Finite Group Databasebeta

← #14769899

Subgroups — #14769899

Order 2816.

1696 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623021C211yesmaximal, characteristic
2#13071432C212yesmaximal, complemented
3#13069599C212yesmaximal, complemented
4#13069068C212yesmaximal, complemented
5#13069067C212yesmaximal, complemented
6#13068689C211yesmaximal, characteristic, complemented
7#13068603C211yesmaximal, characteristic, complemented
8#13068403C211yesmaximal, characteristic, complemented
9C2×#10622164C211yesmaximal, characteristic, complemented
10D11×#342C211yesmaximal, characteristic, complemented
11C11×#1819C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2211yescharacteristic
13C22×#4339C411yescharacteristic, complemented
14C22×C11×C22⋊C4C2211yescharacteristic
15C2×#67006C2211yescharacteristic
16C22×C22⋊Dic11C2212yes—
17C2×#66983C411yescharacteristic, complemented
18C2×#66982C411yescharacteristic, complemented
19C2×C4×C22⋊D11C411yescharacteristic, complemented
20C2×#66938C411yescharacteristic, complemented
21#10623021—22no—
22#10623021—22no—
23#10623021—22no—
24#10623021—22no—
25C2×#66937C411yescharacteristic, complemented
26C2×#66937C411yescharacteristic, complemented
27C2×#66936C411yescharacteristic, complemented
28C2×#66935C2211yescharacteristic
29C2×(C22⋊D11)⋊C4—22no—
30C2×(C22⋊D11)⋊C4C2211yescharacteristic
31C2×C22⋊C4×D11C2211yescharacteristic
32C2×C22⋊C4×D11C2212yes—
33C2×#66931C2211yescharacteristic
34C11×#379C2212yes—
35#10622571—22no—
36#10622570—22no—
37#10622569—22no—
38#10622568C2212yes—
39C2×#66870C2212yes—
40C2×#66870C2212yes—
41#10622555C2212yes—
42C22⋊C4×Dic11C2212yes—
43C11×#342C2212yes—
44C11×#342C2211yescharacteristic
45C11×#342C2211yescharacteristic
46#10622165C2212yes—
47#10622165C2212yes—
48#10622164C2212yes—
49#10622164C2211yescharacteristic
50#10622164C2211yescharacteristic
51C25×C11C2311yescharacteristic
52C24×D11C2311yescharacteristic
53C23×C4×C11C2×C411yescharacteristic, complemented
54C23×C4×C11C2×C411yescharacteristic, complemented
55C22×C22⋊D11—44no—
56C22×C22⋊D11C2×C411yescharacteristic
57C22×C22⋊D11C2×C411yescharacteristic
58C22×C22⋊D11C2×C411yescharacteristic
59C22×C22⋊D11C2×C411yescharacteristic
60C22×C22⋊D11C2×C411yescharacteristic, complemented
61C22×C22⋊D11C2×C411yescharacteristic, complemented
62C22×C22⋊D11D412yes—
63C22×C22⋊D11D412yes—
64C22×C22⋊D11D412yes—
65C22×C22⋊D11D412yes—
66C22×C22⋊D11C2311yescharacteristic
67C23×Dic11—22no—
68C23×Dic11C2311yescharacteristic
69C2×#4339—21no—
70C2×#4339—21no—
71C2×#4339—21no—
72C2×#4339—21no—
73C2×#4339—44no—
74C22×D44C2×C411yescharacteristic, complemented
75C22×D44C2×C411yescharacteristic, complemented
76C22×C4×D11—22no—
77C22×C4×D11C2×C411yescharacteristic, complemented
78C22×C4×D11C2×C411yescharacteristic, complemented
79C22×C4×D11C2×C411yescharacteristic, complemented
80C22×Dic22C2×C411yescharacteristic, complemented
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4C2×C411yescharacteristic, complemented
86C2×C11×C22⋊C4C2×C411yescharacteristic, complemented
87C2×C11×C22⋊C4C2312yes—
88C2×C11×C22⋊C4C2312yes—
89C2×C11×C22⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4C2311yescharacteristic
91#67006—22no—
92#67006—22no—
93C2×C22⋊Dic11—24no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—42no—
96C2×C22⋊Dic11C2×C411yescharacteristic, complemented
97C2×C22⋊Dic11C2×C411yescharacteristic, complemented
98C2×C22⋊Dic11C2312yes—
99C2×C22⋊Dic11C2311yescharacteristic
100C2×C22⋊Dic11C2312yes—
101#66983—22no—
102#66983—22no—
103#66982—22no—
104#66982—22no—
105C4×C22⋊D11—21no—
106C4×C22⋊D11—21no—
107C4×C22⋊D11—21no—
108C4×C22⋊D11—21no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4C2×C411yescharacteristic, complemented
113C2×(C2×D11)⋊C4C2×C411yescharacteristic, complemented
114C2×(C2×D11)⋊C4C2×C411yescharacteristic, complemented
115C2×(C2×D11)⋊C4C2×C411yescharacteristic, complemented
116C2×(C2×D11)⋊C4C2×C411yescharacteristic, complemented
117C2×C4⋊Dic11C2×C411yescharacteristic, complemented
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4C2×C411yescharacteristic, complemented
120C2×Dic11⋊C4C2×C411yescharacteristic, complemented
121C2×Dic11⋊C4C2×C411yescharacteristic, complemented
122C2×C4×Dic11—22no—
123C2×C4×Dic11C2×C411yescharacteristic, complemented
124#66938—22no—
125#66938—22no—
126#66937—22no—
127#66937—22no—
128#66937—22no—
129#66937—22no—
130#66936—22no—
131#66936—22no—
132#66935—22no—
133#66935—22no—
134(C22⋊D11)⋊C4—22no—
135(C22⋊D11)⋊C4—22no—
136(C22⋊D11)⋊C4—48no—
137C22⋊C4×D11—22no—
138C22⋊C4×D11—22no—
139C22⋊C4×D11—24no—
140C22⋊C4×D11—42no—
141#66931—22no—
142#66931—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145#66870—24no—
146#66870—42no—
147#22476—111nomaximal, Sylow
148C24×C11—22no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—42no—
152C24×C11—81no—
153C24×C11C22×C411yescharacteristic
154C24×C11C22×C411yescharacteristic
155C24×C11C2×D412yes—
156C24×C11C2×D412yes—
157C24×C11C2411yescharacteristic
158C23×D11—22no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11—42no—
162C23×D11—81no—
163C23×D11C22×C411yescharacteristic
164C23×D11C22×C411yescharacteristic
165C23×D11C22×C411yescharacteristic
166C23×D11C2×D412yes—
167C23×D11C2×D412yes—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—42no—
175C22×C4×C11—81no—
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C22×C411yescharacteristic
178C22×C4×C11C22×C411yescharacteristic
179C22×C4×C11C22×C411yescharacteristic
180C2×C22⋊D11—28no—
181C2×C22⋊D11—24no—
182C2×C22⋊D11—21no—
183C2×C22⋊D11—21no—
184C2×C22⋊D11—22no—
185C2×C22⋊D11—22no—
186C2×C22⋊D11—22no—
187C2×C22⋊D11—21no—
188C2×C22⋊D11—21no—
189C2×C22⋊D11—42no—
190C2×C22⋊D11—44no—
191C2×C22⋊D11—42no—
192C2×C22⋊D11—44no—
193C2×C22⋊D11—42no—
194C2×C22⋊D11—42no—
195C2×C22⋊D11—44no—
196C2×C22⋊D11—81no—
197C2×C22⋊D11C22⋊C412yes—
198C2×C22⋊D11C22⋊C412yes—
199C2×C22⋊D11C22⋊C411yescharacteristic
200C2×C22⋊D11C22⋊C411yescharacteristic
201C2×C22⋊D11C22⋊C411yescharacteristic
202C2×C22⋊D11C22⋊C412yes—
203C2×C22⋊D11C22⋊C412yes—
204C2×C22⋊D11C22⋊C412yes—
205C2×C22⋊D11C22⋊C412yes—
206C2×C22⋊D11C22⋊C411yescharacteristic
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—44no—
210C22×Dic11—44no—
211C22×Dic11—42no—
212C22×Dic11—82no—
213C22×Dic11C22×C411yescharacteristic
214C22×Dic11C22×C411yescharacteristic
215C22×Dic11C22×C411yescharacteristic
216C22×Dic11C22×C411yescharacteristic
217C22×Dic11C22×C411yescharacteristic
218C22×Dic11C2×D412yes—
219C22×Dic11C2×D412yes—
220#4339—44no—
221#4339—44no—
222#4339—44no—
223#4339—44no—
224C2×D44—21no—
225C2×D44—21no—
226C2×D44—22no—
227C2×D44—42no—
228C2×D44—81no—
229C2×C4×D11—21no—
230C2×C4×D11—21no—
231C2×C4×D11—21no—
232C2×C4×D11—21no—
233C2×C4×D11—21no—
234C2×C4×D11—21no—
235C2×C4×D11—42no—
236C2×C4×D11—44no—
237C2×C4×D11—44no—
238C2×C4×D11—42no—
239C2×C4×D11—82no—
240C2×C4×D11—81no—
241C2×Dic22—21no—
242C2×Dic22—21no—
243C2×Dic22—42no—
244C11×C22⋊C4—22no—
245C11×C22⋊C4—22no—
246C11×C22⋊C4—22no—
247C11×C22⋊C4—22no—
248C11×C22⋊C4—22no—
249C11×C22⋊C4—22no—
250C11×C22⋊C4—22no—
251C11×C22⋊C4—22no—
252C11×C22⋊C4—44no—
253C11×C22⋊C4—82no—
254C22⋊Dic11—22no—
255C22⋊Dic11—21no—
256C22⋊Dic11—21no—
257C22⋊Dic11—22no—
258C22⋊Dic11—22no—
259C22⋊Dic11—22no—
260C22⋊Dic11—22no—
261C22⋊Dic11—44no—
262C22⋊Dic11#4114yescomplemented
263(C2×D11)⋊C4—22no—
264(C2×D11)⋊C4—22no—
265(C2×D11)⋊C4—22no—
266(C2×D11)⋊C4—21no—
267(C2×D11)⋊C4—21no—
268(C2×D11)⋊C4—22no—
269(C2×D11)⋊C4—44no—
270(C2×D11)⋊C4—44no—
271(C2×D11)⋊C4—82no—
272C4⋊Dic11—22no—
273Dic11⋊C4—21no—
274Dic11⋊C4—21no—
275Dic11⋊C4—22no—
276Dic11⋊C4—22no—
277Dic11⋊C4—44no—
278C4×Dic11—21no—
279C4×Dic11—21no—
280C4×Dic11—44no—
281C2×#546—111no—
282D4×C22⋊C4—112no—
283#1996—112no—
284#1898—112no—
285#1898—112no—
286#1819—111no—
287#1819D1111yescharacteristic, complemented
288#1799—111no—
289C4×#99—111no—
290C2×#342—111no—
291C2×#342—111no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—24no—
297C23×C11—22no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—41no—
303C23×C11—42no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—42no—
307C23×C11—41no—
308C23×C11—42no—
309C23×C11—41no—
310C23×C11—84no—
311C23×C11—82no—
312C23×C11—82no—
313C23×C11C2×C22⋊C412yes—
314C23×C11C2×C22⋊C411yescharacteristic
315C23×C11C2×C22⋊C411yescharacteristic
316C23×C11C23×C411yescharacteristic
317C23×C11C22×D412yes—
318C23×C11C2×#4112yes—
319C23×C11H(5,𝔽2)11yescharacteristic
320C23×C112−1+411yescharacteristic
321C22×D11—21no—
322C22×D11—21no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—21no—
326C22×D11—21no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—24no—
330C22×D11—22no—
331C22×D11—21no—
332C22×D11—21no—
333C22×D11—21no—
334C22×D11—41no—
335C22×D11—42no—
336C22×D11—42no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—42no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—82no—
343C22×D11—84no—
344C22×D11—82no—
345C22×D11C2×C22⋊C412yes—
346C22×D11C2×C22⋊C411yescharacteristic
347C22×D11C2×C22⋊C411yescharacteristic
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—42no—
353C2×C4×C11—42no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—42no—
359C2×C4×C11—42no—
360C2×C4×C11—42no—
361C2×C4×C11—42no—
362C2×C4×C11—42no—
363C2×C4×C11—42no—
364C2×C4×C11—81no—
365C2×C4×C11—81no—
366C22⋊D11—22no—
367C22⋊D11—24no—
368C22⋊D11—22no—
369C22⋊D11—24no—
370C22⋊D11—22no—
371C22⋊D11—24no—
372C22⋊D11—42no—
373C22⋊D11—42no—
374C22⋊D11—42no—
375C22⋊D11—42no—
376C22⋊D11—42no—
377C22⋊D11—42no—
378C22⋊D11—42no—
379C22⋊D11—82no—
380C22⋊D11#9914yescomplemented
381C2×Dic11—24no—
382C2×Dic11—22no—
383C2×Dic11—21no—
384C2×Dic11—21no—
385C2×Dic11—21no—
386C2×Dic11—21no—
387C2×Dic11—21no—
388C2×Dic11—24no—
389C2×Dic11—41no—
390C2×Dic11—42no—
391C2×Dic11—42no—
392C2×Dic11—42no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—42no—
396C2×Dic11—42no—
397C2×Dic11—42no—
398C2×Dic11—88no—
399C2×Dic11C2×C22⋊C411yescharacteristic
400C2×Dic11C2×C22⋊C412yes—
401C2×Dic11C2×C22⋊C411yescharacteristic
402D44—42no—
403D44—42no—
404D44—82no—
405C4×D11—42no—
406C4×D11—42no—
407C4×D11—42no—
408C4×D11—42no—
409C4×D11—81no—
410C4×D11—81no—
411C4×D11—88no—
412Dic22—42no—
413Dic22—42no—
414C22×#41—111no—
415C23×D4—111no—
416#546—222no—
417#546—222no—
418#546—222no—
419#546—222no—
420C2×#124—111no—
421C2×#123—111no—
422C2×#123—111no—
423C2×C22⋊Q8—111no—
424C2×#121—111no—
425C2×#121—111no—
426C2×#121—111no—
427C2×#120—111no—
428C2×#120—111no—
429C2×C4×D4—111no—
430C2×C4×D4—111no—
431C2×C4×D4—222no—
432C22×C22⋊C4—111no—
433C22×C22⋊C4—112no—
434C22×C22⋊C4—112no—
435C22×C22⋊C4C2×D1111yescharacteristic
436C2×#99—112no—
437C2×#99—112no—
438#390—222no—
439#386—222no—
440#386—222no—
441#380—112no—
442#379—112no—
443#379C2×D1112yes—
444C4×C22⋊C4—112no—
445#342—111no—
446#342—112no—
447#342—112no—
448#342—112no—
449#342—111no—
450#342C2×D1111yescharacteristic
451#342C2×D1111yescharacteristic
452#342C2×D1112yes—
453C22×C11—21no—
454C22×C11—21no—
455C22×C11—22no—
456C22×C11—21no—
457C22×C11—22no—
458C22×C11—21no—
459C22×C11—21no—
460C22×C11—22no—
461C22×C11—21no—
462C22×C11—22no—
463C22×C11—21no—
464C22×C11—22no—
465C22×C11—42no—
466C22×C11—41no—
467C22×C11—41no—
468C22×C11—44no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—44no—
472C22×C11—82no—
473C22×C11—82no—
474C22×C11—81no—
475C22×C11—81no—
476C22×C11C2×#9912yes—
477C22×C11C22×C22⋊C411yescharacteristic
478C22×C11C4×#4111yescharacteristic
479C22×C11#52011yescharacteristic
480C22×C11#54612yes—
481C22×C11#54712yes—
482C2×D11—21no—
483C2×D11—21no—
484C2×D11—21no—
485C2×D11—22no—
486C2×D11—21no—
487C2×D11—22no—
488C2×D11—21no—
489C2×D11—22no—
490C2×D11—44no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—44no—
494C2×D11—41no—
495C2×D11—41no—
496C2×D11—41no—
497C2×D11—82no—
498C2×D11—82no—
499C2×D11—81no—
500C2×D11—81no—
501C2×D11—81no—
502C2×D11—81no—
503C2×D11C2×#9912yes—
504C4×C11—41no—
505C4×C11—41no—
506C4×C11—41no—
507C4×C11—41no—
508C4×C11—82no—
509C4×C11—82no—
510Dic11—21no—
511Dic11—22no—
512Dic11—44no—
513Dic11—41no—
514Dic11—41no—
515Dic11—41no—
516Dic11—82no—
517Dic11C2×#9912yes—
518C25—111no—
519C25C22×D1111yescharacteristic
520C2×#41—221no—
521C2×#41—221no—
522C2×#41—221no—
523C2×#41—221no—
524C2×#41—444no—
525C22×Q8—111no—
526C22×D4—111no—
527C22×D4—112no—
528C22×D4—111no—
529C22×D4—111no—
530C22×D4—111no—
531C22×D4—112no—
532C22×D4—112no—
533C22×D4—112no—
534C22×D4—111no—
535C22×D4—111no—
536C22×D4—111no—
537C22×D4—111no—
538C22×D4—111no—
539C22×D4—444no—
540C23×C4—111no—
541C23×C4—111no—
542C23×C4—111no—
543C23×C4—111no—
544C23×C4—222no—
545C23×C4—222no—
546C23×C4C4×D1111yescharacteristic, complemented
547C23×C4C4×D1111yescharacteristic, complemented
548#124—222no—
549#124—222no—
550#123—222no—
551#123—222no—
552#123—222no—
553#123—222no—
554C22⋊Q8—222no—
555C22⋊Q8—222no—
556#121—222no—
557#121—222no—
558#121—222no—
559#121—222no—
560#121—222no—
561#121—222no—
562#120—222no—
563#120—222no—
564#120—222no—
565#120—222no—
566C4×D4—222no—
567C4×D4—222no—
568C4×D4—221no—
569C4×D4—221no—
570C4×D4—221no—
571C4×D4—221no—
572C4×D4—448no—
573C2×C4⋊C4—111no—
574C2×C4⋊C4—111no—
575C2×C4⋊C4—111no—
576C2×C4⋊C4—111no—
577C2×C4⋊C4—222no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—112no—
583C2×C22⋊C4—111no—
584C2×C22⋊C4—111no—
585C2×C22⋊C4—111no—
586C2×C22⋊C4—111no—
587C2×C22⋊C4—111no—
588C2×C22⋊C4—111no—
589C2×C22⋊C4—111no—
590C2×C22⋊C4—111no—
591C2×C22⋊C4—112no—
592C2×C22⋊C4—224no—
593C2×C22⋊C4—222no—
594C2×C22⋊C4—222no—
595C2×C22⋊C4—224no—
596C2×C22⋊C4—222no—
597C2×C22⋊C4—222no—
598C2×C22⋊C4—222no—
599C2×C22⋊C4—222no—
600C2×C22⋊C4—442no—
601C2×C22⋊C4—442no—
602C2×C22⋊C4C4×D1111yescharacteristic, complemented
603C2×C22⋊C4C4×D1111yescharacteristic, complemented
604C2×C22⋊C4C22×D1112yes—
605C2×C22⋊C4C22×D1112yes—
606C2×C22⋊C4C22×D1111yescharacteristic
607C2×C22⋊C4C22×D1111yescharacteristic
608C2×C42—111no—
609C2×C42—222no—
610#99—224no—
611#99—442no—
612#95—222no—
613#95—222no—
614C2×C11—22no—
615C2×C11—22no—
616C2×C11—21no—
617C2×C11—21no—
618C2×C11—22no—
619C2×C11—41no—
620C2×C11—42no—
621C2×C11#233911yescharacteristic
622C2×C11C22×#9911yescharacteristic
623C2×C11#288311yescharacteristic
624D11—22no—
625D11—41no—
626D11—42no—
627D11—81no—
628C24—22no—
629C24—21no—
630C24—21no—
631C24—42no—
632C24—81no—
633C24—111no—
634C24—112no—
635C24—111no—
636C24—112no—
637C24—111no—
638C24—222no—
639C24—221no—
640C24—221no—
641C24—442no—
642C24—881no—
643C24C2×C4×D1111yescharacteristic
644C24C2×C4×D1111yescharacteristic
645C24D4×D1112yes—
646C24D4×D1112yes—
647C24C23×D1111yescharacteristic
648#41—444no—
649#41—444no—
650#41—444no—
651#41—444no—
652C2×Q8—221no—
653C2×Q8—221no—
654C2×Q8—442no—
655C2×D4—111no—
656C2×D4—111no—
657C2×D4—111no—
658C2×D4—111no—
659C2×D4—112no—
660C2×D4—112no—
661C2×D4—112no—
662C2×D4—112no—
663C2×D4—112no—
664C2×D4—112no—
665C2×D4—221no—
666C2×D4—221no—
667C2×D4—222no—
668C2×D4—228no—
669C2×D4—224no—
670C2×D4—221no—
671C2×D4—221no—
672C2×D4—222no—
673C2×D4—222no—
674C2×D4—221no—
675C2×D4—221no—
676C2×D4—222no—
677C2×D4—442no—
678C2×D4—444no—
679C2×D4—442no—
680C2×D4—444no—
681C2×D4—442no—
682C2×D4—444no—
683C2×D4—442no—
684C2×D4—442no—
685C2×D4—881no—
686C2×D4—881no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—42no—
694C22×C4—81no—
695C22×C4—111no—
696C22×C4—112no—
697C22×C4—111no—
698C22×C4—112no—
699C22×C4—111no—
700C22×C4—111no—
701C22×C4—111no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—222no—
709C22×C4—222no—
710C22×C4—442no—
711C22×C4—444no—
712C22×C4—442no—
713C22×C4—444no—
714C22×C4—442no—
715C22×C4—444no—
716C22×C4—444no—
717C22×C4—882no—
718C22×C4—881no—
719C22×C4—882no—
720C22×C4C2×C4×D1111yescharacteristic
721C22×C4C2×C4×D1111yescharacteristic
722C22×C4C2×C4×D1111yescharacteristic
723C22×C4C2×C4×D1111yescharacteristic
724C4⋊C4—221no—
725C4⋊C4—221no—
726C4⋊C4—222no—
727C4⋊C4—222no—
728C4⋊C4—222no—
729C4⋊C4—444no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—44no—
739C22⋊C4—82no—
740C22⋊C4—114no—
741C22⋊C4—222no—
742C22⋊C4—222no—
743C22⋊C4—222no—
744C22⋊C4—221no—
745C22⋊C4—221no—
746C22⋊C4—222no—
747C22⋊C4—221no—
748C22⋊C4—221no—
749C22⋊C4—222no—
750C22⋊C4—222no—
751C22⋊C4—222no—
752C22⋊C4—222no—
753C22⋊C4—222no—
754C22⋊C4—444no—
755C22⋊C4—444no—
756C22⋊C4—444no—
757C22⋊C4—882no—
758C42—221no—
759C42—221no—
760C42—444no—
761C11#2247611yescharacteristic, complemented, Sylow
762C23—21no—
763C23—21no—
764C23—24no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—41no—
773C23—41no—
774C23—42no—
775C23—41no—
776C23—42no—
777C23—41no—
778C23—42no—
779C23—41no—
780C23—84no—
781C23—82no—
782C23—82no—
783C23—111no—
784C23—112no—
785C23—111no—
786C23—224no—
787C23—222no—
788C23—221no—
789C23—221no—
790C23—222no—
791C23—222no—
792C23—221no—
793C23—221no—
794C23—222no—
795C23—222no—
796C23—221no—
797C23—221no—
798C23—221no—
799C23—442no—
800C23—441no—
801C23—442no—
802C23—442no—
803C23—441no—
804C23—441no—
805C23—441no—
806C23—441no—
807C23—884no—
808C23—882no—
809C23—882no—
810C23C22⋊C4×D1112yes—
811C23C22⋊C4×D1111yescharacteristic
812C23C22⋊C4×D1111yescharacteristic
813C23C22×C4×D1111yescharacteristic
814C23C2×D4×D1112yes—
815C23#41×D1112yes—
816C23#6704211yescharacteristic
817C23#6704311yescharacteristic
818Q8—442no—
819Q8—442no—
820D4—114no—
821D4—222no—
822D4—224no—
823D4—222no—
824D4—224no—
825D4—222no—
826D4—224no—
827D4—442no—
828D4—442no—
829D4—442no—
830D4—442no—
831D4—442no—
832D4—442no—
833D4—442no—
834D4—442no—
835D4—442no—
836D4—882no—
837D4—882no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—111no—
857C2×C4—111no—
858C2×C4—112no—
859C2×C4—224no—
860C2×C4—222no—
861C2×C4—221no—
862C2×C4—221no—
863C2×C4—221no—
864C2×C4—221no—
865C2×C4—221no—
866C2×C4—224no—
867C2×C4—442no—
868C2×C4—442no—
869C2×C4—442no—
870C2×C4—442no—
871C2×C4—442no—
872C2×C4—441no—
873C2×C4—442no—
874C2×C4—442no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—442no—
878C2×C4—442no—
879C2×C4—442no—
880C2×C4—881no—
881C2×C4—881no—
882C2×C4—888no—
883C2×C4—888no—
884C22—22no—
885C22—21no—
886C22—21no—
887C22—22no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—22no—
892C22—21no—
893C22—22no—
894C22—21no—
895C22—22no—
896C22—42no—
897C22—41no—
898C22—41no—
899C22—44no—
900C22—44no—
901C22—42no—
902C22—42no—
903C22—82no—
904C22—82no—
905C22—81no—
906C22—81no—
907C22—112no—
908C22—221no—
909C22—221no—
910C22—221no—
911C22—222no—
912C22—222no—
913C22—221no—
914C22—221no—
915C22—222no—
916C22—444no—
917C22—444no—
918C22—442no—
919C22—442no—
920C22—441no—
921C22—441no—
922C22—441no—
923C22—882no—
924C22—882no—
925C22—881no—
926C22—881no—
927C22—881no—
928C22—881no—
929C22D11×#9912yes—
930C22C2×C22⋊C4×D1111yescharacteristic
931C22#1062305311yescharacteristic
932C22#1062305411yescharacteristic
933C22#1062318512yes—
934C22#1062318612yes—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—82no—
940C4—82no—
941C4—112no—
942C4—221no—
943C4—222no—
944C4—444no—
945C4—441no—
946C4—441no—
947C4—441no—
948C4—882no—
949C2—22no—
950C2—22no—
951C2—22no—
952C2—21no—
953C2—21no—
954C2—41no—
955C2—42no—
956C2—222no—
957C2—441no—
958C2—442no—
959C2—881no—
960C2#1307144011yescharacteristic
961C2C2×D11×#9911yescharacteristic
962C2#1307707411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#1819C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623021C2
cosocleC24×C11C24
hypercenter#1819D11
hypocenterC11#22476
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
2. #13071432C2semidirect
3. #13069599C2semidirect
4. #13069068C2semidirect
5. #13069067C2semidirect
6. #13068689C2semidirect
7. #13068603C2semidirect
8. #13068403C2semidirect
9. C2×#10622164C2semidirect
10. D11×#342C2semidirect
11. C11×#1819C2semidirect
13. C22×#4339C4semidirect
17. C2×#66983C4semidirect
18. C2×#66982C4semidirect
19. C2×C4×C22⋊D11C4semidirect
20. C2×#66938C4semidirect
25. C2×#66937C4semidirect
26. C2×#66937C4semidirect
27. C2×#66936C4semidirect
53. C23×C4×C11C2×C4semidirect
54. C23×C4×C11C2×C4semidirect
60. C22×C22⋊D11C2×C4semidirect
61. C22×C22⋊D11C2×C4semidirect
74. C22×D44C2×C4semidirect
75. C22×D44C2×C4semidirect
77. C22×C4×D11C2×C4semidirect
78. C22×C4×D11C2×C4semidirect
79. C22×C4×D11C2×C4semidirect
80. C22×Dic22C2×C4semidirect
85. C2×C11×C22⋊C4C2×C4semidirect
86. C2×C11×C22⋊C4C2×C4semidirect
96. C2×C22⋊Dic11C2×C4semidirect
97. C2×C22⋊Dic11C2×C4semidirect
112. C2×(C2×D11)⋊C4C2×C4semidirect
113. C2×(C2×D11)⋊C4C2×C4semidirect
114. C2×(C2×D11)⋊C4C2×C4semidirect
115. C2×(C2×D11)⋊C4C2×C4semidirect
116. C2×(C2×D11)⋊C4C2×C4semidirect
117. C2×C4⋊Dic11C2×C4semidirect
119. C2×Dic11⋊C4C2×C4semidirect
120. C2×Dic11⋊C4C2×C4semidirect
121. C2×Dic11⋊C4C2×C4semidirect
123. C2×C4×Dic11C2×C4semidirect
262. C22⋊Dic11#41semidirect
287. #1819D11semidirect
380. C22⋊D11#99semidirect
546. C23×C4C4×D11semidirect
547. C23×C4C4×D11semidirect
602. C2×C22⋊C4C4×D11semidirect
603. C2×C22⋊C4C4×D11semidirect
761. C11#22476semidirect

Maximal subgroups

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

subgroupindex
C2×#106230212
#130714322
#130695992
#130690682
#130690672
#130686892
#130686032
#130684032
C2×#106221642
D11×#3422
C11×#18192
#2247611