Finite Group Databasebeta

← C2×#13080863 #15630620

Subgroups — C2×#13080863 #15630620

Order 2816.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623083C211yesmaximal, characteristic, complemented
2#13080863C2116yesmaximal, direct product factor
3C2×#10622681C211yesmaximal, characteristic, complemented
4C2×#10622616C211yesmaximal, characteristic, complemented
5C2×#10622584C211yesmaximal, characteristic, complemented
6C2×#10622676C211yesmaximal, characteristic, complemented
7C2×#10622652C211yesmaximal, characteristic, complemented
8C2×#10622655C211yesmaximal, characteristic, complemented
9C2×#10622629C211yesmaximal, characteristic, complemented
10C2×#10622650C211yesmaximal, characteristic, complemented
11C2×#10622653C211yesmaximal, characteristic, complemented
12C2×C4×#4324C211yesmaximal, characteristic, complemented
13C2×#10622625C211yesmaximal, characteristic, complemented
14C2×#10622579C211yesmaximal, characteristic, complemented
15C2×#10622617C211yesmaximal, characteristic, complemented
16C2×C11×#553C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C11×#553—24no—
20C11×#553C2218yescomplemented
21C2×C11×#126—21no—
22C2×C11×#125C2211yescharacteristic
23C2×C11×#123—21no—
24C2×C11×#121—21no—
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117C2211yescharacteristic
31C22×C11×C4⋊C4C2211yescharacteristic
32C2×#66992—21no—
33C22×#4324C2211yescharacteristic
34C22×#4324C2211yescharacteristic
35C22×#4323C2211yescharacteristic
36C2×#66983C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38C22×#4318C2211yescharacteristic
39C22×#4318C2211yescharacteristic
40#10623083—24no—
41#10623083C2218yescomplemented
42C2×#66949—21no—
43C2×#66938—21no—
44C2×(C22⋊D11)⋊C4—21no—
45C2×#66928C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic
50#10622681C2218yescomplemented
51#10622676C2218yescomplemented
52#10622655C2218yescomplemented
53#10622653C2218yescomplemented
54#10622652C2218yescomplemented
55#10622650C2218yescomplemented
56C4×#4324C2218yescomplemented
57#10622629C2218yescomplemented
58#10622625C2218yescomplemented
59#10622617C2218yescomplemented
60#10622616C2218yescomplemented
61#10622584C2218yescomplemented
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64C2×#66874C2211yescharacteristic
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66874C2211yescharacteristic
68#10622579C2218yescomplemented
69C2×#66873C2211yescharacteristic
70C2×#66873C2211yescharacteristic
71C2×#66873C2211yescharacteristic
72C2×#66872C2211yescharacteristic
73C2×#66872C2211yescharacteristic
74C2×#66871C2211yescharacteristic
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11D411yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11—21no—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C23×Dic11—21no—
88C2×#4339—22no—
89C2×#4339—24no—
90C2×#4339—42no—
91C2×#4339C2314yes—
92C22×D44C2311yescharacteristic
93C22×C4×D11—21no—
94C22×Dic22—24no—
95C22×Dic22—21no—
96C22×Dic22—22no—
97C22×Dic22—42no—
98C22×Dic22C2311yescharacteristic
99C22×Dic22C2314yes—
100C22×Dic22C2311yescharacteristic
101C11×#126—28no—
102C11×#125—22no—
103C11×#125C2314yes—
104C11×#123—28no—
105C11×#121—28no—
106C11×#121—22no—
107C11×#121—22no—
108C11×#121C2314yes—
109C11×#121C2314yes—
110C4×D4×C11—28no—
111C4×D4×C11—22no—
112C4×D4×C11D414yes—
113C4×D4×C11C2314yes—
114C4×D4×C11C2314yes—
115C11×#117—22no—
116C11×#117C2314yes—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—22no—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4D411yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C4⋊C4C2314yes—
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4—21no—
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4D411yescharacteristic
131C2×C11×C22⋊C4D411yescharacteristic
132C2×C42×C11—21no—
133C2×C42×C11C2311yescharacteristic
134C2×C22⋊Dic11—21no—
135#66992—28no—
136C2×#4324—24no—
137C2×#4324—42no—
138C2×#4324C2314yes—
139C2×#4324C2314yes—
140C2×#4323—42no—
141C2×#4323C2314yes—
142#66983—22no—
143#66983C2314yes—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×C4⋊Dic11C2311yescharacteristic
148#66977—22no—
149#66977C2314yes—
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×C4×Dic11—21no—
153C2×#4318—42no—
154C2×#4318—42no—
155C2×#4318C2314yes—
156C2×#4318C2314yes—
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161#66949—28no—
162#66938—28no—
163(C22⋊D11)⋊C4—28no—
164#66928—22no—
165#66928C2314yes—
166C4×Dic22—22no—
167C4×Dic22C2314yes—
168#66896C2314yes—
169C22⋊(C11⋊C8)C2314yes—
170C22⋊(C11⋊C8)C2314yes—
171#66874C2314yes—
172#66874C2314yes—
173#66874C2314yes—
174#66874C2314yes—
175#66874C2314yes—
176#66874C2314yes—
177#66873C2314yes—
178#66873C2314yes—
179#66873C2314yes—
180#66872C2314yes—
181#66872C2314yes—
182#66871C2314yes—
183C4⋊(C11⋊C8)C2314yes—
184C4×C11⋊C8C2314yes—
185C2×#3326—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11C2×D411yescharacteristic
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
190C2×D4×C11—24no—
191C2×D4×C11—24no—
192C2×D4×C11—21no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—42no—
196C2×D4×C11—44no—
197C2×D4×C11—82no—
198C2×D4×C11C2×D414yes—
199C2×D4×C11C2412yes—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—24no—
208C22×C4×C11—24no—
209C22×C4×C11—82no—
210C22×C4×C11—82no—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2411yescharacteristic
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—44no—
224C22×Dic11—21no—
225C22×Dic11—24no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—44no—
229#4339—28no—
230#4339—44no—
231#4339—48no—
232C2×D44—21no—
233C2×D44—22no—
234C2×D44—22no—
235C2×D44C2412yes—
236C2×C4×D11—24no—
237C2×C4×D11—44no—
238C2×Dic22—28no—
239C2×Dic22—21no—
240C2×Dic22—21no—
241C2×Dic22—24no—
242C2×Dic22—22no—
243C2×Dic22—22no—
244C2×Dic22—22no—
245C2×Dic22—44no—
246C2×Dic22—48no—
247C2×Dic22—44no—
248C2×Dic22#4114yes—
249C2×Dic22C2412yes—
250C2×Dic22C2412yes—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—24no—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4C2×D414yes—
258C11×C4⋊C4C2412yes—
259C11×C4⋊C4C2412yes—
260C11×C4⋊C4C2412yes—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—24no—
263C11×C22⋊C4—24no—
264C11×C22⋊C4—24no—
265C11×C22⋊C4C2×D414yes—
266C11×C22⋊C4C2×D414yes—
267C42×C11—24no—
268C42×C11C2×D412yes—
269C42×C11C2412yes—
270C22⋊Dic11—24no—
271#4324—28no—
272#4324—44no—
273#4323—44no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277C4⋊Dic11—21no—
278C4⋊Dic11C2412yes—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281C4×Dic11—24no—
282#4318—44no—
283#4318—44no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8—22no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8C2412yes—
289C2×C11⋊C8C2412yes—
290C2×C11⋊C8C2412yes—
291C2×C11⋊C8C2412yes—
292C2×#553D1111yescharacteristic, complemented
293C2×#548—111no—
294#3326—1116no—
295C2×#488—111no—
296C2×#482—111no—
297C2×#483—111no—
298C2×#479—111no—
299C2×#469—111no—
300C2×#468—111no—
301C2×#463—111no—
302C2×#449—111no—
303C2×#448—111no—
304C2×C4×SD16—111no—
305C2×#436—111no—
306C2×#417—111no—
307C2×#419—111no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11C22×D412yes—
319C23×C11C22×D412yes—
320C23×C11C22×D411yescharacteristic
321C22×D11—22no—
322C22×D11—42no—
323C22×D11—42no—
324C22×D11—42no—
325D4×C11—22no—
326D4×C11—22no—
327D4×C11—44no—
328D4×C11—48no—
329D4×C11—42no—
330D4×C11—84no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—24no—
336C2×C4×C11—24no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—42no—
345C2×C4×C11—42no—
346C2×C4×C11—42no—
347C2×C4×C11—84no—
348C2×C4×C11—84no—
349C2×C4×C11C22×D412yes—
350C2×C4×C11C22×D412yes—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C2×#4112yes—
355C2×C4×C11H(5,𝔽2)12yes—
356C2×C4×C11C2511yescharacteristic
357C22⋊D11—48no—
358C22⋊D11—48no—
359C2×Dic11—24no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—48no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366D44—22no—
367D44—22no—
368D44—42no—
369C4×D11—48no—
370Dic22—24no—
371Dic22—22no—
372Dic22—22no—
373Dic22—22no—
374Dic22—48no—
375Dic22—42no—
376Dic22C2×#4114yes—
377C11⋊C8—22no—
378C11⋊C8—22no—
379C11⋊C8—22no—
380C11⋊C8—22no—
381C22×#41—111no—
382C23×Q8—111no—
383C22×SD16—111no—
384C22×SD16—111no—
385C22×D8—111no—
386C22×M16—111no—
387C22×M16—111no—
388#553—24no—
389#553C2×D1118yescomplemented
390#548—118no—
391#548—224no—
392C2×#126—21no—
393C2×#125C2×D1111yescharacteristic
394C2×#124—111no—
395C2×#124—221no—
396C2×#123—21no—
397C2×C22⋊Q8—111no—
398C2×C22⋊Q8—221no—
399C2×#121—21no—
400C2×#121—111no—
401C2×#121—221no—
402C2×#121C2×D1111yescharacteristic
403C2×#121C2×D1111yescharacteristic
404C2×C4×Q8—111no—
405C2×C4×D4—21no—
406C2×C4×D4—221no—
407C2×C4×D4C2×D1111yescharacteristic
408C2×C4×D4C2×D1111yescharacteristic
409C2×#117C2×D1111yescharacteristic
410C22×C4⋊C4C2×D1111yescharacteristic
411#488—118no—
412#483—118no—
413#482—118no—
414#479—118no—
415#469—118no—
416#468—118no—
417#463—118no—
418#449—118no—
419#448—118no—
420C4×SD16—118no—
421#436—118no—
422C2×#107—111no—
423C2×#106—111no—
424C2×#106—111no—
425C2×C4⋊C8—111no—
426#419—118no—
427#417—118no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#103—111no—
433C2×#103—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×C22⋊C8—111no—
439C2×C22⋊C8—111no—
440C2×C4×C8—111no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—44no—
448C22×C11—44no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—84no—
453C22×C11#54612yes—
454C22×C11#57512yes—
455C22×C11#57712yes—
456C22×C11C23×D411yescharacteristic
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—84no—
461C4×C11—22no—
462C4×C11—22no—
463C4×C11—22no—
464C4×C11—22no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11#54612yes—
469C4×C11C22×#4111yescharacteristic
470C4×C11C2×H(5,𝔽2)11yescharacteristic
471Dic11—24no—
472Dic11—42no—
473Dic11—42no—
474C2×#41—114no—
475C2×#41—224no—
476C2×#41—222no—
477C2×#41—442no—
478C22×Q8—111no—
479C22×Q8—111no—
480C22×Q8—114no—
481C22×Q8—224no—
482C22×Q8—221no—
483C22×Q8—222no—
484C22×Q8—442no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—111no—
488C22×D4—221no—
489C22×D4—221no—
490C22×D4C22⋊D1111yescharacteristic
491C22×D4C22×D1111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—221no—
495C23×C4—221no—
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C2×SD16—114no—
499C2×SD16—114no—
500C2×SD16—224no—
501C2×SD16—442no—
502C2×D8—114no—
503C2×D8—442no—
504C2×M16—114no—
505C2×M16—114no—
506C2×M16—442no—
507C2×M16—442no—
508C22×C8—111no—
509C22×C8—111no—
510C22×C8—111no—
511C22×C8—111no—
512#126—28no—
513#125—22no—
514#125C22×D1114yes—
515#124—114no—
516#124—228no—
517#124—222no—
518#123—28no—
519C22⋊Q8—114no—
520C22⋊Q8—222no—
521C22⋊Q8—228no—
522#121—28no—
523#121—22no—
524#121—22no—
525#121—114no—
526#121—228no—
527#121—222no—
528#121C22×D1114yes—
529#121C22×D1114yes—
530C4×Q8—114no—
531C4×Q8—222no—
532C4×D4—28no—
533C4×D4—22no—
534C4×D4—228no—
535C4×D4C22⋊D1114yes—
536C4×D4C22×D1114yes—
537C4×D4C22×D1114yes—
538#117—22no—
539#117C22×D1114yes—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4C22⋊D1111yescharacteristic
548C2×C4⋊C4C22×D1111yescharacteristic
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1114yes—
551C2×C4⋊C4C22×D1111yescharacteristic
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4C22⋊D1111yescharacteristic
561C2×C22⋊C4C22⋊D1111yescharacteristic
562C2×C42—21no—
563C2×C42—221no—
564C2×C42C22×D1111yescharacteristic
565#107—114no—
566#106—114no—
567#106—114no—
568C4⋊C8—114no—
569#103—114no—
570#103—114no—
571#103—114no—
572#103—114no—
573#103—114no—
574#103—114no—
575#102—114no—
576#102—114no—
577#102—114no—
578#102—114no—
579C22⋊C8—114no—
580C22⋊C8—114no—
581C4×C8—114no—
582C2×C11—42no—
583C2×C11—42no—
584C2×C11—82no—
585C2×C11#332614yescomplemented
586C2×C11C2×#54611yescharacteristic
587C2×C11C2×#57511yescharacteristic
588C2×C11C2×#57711yescharacteristic
589D11—82no—
590C24—21no—
591C24—221no—
592C24C2×C22⋊D1111yescharacteristic
593C24C2×C22⋊D1111yescharacteristic
594#41—228no—
595#41—444no—
596#41—448no—
597C2×Q8—114no—
598C2×Q8—112no—
599C2×Q8—112no—
600C2×Q8—228no—
601C2×Q8—222no—
602C2×Q8—221no—
603C2×Q8—224no—
604C2×Q8—221no—
605C2×Q8—222no—
606C2×Q8—222no—
607C2×Q8—444no—
608C2×Q8—444no—
609C2×Q8—448no—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—21no—
615C2×D4—42no—
616C2×D4—44no—
617C2×D4—82no—
618C2×D4—112no—
619C2×D4—224no—
620C2×D4—224no—
621C2×D4—222no—
622C2×D4—222no—
623C2×D4—221no—
624C2×D4—444no—
625C2×D4—444no—
626C2×D4C2×C22⋊D1114yes—
627C2×D4C23×D1112yes—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—24no—
636C22×C4—24no—
637C22×C4—82no—
638C22×C4—82no—
639C22×C4—221no—
640C22×C4—224no—
641C22×C4—221no—
642C22×C4—221no—
643C22×C4—224no—
644C22×C4—444no—
645C22×C4—444no—
646C22×C4C2×C22⋊D1112yes—
647C22×C4C2×C22⋊D1112yes—
648C22×C4C2×C22⋊D1111yescharacteristic
649C22×C4C2×C22⋊D1111yescharacteristic
650C22×C4C2×C22⋊D1111yescharacteristic
651C22×C4C2×C22⋊D1111yescharacteristic
652C22×C4C23×D1112yes—
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655SD16—228no—
656SD16—444no—
657D8—444no—
658M16—444no—
659M16—444no—
660C2×C8—112no—
661C2×C8—112no—
662C2×C8—112no—
663C2×C8—112no—
664C2×C8—222no—
665C2×C8—222no—
666C2×C8—222no—
667C2×C8—222no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—21no—
674C4⋊C4—112no—
675C4⋊C4—221no—
676C4⋊C4—224no—
677C4⋊C4—224no—
678C4⋊C4C2×C22⋊D1114yes—
679C4⋊C4C23×D1112yes—
680C4⋊C4C23×D1112yes—
681C4⋊C4C23×D1112yes—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4C2×C22⋊D1114yes—
691C22⋊C4C2×C22⋊D1114yes—
692C42—24no—
693C42—224no—
694C42C2×C22⋊D1112yes—
695C42C23×D1112yes—
696C11C2×#332611yescharacteristic, complemented, Sylow
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—222no—
708C23—442no—
709C23—442no—
710C23—442no—
711C23C22×C22⋊D1112yes—
712C23C22×C22⋊D1112yes—
713C23C22×C22⋊D1111yescharacteristic
714Q8—114no—
715Q8—224no—
716Q8—222no—
717Q8—222no—
718Q8—222no—
719Q8—448no—
720Q8—442no—
721D4—22no—
722D4—22no—
723D4—44no—
724D4—48no—
725D4—42no—
726D4—84no—
727D4—222no—
728D4—222no—
729D4—448no—
730D4—448no—
731D4—442no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4—224no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—448no—
755C2×C4—448no—
756C2×C4—442no—
757C2×C4—442no—
758C2×C4#41×D1112yes—
759C2×C4#6704212yes—
760C2×C4C22×C22⋊D1112yes—
761C2×C4C22×C22⋊D1112yes—
762C2×C4C22×C22⋊D1112yes—
763C2×C4C22×C22⋊D1112yes—
764C2×C4C22×C22⋊D1111yescharacteristic
765C2×C4C24×D1111yescharacteristic
766C8—222no—
767C8—222no—
768C8—222no—
769C8—222no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—884no—
786C22#1062335312yes—
787C22#1062336012yes—
788C22#1062336712yes—
789C22C23×C22⋊D1111yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—224no—
798C4—442no—
799C4—442no—
800C4#1062336012yes—
801C4C2×#41×D1111yescharacteristic
802C4C2×#6704211yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—882no—
807C2#1308086314yesdirect product factor
808C2C2×#1062336011yescharacteristic
809C2C2×#1062335311yescharacteristic
810C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#553C2
socleC23×C11C22×D4
hypercenterC2×#553D11
hypocenterC11C2×#3326
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#10623083C2semidirect
2. #13080863C2direct (N × H)
3. C2×#10622681C2semidirect
4. C2×#10622616C2semidirect
5. C2×#10622584C2semidirect
6. C2×#10622676C2semidirect
7. C2×#10622652C2semidirect
8. C2×#10622655C2semidirect
9. C2×#10622629C2semidirect
10. C2×#10622650C2semidirect
11. C2×#10622653C2semidirect
12. C2×C4×#4324C2semidirect
13. C2×#10622625C2semidirect
14. C2×#10622579C2semidirect
15. C2×#10622617C2semidirect
16. C2×C11×#553C2semidirect
20. C11×#553C22semidirect
41. #10623083C22semidirect
50. #10622681C22semidirect
51. #10622676C22semidirect
52. #10622655C22semidirect
53. #10622653C22semidirect
54. #10622652C22semidirect
55. #10622650C22semidirect
56. C4×#4324C22semidirect
57. #10622629C22semidirect
58. #10622625C22semidirect
59. #10622617C22semidirect
60. #10622616C22semidirect
61. #10622584C22semidirect
68. #10622579C22semidirect
292. C2×#553D11semidirect
389. #553C2×D11semidirect
585. C2×C11#3326semidirect
696. C11C2×#3326semidirect
807. C2#13080863direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230832
#130808632
C2×#106226812
C2×#106226162
C2×#106225842
C2×#106226762
C2×#106226522
C2×#106226552
C2×#106226292
C2×#106226502
C2×#106226532
C2×C4×#43242
C2×#106226252
C2×#106225792
C2×#106226172
C2×C11×#5532
C2×#332611