Finite Group Databasebeta

← #14681121

Subgroups — #14681121

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×#66931C211yesmaximal, characteristic
2C2×#10622259C211yesmaximal, characteristic, complemented
3C2×#10622541C211yesmaximal, characteristic, complemented
4C2×#10622267C211yesmaximal, characteristic, complemented
5C2×#10622555C211yesmaximal, characteristic
6#13066886C211yesmaximal, characteristic, complemented
7#13066870C211yesmaximal, characteristic, complemented
8#13066867C211yesmaximal, characteristic, complemented
9#13066867C211yesmaximal, characteristic, complemented
10#13066861C211yesmaximal, characteristic
11#13066859C211yesmaximal, characteristic
12#13066853C211yesmaximal, characteristic
13#13066849C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic
15C11×#1437C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C2×#66931—24no—
34C2×#66931—24no—
35C2×#66931C418yescomplemented
36C2×C11×#95C2211yescharacteristic
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
54#10622555—24no—
55#10622541—24no—
56#10622267—24no—
57#10622259—24no—
58C25×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—41no—
70C23×Dic11—41no—
71C23×Dic11C2×C414yes—
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×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—41no—
92C2×C11×C22⋊C4—41no—
93C2×C11×C22⋊C4—41no—
94C2×C11×C22⋊C4C2×C414yes—
95C2×C11×C22⋊C4Q814yescomplemented
96C2×C42×C11—22no—
97C2×C42×C11—41no—
98C2×C42×C11—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⋊Dic11C2×C414yes—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—41no—
110C2×C4⋊Dic11—41no—
111C2×C4⋊Dic11C2×C414yes—
112C2×C4⋊Dic11D414yes—
113C2×C4⋊Dic11D414yes—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—22no—
121C2×Dic11⋊C4—22no—
122C2×Dic11⋊C4—22no—
123C2×Dic11⋊C4—22no—
124C2×Dic11⋊C4—41no—
125C2×Dic11⋊C4—41no—
126C2×Dic11⋊C4—41no—
127C2×Dic11⋊C4C2×C414yes—
128C2×Dic11⋊C4C2×C414yes—
129C2×C4×Dic11—22no—
130C2×C4×Dic11—22no—
131C2×C4×Dic11—41no—
132#66931—232no—
133C11×#95—22no—
134C11×#95—22no—
135C11×#95—41no—
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⋊#95D414yes—
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—21no—
189C22×C4×C11—21no—
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×C11C22×C412yes—
204C22×C4×C11C22×C412yes—
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2×D412yes—
208C22×C4×C11C2×Q812yes—
209C22×C4×C11C2×Q812yes—
210C22×Dic11—28no—
211C22×Dic11—28no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
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—44no—
258C22×Dic11—44no—
259C22×Dic11—44no—
260C22×Dic11—44no—
261C22×Dic11—44no—
262C22×Dic11C22×C412yes—
263C22×Dic11C22×C412yes—
264C22×Dic11C22×C412yes—
265C22×Dic11C22×C412yes—
266C22×Dic11C2×D412yes—
267C22×Dic11C2×D412yes—
268C22×Dic11C2×D412yes—
269C22×Dic11C2×D412yes—
270C22×Dic11C2×D412yes—
271C22×Dic11C2×D412yes—
272C22×Dic11#4112yes—
273C2×Dic22—28no—
274C2×Dic22—28no—
275C2×Dic22—44no—
276C2×Dic22—44no—
277C2×Dic22—44no—
278C2×Dic22—44no—
279C2×Dic22—44no—
280C11×C22⋊C4—28no—
281C11×C22⋊C4—44no—
282C11×C22⋊C4—44no—
283C42×C11—44no—
284C22⋊Dic11—28no—
285C22⋊Dic11—44no—
286C22⋊Dic11—44no—
287C4⋊Dic11—44no—
288C4⋊Dic11C22⋊C4116yescomplemented
289Dic11⋊C4—28no—
290Dic11⋊C4—28no—
291Dic11⋊C4—44no—
292Dic11⋊C4—44no—
293Dic11⋊C4—44no—
294C4×Dic11—44no—
295C22×C22⋊Q8—111no—
296C2×#391—111no—
297C2×#389—111no—
298C2×#387—111no—
299C2×#380—111no—
300#1446—111no—
301#1441—111no—
302#1441—111no—
303#1441—111no—
304#1439—111no—
305#1439—111no—
306#1437—111no—
307#1437D1111yescharacteristic
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—41no—
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×Dic11—22no—
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—416no—
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×Dic11C2×C22⋊C414yes—
457C2×Dic11C2×C22⋊C414yes—
458C2×Dic11C4×D414yes—
459Dic22—416no—
460C23×Q8—111no—
461C24×C4—111no—
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⋊C4—111no—
471C22×C4⋊C4—111no—
472C22×C22⋊C4—111no—
473C22×C22⋊C4—111no—
474C22×C22⋊C4—111no—
475C22×C22⋊C4C2×D1111yescharacteristic
476C22×C22⋊C4C2×D1111yescharacteristic
477C22×C22⋊C4C2×D1111yescharacteristic
478C22×C42—111no—
479C22×C42C2×D1111yescharacteristic
480#391—224no—
481#389—224no—
482#387—224no—
483#380—224no—
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×#95C2×D1111yescharacteristic
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—42no—
554C4×C11—42no—
555C4×C11—42no—
556C4×C11—42no—
557C4×C11—81no—
558Dic11—24no—
559Dic11—24no—
560Dic11—24no—
561Dic11—42no—
562Dic11—42no—
563Dic11—81no—
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—111no—
575C23×C4—111no—
576C23×C4—111no—
577C23×C4—111no—
578C23×C4—111no—
579C23×C4—114no—
580C23×C4—111no—
581C23×C4—111no—
582C23×C4—111no—
583C23×C4—222no—
584C23×C4—222no—
585C23×C4—222no—
586C23×C4—222no—
587C23×C4—441no—
588C23×C4—441no—
589C23×C4C22×D1111yescharacteristic
590C23×C4C22×D1111yescharacteristic
591C23×C4C22×D1111yescharacteristic
592C23×C4C22×D1111yescharacteristic
593C23×C4C22×D1111yescharacteristic
594C23×C4C22×D1111yescharacteristic
595C22⋊Q8—2232no—
596C2×C4⋊C4—114no—
597C2×C4⋊C4—114no—
598C2×C4⋊C4—114no—
599C2×C4⋊C4—114no—
600C2×C4⋊C4—114no—
601C2×C4⋊C4—222no—
602C2×C4⋊C4—222no—
603C2×C4⋊C4—222no—
604C2×C4⋊C4—222no—
605C2×C4⋊C4—222no—
606C2×C4⋊C4—222no—
607C2×C4⋊C4—222no—
608C2×C4⋊C4—222no—
609C2×C4⋊C4—222no—
610C2×C4⋊C4—222no—
611C2×C4⋊C4—222no—
612C2×C4⋊C4—441no—
613C2×C4⋊C4—441no—
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—41no—
624C2×C22⋊C4—114no—
625C2×C22⋊C4—222no—
626C2×C22⋊C4—222no—
627C2×C22⋊C4—222no—
628C2×C22⋊C4—222no—
629C2×C22⋊C4—222no—
630C2×C22⋊C4—441no—
631C2×C22⋊C4—441no—
632C2×C22⋊C4—441no—
633C2×C22⋊C4Dic2214yescomplemented
634C2×C22⋊C4C4×D1114yes—
635C2×C42—22no—
636C2×C42—41no—
637C2×C42—41no—
638C2×C42—222no—
639C2×C42—222no—
640C2×C42—441no—
641#95—22no—
642#95—22no—
643#95—41no—
644#95—114no—
645#95—222no—
646#95—222no—
647#95—222no—
648#95—222no—
649#95—222no—
650#95—222no—
651#95—222no—
652#95—222no—
653#95—222no—
654#95—441no—
655#95—441no—
656#95—441no—
657#95—441no—
658#95—441no—
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×Dic2212yes—
688C24C2×C4×D1112yes—
689C24#433912yes—
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—21no—
719C22×C4—21no—
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—112no—
734C22×C4—112no—
735C22×C4—112no—
736C22×C4—112no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—112no—
743C22×C4—112no—
744C22×C4—228no—
745C22×C4—228no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
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—444no—
792C22×C4—444no—
793C22×C4—444no—
794C22×C4—444no—
795C22×C4—444no—
796C22×C4C2×Dic2212yes—
797C22×C4C2×Dic2212yes—
798C22×C4C2×C4×D1112yes—
799C22×C4C2×C4×D1112yes—
800C22×C4D4×D1112yes—
801C22×C4D4×D1112yes—
802C22×C4D4×D1112yes—
803C4⋊C4—1116no—
804C4⋊C4—228no—
805C4⋊C4—228no—
806C4⋊C4—444no—
807C4⋊C4—444no—
808C4⋊C4—444no—
809C4⋊C4—444no—
810C22⋊C4—28no—
811C22⋊C4—44no—
812C22⋊C4—44no—
813C22⋊C4—228no—
814C22⋊C4—444no—
815C22⋊C4—444no—
816C42—44no—
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—
853C23C4×Dic2214yes—
854C23C22×Dic2211yescharacteristic
855C23C22×C4×D1111yescharacteristic
856C23C2×#433911yescharacteristic
857C23C2×D4×D1111yescharacteristic
858C23C2×D4×D1111yescharacteristic
859C23C2×D4×D1111yescharacteristic
860C23#6703711yescharacteristic
861C23#6703711yescharacteristic
862C23#6703711yescharacteristic
863C23#41×D1111yescharacteristic
864C23#6704211yescharacteristic
865C23#6704311yescharacteristic
866C23#6704311yescharacteristic
867C23#6704311yescharacteristic
868C23#6704311yescharacteristic
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—41no—
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—114no—
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—222no—
938C2×C4—4416no—
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×C4—441no—
968C2×C4C22⋊C4×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×C4×Dic2211yescharacteristic
985C22#1062301411yescharacteristic
986C22C2×C22⋊C4×D1111yescharacteristic
987C22#1062302111yescharacteristic
988C22#1062304711yescharacteristic
989C22#1062305011yescharacteristic
990C22#1062306211yescharacteristic
991C22D4×Dic2211yescharacteristic
992C22D4×Dic2211yescharacteristic
993C22D4×Dic2211yescharacteristic
994C22#1062307011yescharacteristic
995C22C4×D4×D1111yescharacteristic
996C22#1062307611yescharacteristic
997C22#1062307711yescharacteristic
998C22#1062307711yescharacteristic
999C22#1062308311yescharacteristic
1000C22#1062308311yescharacteristic
1001C22#1062309111yescharacteristic
1002C22#1062309511yescharacteristic
1003C22#1062312311yescharacteristic
1004C22#1062312811yescharacteristic
1005C22#1062312811yescharacteristic
1006C22#1062312811yescharacteristic
1007C22#1062314011yescharacteristic
1008C22#1062314311yescharacteristic
1009C22#1062315211yescharacteristic
1010C22#1062317911yescharacteristic
1011C22#1062319311yescharacteristic
1012C22#1062319811yescharacteristic
1013C22#1062320311yescharacteristic
1014C22#1062320611yescharacteristic
1015C22#1062320711yescharacteristic
1016C22#1062323211yescharacteristic
1017C22#1062324311yescharacteristic
1018C22#1062324811yescharacteristic
1019C4—24no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—81no—
1025C4—224no—
1026C4—224no—
1027C4—224no—
1028C4—442no—
1029C4—442no—
1030C4—881no—
1031C4—881no—
1032C4—881no—
1033C2—44no—
1034C2#1307120311yescharacteristic
1035C2#1307129111yescharacteristic
1036C2#1307134411yescharacteristic
1037C2#1307143711yescharacteristic
1038C2C22⋊C4×Dic2211yescharacteristic
1039C2#1307162211yescharacteristic
1040C2#1307177611yescharacteristic
1041C2#1307491811yescharacteristic
1042C2#1307492811yescharacteristic
1043C2#1307496511yescharacteristic
1044C2#1307498811yescharacteristic
1045C2#1307508311yescharacteristic
1046C2#1307511311yescharacteristic
1047C2#1307524111yescharacteristic
1048C2#1307527111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1437D11
hypocenterC11#14362
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#10622259C2semidirect
3. C2×#10622541C2semidirect
4. C2×#10622267C2semidirect
6. #13066886C2semidirect
7. #13066870C2semidirect
8. #13066867C2semidirect
9. #13066867C2semidirect
13. #13066849C2semidirect
35. C2×#66931C4semidirect
95. C2×C11×C22⋊C4Q8semidirect
288. C4⋊Dic11C22⋊C4semidirect
633. C2×C22⋊C4Dic22semidirect
818. C11#14362semidirect

Maximal subgroups

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

subgroupindex
C22×#669312
C2×#106222592
C2×#106225412
C2×#106222672
C2×#106225552
#130668862
#130668702
#130668672
#130668612
#130668592
#130668532
#130668492
#130668382
C11×#14372
#1436211