574#103—114no—
575#103—114no—
576#103—114no—
577#103—114no—
578#103—114no—
579#102—114no—
580#102—114no—
581C22⋊C8—114no—
582C22⋊C8—114no—
583#97—114no—
584C4×C8—114no—
585C2×C11—42no—
586C2×C11—82no—
587C2×C11#322514yescomplemented
588C2×C11C2×#53511yescharacteristic
589C2×C11C2×#57711yescharacteristic
590C2×C11C2×#57811yescharacteristic
591D11—82no—
592C24—21no—
593C24—221no—
594C24C2×C22⋊D1111yescharacteristic
595#41—44no—
596#41—44no—
597#41—48no—
598C2×Q8—24no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—44no—
609C2×Q8—44no—
610C2×Q8—44no—
611C2×Q8—48no—
612C2×Q8—112no—
613C2×Q8—221no—
614C2×Q8—224no—
615C2×Q8—222no—
616C2×Q8—222no—
617C2×Q8—882no—
618C2×Q8C23×D1112yes—
619C2×Q8C23×D1112yes—
620C2×Q8C23×D1112yes—
621C2×D4—24no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—21no—
625C2×D4—44no—
626C2×D4—112no—
627C2×D4—224no—
628C2×D4—222no—
629C2×D4—222no—
630C2×D4—221no—
631C2×D4—882no—
632C2×D4C23×D1112yes—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—24no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—224no—
646C22×C4—882no—
647C22×C4C2×C22⋊D1112yes—
648C22×C4C2×C22⋊D1111yescharacteristic
649C22×C4C2×C22⋊D1111yescharacteristic
650C22×C4C2×C22⋊D1111yescharacteristic
651C22×C4C2×C22⋊D1111yescharacteristic
652C22×C4C2×C22⋊D1111yescharacteristic
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655Q16—444no—
656Q16—444no—
657Q16—444no—
658SD16—444no—
659SD16—444no—
660SD16—444no—
661SD16—444no—
662D8—444no—
663C2×C8—112no—
664C2×C8—112no—
665C2×C8—112no—
666C2×C8—112no—
667C2×C8—222no—
668C2×C8—222no—
669C2×C8—222no—
670C2×C8—222no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—112no—
676C4⋊C4—112no—
677C4⋊C4—221no—
678C4⋊C4—221no—
679C4⋊C4—224no—
680C4⋊C4—224no—
681C4⋊C4—224no—
682C4⋊C4C2×C22⋊D1114yes—
683C4⋊C4C2×C22⋊D1114yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C22⋊C4—224no—
693C22⋊C4C2×C22⋊D1114yes—
694C22⋊C4C2×C22⋊D1114yes—
695C42—224no—
696C42C2×C22⋊D1112yes—
697C42C2×C22⋊D1112yes—
698C42C23×D1112yes—
699C42C23×D1112yes—
700C11C2×#322511yescharacteristic, complemented, Sylow
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—222no—
709C23—442no—
710C23—442no—
711C23—442no—
712C23C22×C22⋊D1112yes—
713C23C22×C22⋊D1111yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—48no—
721Q8—42no—
722Q8—42no—
723Q8—42no—
724Q8—222no—
725Q8—222no—
726Q8—442no—
727Q8—884no—
728D4—22no—
729D4—22no—
730D4—48no—
731D4—42no—
732D4—222no—
733D4—222no—
734D4—442no—
735D4—884no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—442no—
756C2×C4—442no—
757C2×C4—442no—
758C2×C4—884no—
759C2×C4#6703712yes—
760C2×C4#6703712yes—
761C2×C4C22×C22⋊D1112yes—
762C2×C4C22×C22⋊D1112yes—
763C2×C4C22×C22⋊D1112yes—
764C2×C4C22×C22⋊D1112yes—
765C2×C4C22×C22⋊D1112yes—
766C2×C4C22×C22⋊D1111yescharacteristic
767C2×C4C24×D1111yescharacteristic
768C8—222no—
769C8—222no—
770C8—222no—
771C8—222no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—442no—
781C22—442no—
782C22—442no—
783C22—884no—
784C22#1062333612yes—
785C22#1062336812yes—
786C22#1062336912yes—
787C22C23×C22⋊D1111yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—442no—
797C4—442no—
798C4—442no—
799C4#1062333612yes—
800C4C2×#6703711yescharacteristic
801C4C2×#6703711yescharacteristic
802C2—42no—
803C2—82no—
804C2—882no—
805C2#1307972514yesdirect product factor
806C2C2×#1062333611yescharacteristic
807C2C2×#1062336811yescharacteristic
808C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#536C2
socleC23×C11C22×D4
prime radicalC2×#10622851C2
hypercenterC2×#536D11
hypocenterC11C2×#3225
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#10623065C2semidirect
2. #13079725C2direct (N × H)
3. C2×#10622699C2semidirect
4. C2×#10622672C2semidirect
5. C2×#10622668C2semidirect
6. C2×#10622694C2semidirect
7. C2×#10622667C2semidirect
8. C2×#10622703C2semidirect
9. C2×#10622670C2semidirect
10. C2×#10622696C2semidirect
11. C2×#10622852C2semidirect
13. C2×#10622841C2semidirect
14. C2×#10622840C2semidirect
15. C2×#10622613C2semidirect
16. C2×C11×#536C2semidirect
20. C11×#536C22semidirect
41. #10623065C22semidirect
50. #10622852C22semidirect
52. #10622841C22semidirect
53. #10622840C22semidirect
64. #10622703C22semidirect
65. #10622699C22semidirect
66. #10622696C22semidirect
67. #10622694C22semidirect
68. #10622672C22semidirect
69. #10622670C22semidirect
70. #10622668C22semidirect
71. #10622667C22semidirect
72. #10622613C22semidirect
298. C2×#536D11semidirect
397. #536C2×D11semidirect
587. C2×C11#3225semidirect
700. C11C2×#3225semidirect
805. C2#13079725direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230652
#130797252
C2×#106226992
C2×#106226722
C2×#106226682
C2×#106226942
C2×#106226672
C2×#106227032
C2×#106226702
C2×#106226962
C2×#106228522
C2×#106228512
C2×#106228412
C2×#106228402
C2×#106226132
C2×C11×#5362
C2×#322511