Finite Group Databasebeta

← #14769373

Subgroups — #14769373

Order 2816.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622625C211yesmaximal, characteristic, complemented
2C2×#10622845C211yesmaximal, characteristic, complemented
3C2×#10622828C211yesmaximal, characteristic, complemented
4#13071545C211yesmaximal, characteristic, complemented
5#13069549C211yesmaximal, characteristic, complemented
6#13069428C211yesmaximal, characteristic, complemented
7#13069055C211yesmaximal, characteristic, complemented
8#13069050C211yesmaximal, characteristic, complemented
9#13068934C211yesmaximal, characteristic, complemented
10#13068929C211yesmaximal, characteristic, complemented
11#13068626C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic, complemented
13#13068547C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, 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×#66979C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic, complemented
31C22×#4318C2211yescharacteristic
32C22×#4318C2211yescharacteristic, complemented
33#10622845—24no—
34C2×#66899C2211yescharacteristic, complemented
35C2×#66899C2211yescharacteristic, complemented
36C2×#66899C2211yescharacteristic, complemented
37C2×#66899C2211yescharacteristic, complemented
38#10622833—21no—
39#10622828—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#10622625—24no—
53#10622594—21no—
54#10622564—21no—
55C22⋊C4×Dic11—21no—
56#10622549C2211yescharacteristic, complemented
57C4×C4⋊Dic11C2211yescharacteristic, complemented
58C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
59C2×C4×C11⋊C8C2211yescharacteristic, 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×C414yes—
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—
89C11×#124—22no—
90C11×#124C2×C414yescomplemented
91C11×#123—28no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8C2×C414yescomplemented
94C11×#121—22no—
95C11×#121—28no—
96C11×#121C2×C414yes—
97C11×#120—28no—
98C4×D4×C11—22no—
99C4×D4×C11C2×C414yes—
100C4×D4×C11C2×C414yescomplemented
101C4×D4×C11D414yes—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4D411yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—28no—
111C2×C11×C22⋊C4D411yescharacteristic
112C2×C11×C22⋊C4D411yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117#66979—22no—
118#66979—41no—
119C2×C4⋊Dic11—22no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—41no—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4×Dic11—21no—
127C2×C4×Dic11—21no—
128C2×#4318—22no—
129C2×#4318—22no—
130C2×#4318—22no—
131C2×#4318—22no—
132C2×#4318—41no—
133C2×#4318—41no—
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138#66899—22no—
139#66899—22no—
140#66899—41no—
141#66899—41no—
142#66896—22no—
143#66896—22no—
144#66896—22no—
145#66896—22no—
146#66896—22no—
147#66896—41no—
148#66896—41no—
149#66896D414yescomplemented
150C11⋊#95—21no—
151C11⋊#95—21no—
152C11⋊#95—21no—
153C11⋊#95—21no—
154C11⋊#95—21no—
155C22⋊(C11⋊C8)—22no—
156C22⋊(C11⋊C8)—22no—
157C4⋊(C11⋊C8)—22no—
158C4×C11⋊C8—22no—
159#22427—111nomaximal, Sylow
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—24no—
163C24×C11—42no—
164C24×C11—42no—
165C24×C11—42no—
166C24×C11—42no—
167C24×C11—81no—
168C24×C11—81no—
169C24×C11C2×D411yescharacteristic
170C24×C11C2×D411yescharacteristic
171C11×#41—28no—
172C11×#41—44no—
173C11×#41—44no—
174C11×#41—44no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11C22×C412yes—
181C2×D4×C11—28no—
182C2×D4×C11—24no—
183C2×D4×C11—24no—
184C2×D4×C11—24no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11—44no—
196C2×D4×C11—41no—
197C2×D4×C11—41no—
198C2×D4×C11—42no—
199C2×D4×C11—42no—
200C2×D4×C11—42no—
201C2×D4×C11—42no—
202C2×D4×C11—81no—
203C2×D4×C11—81no—
204C2×D4×C11C22⋊C414yes—
205C2×D4×C11C22×C412yes—
206C2×D4×C11C22×C412yes—
207C2×D4×C11C2×D412yes—
208C2×D4×C11#4112yes—
209C22×C4×C11—21no—
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—24no—
220C22×C4×C11—24no—
221C22×C4×C11—42no—
222C22×C4×C11—42no—
223C22×C4×C11—81no—
224C22×C4×C11—81no—
225C22×C4×C11C22×C412yes—
226C22×C4×C11C22×C412yes—
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2411yescharacteristic
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—42no—
239C22×Dic11—42no—
240C22×Dic11—81no—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4C22⋊C414yes—
244C11×C4⋊C4C22×C412yes—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—24no—
249C11×C22⋊C4—24no—
250C11×C22⋊C4C22⋊C414yes—
251C11×C22⋊C4C22⋊C414yes—
252C42×C11C22×C412yes—
253C42×C11C2×D412yes—
254C22⋊Dic11—42no—
255C22⋊Dic11—42no—
256C22⋊Dic11—81no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—42no—
265C4⋊Dic11C2×D412yes—
266C4×Dic11—42no—
267C4×Dic11—81no—
268#4318—44no—
269#4318—44no—
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⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—21no—
281C2×C11⋊C8C2×D412yes—
282C2×#546D1111yescharacteristic
283C2×#436—111no—
284C2×#417—111no—
285C2×#418—111no—
286#2352—111no—
287#1983—111no—
288#1958—111no—
289#1895—111no—
290#1894—111no—
291#1874—111no—
292#1873—111no—
293#1804—111no—
294#1788—111no—
295#1786—111no—
296C4×#102—111no—
297C23×C11—22no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—22no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—22no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—22no—
313C23×C11—48no—
314C23×C11—48no—
315C23×C11—41no—
316C23×C11—41no—
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—84no—
326C23×C11—84no—
327C23×C11—84no—
328C23×C11—84no—
329C23×C11—84no—
330C23×C11C2×C22⋊C412yes—
331C23×C11C2×C22⋊C412yes—
332C23×C11C22×D411yescharacteristic
333Q8×C11—22no—
334Q8×C11—22no—
335Q8×C11—41no—
336Q8×C11—41no—
337D4×C11—22no—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—22no—
341D4×C11—22no—
342D4×C11—44no—
343D4×C11—48no—
344D4×C11—48no—
345D4×C11—41no—
346D4×C11—41no—
347D4×C11—84no—
348D4×C11C4×D414yes—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
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—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—48no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—84no—
373C2×C4×C11C2×C22⋊C412yes—
374C2×C4×C11C2×C22⋊C412yes—
375C2×C4×C11C2×C22⋊C412yes—
376C2×C4×C11C2×C22⋊C412yes—
377C2×C4×C11C23×C411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C2×#4111yescharacteristic
381C2×C4×C11H(5,𝔽2)11yescharacteristic
382C2×C4×C11H(5,𝔽2)11yescharacteristic
383C2×Dic11—22no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389C2×Dic11—41no—
390C2×Dic11—41no—
391C2×Dic11—41no—
392C2×Dic11—41no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—84no—
396C11⋊C8—22no—
397C11⋊C8—41no—
398C11⋊C8—41no—
399C11⋊C8—41no—
400C22×#41C2×D1111yescharacteristic
401C23×D4C2×D1111yescharacteristic
402C22×M16—111no—
403C22×M16—111no—
404#546—24no—
405#546Dic1118yescomplemented
406C2×#124C2×D1111yescharacteristic
407C2×#123—21no—
408C2×C22⋊Q8C2×D1111yescharacteristic
409C2×#121—21no—
410C2×#121C2×D1111yescharacteristic
411C2×#120—21no—
412C2×C4×D4C2×D1111yescharacteristic
413C2×C4×D4C2×D1111yescharacteristic
414C2×#117—111no—
415C22×C4⋊C4—111no—
416C22×C22⋊C4—21no—
417#436—224no—
418C2×C4⋊C8—111no—
419#418—224no—
420#417—224no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#103—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×C22⋊C8—111no—
434C2×C22⋊C8—111no—
435C2×C4×C8—111no—
436#388—221no—
437#387—221no—
438#386—221no—
439#382—111no—
440#380—111no—
441#380—111no—
442C4×C4⋊C4—111no—
443C4×C22⋊C4—221no—
444#340—111no—
445#340—111no—
446#340—111no—
447#340—111no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—24no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—22no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—42no—
460C22×C11—41no—
461C22×C11—41no—
462C22×C11—42no—
463C22×C11—41no—
464C22×C11—41no—
465C22×C11—42no—
466C22×C11—41no—
467C22×C11—41no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—816no—
473C22×C11—81no—
474C22×C11—81no—
475C22×C11—81no—
476C22×C11—81no—
477C22×C11C22×C22⋊C411yescharacteristic
478C22×C11D4211yescharacteristic
479C22×C11#54611yescharacteristic
480C22×C11#57511yescharacteristic
481C22×C11#57511yescharacteristic
482C22×C11#57611yescharacteristic
483C22×C11#57711yescharacteristic
484C4×C11—22no—
485C4×C11—22no—
486C4×C11—22no—
487C4×C11—22no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11C2×C4×D411yescharacteristic
491C4×C11#51811yescharacteristic
492C4×C11D4211yescharacteristic
493C4×C11#54611yescharacteristic
494Dic11—42no—
495Dic11—81no—
496Dic11—81no—
497Dic11—81no—
498C25—21no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41C2×Dic1114yes—
505C22×Q8C22×D1111yescharacteristic
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—22no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4C2×Dic1114yescomplemented
515C22×D4C22⋊D1111yescharacteristic
516C22×D4C22×D1111yescharacteristic
517C22×D4C22×D1111yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—221no—
521C23×C4C22×D1111yescharacteristic
522C23×C4C22×D1111yescharacteristic
523C2×M16—222no—
524C2×M16—222no—
525C2×M16—222no—
526C2×M16—222no—
527C2×M16—441no—
528C2×M16—441no—
529C22×C8—111no—
530C22×C8—111no—
531C22×C8—111no—
532C22×C8—111no—
533#124—22no—
534#124C2×Dic1114yescomplemented
535#123—28no—
536C22⋊Q8—22no—
537C22⋊Q8C2×Dic1114yescomplemented
538#121—22no—
539#121—28no—
540#121C2×Dic1114yes—
541#120—28no—
542C4×D4—22no—
543C4×D4C2×Dic1114yes—
544C4×D4C2×Dic1114yescomplemented
545C4×D4C22⋊D1114yes—
546#117—222no—
547#117—441no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—111no—
553C2×C4⋊C4—222no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—441no—
556C2×C4⋊C4C22⋊D1111yescharacteristic
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—28no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4C22⋊D1111yescharacteristic
568C2×C22⋊C4C22⋊D1111yescharacteristic
569C2×C42—221no—
570C2×C42—221no—
571C2×C42C22×D1111yescharacteristic
572C4⋊C8—222no—
573#103—222no—
574#103—222no—
575#103—441no—
576#103—441no—
577#102—114no—
578#102—222no—
579#102—222no—
580#102—222no—
581#102—222no—
582#102—222no—
583#102—441no—
584#102—441no—
585C22⋊C8—222no—
586C22⋊C8—222no—
587C4×C8—222no—
588#95—221no—
589#95—221no—
590#95—221no—
591#95—221no—
592#95—221no—
593C2×C11—42no—
594C2×C11—42no—
595C2×C11—44no—
596C2×C11—82no—
597C2×C11D4×C22⋊C411yescharacteristic
598C2×C11#289611yescharacteristic
599C2×C11#289711yescharacteristic
600C2×C11#327311yescharacteristic
601C2×C11#327511yescharacteristic
602C2×C11#332211yescharacteristic
603C2×C11#332311yescharacteristic
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×C22⋊D1111yescharacteristic
614C24C2×C22⋊D1111yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×Dic1112yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊Dic1114yes—
649C2×D4D4×D1112yes—
650C2×D4#434112yes—
651C2×D4C22×Dic1112yes—
652C2×D4C22×Dic1112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—81no—
668C22×C4—81no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—442no—
674C22×C4—442no—
675C22×C4—881no—
676C22×C4C22×Dic1112yes—
677C22×C4C22×Dic1112yes—
678C22×C4C2×C22⋊D1111yescharacteristic
679C22×C4C2×C22⋊D1111yescharacteristic
680C22×C4C2×C22⋊D1111yescharacteristic
681C22×C4C2×C22⋊D1111yescharacteristic
682C22×C4C2×C22⋊D1112yes—
683C22×C4C2×C22⋊D1112yes—
684C22×C4C23×D1111yescharacteristic
685M16—444no—
686M16—444no—
687C2×C8—112no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—221no—
695C2×C8—221no—
696C2×C8—221no—
697C2×C8—221no—
698C2×C8—221no—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—112no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—442no—
710C4⋊C4C22⋊Dic1114yes—
711C4⋊C4C22×Dic1112yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—442no—
718C22⋊C4—442no—
719C22⋊C4—881no—
720C22⋊C4C22⋊Dic1114yes—
721C22⋊C4C22⋊Dic1114yes—
722C42—442no—
723C42—881no—
724C42C22×Dic1112yes—
725C42C2×C22⋊D1112yes—
726C11#2242711yescharacteristic, complemented, Sylow
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—22no—
743C23—48no—
744C23—48no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23C2×C22⋊Dic1112yes—
761C23C2×C22⋊Dic1112yes—
762C23C22×C22⋊D1111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—44no—
773D4—48no—
774D4—48no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4D4×Dic1114yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—84no—
803C2×C4—222no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—884no—
816C2×C4C2×C22⋊Dic1112yes—
817C2×C4C2×C22⋊Dic1112yes—
818C2×C4C2×C22⋊Dic1112yes—
819C2×C4C2×C22⋊Dic1112yes—
820C2×C4C2×D4×D1111yescharacteristic
821C2×C4C2×#434111yescharacteristic
822C2×C4#6703711yescharacteristic
823C2×C4#6703711yescharacteristic
824C2×C4C23×Dic1111yescharacteristic
825C2×C4C22×C22⋊D1111yescharacteristic
826C8—222no—
827C8—441no—
828C8—441no—
829C8—441no—
830C22—22no—
831C22—22no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—41no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—41no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—816no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22D4×C22⋊D1111yescharacteristic
860C22#1062333711yescharacteristic
861C22#1062335311yescharacteristic
862C22#1062335311yescharacteristic
863C22#1062336611yescharacteristic
864C22#1062336711yescharacteristic
865C22C22×C22⋊Dic1111yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—442no—
873C4—881no—
874C4—881no—
875C4—881no—
876C4C2×D4×Dic1111yescharacteristic
877C4#1062332911yescharacteristic
878C4D4×C22⋊D1111yescharacteristic
879C4#1062333711yescharacteristic
880C2—42no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2D4×C22⋊Dic1111yescharacteristic
885C2#1307713511yescharacteristic
886C2#1307714211yescharacteristic
887C2#1308022311yescharacteristic
888C2#1308024311yescharacteristic
889C2#1308081711yescharacteristic
890C2#1308083211yescharacteristic
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#22427
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×#10622625C2semidirect
2. C2×#10622845C2semidirect
3. C2×#10622828C2semidirect
4. #13071545C2semidirect
5. #13069549C2semidirect
6. #13069428C2semidirect
7. #13069055C2semidirect
8. #13069050C2semidirect
9. #13068934C2semidirect
10. #13068929C2semidirect
11. #13068626C2semidirect
12. #13068556C2semidirect
13. #13068547C2semidirect
14. C4×#66896C2semidirect
19. C11×#546C4semidirect
30. C22×C4⋊Dic11C22semidirect
32. C22×#4318C22semidirect
34. C2×#66899C22semidirect
35. C2×#66899C22semidirect
36. C2×#66899C22semidirect
37. C2×#66899C22semidirect
49. #10622825C22semidirect
51. C2×C22⋊(C11⋊C8)C22semidirect
56. #10622549C22semidirect
57. C4×C4⋊Dic11C22semidirect
58. C2×C4⋊(C11⋊C8)C22semidirect
59. C2×C4×C11⋊C8C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
80. C22×D4×C11C2×C4semidirect
90. C11×#124C2×C4semidirect
93. C11×C22⋊Q8C2×C4semidirect
100. C4×D4×C11C2×C4semidirect
149. #66896D4semidirect
405. #546Dic11semidirect
514. C22×D4C2×Dic11semidirect
534. #124C2×Dic11semidirect
537. C22⋊Q8C2×Dic11semidirect
544. C4×D4C2×Dic11semidirect
726. C11#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#106226252
C2×#106228452
C2×#106228282
#130715452
#130695492
#130694282
#130690552
#130690502
#130689342
#130689292
#130686262
#130685562
#130685472
C4×#668962
C2×C11×#5462
#2242711