Finite Group Databasebeta

← C2×#13080616 #15630469

Subgroups — C2×#13080616 #15630469

Order 2816.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623084C211yesmaximal, characteristic, complemented
2#13080616C2116yesmaximal, direct product factor
3C2×#10622680C211yesmaximal, characteristic, complemented
4C2×#10622616C211yesmaximal, characteristic, complemented
5C2×#10622580C211yesmaximal, characteristic, complemented
6C2×#10622676C211yesmaximal, characteristic, complemented
7C2×#10622652C211yesmaximal, characteristic, complemented
8C2×#10622651C211yesmaximal, characteristic, complemented
9C2×#10622628C211yesmaximal, characteristic, complemented
10C2×#10622650C211yesmaximal, characteristic, complemented
11C2×#10622650C211yesmaximal, characteristic, complemented
12C2×#10622631C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622579C211yesmaximal, characteristic, complemented
15C2×#10622615C211yesmaximal, characteristic, complemented
16C2×C11×#553C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C22×#4339C2211yescharacteristic
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×#66993—21no—
33C22×#4324C2211yescharacteristic
34C22×#4323C2211yescharacteristic
35C22×#4323C2211yescharacteristic
36C2×#66983C2211yescharacteristic
37C2×#66983C2211yescharacteristic
38C22×#4318C2211yescharacteristic
39C23×C11⋊C8C2211yescharacteristic
40#10623084—24no—
41#10623084C2218yescomplemented
42C2×#66946—21no—
43C2×#66937—21no—
44C2×#66937—21no—
45C2×#66927C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic
50#10622680C2218yescomplemented
51#10622676C2218yescomplemented
52#10622652C2218yescomplemented
53#10622651C2218yescomplemented
54#10622650C2218yescomplemented
55#10622650C2218yescomplemented
56#10622631C2218yescomplemented
57#10622628C2218yescomplemented
58#10622624C2218yescomplemented
59#10622616C2218yescomplemented
60#10622615C2218yescomplemented
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64#10622580C2218yescomplemented
65#10622579C2218yescomplemented
66C2×#66873C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66873C2211yescharacteristic
70C2×#66873C2211yescharacteristic
71C2×#66873C2211yescharacteristic
72C2×#66872C2211yescharacteristic
73C2×#66871C2211yescharacteristic
74C2×#66871C2211yescharacteristic
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×#66867C2211yescharacteristic
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—
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C2×#4339—22no—
90C2×#4339—22no—
91C2×#4339—24no—
92C2×#4339—24no—
93C2×#4339—42no—
94C2×#4339—42no—
95C2×#4339C2314yes—
96C2×#4339C2314yes—
97C22×D44—21no—
98C22×D44—21no—
99C22×D44C2311yescharacteristic
100C22×D44C2311yescharacteristic
101C22×C4×D11—21no—
102C22×C4×D11—21no—
103C22×Dic22C2311yescharacteristic
104C11×#126—28no—
105C11×#125—22no—
106C11×#125C2314yes—
107C11×#123—28no—
108C11×#121—28no—
109C11×#121—22no—
110C11×#121—22no—
111C11×#121C2314yes—
112C11×#121C2314yes—
113C4×D4×C11—28no—
114C4×D4×C11—22no—
115C4×D4×C11D414yes—
116C4×D4×C11C2314yes—
117C4×D4×C11C2314yes—
118C11×#117—22no—
119C11×#117C2314yes—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4—22no—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4D411yescharacteristic
125C2×C11×C4⋊C4C2311yescharacteristic
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C4⋊C4C2314yes—
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4D411yescharacteristic
134C2×C11×C22⋊C4D411yescharacteristic
135C2×C42×C11—21no—
136C2×C42×C11C2311yescharacteristic
137#66993—28no—
138C2×#4324—24no—
139C2×#4324C2314yes—
140C2×#4323—42no—
141C2×#4323—42no—
142C2×#4323C2314yes—
143C2×#4323C2314yes—
144#66983—22no—
145#66983—22no—
146#66983C2314yes—
147#66983C2314yes—
148C2×(C2×D11)⋊C4—21no—
149C2×(C2×D11)⋊C4—21no—
150C2×C4⋊Dic11C2311yescharacteristic
151C2×Dic11⋊C4—21no—
152C2×C4×Dic11—21no—
153C2×#4318—42no—
154C2×#4318C2314yes—
155C22×C11⋊C8—42no—
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2314yes—
161#66946—28no—
162#66937—28no—
163#66937—28no—
164#66927—22no—
165#66927C2314yes—
166C4×Dic22—22no—
167C4×Dic22C2314yes—
168#66896C2314yes—
169C22⋊(C11⋊C8)C2314yes—
170C22⋊(C11⋊C8)C2314yes—
171#66874C2314yes—
172#66874C2314yes—
173#66874C2314yes—
174#66873C2314yes—
175#66873C2314yes—
176#66873C2314yes—
177#66873C2314yes—
178#66873C2314yes—
179#66873C2314yes—
180#66872C2314yes—
181#66871C2314yes—
182#66871C2314yes—
183C4⋊(C11⋊C8)C2314yes—
184#66867C2314yes—
185C2×#3309—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11C2×D411yescharacteristic
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
190C23×D11—21no—
191C2×D4×C11—24no—
192C2×D4×C11—24no—
193C2×D4×C11—21no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—42no—
197C2×D4×C11—44no—
198C2×D4×C11—82no—
199C2×D4×C11C2×D414yes—
200C2×D4×C11C2412yes—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—24no—
209C22×C4×C11—24no—
210C22×C4×C11—82no—
211C22×C4×C11—82no—
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2×D412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2411yescharacteristic
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—82no—
228C2×C22⋊D11—82no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231#4339—28no—
232#4339—28no—
233#4339—44no—
234#4339—44no—
235#4339—48no—
236#4339—48no—
237C2×D44—21no—
238C2×D44—21no—
239C2×D44—24no—
240C2×D44—24no—
241C2×D44—22no—
242C2×D44—22no—
243C2×D44—22no—
244C2×D44—22no—
245C2×D44—44no—
246C2×D44—82no—
247C2×D44C2412yes—
248C2×D44C2412yes—
249C2×C4×D11—24no—
250C2×C4×D11—24no—
251C2×C4×D11—44no—
252C2×C4×D11—44no—
253C2×Dic22—21no—
254C2×Dic22—22no—
255C2×Dic22#4114yes—
256C2×Dic22C2412yes—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—24no—
260C11×C4⋊C4—24no—
261C11×C4⋊C4—24no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4C2×D414yes—
264C11×C4⋊C4C2412yes—
265C11×C4⋊C4C2412yes—
266C11×C4⋊C4C2412yes—
267C11×C22⋊C4—24no—
268C11×C22⋊C4—24no—
269C11×C22⋊C4—24no—
270C11×C22⋊C4—24no—
271C11×C22⋊C4C2×D414yes—
272C11×C22⋊C4C2×D414yes—
273C42×C11—24no—
274C42×C11C2×D412yes—
275C42×C11C2412yes—
276#4324—28no—
277#4323—44no—
278#4323—44no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281C4⋊Dic11—21no—
282C4⋊Dic11C2412yes—
283Dic11⋊C4—24no—
284C4×Dic11—24no—
285#4318—44no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8—22no—
289C2×C11⋊C8—22no—
290C2×C11⋊C8—44no—
291C2×C11⋊C8C2412yes—
292C2×C11⋊C8C2412yes—
293C2×C11⋊C8C2412yes—
294C2×C11⋊C8C2412yes—
295C2×#553D1111yescharacteristic, complemented
296C2×#550—111no—
297#3309—1116no—
298C2×#490—111no—
299C2×#482—111no—
300C2×#480—111no—
301C2×#479—111no—
302C2×#469—111no—
303C2×#466—111no—
304C2×#459—111no—
305C2×#449—111no—
306C2×#449—111no—
307C2×#440—111no—
308C2×#435—111no—
309C2×#417—111no—
310C2×#416—111no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11C22×D412yes—
322C23×C11C22×D412yes—
323C23×C11C22×D411yescharacteristic
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—42no—
327C22×D11—42no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—44no—
335D4×C11—48no—
336D4×C11—42no—
337D4×C11—84no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—24no—
343C2×C4×C11—24no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—42no—
352C2×C4×C11—42no—
353C2×C4×C11—42no—
354C2×C4×C11—84no—
355C2×C4×C11—84no—
356C2×C4×C11C22×D412yes—
357C2×C4×C11C22×D412yes—
358C2×C4×C11C22×D412yes—
359C2×C4×C11C22×D412yes—
360C2×C4×C11C22×D411yescharacteristic
361C2×C4×C11C2×#4112yes—
362C2×C4×C11H(5,𝔽2)12yes—
363C2×C4×C11C2511yescharacteristic
364C22⋊D11—48no—
365C22⋊D11—48no—
366C22⋊D11—84no—
367C22⋊D11—84no—
368C2×Dic11—24no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—42no—
372D44—22no—
373D44—22no—
374D44—22no—
375D44—22no—
376D44—48no—
377D44—42no—
378D44—42no—
379D44—84no—
380C4×D11—48no—
381C4×D11—48no—
382Dic22—24no—
383Dic22—22no—
384Dic22C2×#4114yes—
385C11⋊C8—22no—
386C11⋊C8—22no—
387C11⋊C8—22no—
388C11⋊C8—22no—
389C22×#41—111no—
390C22×#41—111no—
391C22×SD16—111no—
392C22×D8—111no—
393C22×D8—111no—
394C22×M16—111no—
395C23×C8—111no—
396#553—24no—
397#553C2×D1118yescomplemented
398#550—118no—
399#550—224no—
400C2×#127—111no—
401C2×#127—221no—
402C2×#126—21no—
403C2×#125C2×D1111yescharacteristic
404C2×#123—21no—
405C2×#121—21no—
406C2×#121—111no—
407C2×#121—111no—
408C2×#121—221no—
409C2×#121—221no—
410C2×#121C2×D1111yescharacteristic
411C2×#121C2×D1111yescharacteristic
412C2×C4×Q8—111no—
413C2×C4×D4—21no—
414C2×C4×D4—221no—
415C2×C4×D4C2×D1111yescharacteristic
416C2×C4×D4C2×D1111yescharacteristic
417C2×#117C2×D1111yescharacteristic
418C22×C4⋊C4C2×D1111yescharacteristic
419#490—118no—
420#482—118no—
421#480—118no—
422#479—118no—
423#469—118no—
424#466—118no—
425#459—118no—
426#449—118no—
427#449—118no—
428#440—118no—
429#435—118no—
430C2×#107—111no—
431C2×#107—111no—
432C2×#106—111no—
433C2×C4⋊C8—111no—
434#417—118no—
435#416—118no—
436C2×#103—111no—
437C2×#103—111no—
438C2×#103—111no—
439C2×#102—111no—
440C2×#102—111no—
441C2×#102—111no—
442C2×#102—111no—
443C2×#102—111no—
444C2×#102—111no—
445C2×#102—111no—
446C2×C22⋊C8—111no—
447C2×C22⋊C8—111no—
448C2×#97—111no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—22no—
455C22×C11—44no—
456C22×C11—44no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—84no—
461C22×C11#54612yes—
462C22×C11#57512yes—
463C22×C11#57612yes—
464C22×C11C23×D411yescharacteristic
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—84no—
472C2×D11—84no—
473C4×C11—22no—
474C4×C11—22no—
475C4×C11—22no—
476C4×C11—22no—
477C4×C11—42no—
478C4×C11—42no—
479C4×C11—42no—
480C4×C11#54612yes—
481C4×C11C22×#4111yescharacteristic
482C4×C11C2×H(5,𝔽2)11yescharacteristic
483Dic11—24no—
484Dic11—42no—
485C2×#41—114no—
486C2×#41—114no—
487C2×#41—224no—
488C2×#41—224no—
489C2×#41—222no—
490C2×#41—222no—
491C2×#41—442no—
492C2×#41—442no—
493C22×Q8—111no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—111no—
497C22×D4—111no—
498C22×D4—221no—
499C22×D4—221no—
500C22×D4—221no—
501C22×D4—221no—
502C22×D4—221no—
503C22×D4—221no—
504C22×D4C22⋊D1111yescharacteristic
505C22×D4C22×D1111yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—221no—
509C23×C4—221no—
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1111yescharacteristic
512C2×SD16—114no—
513C2×SD16—224no—
514C2×D8—114no—
515C2×D8—114no—
516C2×D8—442no—
517C2×D8—442no—
518C2×M16—114no—
519C2×M16—442no—
520C22×C8—111no—
521C22×C8—111no—
522C22×C8—111no—
523C22×C8—111no—
524C22×C8—114no—
525C22×C8—442no—
526#127—114no—
527#127—228no—
528#127—222no—
529#126—28no—
530#125—22no—
531#125C22×D1114yes—
532#123—28no—
533#121—28no—
534#121—22no—
535#121—22no—
536#121—114no—
537#121—114no—
538#121—222no—
539#121—222no—
540#121—228no—
541#121—228no—
542#121C22×D1114yes—
543#121C22×D1114yes—
544C4×Q8—114no—
545C4×Q8—222no—
546C4×D4—28no—
547C4×D4—22no—
548C4×D4—228no—
549C4×D4C22⋊D1114yes—
550C4×D4C22×D1114yes—
551C4×D4C22×D1114yes—
552#117—22no—
553#117C22×D1114yes—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—111no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4C22⋊D1111yescharacteristic
561C2×C4⋊C4C22×D1111yescharacteristic
562C2×C4⋊C4C22×D1111yescharacteristic
563C2×C4⋊C4C22×D1114yes—
564C2×C4⋊C4C22×D1111yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4C22⋊D1111yescharacteristic
572C2×C22⋊C4C22⋊D1111yescharacteristic
573C2×C42—21no—
574C2×C42—221no—
575C2×C42C22×D1111yescharacteristic
576#107—114no—
577#107—114no—
578#106—114no—
579C4⋊C8—114no—
580#103—114no—
581#103—114no—
582#103—114no—
583#102—114no—
584#102—114no—
585#102—114no—
586#102—114no—
587#102—114no—
588#102—114no—
589#102—114no—
590C22⋊C8—114no—
591C22⋊C8—114no—
592#97—114no—
593C2×C11—42no—
594C2×C11—42no—
595C2×C11—82no—
596C2×C11#330914yescomplemented
597C2×C11C2×#54611yescharacteristic
598C2×C11C2×#57511yescharacteristic
599C2×C11C2×#57611yescharacteristic
600D11—82no—
601D11—82no—
602C24—21no—
603C24—221no—
604C24—221no—
605C24C2×C22⋊D1111yescharacteristic
606C24C2×C22⋊D1111yescharacteristic
607#41—228no—
608#41—228no—
609#41—444no—
610#41—444no—
611#41—448no—
612#41—448no—
613C2×Q8—114no—
614C2×Q8—112no—
615C2×Q8—222no—
616C2×Q8—221no—
617C2×D4—24no—
618C2×D4—24no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—21no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—82no—
625C2×D4—112no—
626C2×D4—112no—
627C2×D4—224no—
628C2×D4—224no—
629C2×D4—224no—
630C2×D4—224no—
631C2×D4—222no—
632C2×D4—222no—
633C2×D4—222no—
634C2×D4—222no—
635C2×D4—224no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—224no—
639C2×D4—444no—
640C2×D4—444no—
641C2×D4—444no—
642C2×D4—882no—
643C2×D4—882no—
644C2×D4—882no—
645C2×D4C2×C22⋊D1114yes—
646C2×D4C23×D1112yes—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—82no—
657C22×C4—82no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—224no—
661C22×C4—224no—
662C22×C4—444no—
663C22×C4—444no—
664C22×C4C2×C22⋊D1112yes—
665C22×C4C2×C22⋊D1112yes—
666C22×C4C2×C22⋊D1111yescharacteristic
667C22×C4C2×C22⋊D1111yescharacteristic
668C22×C4C2×C22⋊D1111yescharacteristic
669C22×C4C2×C22⋊D1111yescharacteristic
670C22×C4C23×D1112yes—
671C22×C4C23×D1112yes—
672C22×C4C23×D1111yescharacteristic
673SD16—228no—
674D8—444no—
675D8—444no—
676M16—444no—
677C2×C8—112no—
678C2×C8—112no—
679C2×C8—112no—
680C2×C8—112no—
681C2×C8—222no—
682C2×C8—222no—
683C2×C8—222no—
684C2×C8—222no—
685C2×C8—444no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—24no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—21no—
692C4⋊C4—112no—
693C4⋊C4—221no—
694C4⋊C4—224no—
695C4⋊C4C2×C22⋊D1114yes—
696C4⋊C4C23×D1112yes—
697C4⋊C4C23×D1112yes—
698C4⋊C4C23×D1112yes—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4C2×C22⋊D1114yes—
706C22⋊C4C2×C22⋊D1114yes—
707C42—24no—
708C42—224no—
709C42C2×C22⋊D1112yes—
710C42C23×D1112yes—
711C11C2×#330911yescharacteristic, complemented, Sylow
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—222no—
723C23—222no—
724C23—442no—
725C23—442no—
726C23—442no—
727C23—442no—
728C23—442no—
729C23—442no—
730C23C22×C22⋊D1112yes—
731C23C22×C22⋊D1112yes—
732C23C22×C22⋊D1111yescharacteristic
733Q8—114no—
734Q8—224no—
735Q8—222no—
736D4—22no—
737D4—22no—
738D4—44no—
739D4—48no—
740D4—42no—
741D4—84no—
742D4—222no—
743D4—222no—
744D4—222no—
745D4—222no—
746D4—448no—
747D4—448no—
748D4—448no—
749D4—442no—
750D4—442no—
751D4—884no—
752D4—884no—
753D4—884no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—84no—
771C2×C4—84no—
772C2×C4—224no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—448no—
776C2×C4—448no—
777C2×C4—442no—
778C2×C4#41×D1112yes—
779C2×C4#6704212yes—
780C2×C4C22×C22⋊D1112yes—
781C2×C4C22×C22⋊D1112yes—
782C2×C4C22×C22⋊D1112yes—
783C2×C4C22×C22⋊D1112yes—
784C2×C4C22×C22⋊D1111yescharacteristic
785C2×C4C24×D1111yescharacteristic
786C8—222no—
787C8—222no—
788C8—222no—
789C8—222no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—84no—
802C22—442no—
803C22—442no—
804C22—442no—
805C22—442no—
806C22—442no—
807C22—442no—
808C22—884no—
809C22—884no—
810C22#1062335312yes—
811C22#1062336012yes—
812C22#1062336612yes—
813C22C23×C22⋊D1111yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—224no—
822C4—442no—
823C4#1062336012yes—
824C4C2×#41×D1111yescharacteristic
825C4C2×#6704211yescharacteristic
826C2—42no—
827C2—42no—
828C2—82no—
829C2—882no—
830C2—882no—
831C2#1308061614yesdirect product factor
832C2C2×#1062336011yescharacteristic
833C2C2×#1062335311yescharacteristic
834C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#553C2
socleC23×C11C22×D4
hypercenterC2×#553D11
hypocenterC11C2×#3309
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×#10623084C2semidirect
2. #13080616C2direct (N × H)
3. C2×#10622680C2semidirect
4. C2×#10622616C2semidirect
5. C2×#10622580C2semidirect
6. C2×#10622676C2semidirect
7. C2×#10622652C2semidirect
8. C2×#10622651C2semidirect
9. C2×#10622628C2semidirect
10. C2×#10622650C2semidirect
11. C2×#10622650C2semidirect
12. C2×#10622631C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622579C2semidirect
15. C2×#10622615C2semidirect
16. C2×C11×#553C2semidirect
20. C11×#553C22semidirect
41. #10623084C22semidirect
50. #10622680C22semidirect
51. #10622676C22semidirect
52. #10622652C22semidirect
53. #10622651C22semidirect
54. #10622650C22semidirect
55. #10622650C22semidirect
56. #10622631C22semidirect
57. #10622628C22semidirect
58. #10622624C22semidirect
59. #10622616C22semidirect
60. #10622615C22semidirect
64. #10622580C22semidirect
65. #10622579C22semidirect
295. C2×#553D11semidirect
397. #553C2×D11semidirect
596. C2×C11#3309semidirect
711. C11C2×#3309semidirect
831. C2#13080616direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230842
#130806162
C2×#106226802
C2×#106226162
C2×#106225802
C2×#106226762
C2×#106226522
C2×#106226512
C2×#106226282
C2×#106226502
C2×#106226312
C2×#106226242
C2×#106225792
C2×#106226152
C2×C11×#5532
C2×#330911