Finite Group Databasebeta

← #14681120

Subgroups — #14681120

Order 2816.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic
2C2×#10622259C211yesmaximal, characteristic, complemented
3C2×#10622585C211yesmaximal, characteristic, complemented
4C2×#10622591C211yesmaximal, characteristic, complemented
5#13066886C211yesmaximal, characteristic, complemented
6#13066868C211yesmaximal, characteristic, complemented
7#13066866C211yesmaximal, characteristic, complemented
8#13066866C211yesmaximal, characteristic, complemented
9#13066859C211yesmaximal, characteristic
10#13066859C211yesmaximal, characteristic
11#13066853C211yesmaximal, characteristic
12#13066853C211yesmaximal, characteristic
13#13066850C211yesmaximal, characteristic, complemented
14#13066839C211yesmaximal, characteristic
15C2×C11×#380C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C2×#66977—24no—
28C2×#66977—24no—
29C2×#66977C418yescomplemented
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C11×#380—24no—
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622591—24no—
56#10622585—24no—
57#10622259—24no—
58C25×C11C2311yescharacteristic
59C23×C4×C11—22no—
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11—41no—
64C23×C4×C11—41no—
65C23×C4×C11C2×C414yes—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C22×Dic22—22no—
81C22×Dic22—22no—
82C22×Dic22—22no—
83C22×Dic22—22no—
84C22×Dic22—41no—
85C22×Dic22—41no—
86C22×Dic22C2×C414yes—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—41no—
92C2×C11×C4⋊C4—41no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—41no—
98C2×C11×C22⋊C4—41no—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—41no—
105C2×C22⋊Dic11—41no—
106C2×C22⋊Dic11—41no—
107C2×C22⋊Dic11—41no—
108C2×C22⋊Dic11C2×C414yes—
109C2×C22⋊Dic11C2×C414yes—
110C2×C22⋊Dic11Q814yescomplemented
111C2×C4⋊Dic11—22no—
112C2×C4⋊Dic11—22no—
113C2×C4⋊Dic11C2×C414yes—
114#66977—232no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—41no—
121C2×Dic11⋊C4—41no—
122C2×Dic11⋊C4—41no—
123C2×Dic11⋊C4C2×C414yes—
124C2×Dic11⋊C4C2×C414yes—
125C2×Dic11⋊C4D414yes—
126C2×Dic11⋊C4D414yes—
127C2×C4×Dic11—22no—
128C2×C4×Dic11—22no—
129C2×C4×Dic11—22no—
130C2×C4×Dic11—41no—
131C2×C4×Dic11—41no—
132C2×C4×Dic11—41no—
133C11×#95—22no—
134C11×#95D414yes—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—41no—
146C11⋊#95—41no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151#14362—111nomaximal, Sylow
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11C22×C412yes—
165C24×C11C2×Q812yes—
166C24×C11#4112yes—
167C24×C11C2411yescharacteristic
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—28no—
189C22×C4×C11—28no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—44no—
205C22×C4×C11—44no—
206C22×C4×C11—44no—
207C22×C4×C11—44no—
208C22×C4×C11—44no—
209C22×C4×C11C22×C412yes—
210C22×C4×C11C22×C412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2×D412yes—
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2×D412yes—
216C22×C4×C11#4112yes—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11C22×C412yes—
264C22×Dic11C22×C412yes—
265C22×Dic11C22×C412yes—
266C22×Dic11C22×C412yes—
267C22×Dic11C2×D412yes—
268C22×Dic11C2×D412yes—
269C22×Dic11C2×D412yes—
270C22×Dic11C2×D412yes—
271C22×Dic11C2×Q812yes—
272C22×Dic11C2×Q812yes—
273C2×Dic22—28no—
274C2×Dic22—28no—
275C2×Dic22—44no—
276C2×Dic22—44no—
277C2×Dic22—44no—
278C2×Dic22—44no—
279C2×Dic22—44no—
280C11×C4⋊C4—44no—
281C11×C4⋊C4—44no—
282C11×C22⋊C4—44no—
283C11×C22⋊C4—44no—
284C22⋊Dic11—28no—
285C22⋊Dic11—28no—
286C22⋊Dic11—44no—
287C22⋊Dic11—44no—
288C4⋊Dic11—28no—
289Dic11⋊C4—28no—
290Dic11⋊C4—44no—
291Dic11⋊C4—44no—
292Dic11⋊C4C22⋊C4116yescomplemented
293C4×Dic11—44no—
294C4×Dic11—44no—
295C22×C22⋊Q8—111no—
296C2×#391—111no—
297C2×#389—111no—
298C2×#387—111no—
299C2×#380D1111yescharacteristic
300#1446—111no—
301#1441—111no—
302#1441—111no—
303#1441—111no—
304#1439—111no—
305#1439—111no—
306#1437—111no—
307#1437—111no—
308#1436—111no—
309C22⋊#95—111no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11—41no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11C4×Q814yes—
345C23×C11C23×C411yescharacteristic
346C23×C11C22×D411yescharacteristic
347C23×C11C22×D411yescharacteristic
348C23×C11C22×D411yescharacteristic
349C23×C11C22×Q811yescharacteristic
350C23×C11C2×#4111yescharacteristic
351C23×C11C2×#4111yescharacteristic
352C23×C11H(5,𝔽2)11yescharacteristic
353C23×C11H(5,𝔽2)11yescharacteristic
354C23×C11H(5,𝔽2)11yescharacteristic
355C23×C11H(5,𝔽2)11yescharacteristic
356C23×C112−1+411yescharacteristic
357C23×C112−1+411yescharacteristic
358C23×C112−1+411yescharacteristic
359C23×C112−1+411yescharacteristic
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—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—416no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11C2×C22⋊C414yes—
402C2×C4×C11C4×D414yes—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11—41no—
450C2×Dic11—41no—
451C2×Dic11—41no—
452C2×Dic11—41no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11C2×C22⋊C414yes—
458C2×Dic11C2×C22⋊C414yes—
459Dic22—416no—
460C23×Q8—111no—
461C24×C4C2×D1111yescharacteristic
462C2×C22⋊Q8—118no—
463C2×C22⋊Q8—224no—
464C2×C22⋊Q8—224no—
465C22×C4⋊C4—111no—
466C22×C4⋊C4—111no—
467C22×C4⋊C4—111no—
468C22×C4⋊C4—111no—
469C22×C4⋊C4—111no—
470C22×C4⋊C4C2×D1111yescharacteristic
471C22×C4⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4—111no—
473C22×C22⋊C4—111no—
474C22×C22⋊C4—111no—
475C22×C22⋊C4—111no—
476C22×C22⋊C4C2×D1111yescharacteristic
477C22×C22⋊C4C2×D1111yescharacteristic
478C22×C42—111no—
479C22×C42—111no—
480#391—224no—
481#389—224no—
482#387—224no—
483#380—24no—
484C2×#95—111no—
485C2×#95—111no—
486C2×#95—111no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95—111no—
493C2×#95—111no—
494C2×#95—111no—
495C2×#95—111no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95C2×D1111yescharacteristic
501C2×#95C2×D1111yescharacteristic
502C22×C11—24no—
503C22×C11—24no—
504C22×C11—24no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—42no—
517C22×C11C22×C22⋊C411yescharacteristic
518C22×C11C2×C4×D411yescharacteristic
519C22×C11C2×C4×Q811yescharacteristic
520C22×C11#51811yescharacteristic
521C22×C11#51911yescharacteristic
522C22×C11#52011yescharacteristic
523C22×C11#52011yescharacteristic
524C22×C11#53511yescharacteristic
525C22×C11#53611yescharacteristic
526C22×C11#53611yescharacteristic
527C22×C11#53711yescharacteristic
528C22×C11#53711yescharacteristic
529C22×C11#53711yescharacteristic
530C22×C11#53811yescharacteristic
531C22×C11#53911yescharacteristic
532C22×C11#54111yescharacteristic
533C22×C11#54211yescharacteristic
534C22×C11#54311yescharacteristic
535C22×C11#54411yescharacteristic
536C22×C11D4211yescharacteristic
537C22×C11D4211yescharacteristic
538C22×C11#54611yescharacteristic
539C22×C11#54611yescharacteristic
540C22×C11#54611yescharacteristic
541C22×C11#54811yescharacteristic
542C22×C11#54811yescharacteristic
543C22×C11D4×Q811yescharacteristic
544C22×C11D4×Q811yescharacteristic
545C22×C11D4×Q811yescharacteristic
546C22×C11#55211yescharacteristic
547C22×C11#55411yescharacteristic
548C22×C11#56211yescharacteristic
549C22×C11#56211yescharacteristic
550C22×C11#56311yescharacteristic
551C22×C11#56311yescharacteristic
552C4×C11—24no—
553C4×C11—24no—
554C4×C11—42no—
555C4×C11—42no—
556C4×C11—81no—
557C4×C11—81no—
558Dic11—24no—
559Dic11—24no—
560Dic11—42no—
561Dic11—42no—
562Dic11—42no—
563Dic11—42no—
564Dic11—81no—
565Dic11—81no—
566C25C22×D1111yescharacteristic
567C22×Q8—114no—
568C22×Q8—222no—
569C22×Q8—222no—
570C22×Q8—222no—
571C22×Q8—222no—
572C22×Q8—441no—
573C22×Q8—441no—
574C23×C4—22no—
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—41no—
579C23×C4—41no—
580C23×C4—111no—
581C23×C4—111no—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4C4×D1114yes—
589C23×C4C22×D1111yescharacteristic
590C23×C4C22×D1111yescharacteristic
591C23×C4C22×D1111yescharacteristic
592C23×C4C22×D1111yescharacteristic
593C23×C4C22×D1111yescharacteristic
594C23×C4C22×D1111yescharacteristic
595C22⋊Q8—2232no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—114no—
603C2×C4⋊C4—114no—
604C2×C4⋊C4—114no—
605C2×C4⋊C4—114no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—222no—
608C2×C4⋊C4—222no—
609C2×C4⋊C4—222no—
610C2×C4⋊C4—222no—
611C2×C4⋊C4—222no—
612C2×C4⋊C4—222no—
613C2×C4⋊C4—222no—
614C2×C4⋊C4—441no—
615C2×C4⋊C4—441no—
616C2×C4⋊C4—441no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—114no—
624C2×C22⋊C4—114no—
625C2×C22⋊C4—114no—
626C2×C22⋊C4—222no—
627C2×C22⋊C4—222no—
628C2×C22⋊C4—222no—
629C2×C22⋊C4—222no—
630C2×C22⋊C4—222no—
631C2×C22⋊C4—441no—
632C2×C22⋊C4—441no—
633C2×C22⋊C4—441no—
634C2×C22⋊C4—441no—
635C2×C42—222no—
636C2×C42—222no—
637C2×C42—222no—
638C2×C42—441no—
639C2×C42—441no—
640C2×C42—441no—
641#95—22no—
642#95—222no—
643#95—222no—
644#95—222no—
645#95—222no—
646#95—222no—
647#95—222no—
648#95—222no—
649#95—222no—
650#95—222no—
651#95—222no—
652#95—441no—
653#95—441no—
654#95—441no—
655#95—441no—
656#95—441no—
657#95—441no—
658#95C22⋊D1114yes—
659C2×C11—44no—
660C2×C11#231111yescharacteristic
661C2×C11#232311yescharacteristic
662C2×C11#232911yescharacteristic
663C2×C11D4×C22⋊C411yescharacteristic
664C2×C11Q8×C22⋊C411yescharacteristic
665C2×C11#236011yescharacteristic
666C2×C11#237811yescharacteristic
667C2×C11#267611yescharacteristic
668C2×C11#267711yescharacteristic
669C2×C11#268111yescharacteristic
670C2×C11#268311yescharacteristic
671C2×C11#269011yescharacteristic
672C2×C11#269211yescharacteristic
673C2×C11#270211yescharacteristic
674C2×C11#270411yescharacteristic
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24C2×C4×D1112yes—
688C24#434112yes—
689C24Q8×D1112yes—
690C24C23×D1111yescharacteristic
691C2×Q8—228no—
692C2×Q8—228no—
693C2×Q8—444no—
694C2×Q8—444no—
695C2×Q8—444no—
696C2×Q8—444no—
697C2×Q8—444no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—112no—
743C22×C4—112no—
744C22×C4—112no—
745C22×C4—112no—
746C22×C4—112no—
747C22×C4—112no—
748C22×C4—112no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—221no—
761C22×C4—221no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4—221no—
785C22×C4—221no—
786C22×C4—221no—
787C22×C4—221no—
788C22×C4—221no—
789C22×C4—221no—
790C22×C4—221no—
791C22×C4—221no—
792C22×C4—221no—
793C22×C4—221no—
794C22×C4—221no—
795C22×C4C2×C4×D1112yes—
796C22×C4C2×C4×D1112yes—
797C22×C4#433912yes—
798C22×C4D4×D1112yes—
799C22×C4D4×D1112yes—
800C22×C4C2×C22⋊D1112yes—
801C22×C4C2×C22⋊D1112yes—
802C22×C4C2×C22⋊D1112yes—
803C4⋊C4—44no—
804C4⋊C4—44no—
805C4⋊C4—1116no—
806C4⋊C4—228no—
807C4⋊C4—228no—
808C4⋊C4—444no—
809C4⋊C4—444no—
810C22⋊C4—44no—
811C22⋊C4—44no—
812C22⋊C4—228no—
813C22⋊C4—228no—
814C22⋊C4—444no—
815C22⋊C4—444no—
816C42—444no—
817C42—444no—
818C11#1436211yescharacteristic, complemented, Sylow
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23#6694014yes—
854C23C22×C4×D1111yescharacteristic
855C23C2×#433911yescharacteristic
856C23C2×D4×D1111yescharacteristic
857C23C2×D4×D1111yescharacteristic
858C23C2×#434111yescharacteristic
859C23#6703711yescharacteristic
860C23#6703711yescharacteristic
861C23#6703711yescharacteristic
862C23C2×Q8×D1111yescharacteristic
863C23#6704011yescharacteristic
864C23#6704211yescharacteristic
865C23#6704311yescharacteristic
866C23#6704311yescharacteristic
867C23#6704311yescharacteristic
868C23C22×C22⋊D1111yescharacteristic
869Q8—4416no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—416no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—114no—
912C2×C4—114no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—441no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—441no—
945C2×C4—441no—
946C2×C4—441no—
947C2×C4—441no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—441no—
951C2×C4—441no—
952C2×C4—441no—
953C2×C4—441no—
954C2×C4—441no—
955C2×C4—441no—
956C2×C4—441no—
957C2×C4—441no—
958C2×C4—441no—
959C2×C4—441no—
960C2×C4—441no—
961C2×C4—441no—
962C2×C4—441no—
963C2×C4—441no—
964C2×C4—441no—
965C2×C4—441no—
966C2×C4—441no—
967C2×C4C22⋊C4×D1114yes—
968C2×C4C4×C22⋊D1114yes—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22C2×C22⋊C4×D1111yescharacteristic
985C22#1062301711yescharacteristic
986C22#1062302111yescharacteristic
987C22#1062302111yescharacteristic
988C22C2×#6694011yescharacteristic
989C22#1062303511yescharacteristic
990C22#1062304211yescharacteristic
991C22#1062304411yescharacteristic
992C22#1062304711yescharacteristic
993C22#1062304911yescharacteristic
994C22#1062305411yescharacteristic
995C22#1062306511yescharacteristic
996C22#1062312911yescharacteristic
997C22#1062312911yescharacteristic
998C22#1062313311yescharacteristic
999C22#1062313811yescharacteristic
1000C22#1062313911yescharacteristic
1001C22#1062314811yescharacteristic
1002C22#1062315211yescharacteristic
1003C22#1062315211yescharacteristic
1004C22#1062315411yescharacteristic
1005C22#1062315911yescharacteristic
1006C22#1062316011yescharacteristic
1007C22#1062316311yescharacteristic
1008C22#1062316311yescharacteristic
1009C22#1062316511yescharacteristic
1010C22#1062317711yescharacteristic
1011C22#1062317711yescharacteristic
1012C22C2×C4×C22⋊D1111yescharacteristic
1013C22D4×C22⋊D1111yescharacteristic
1014C22D4×C22⋊D1111yescharacteristic
1015C22#1062333711yescharacteristic
1016C22Q8×C22⋊D1111yescharacteristic
1017C22#1062335611yescharacteristic
1018C22#1062336411yescharacteristic
1019C4—24no—
1020C4—24no—
1021C4—42no—
1022C4—42no—
1023C4—81no—
1024C4—81no—
1025C4—224no—
1026C4—224no—
1027C4—442no—
1028C4—442no—
1029C4—442no—
1030C4—442no—
1031C4—881no—
1032C4—881no—
1033C2—44no—
1034C2#1307120511yescharacteristic
1035C2#1307129811yescharacteristic
1036C2#1307134611yescharacteristic
1037C2C22⋊C4×C22⋊D1111yescharacteristic
1038C2#1307144811yescharacteristic
1039C2#1307162111yescharacteristic
1040C2#1307177911yescharacteristic
1041C2#1307491711yescharacteristic
1042C2#1307492711yescharacteristic
1043C2#1307496211yescharacteristic
1044C2#1307498611yescharacteristic
1045C2#1307508211yescharacteristic
1046C2#1307511211yescharacteristic
1047C2#1307524411yescharacteristic
1048C2#1307527411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11#14362
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#10622259C2semidirect
3. C2×#10622585C2semidirect
4. C2×#10622591C2semidirect
5. #13066886C2semidirect
6. #13066868C2semidirect
7. #13066866C2semidirect
8. #13066866C2semidirect
13. #13066850C2semidirect
29. C2×#66977C4semidirect
110. C2×C22⋊Dic11Q8semidirect
292. Dic11⋊C4C22⋊C4semidirect
818. C11#14362semidirect

Maximal subgroups

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

subgroupindex
C22×#669772
C2×#106222592
C2×#106225852
C2×#106225912
#130668862
#130668682
#130668662
#130668592
#130668532
#130668502
#130668392
C2×C11×#3802
#1436211