Finite Group Databasebeta

← #14769554

Subgroups — #14769554

Order 2816.

1622 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67002C211yesmaximal, characteristic
2C2×#10622639C211yesmaximal, characteristic, complemented
3C2×C4×#4325C211yesmaximal, characteristic, complemented
4C22⋊C4×D44C211yesmaximal, characteristic, complemented
5#13069491C211yesmaximal, characteristic, complemented
6#13069481C211yesmaximal, characteristic, complemented
7#13068971C211yesmaximal, characteristic, complemented
8#13068971C211yesmaximal, characteristic, complemented
9#13068967C211yesmaximal, characteristic, complemented
10#13068967C211yesmaximal, characteristic, complemented
11#13068647C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic, complemented
13#13068546C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15C11×#2341C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic, complemented
19C2×C4×Q8×C11C2211yescharacteristic, complemented
20C2×#67002—24no—
21C2×#67002—24no—
22C2×#67002C418yescomplemented
23C22×#4325C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C22×#4323C2211yescharacteristic
26C22×#4323C2211yescharacteristic
27C22×#4318C2211yescharacteristic
28C2×C22⋊C4×D11—21no—
29C2×C4×D44C2211yescharacteristic
30C2×C4×D44C2211yescharacteristic
31C11×#390—21no—
32C11×#390—21no—
33C11×#390C2211yescharacteristic, complemented
34C11×#390C2211yescharacteristic, complemented
35C11×#380—21no—
36C11×#380C2211yescharacteristic
37C4×C11×C22⋊C4—21no—
38C4×C11×C22⋊C4C2211yescharacteristic
39C2×#66899C2211yescharacteristic, complemented
40C2×#66899C2211yescharacteristic, complemented
41C2×#66896C2211yescharacteristic, complemented
42C2×#66896C2211yescharacteristic, complemented
43#10622825C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45#10622639—24no—
46C4×#4325—24no—
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66872C2211yescharacteristic, complemented
52C2×#66871C2211yescharacteristic, complemented
53#10622568—21no—
54#10622552C2211yescharacteristic
55#10622552C2211yescharacteristic
56C2×#66867C2211yescharacteristic, complemented
57C2×C4×C11⋊C8C2211yescharacteristic, complemented
58#10622278—21no—
59#10622278—21no—
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622162C2211yescharacteristic, complemented
63#10622162C2211yescharacteristic, complemented
64C24×D11—21no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—41no—
69C2×C11×#41—41no—
70C2×C11×#41C2×C414yescomplemented
71C22×Q8×C11C2311yescharacteristic
72C22×D4×C11—21no—
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C22×D44—22no—
77C22×D44—22no—
78C22×D44—21no—
79C22×D44—22no—
80C22×D44—41no—
81C22×D44—41no—
82C22×D44C2×C414yes—
83C22×D44C2311yescharacteristic
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C4×Q8×C11—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—41no—
90C4×Q8×C11—41no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4D411yescharacteristic
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C42×C11—21no—
103C2×C42×C11—21no—
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11—21no—
107#67002—232no—
108C2×#4325—22no—
109C2×#4325—22no—
110C2×#4325C2×C414yes—
111C2×#4325C2×C414yescomplemented
112C2×#4325D414yes—
113C2×#4325D414yes—
114C2×#4323—22no—
115C2×#4323—22no—
116C2×#4323—22no—
117C2×#4323—22no—
118C2×#4323C2×C414yes—
119C2×#4323C2×C414yescomplemented
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×#4318—22no—
129C2×#4318—22no—
130C2×#4318C2×C414yescomplemented
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C22⋊C4×D11—44no—
136C4×D44—22no—
137C4×D44—22no—
138C4×D44—41no—
139C4×D44—41no—
140C11×#95—21no—
141C11×#95D411yescharacteristic
142C11×#95D411yescharacteristic
143#66899—22no—
144#66899—22no—
145#66896—41no—
146#66896—41no—
147C11⋊#95—21no—
148C22⋊(C11⋊C8)—22no—
149#66873—22no—
150#66873—22no—
151#66873—41no—
152#66873—41no—
153#66872—22no—
154#66871—22no—
155#66867—22no—
156C4×C11⋊C8—22no—
157#22443—111nomaximal, Sylow
158C24×C11—21no—
159C24×C11C2×D411yescharacteristic
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—24no—
163C23×D11—42no—
164C23×D11—42no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—81no—
168C23×D11—81no—
169C11×#41—28no—
170C11×#41—44no—
171C11×#41—44no—
172C11×#41—44no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11C22×C412yes—
177C2×Q8×C11C2×D412yes—
178C2×Q8×C11C2×D412yes—
179C2×D4×C11—24no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—42no—
186C2×D4×C11—42no—
187C2×D4×C11C22×C412yes—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—24no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—42no—
197C22×C4×C11—42no—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11#4112yes—
205C22×C4×C11C2411yescharacteristic
206C22×Dic11—21no—
207C22×Dic11—21no—
208C2×D44—28no—
209C2×D44—24no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—42no—
219C2×D44—42no—
220C2×D44—44no—
221C2×D44—44no—
222C2×D44—44no—
223C2×D44C22×C412yes—
224C2×D44C22×C412yes—
225C2×D44C2×D412yes—
226C2×D44C2×D412yes—
227C2×C4×D11—42no—
228C2×C4×D11—42no—
229C2×C4×D11—42no—
230C2×C4×D11—42no—
231C2×C4×D11—81no—
232C2×C4×D11—81no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—42no—
238C11×C4⋊C4—42no—
239C11×C22⋊C4—22no—
240C11×C22⋊C4—41no—
241C11×C22⋊C4—42no—
242C11×C22⋊C4—42no—
243C11×C22⋊C4—81no—
244C11×C22⋊C4—81no—
245C11×C22⋊C4—81no—
246C42×C11—21no—
247C42×C11—21no—
248C42×C11—21no—
249C42×C11—21no—
250C42×C11—42no—
251C42×C11—42no—
252C22⋊Dic11—42no—
253#4325—28no—
254#4325C22⋊C4116yescomplemented
255#4323—28no—
256#4323—28no—
257(C2×D11)⋊C4—42no—
258(C2×D11)⋊C4—42no—
259(C2×D11)⋊C4—42no—
260(C2×D11)⋊C4—42no—
261(C2×D11)⋊C4—81no—
262(C2×D11)⋊C4—81no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267#4318—28no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8C22×C412yes—
277C2×C11⋊C8C22×C412yes—
278C2×C11⋊C8C2×D412yes—
279C2×C11⋊C8C2×D412yes—
280C22×AGL(1,ℤ/8)—111no—
281C2×#440—111no—
282C2×C4×SD16—111no—
283#2341D1111yescharacteristic, complemented
284D4×C22⋊C4—111no—
285#1972—111no—
286#1970—111no—
287#1880—111no—
288#1880—111no—
289#1879—111no—
290#1879—111no—
291#1809—111no—
292#1788—111no—
293#1786—111no—
294#1753—111no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—22no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11C4×D412yes—
309C23×C11C22×D411yescharacteristic
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—48no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—48no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—84no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—22no—
334Q8×C11C2×C22⋊C414yescomplemented
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—48no—
338D4×C11—41no—
339D4×C11—41no—
340C2×C4×C11—22no—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—21no—
359C2×C4×C11—21no—
360C2×C4×C11—48no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11C4×D412yes—
368C2×C4×C11AGL(1,ℤ/8)12yescomplemented
369C2×C4×C11C23×C411yescharacteristic
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C2×#4111yescharacteristic
373C2×C4×C11H(5,𝔽2)11yescharacteristic
374C2×C4×C11H(5,𝔽2)11yescharacteristic
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381D44—22no—
382D44—22no—
383D44—22no—
384D44—22no—
385D44—22no—
386D44—48no—
387D44—41no—
388D44—41no—
389D44C2×C22⋊C414yes—
390C4×D11—84no—
391C4×D11—84no—
392C11⋊C8—22no—
393C11⋊C8—41no—
394C11⋊C8—41no—
395C11⋊C8C2×C22⋊C414yescomplemented
396C22×#41C2×D1111yescharacteristic
397C23×D4—111no—
398C2×AGL(1,ℤ/8)—118no—
399C2×AGL(1,ℤ/8)—224no—
400C2×AGL(1,ℤ/8)—224no—
401C22×SD16—111no—
402C22×SD16—111no—
403C22×D8—111no—
404C22×D8—111no—
405C22×M16—111no—
406C2×C4×Q8C2×D1111yescharacteristic, complemented
407C2×C4×Q8C2×D1111yescharacteristic, complemented
408C2×C4×D4—111no—
409C2×C4×D4—111no—
410C22×C22⋊C4—221no—
411#440—224no—
412C4×SD16—224no—
413C2×#107—111no—
414C2×#106—111no—
415C2×#103—111no—
416C2×#103—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×C22⋊C8—111no—
424C2×#97—111no—
425C2×C4×C8—111no—
426#390—21no—
427#390—21no—
428#390—111no—
429#390—111no—
430#390C2×D1111yescharacteristic, complemented
431#390C2×D1111yescharacteristic, complemented
432#386—221no—
433#386—221no—
434#380—21no—
435#380—111no—
436#380C2×D1111yescharacteristic
437#379—221no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4C2×D1111yescharacteristic
440#340—111no—
441#340—111no—
442#336—111no—
443#336—111no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—81no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11—81no—
458C22×C11C2×C4×D411yescharacteristic
459C22×C11D4211yescharacteristic
460C22×C11D4211yescharacteristic
461C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
462C22×C11#57511yescharacteristic
463C22×C11#57611yescharacteristic
464C22×C11#57711yescharacteristic
465C2×D11—24no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—816no—
476C2×D11—81no—
477C2×D11—81no—
478C2×D11—81no—
479C2×D11—81no—
480C4×C11—22no—
481C4×C11—24no—
482C4×C11—22no—
483C4×C11—41no—
484C4×C11—41no—
485C4×C11—41no—
486C4×C11—81no—
487C4×C11—81no—
488C4×C11C22×C22⋊C411yescharacteristic
489C4×C11#51811yescharacteristic
490C4×C11#54611yescharacteristic
491C4×C11#54611yescharacteristic
492Dic11—81no—
493Dic11—81no—
494C25—221no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41C4×D1114yescomplemented
501C22×Q8C22×D1111yescharacteristic
502C22×D4—21no—
503C22×D4—114no—
504C22×D4—111no—
505C22×D4—111no—
506C22×D4—222no—
507C22×D4—222no—
508C22×D4—222no—
509C22×D4—221no—
510C22×D4—441no—
511C22×D4—441no—
512C22×D4C22×D1111yescharacteristic
513C23×C4—21no—
514C23×C4—221no—
515C23×C4—221no—
516C23×C4C22×D1111yescharacteristic
517AGL(1,ℤ/8)—2232no—
518C2×SD16—114no—
519C2×SD16—114no—
520C2×SD16—114no—
521C2×SD16—114no—
522C2×SD16—222no—
523C2×SD16—222no—
524C2×D8—114no—
525C2×D8—114no—
526C2×D8—222no—
527C2×D8—222no—
528C2×D8—222no—
529C2×D8—222no—
530C2×M16—114no—
531C2×M16—222no—
532C2×M16—222no—
533C22×C8—111no—
534C22×C8—111no—
535C22×C8—111no—
536C22×C8—111no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×D4—222no—
542C4×D4—222no—
543C4×D4—441no—
544C4×D4—441no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C22⋊C4—21no—
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⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—444no—
564C2×C22⋊C4C22⋊D1111yescharacteristic
565C2×C22⋊C4C22⋊D1111yescharacteristic
566C2×C42—21no—
567C2×C42—21no—
568C2×C42C22×D1111yescharacteristic
569C2×C42C22×D1111yescharacteristic
570#107—222no—
571#106—222no—
572#103—222no—
573#103—222no—
574#102—222no—
575#102—222no—
576#102—441no—
577#102—441no—
578#102—441no—
579#102—441no—
580C22⋊C8—222no—
581#97—222no—
582C4×C8—222no—
583#95—21no—
584#95—221no—
585#95C22⋊D1111yescharacteristic
586#95C22⋊D1111yescharacteristic
587C2×C11—42no—
588C2×C11—82no—
589C2×C11D4×C22⋊C411yescharacteristic
590C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
591C2×C11#294611yescharacteristic
592C2×C11#326511yescharacteristic
593C2×C11#326811yescharacteristic
594C2×C11#327411yescharacteristic
595C2×C11#327511yescharacteristic
596D11—44no—
597D11—82no—
598C24—21no—
599C24—221no—
600C24—221no—
601C24—224no—
602C24—442no—
603C24—442no—
604C24—442no—
605C24—442no—
606C24—881no—
607C24—881no—
608C24C2×C22⋊D1111yescharacteristic
609#41—28no—
610#41—44no—
611#41—44no—
612#41—44no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8C2×C4×D1112yes—
617C2×Q8D4×D1112yes—
618C2×Q8D4×D1112yes—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—112no—
628C2×D4—112no—
629C2×D4—112no—
630C2×D4—112no—
631C2×D4—228no—
632C2×D4—224no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—444no—
644C2×D4—442no—
645C2×D4—442no—
646C2×D4C2×C4×D1112yes—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—24no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—442no—
660C22×C4—442no—
661C22×C4—442no—
662C22×C4—442no—
663C22×C4—881no—
664C22×C4—881no—
665C22×C4C2×C4×D1112yes—
666C22×C4#433912yes—
667C22×C4C2×C22⋊D1111yescharacteristic
668C22×C4C2×C22⋊D1111yescharacteristic
669C22×C4C2×C22⋊D1111yescharacteristic
670C22×C4C2×C22⋊D1111yescharacteristic
671C22×C4C2×C22⋊D1111yescharacteristic
672C22×C4C23×D1111yescharacteristic
673SD16—1116no—
674SD16—228no—
675D8—228no—
676D8—228no—
677M16—228no—
678C2×C8—112no—
679C2×C8—112no—
680C2×C8—112no—
681C2×C8—112no—
682C2×C8—221no—
683C2×C8—221no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—221no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—221no—
699C4⋊C4—221no—
700C22⋊C4—22no—
701C22⋊C4—41no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—81no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—442no—
708C22⋊C4—442no—
709C22⋊C4—442no—
710C22⋊C4—442no—
711C22⋊C4—442no—
712C22⋊C4—881no—
713C22⋊C4—881no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—42no—
719C42—42no—
720C11#2244311yescharacteristic, complemented, Sylow
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—22no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—448no—
739C23—448no—
740C23—441no—
741C23—441no—
742C23—441no—
743C23—441no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—884no—
751C23—884no—
752C23—884no—
753C23—884no—
754C23—884no—
755C23C4×C22⋊D1112yes—
756C23C22×C22⋊D1111yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8C22⋊C4×D1114yescomplemented
761D4—22no—
762D4—22no—
763D4—48no—
764D4—41no—
765D4—41no—
766D4—114no—
767D4—222no—
768D4—222no—
769D4—222no—
770D4—222no—
771D4—222no—
772D4—448no—
773D4—441no—
774D4—441no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—441no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—884no—
809C2×C4—884no—
810C2×C4C4×C22⋊D1112yes—
811C2×C4#6700212yescomplemented
812C2×C4C22×C4×D1111yescharacteristic
813C2×C4C2×#433911yescharacteristic
814C2×C4C2×D4×D1111yescharacteristic
815C2×C4C2×D4×D1111yescharacteristic
816C2×C4#6703711yescharacteristic
817C2×C4#6703711yescharacteristic
818C8—114no—
819C8—222no—
820C8—441no—
821C8—441no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—224no—
837C22—442no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—442no—
842C22—442no—
843C22—442no—
844C22—442no—
845C22—442no—
846C22—8816no—
847C22—881no—
848C22—881no—
849C22—881no—
850C22—881no—
851C22C2×C4×C22⋊D1111yescharacteristic
852C22D4×C22⋊D1111yescharacteristic
853C22D4×C22⋊D1111yescharacteristic
854C22C2×#6700211yescharacteristic
855C22#1062335311yescharacteristic
856C22#1062336611yescharacteristic
857C22#1062336811yescharacteristic
858C4—22no—
859C4—22no—
860C4—24no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—881no—
867C4—881no—
868C4C2×C22⋊C4×D1111yescharacteristic
869C4#1062301711yescharacteristic
870C4#1062302111yescharacteristic
871C4#1062302111yescharacteristic
872C2—42no—
873C2—82no—
874C2—444no—
875C2—882no—
876C2C22⋊C4×C22⋊D1111yescharacteristic
877C2C4×#6700211yescharacteristic
878C2#1307744411yescharacteristic
879C2#1308011211yescharacteristic
880C2#1308015711yescharacteristic
881C2#1308023611yescharacteristic
882C2#1308024811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2341C2
socleC23×C11C22×D4
prime radicalC22×#67002C2
cosocleC22×C4×C11C24
hypercenter#2341D11
hypocenterC11#22443
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#10622639C2semidirect
3. C2×C4×#4325C2semidirect
4. C22⋊C4×D44C2semidirect
5. #13069491C2semidirect
6. #13069481C2semidirect
7. #13068971C2semidirect
8. #13068971C2semidirect
9. #13068967C2semidirect
10. #13068967C2semidirect
11. #13068647C2semidirect
12. #13068556C2semidirect
13. #13068546C2semidirect
14. #13068400C2semidirect
15. C11×#2341C2semidirect
18. C2×C4×Q8×C11C22semidirect
19. C2×C4×Q8×C11C22semidirect
22. C2×#67002C4semidirect
33. C11×#390C22semidirect
34. C11×#390C22semidirect
39. C2×#66899C22semidirect
40. C2×#66899C22semidirect
41. C2×#66896C22semidirect
42. C2×#66896C22semidirect
51. C2×#66872C22semidirect
52. C2×#66871C22semidirect
56. C2×#66867C22semidirect
57. C2×C4×C11⋊C8C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622162C22semidirect
63. #10622162C22semidirect
70. C2×C11×#41C2×C4semidirect
111. C2×#4325C2×C4semidirect
119. C2×#4323C2×C4semidirect
130. C2×#4318C2×C4semidirect
254. #4325C22⋊C4semidirect
283. #2341D11semidirect
334. Q8×C11C2×C22⋊C4semidirect
368. C2×C4×C11AGL(1,ℤ/8)semidirect
395. C11⋊C8C2×C22⋊C4semidirect
406. C2×C4×Q8C2×D11semidirect
407. C2×C4×Q8C2×D11semidirect
430. #390C2×D11semidirect
431. #390C2×D11semidirect
500. C2×#41C4×D11semidirect
720. C11#22443semidirect
760. Q8C22⋊C4×D11semidirect
811. C2×C4#67002semidirect

Maximal subgroups

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

subgroupindex
C22×#670022
C2×#106226392
C2×C4×#43252
C22⋊C4×D442
#130694912
#130694812
#130689712
#130689672
#130686472
#130685562
#130685462
#130684002
C11×#23412
#2244311