Finite Group Databasebeta

← #14769253

Subgroups — #14769253

Order 2816.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C211yesmaximal, characteristic, complemented
2C2×#10622845C211yesmaximal, characteristic, complemented
3C22×#66896C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic11C211yesmaximal, characteristic, complemented
5#13069549C211yesmaximal, characteristic, complemented
6#13069433C211yesmaximal, characteristic, complemented
7#13069055C211yesmaximal, characteristic, complemented
8#13069040C211yesmaximal, characteristic, complemented
9#13068934C211yesmaximal, characteristic, complemented
10#13068924C211yesmaximal, characteristic, complemented
11#13068616C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic, complemented
13#13068547C211yesmaximal, characteristic, complemented
14#13068441C211yesmaximal, characteristic, complemented
15C2×C11×#546C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C11×#546—24no—
19C11×#546C418yescomplemented
20C2×C11×#124C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#120—21no—
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C22×C11×C22⋊C4—21no—
29C2×D4×Dic11—21no—
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic, complemented
32C22×#4318C2211yescharacteristic, complemented
33C23×C11⋊C8C2211yescharacteristic
34#10622845—24no—
35C2×#66899C2211yescharacteristic, complemented
36C2×#66899C2211yescharacteristic, complemented
37C2×#66899C2211yescharacteristic, complemented
38C2×#66899C2211yescharacteristic, complemented
39C2×#66896—24no—
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44C2×#66896C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46C2×#66896C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48#10622825C2211yescharacteristic
49#10622825C2211yescharacteristic, complemented
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
52#10622624—24no—
53#10622598—21no—
54#10622563—21no—
55#10622563—21no—
56#10622548C2211yescharacteristic, complemented
57C4×C4⋊Dic11C2211yescharacteristic, complemented
58C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
59C2×#66867C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C25×C11—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—22no—
73C22×D4×C11—22no—
74C22×D4×C11—21no—
75C22×D4×C11—21no—
76C22×D4×C11—21no—
77C22×D4×C11—22no—
78C22×D4×C11—41no—
79C22×D4×C11—41no—
80C22×D4×C11C2×C414yescomplemented
81C22×D4×C11D411yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×Dic11—21no—
89C23×Dic11—21no—
90C11×#124—22no—
91C11×#124C2×C414yescomplemented
92C11×#123—28no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8C2×C414yescomplemented
95C11×#121—22no—
96C11×#121—28no—
97C11×#121C2×C414yescomplemented
98C11×#120—28no—
99C4×D4×C11—22no—
100C4×D4×C11C2×C414yes—
101C4×D4×C11C2×C414yescomplemented
102C4×D4×C11D414yes—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4D411yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—28no—
112C2×C11×C22⋊C4D411yescharacteristic
113C2×C11×C22⋊C4D411yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117D4×Dic11—44no—
118C2×C4⋊Dic11—22no—
119C2×C4⋊Dic11—22no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11—41no—
125C2×C4⋊Dic11—41no—
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4×Dic11—21no—
131C2×#4318—22no—
132C2×#4318—22no—
133C2×#4318—41no—
134C22×C11⋊C8—22no—
135C22×C11⋊C8—22no—
136C22×C11⋊C8—41no—
137C22×C11⋊C8C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141#66899—22no—
142#66899—22no—
143#66899—41no—
144#66899—41no—
145#66896—22no—
146#66896—22no—
147#66896—22no—
148#66896—22no—
149#66896—22no—
150#66896—41no—
151#66896—41no—
152#66896D414yescomplemented
153C11⋊#95—21no—
154C11⋊#95—21no—
155C11⋊#95—21no—
156C22⋊(C11⋊C8)—22no—
157C22⋊(C11⋊C8)—22no—
158C4⋊(C11⋊C8)—22no—
159#66867—22no—
160#22419—111nomaximal, Sylow
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—24no—
164C24×C11—42no—
165C24×C11—42no—
166C24×C11—42no—
167C24×C11—42no—
168C24×C11—81no—
169C24×C11—81no—
170C24×C11C2×D411yescharacteristic
171C24×C11C2×D411yescharacteristic
172C11×#41—28no—
173C11×#41—44no—
174C11×#41—44no—
175C11×#41—44no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11C22×C412yes—
182C2×D4×C11—22no—
183C2×D4×C11—22no—
184C2×D4×C11—28no—
185C2×D4×C11—24no—
186C2×D4×C11—24no—
187C2×D4×C11—24no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—44no—
197C2×D4×C11—44no—
198C2×D4×C11—44no—
199C2×D4×C11—42no—
200C2×D4×C11—42no—
201C2×D4×C11—42no—
202C2×D4×C11—42no—
203C2×D4×C11—81no—
204C2×D4×C11—81no—
205C2×D4×C11C22⋊C414yes—
206C2×D4×C11C22×C412yes—
207C2×D4×C11C22×C412yes—
208C2×D4×C11C2×D412yes—
209C2×D4×C11#4112yes—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—24no—
221C22×C4×C11—24no—
222C22×C4×C11—42no—
223C22×C4×C11—42no—
224C22×C4×C11—81no—
225C22×C4×C11—81no—
226C22×C4×C11C22×C412yes—
227C22×C4×C11C22×C412yes—
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2411yescharacteristic
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—42no—
240C22×Dic11—42no—
241C22×Dic11—42no—
242C22×Dic11—42no—
243C22×Dic11—81no—
244C22×Dic11—81no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4C22⋊C414yes—
248C11×C4⋊C4C22×C412yes—
249C11×C22⋊C4—24no—
250C11×C22⋊C4—24no—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—24no—
253C11×C22⋊C4—24no—
254C11×C22⋊C4C22⋊C414yes—
255C11×C22⋊C4C22⋊C414yes—
256C42×C11C22×C412yes—
257C42×C11C2×D412yes—
258C22⋊Dic11—42no—
259C22⋊Dic11—42no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—42no—
268C4⋊Dic11—42no—
269C4⋊Dic11—42no—
270C4⋊Dic11—81no—
271C4⋊Dic11C2×D412yes—
272C4×Dic11—42no—
273#4318—44no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—21no—
281C2×C11⋊C8—21no—
282C2×C11⋊C8—21no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8—21no—
285C2×C11⋊C8—44no—
286C2×C11⋊C8C2×D412yes—
287C2×#546D1111yescharacteristic
288C2×#435—111no—
289C2×#417—111no—
290C22×#102—111no—
291D4×C4⋊C4—111no—
292#1983—111no—
293#1959—111no—
294#1895—111no—
295#1892—111no—
296#1874—111no—
297#1872—111no—
298#1802—111no—
299#1788—111no—
300#1786—111no—
301#1762—111no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—22no—
307C23×C11—21no—
308C23×C11—22no—
309C23×C11—21no—
310C23×C11—22no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—22no—
316C23×C11—48no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—48no—
328C23×C11—84no—
329C23×C11—84no—
330C23×C11—84no—
331C23×C11—84no—
332C23×C11—84no—
333C23×C11C2×C22⋊C412yes—
334C23×C11C2×C22⋊C412yes—
335C23×C11AGL(1,ℤ/8)12yes—
336C23×C11#13712yes—
337C23×C11C22×D411yescharacteristic
338Q8×C11—22no—
339Q8×C11—22no—
340Q8×C11—41no—
341Q8×C11—41no—
342D4×C11—28no—
343D4×C11—22no—
344D4×C11—22no—
345D4×C11—22no—
346D4×C11—22no—
347D4×C11—22no—
348D4×C11—48no—
349D4×C11—48no—
350D4×C11—41no—
351D4×C11—41no—
352D4×C11—84no—
353D4×C11C4×D414yescomplemented
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—21no—
361C2×C4×C11—21no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—48no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—84no—
378C2×C4×C11C2×C22⋊C412yes—
379C2×C4×C11C2×C22⋊C412yes—
380C2×C4×C11C2×C22⋊C412yes—
381C2×C4×C11C2×C22⋊C412yes—
382C2×C4×C11C23×C411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C2×#4111yescharacteristic
386C2×C4×C11H(5,𝔽2)11yescharacteristic
387C2×C4×C11H(5,𝔽2)11yescharacteristic
388C2×Dic11—22no—
389C2×Dic11—41no—
390C2×Dic11—41no—
391C2×Dic11—41no—
392C2×Dic11—41no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—84no—
401C2×Dic11—84no—
402C11⋊C8—22no—
403C11⋊C8—41no—
404C11⋊C8—41no—
405C11⋊C8—41no—
406C22×#41C2×D1111yescharacteristic
407C23×D4C2×D1111yescharacteristic
408C22×M16—111no—
409C23×C8—111no—
410#546—24no—
411#546Dic1118yescomplemented
412C2×#124C2×D1111yescharacteristic
413C2×#123—21no—
414C2×C22⋊Q8C2×D1111yescharacteristic
415C2×#121—21no—
416C2×#121C2×D1111yescharacteristic
417C2×#120—21no—
418C2×C4×D4—221no—
419C2×C4×D4C2×D1111yescharacteristic
420C2×C4×D4C2×D1111yescharacteristic
421C22×C4⋊C4—111no—
422C22×C4⋊C4—111no—
423C22×C22⋊C4—21no—
424#435—224no—
425C2×C4⋊C8—111no—
426#417—224no—
427C2×#103—111no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×#102—111no—
439C2×#102—224no—
440C2×C22⋊C8—111no—
441C2×C22⋊C8—111no—
442C2×#97—111no—
443#389—221no—
444#385—221no—
445#385—221no—
446#384—111no—
447#380—111no—
448#380—111no—
449C4×C4⋊C4—111no—
450#340—111no—
451#340—111no—
452#340—111no—
453#340—111no—
454C22×C11—22no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—22no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—24no—
462C22×C11—22no—
463C22×C11—22no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—41no—
467C22×C11—42no—
468C22×C11—41no—
469C22×C11—42no—
470C22×C11—41no—
471C22×C11—42no—
472C22×C11—41no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—816no—
478C22×C11—81no—
479C22×C11—81no—
480C22×C11—81no—
481C22×C11—81no—
482C22×C11#41714yescomplemented
483C22×C11C22×C22⋊C411yescharacteristic
484C22×C11D4211yescharacteristic
485C22×C11#54611yescharacteristic
486C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
487C22×C11C2×#13711yescharacteristic
488C22×C11#57611yescharacteristic
489C22×C11#57711yescharacteristic
490C4×C11—22no—
491C4×C11—22no—
492C4×C11—22no—
493C4×C11—22no—
494C4×C11—42no—
495C4×C11—42no—
496C4×C11C2×C4×D411yescharacteristic
497C4×C11#51811yescharacteristic
498C4×C11D4211yescharacteristic
499C4×C11#54611yescharacteristic
500Dic11—42no—
501Dic11—81no—
502Dic11—81no—
503Dic11—81no—
504C25—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41C2×Dic1114yescomplemented
511C22×Q8C22×D1111yescharacteristic
512C22×D4—22no—
513C22×D4—22no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—22no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C2×Dic1114yescomplemented
521C22×D4C22⋊D1111yescharacteristic
522C22×D4C22×D1111yescharacteristic
523C22×D4C22×D1111yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—221no—
527C23×C4—221no—
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530C2×M16—222no—
531C2×M16—222no—
532C2×M16—441no—
533C22×C8—111no—
534C22×C8—111no—
535C22×C8—111no—
536C22×C8—111no—
537C22×C8—222no—
538C22×C8—222no—
539C22×C8—441no—
540#124—22no—
541#124C2×Dic1114yescomplemented
542#123—28no—
543C22⋊Q8—22no—
544C22⋊Q8C2×Dic1114yescomplemented
545#121—22no—
546#121—28no—
547#121C2×Dic1114yescomplemented
548#120—28no—
549C4×D4—22no—
550C4×D4—444no—
551C4×D4C2×Dic1114yes—
552C4×D4C2×Dic1114yescomplemented
553C4×D4C22⋊D1114yes—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—111no—
559C2×C4⋊C4—222no—
560C2×C4⋊C4—222no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—221no—
563C2×C4⋊C4—221no—
564C2×C4⋊C4—221no—
565C2×C4⋊C4—441no—
566C2×C4⋊C4—441no—
567C2×C4⋊C4C22⋊D1111yescharacteristic
568C2×C4⋊C4C22×D1111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—221no—
576C2×C22⋊C4—221no—
577C2×C22⋊C4C22⋊D1111yescharacteristic
578C2×C22⋊C4C22⋊D1111yescharacteristic
579C2×C42—221no—
580C2×C42C22×D1111yescharacteristic
581C4⋊C8—222no—
582#103—222no—
583#103—222no—
584#103—441no—
585#103—441no—
586#102—114no—
587#102—222no—
588#102—222no—
589#102—222no—
590#102—222no—
591#102—222no—
592#102—441no—
593#102—441no—
594C22⋊C8—222no—
595C22⋊C8—222no—
596#97—222no—
597#95—221no—
598#95—221no—
599#95—221no—
600C2×C11—24no—
601C2×C11—42no—
602C2×C11—44no—
603C2×C11—82no—
604C2×C11D4×C22⋊C411yescharacteristic
605C2×C11C2×#41711yescharacteristic
606C2×C11#289711yescharacteristic
607C2×C11#326411yescharacteristic
608C2×C11#326611yescharacteristic
609C2×C11#330611yescharacteristic
610C2×C11#331411yescharacteristic
611C24—21no—
612C24—21no—
613C24—24no—
614C24—42no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—81no—
619C24—81no—
620C24C2×C22⋊D1111yescharacteristic
621C24C2×C22⋊D1111yescharacteristic
622#41—28no—
623#41—44no—
624#41—44no—
625#41—44no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8C22×Dic1112yes—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—28no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—44no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—81no—
654C2×D4—81no—
655C2×D4C22⋊Dic1114yes—
656C2×D4D4×D1112yes—
657C2×D4#434112yes—
658C2×D4C22×Dic1112yes—
659C2×D4C22×Dic1112yes—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—81no—
675C22×C4—81no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—221no—
679C22×C4—221no—
680C22×C4—442no—
681C22×C4—442no—
682C22×C4—442no—
683C22×C4—442no—
684C22×C4—881no—
685C22×C4—881no—
686C22×C4C22×Dic1112yes—
687C22×C4C22×Dic1112yes—
688C22×C4C2×C22⋊D1111yescharacteristic
689C22×C4C2×C22⋊D1111yescharacteristic
690C22×C4C2×C22⋊D1111yescharacteristic
691C22×C4C2×C22⋊D1111yescharacteristic
692C22×C4C2×C22⋊D1112yes—
693C22×C4C2×C22⋊D1112yes—
694C22×C4C23×D1111yescharacteristic
695M16—444no—
696C2×C8—112no—
697C2×C8—221no—
698C2×C8—221no—
699C2×C8—221no—
700C2×C8—221no—
701C2×C8—221no—
702C2×C8—221no—
703C2×C8—221no—
704C2×C8—221no—
705C2×C8—221no—
706C2×C8—221no—
707C2×C8—221no—
708C2×C8—444no—
709C4⋊C4—24no—
710C4⋊C4—21no—
711C4⋊C4—112no—
712C4⋊C4—221no—
713C4⋊C4—221no—
714C4⋊C4—221no—
715C4⋊C4—221no—
716C4⋊C4—221no—
717C4⋊C4—221no—
718C4⋊C4—221no—
719C4⋊C4—442no—
720C4⋊C4—442no—
721C4⋊C4—442no—
722C4⋊C4—881no—
723C4⋊C4C22⋊Dic1114yes—
724C4⋊C4C22×Dic1112yes—
725C22⋊C4—24no—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—442no—
731C22⋊C4—442no—
732C22⋊C4C22⋊Dic1114yes—
733C22⋊C4C22⋊Dic1114yes—
734C42—442no—
735C42C22×Dic1112yes—
736C42C2×C22⋊D1112yes—
737C11#2241911yescharacteristic, complemented, Sylow
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—22no—
744C23—21no—
745C23—22no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—22no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—48no—
762C23—41no—
763C23—41no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23#6700212yes—
770C23#6700412yes—
771C23C2×C22⋊Dic1112yes—
772C23C2×C22⋊Dic1112yes—
773C23C22×C22⋊D1111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4D4×Dic1114yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—48no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—84no—
814C2×C4—222no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—441no—
818C2×C4—441no—
819C2×C4—441no—
820C2×C4—441no—
821C2×C4—441no—
822C2×C4—441no—
823C2×C4—441no—
824C2×C4—441no—
825C2×C4—441no—
826C2×C4—884no—
827C2×C4—884no—
828C2×C4C2×C22⋊Dic1112yes—
829C2×C4C2×C22⋊Dic1112yes—
830C2×C4C2×C22⋊Dic1112yes—
831C2×C4C2×C22⋊Dic1112yes—
832C2×C4C2×D4×D1111yescharacteristic
833C2×C4C2×#434111yescharacteristic
834C2×C4#6703711yescharacteristic
835C2×C4#6703711yescharacteristic
836C2×C4C23×Dic1111yescharacteristic
837C2×C4C22×C22⋊D1111yescharacteristic
838C8—222no—
839C8—441no—
840C8—441no—
841C8—441no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—42no—
854C22—41no—
855C22—42no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22#1062284514yescomplemented
871C22D4×C22⋊D1111yescharacteristic
872C22#1062333711yescharacteristic
873C22C2×#6700211yescharacteristic
874C22C2×#6700411yescharacteristic
875C22#1062336611yescharacteristic
876C22#1062336711yescharacteristic
877C22C22×C22⋊Dic1111yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—442no—
885C4—881no—
886C4—881no—
887C4—881no—
888C4C2×D4×Dic1111yescharacteristic
889C4#1062332911yescharacteristic
890C4D4×C22⋊D1111yescharacteristic
891C4#1062333711yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊Dic1111yescharacteristic
897C2C2×#1062284511yescharacteristic
898C2#1307714211yescharacteristic
899C2#1308009711yescharacteristic
900C2#1308012211yescharacteristic
901C2#1308057711yescharacteristic
902C2#1308069711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#546C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#546D11
hypocenterC11#22419
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#10622624C2semidirect
2. C2×#10622845C2semidirect
3. C22×#66896C2semidirect
4. D4×C4⋊Dic11C2semidirect
5. #13069549C2semidirect
6. #13069433C2semidirect
7. #13069055C2semidirect
8. #13069040C2semidirect
9. #13068934C2semidirect
10. #13068924C2semidirect
11. #13068616C2semidirect
12. #13068556C2semidirect
13. #13068547C2semidirect
14. #13068441C2semidirect
19. C11×#546C4semidirect
31. C22×C4⋊Dic11C22semidirect
32. C22×#4318C22semidirect
35. C2×#66899C22semidirect
36. C2×#66899C22semidirect
37. C2×#66899C22semidirect
38. C2×#66899C22semidirect
49. #10622825C22semidirect
51. C2×C22⋊(C11⋊C8)C22semidirect
56. #10622548C22semidirect
57. C4×C4⋊Dic11C22semidirect
58. C2×C4⋊(C11⋊C8)C22semidirect
59. C2×#66867C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
70. C2×C11×#41C2×C4semidirect
80. C22×D4×C11C2×C4semidirect
91. C11×#124C2×C4semidirect
94. C11×C22⋊Q8C2×C4semidirect
97. C11×#121C2×C4semidirect
101. C4×D4×C11C2×C4semidirect
152. #66896D4semidirect
353. D4×C11C4×D4semidirect
411. #546Dic11semidirect
482. C22×C11#417semidirect
510. C2×#41C2×Dic11semidirect
520. C22×D4C2×Dic11semidirect
541. #124C2×Dic11semidirect
544. C22⋊Q8C2×Dic11semidirect
547. #121C2×Dic11semidirect
552. C4×D4C2×Dic11semidirect
737. C11#22419semidirect
789. D4D4×Dic11semidirect
870. C22#10622845semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
C2×#106228452
C22×#668962
D4×C4⋊Dic112
#130695492
#130694332
#130690552
#130690402
#130689342
#130689242
#130686162
#130685562
#130685472
#130684412
C2×C11×#5462
#2241911