Finite Group Databasebeta

← C2×#13081700 #15634799

Subgroups — C2×#13081700 #15634799

Order 2816.

2066 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic, complemented
2#13081700C2116yesmaximal, direct product factor
3C2×#10622671C211yesmaximal, characteristic, complemented
4C2×#10622687C211yesmaximal, characteristic, complemented
5C2×#10622672C211yesmaximal, characteristic, complemented
6C2×#10622641C211yesmaximal, characteristic, complemented
7C2×#10622667C211yesmaximal, characteristic, complemented
8C2×#10622629C211yesmaximal, characteristic, complemented
9C2×#10622670C211yesmaximal, characteristic, complemented
10C2×#10622628C211yesmaximal, characteristic, complemented
11C2×#10622685C211yesmaximal, characteristic, complemented
12C2×#10622637C211yesmaximal, characteristic, complemented
13C2×#10622631C211yesmaximal, characteristic, complemented
14C2×#10622639C211yesmaximal, characteristic, complemented
15C2×C4×#4323C211yesmaximal, characteristic, complemented
16C2×C11×#559C211yesmaximal, characteristic, complemented
17C11×#559—24no—
18C11×#559C2218yescomplemented
19C2×C11×#127C2211yescharacteristic
20C2×C11×#124—21no—
21C2×C11×#124C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×C11×#123—21no—
24C2×C11×#123—21no—
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×#67000—21no—
31C22×#4326C2211yescharacteristic
32C22×#4325C2211yescharacteristic
33C22×#4325C2211yescharacteristic
34C22×#4324C2211yescharacteristic
35C22×#4324C2211yescharacteristic
36C22×#4323C2211yescharacteristic
37C22×#4323C2211yescharacteristic
38C22×#4323C2211yescharacteristic
39C22×#4323C2211yescharacteristic
40#10623116—24no—
41#10623116C2218yescomplemented
42C2×#66947—21no—
43C2×#66947—21no—
44C2×#66946—21no—
45C2×#66928C2211yescharacteristic
46C2×#66928C2211yescharacteristic
47C2×#66927C2211yescharacteristic
48C2×C4×D44C2211yescharacteristic
49C2×C4×D44C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622687C2218yescomplemented
55#10622685C2218yescomplemented
56#10622672C2218yescomplemented
57#10622671C2218yescomplemented
58#10622670C2218yescomplemented
59#10622667C2218yescomplemented
60#10622641C2218yescomplemented
61#10622639C2218yescomplemented
62#10622637C2218yescomplemented
63#10622631C2218yescomplemented
64#10622629C2218yescomplemented
65#10622628C2218yescomplemented
66C4×#4323C2218yescomplemented
67C2×#66874C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66873C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×C4⋊(C11⋊C8)C2211yescharacteristic
72C2×C4⋊(C11⋊C8)C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×#66867C2211yescharacteristic
75C2×#66867C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×Q8×C11D411yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11—21no—
85C22×D44—21no—
86C22×D44—21no—
87C22×D44C2311yescharacteristic
88C22×D44C2311yescharacteristic
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C22×Dic22C2311yescharacteristic
92C11×#127—22no—
93C11×#127C2314yes—
94C11×#124—28no—
95C11×#124—22no—
96C11×#124—22no—
97C11×#124C2314yes—
98C11×#124C2314yes—
99C11×#123—28no—
100C11×#123—28no—
101C4×Q8×C11—22no—
102C4×Q8×C11D414yes—
103C4×Q8×C11C2314yes—
104C4×Q8×C11C2314yes—
105C4×D4×C11—28no—
106C4×D4×C11—22no—
107C4×D4×C11—22no—
108C4×D4×C11C2314yes—
109C4×D4×C11C2314yes—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4D411yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4—21no—
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×C42×C11—21no—
122C2×C42×C11C2311yescharacteristic
123C2×C42×C11C2311yescharacteristic
124C2×C42×C11C2311yescharacteristic
125#67000—28no—
126C2×#4326—42no—
127C2×#4326C2314yes—
128C2×#4325—24no—
129C2×#4325—42no—
130C2×#4325C2314yes—
131C2×#4325C2314yes—
132C2×#4324—24no—
133C2×#4324—42no—
134C2×#4324C2314yes—
135C2×#4324C2314yes—
136C2×#4323—24no—
137C2×#4323—42no—
138C2×#4323—42no—
139C2×#4323—42no—
140C2×#4323C2314yes—
141C2×#4323C2314yes—
142C2×#4323C2314yes—
143C2×#4323C2314yes—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—21no—
149C2×(C2×D11)⋊C4—21no—
150C2×C4⋊Dic11C2311yescharacteristic
151C2×Dic11⋊C4—21no—
152C2×C4×Dic11—21no—
153C22×C11⋊C8C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156C22×C11⋊C8C2311yescharacteristic
157#66947—28no—
158#66947—28no—
159#66946—28no—
160#66928—22no—
161#66928—22no—
162#66928C2314yes—
163#66928C2314yes—
164#66927—22no—
165#66927C2314yes—
166C4×D44—22no—
167C4×D44—22no—
168C4×D44C2314yes—
169C4×D44C2314yes—
170C4×Dic22—22no—
171C4×Dic22C2314yes—
172#66899C2314yes—
173#66896C2314yes—
174#66896C2314yes—
175#66874C2314yes—
176#66873C2314yes—
177#66873C2314yes—
178#66871C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180C4⋊(C11⋊C8)C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182#66867C2314yes—
183#66867C2314yes—
184C4×C11⋊C8C2314yes—
185C2×#3403—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C23×D11—21no—
189C23×D11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11—42no—
194C2×Q8×C11C2×D414yes—
195C2×Q8×C11C2412yes—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—24no—
199C2×D4×C11—24no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11—44no—
205C2×D4×C11—82no—
206C2×D4×C11C2412yes—
207C2×D4×C11C2412yes—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—24no—
211C22×C4×C11—24no—
212C22×C4×C11—82no—
213C22×C4×C11—82no—
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2411yescharacteristic
221C22×Dic11—21no—
222C22×Dic11—21no—
223C2×D44—21no—
224C2×D44—21no—
225C2×D44—24no—
226C2×D44—24no—
227C2×D44—22no—
228C2×D44—22no—
229C2×D44—22no—
230C2×D44—22no—
231C2×D44—44no—
232C2×D44—82no—
233C2×D44C2412yes—
234C2×D44C2412yes—
235C2×C4×D11—24no—
236C2×C4×D11—24no—
237C2×C4×D11—82no—
238C2×C4×D11—82no—
239C2×Dic22—21no—
240C2×Dic22—22no—
241C2×Dic22—22no—
242C2×Dic22C2412yes—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4C2×D414yes—
246C11×C4⋊C4C2×D414yes—
247C11×C4⋊C4C2×D414yes—
248C11×C4⋊C4C2412yes—
249C11×C22⋊C4—24no—
250C11×C22⋊C4—24no—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—24no—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—24no—
255C42×C11—24no—
256C42×C11C2×D412yes—
257C42×C11C2×D412yes—
258C42×C11C2×D412yes—
259C42×C11C2412yes—
260C42×C11C2412yes—
261C42×C11C2412yes—
262#4326—44no—
263#4325—28no—
264#4325—44no—
265#4324—28no—
266#4324—44no—
267#4323—28no—
268#4323—44no—
269#4323—44no—
270#4323—44no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277C4⋊Dic11—21no—
278C4⋊Dic11C2412yes—
279Dic11⋊C4—24no—
280C4×Dic11—24no—
281C2×C11⋊C8—22no—
282C2×C11⋊C8—22no—
283C2×C11⋊C8—22no—
284C2×C11⋊C8#4114yes—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2412yes—
287C2×C11⋊C8C2412yes—
288C2×C11⋊C8C2412yes—
289C2×#559—111no—
290C2×#559D1111yescharacteristic, complemented
291#3403—1116no—
292C2×#496—111no—
293C2×#496—111no—
294C2×#495—111no—
295C2×#464—111no—
296C2×#464—111no—
297C2×#463—111no—
298C2×#463—111no—
299C2×#459—111no—
300C2×#459—111no—
301C2×#446—111no—
302C2×#440—111no—
303C2×#440—111no—
304C2×C4×D8—111no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11—42no—
313C23×C11C22×D411yescharacteristic
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—42no—
317C22×D11—42no—
318C22×D11—42no—
319C22×D11—42no—
320C22×D11—42no—
321C22×D11—42no—
322Q8×C11—22no—
323Q8×C11—22no—
324Q8×C11—44no—
325Q8×C11—42no—
326D4×C11—22no—
327D4×C11—22no—
328D4×C11—22no—
329D4×C11—22no—
330D4×C11—48no—
331D4×C11—42no—
332D4×C11—42no—
333D4×C11—84no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—42no—
343C2×C4×C11—42no—
344C2×C4×C11—84no—
345C2×C4×C11—84no—
346C2×C4×C11C22×D412yes—
347C2×C4×C11C22×D412yes—
348C2×C4×C11C22×D412yes—
349C2×C4×C11C22×D412yes—
350C2×C4×C11C22×D412yes—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C2×#4112yes—
354C2×C4×C11H(5,𝔽2)12yes—
355C2×C4×C11C2511yescharacteristic
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360D44—22no—
361D44—22no—
362D44—22no—
363D44—22no—
364D44—48no—
365D44—42no—
366D44—42no—
367D44—84no—
368C4×D11—84no—
369C4×D11—84no—
370Dic22—22no—
371Dic22—22no—
372Dic22—42no—
373C11⋊C8—22no—
374C11⋊C8—22no—
375C11⋊C8—22no—
376C11⋊C8C2×#4114yes—
377C22×Q16—111no—
378C22×SD16—111no—
379C22×SD16—111no—
380C22×SD16—111no—
381C22×SD16—111no—
382C22×D8—111no—
383C22×D8—111no—
384C22×D8—111no—
385C22×D8—111no—
386#559—24no—
387#559—118no—
388#559—224no—
389#559C2×D1118yescomplemented
390C2×#127—111no—
391C2×#127C2×D1111yescharacteristic
392C2×#124—21no—
393C2×#124—111no—
394C2×#124—111no—
395C2×#124—221no—
396C2×#124C2×D1111yescharacteristic
397C2×#124C2×D1111yescharacteristic
398C2×#123—21no—
399C2×#123—21no—
400C2×#123—221no—
401C2×#123—221no—
402C2×C4×Q8—111no—
403C2×C4×Q8C2×D1111yescharacteristic
404C2×C4×Q8C2×D1111yescharacteristic
405C2×C4×D4—21no—
406C2×C4×D4—111no—
407C2×C4×D4—111no—
408C2×C4×D4—221no—
409C2×C4×D4C2×D1111yescharacteristic
410C2×C4×D4C2×D1111yescharacteristic
411#496—118no—
412#496—118no—
413#495—118no—
414#464—118no—
415#464—118no—
416#463—118no—
417#463—118no—
418#459—118no—
419#459—118no—
420#446—118no—
421#440—118no—
422#440—118no—
423C4×D8—118no—
424C2×#107—111no—
425C2×C4⋊C8—111no—
426C2×C4⋊C8—111no—
427C2×C4⋊C8—111no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×#102—111no—
434C2×#97—111no—
435C2×#97—111no—
436C2×C4×C8—111no—
437C22×C11—42no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—84no—
444C22×C11—84no—
445C22×C11#55012yes—
446C22×C11#57512yes—
447C22×C11#57612yes—
448C22×C11C23×D411yescharacteristic
449C2×D11—42no—
450C2×D11—42no—
451C2×D11—42no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—84no—
456C2×D11—84no—
457C4×C11—22no—
458C4×C11—22no—
459C4×C11—22no—
460C4×C11—22no—
461C4×C11—22no—
462C4×C11—22no—
463C4×C11—42no—
464C4×C11—42no—
465C4×C11#55012yes—
466C4×C11C22×#4111yescharacteristic
467C4×C11C2×H(5,𝔽2)11yescharacteristic
468Dic11—42no—
469Dic11—42no—
470C22×Q8—111no—
471C22×Q8C22⋊D1111yescharacteristic
472C22×Q8C22×D1111yescharacteristic
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—111no—
476C22×D4—111no—
477C22×D4—221no—
478C22×D4—221no—
479C22×D4C22×D1111yescharacteristic
480C22×D4C22×D1111yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—221no—
484C23×C4—221no—
485C2×Q16—114no—
486C2×Q16—442no—
487C2×SD16—114no—
488C2×SD16—114no—
489C2×SD16—114no—
490C2×SD16—114no—
491C2×SD16—224no—
492C2×SD16—224no—
493C2×SD16—442no—
494C2×SD16—442no—
495C2×D8—114no—
496C2×D8—114no—
497C2×D8—114no—
498C2×D8—114no—
499C2×D8—224no—
500C2×D8—442no—
501C2×D8—442no—
502C2×D8—442no—
503C22×C8—111no—
504C22×C8—111no—
505C22×C8—111no—
506C22×C8—111no—
507#127—22no—
508#127—114no—
509#127—222no—
510#127C22×D1114yes—
511#124—28no—
512#124—22no—
513#124—22no—
514#124—114no—
515#124—114no—
516#124—228no—
517#124—222no—
518#124—222no—
519#124C22×D1114yes—
520#124C22×D1114yes—
521#123—28no—
522#123—28no—
523#123—228no—
524#123—228no—
525C4×Q8—22no—
526C4×Q8—114no—
527C4×Q8—222no—
528C4×Q8C22⋊D1114yes—
529C4×Q8C22×D1114yes—
530C4×Q8C22×D1114yes—
531C4×D4—28no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—114no—
535C4×D4—114no—
536C4×D4—228no—
537C4×D4—222no—
538C4×D4—222no—
539C4×D4C22×D1114yes—
540C4×D4C22×D1114yes—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—221no—
544C2×C4⋊C4C22⋊D1111yescharacteristic
545C2×C4⋊C4C22⋊D1111yescharacteristic
546C2×C4⋊C4C22⋊D1111yescharacteristic
547C2×C4⋊C4C22×D1111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C42—21no—
561C2×C42—221no—
562C2×C42C22×D1111yescharacteristic
563C2×C42C22×D1111yescharacteristic
564C2×C42C22×D1111yescharacteristic
565#107—114no—
566C4⋊C8—114no—
567C4⋊C8—114no—
568C4⋊C8—114no—
569#103—114no—
570#103—114no—
571#102—114no—
572#102—114no—
573#102—114no—
574#102—114no—
575#97—114no—
576#97—114no—
577C4×C8—114no—
578C2×C11—82no—
579C2×C11—82no—
580C2×C11#340314yescomplemented
581C2×C11C2×#55011yescharacteristic
582C2×C11C2×#57511yescharacteristic
583C2×C11C2×#57611yescharacteristic
584D11—82no—
585D11—82no—
586C24—21no—
587C24—21no—
588C24—221no—
589C24—221no—
590C2×Q8—21no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—42no—
594C2×Q8—112no—
595C2×Q8—221no—
596C2×Q8—222no—
597C2×Q8—222no—
598C2×Q8C2×C22⋊D1114yes—
599C2×Q8C23×D1112yes—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—44no—
609C2×D4—82no—
610C2×D4—112no—
611C2×D4—112no—
612C2×D4—222no—
613C2×D4—222no—
614C2×D4—222no—
615C2×D4—222no—
616C2×D4—224no—
617C2×D4—221no—
618C2×D4—221no—
619C2×D4—224no—
620C2×D4—444no—
621C2×D4—882no—
622C2×D4C23×D1112yes—
623C2×D4C23×D1112yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—82no—
629C22×C4—82no—
630C22×C4—221no—
631C22×C4—221no—
632C22×C4—224no—
633C22×C4—224no—
634C22×C4—882no—
635C22×C4—882no—
636C22×C4C2×C22⋊D1111yescharacteristic
637C22×C4C2×C22⋊D1111yescharacteristic
638C22×C4C2×C22⋊D1111yescharacteristic
639C22×C4C2×C22⋊D1111yescharacteristic
640C22×C4C2×C22⋊D1111yescharacteristic
641C22×C4C2×C22⋊D1111yescharacteristic
642C22×C4C23×D1111yescharacteristic
643Q16—444no—
644SD16—228no—
645SD16—228no—
646SD16—444no—
647SD16—444no—
648D8—228no—
649D8—444no—
650D8—444no—
651D8—444no—
652C2×C8—114no—
653C2×C8—112no—
654C2×C8—112no—
655C2×C8—112no—
656C2×C8—112no—
657C2×C8—222no—
658C2×C8—222no—
659C2×C8—222no—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—112no—
663C4⋊C4—221no—
664C4⋊C4—224no—
665C4⋊C4C2×C22⋊D1114yes—
666C4⋊C4C2×C22⋊D1114yes—
667C4⋊C4C2×C22⋊D1114yes—
668C4⋊C4C23×D1112yes—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C42—24no—
682C42—224no—
683C42C2×C22⋊D1112yes—
684C42C2×C22⋊D1112yes—
685C42C2×C22⋊D1112yes—
686C42C23×D1112yes—
687C42C23×D1112yes—
688C42C23×D1112yes—
689C11C2×#340311yescharacteristic, complemented, Sylow
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—222no—
699C23—222no—
700C23—442no—
701C23—442no—
702C23—442no—
703C23—442no—
704C23—442no—
705C23—442no—
706C23C22×C22⋊D1111yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—44no—
710Q8—42no—
711Q8—222no—
712Q8—222no—
713Q8—442no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—48no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—222no—
723D4—222no—
724D4—222no—
725D4—222no—
726D4—448no—
727D4—442no—
728D4—442no—
729D4—884no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—884no—
747C2×C4—884no—
748C2×C4#41×D1112yes—
749C2×C4#6704212yes—
750C2×C4C22×C22⋊D1112yes—
751C2×C4C22×C22⋊D1112yes—
752C2×C4C22×C22⋊D1112yes—
753C2×C4C22×C22⋊D1112yes—
754C2×C4C22×C22⋊D1112yes—
755C2×C4C22×C22⋊D1112yes—
756C2×C4C22×C22⋊D1111yescharacteristic
757C2×C4C24×D1111yescharacteristic
758C8—114no—
759C8—222no—
760C8—222no—
761C8—222no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22—84no—
770C22—442no—
771C22—442no—
772C22—442no—
773C22—442no—
774C22—442no—
775C22—442no—
776C22—884no—
777C22—884no—
778C22#1062335312yes—
779C22#1062336512yes—
780C22#1062336612yes—
781C22C23×C22⋊D1111yescharacteristic
782C4—22no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—22no—
787C4—22no—
788C4—42no—
789C4—42no—
790C4—442no—
791C4—442no—
792C4#1062336512yes—
793C4C2×#41×D1111yescharacteristic
794C4C2×#6704211yescharacteristic
795C2—82no—
796C2—82no—
797C2—882no—
798C2—882no—
799C2#1308170014yesdirect product factor
800C2C2×#1062336511yescharacteristic
801C2C2×#1062335311yescharacteristic
802C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#559C2
socleC23×C11C22×D4
hypercenterC2×#559D11
hypocenterC11C2×#3403
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#10623116C2semidirect
2. #13081700C2direct (N × H)
3. C2×#10622671C2semidirect
4. C2×#10622687C2semidirect
5. C2×#10622672C2semidirect
6. C2×#10622641C2semidirect
7. C2×#10622667C2semidirect
8. C2×#10622629C2semidirect
9. C2×#10622670C2semidirect
10. C2×#10622628C2semidirect
11. C2×#10622685C2semidirect
12. C2×#10622637C2semidirect
13. C2×#10622631C2semidirect
14. C2×#10622639C2semidirect
15. C2×C4×#4323C2semidirect
16. C2×C11×#559C2semidirect
18. C11×#559C22semidirect
41. #10623116C22semidirect
54. #10622687C22semidirect
55. #10622685C22semidirect
56. #10622672C22semidirect
57. #10622671C22semidirect
58. #10622670C22semidirect
59. #10622667C22semidirect
60. #10622641C22semidirect
61. #10622639C22semidirect
62. #10622637C22semidirect
63. #10622631C22semidirect
64. #10622629C22semidirect
65. #10622628C22semidirect
66. C4×#4323C22semidirect
290. C2×#559D11semidirect
389. #559C2×D11semidirect
580. C2×C11#3403semidirect
689. C11C2×#3403semidirect
799. C2#13081700direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
#130817002
C2×#106226712
C2×#106226872
C2×#106226722
C2×#106226412
C2×#106226672
C2×#106226292
C2×#106226702
C2×#106226282
C2×#106226852
C2×#106226372
C2×#106226312
C2×#106226392
C2×C4×#43232
C2×C11×#5592
C2×#340311