Finite Group Databasebeta

← #14681801

Subgroups — #14681801

Order 2816.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622268C211yesmaximal, characteristic, complemented
2C2×#10622591C211yesmaximal, characteristic, complemented
3C2×#10622823C211yesmaximal, characteristic
4C2×#10622825C211yesmaximal, characteristic
5#13066875C211yesmaximal, characteristic, complemented
6#13066872C211yesmaximal, characteristic, complemented
7#13066870C211yesmaximal, characteristic, complemented
8#13066866C211yesmaximal, characteristic, complemented
9#13066863C211yesmaximal, characteristic
10#13066863C211yesmaximal, characteristic
11#13066853C211yesmaximal, characteristic
12#13066853C211yesmaximal, characteristic
13#13066850C211yesmaximal, characteristic, complemented
14#13066848C211yesmaximal, characteristic, complemented
15C2×C11×#380C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C11×#380—24no—
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34#10622825—24no—
35#10622823C418yescomplemented
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#10622591—24no—
55#10622268—24no—
56C25×C11C2311yescharacteristic
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—22no—
60C23×C4×C11—22no—
61C23×C4×C11—41no—
62C23×C4×C11—41no—
63C23×C4×C11C2×C414yes—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—41no—
83C2×C11×C4⋊C4—41no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—41no—
89C2×C11×C22⋊C4—41no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—41no—
97C2×C22⋊Dic11—41no—
98C2×C22⋊Dic11—41no—
99C2×C22⋊Dic11—41no—
100C2×C22⋊Dic11C2×C414yes—
101C2×C22⋊Dic11C2×C414yes—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—41no—
107C2×C4⋊Dic11—41no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4C2×C414yes—
113C2×Dic11⋊C4C2×C414yes—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—41no—
117C2×C4×Dic11—41no—
118C2×C4×Dic11—41no—
119C2×C4×Dic11—41no—
120C11×#95—22no—
121C11×#95D414yes—
122C11⋊#95—22no—
123C11⋊#95—22no—
124C11⋊#95—22no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—41no—
130C11⋊#95—41no—
131C11⋊#95—41no—
132C11⋊#95—41no—
133C11⋊#95—41no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95C2×C414yes—
138C11⋊#95C2×C414yes—
139C11⋊#95D414yes—
140#14409—111nomaximal, Sylow
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—21no—
145C24×C11—21no—
146C24×C11—21no—
147C24×C11—21no—
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11—21no—
153C24×C11C22×C412yes—
154C24×C11#4112yes—
155C24×C11#4112yes—
156C24×C11C2411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
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—28no—
178C22×C4×C11—28no—
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—44no—
194C22×C4×C11—44no—
195C22×C4×C11—44no—
196C22×C4×C11—44no—
197C22×C4×C11—44no—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C22×C412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2×D412yes—
204C22×C4×C11#4112yes—
205C22×C4×C11#4112yes—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
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×Dic11C22×C412yes—
257C22×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C22×C412yes—
260C22×Dic11C2×D412yes—
261C22×Dic11C2×D412yes—
262C11×C4⋊C4—44no—
263C11×C4⋊C4—44no—
264C11×C22⋊C4—44no—
265C11×C22⋊C4—44no—
266C22⋊Dic11—28no—
267C22⋊Dic11—44no—
268C22⋊Dic11—44no—
269C22⋊Dic11—44no—
270C4⋊Dic11—44no—
271C4⋊Dic11—44no—
272Dic11⋊C4—28no—
273Dic11⋊C4—28no—
274C4×Dic11—44no—
275C4×Dic11—44no—
276C2×#387—111no—
277C2×#387—111no—
278C2×#385—111no—
279C2×#380—111no—
280C2×#380D1111yescharacteristic
281#1442—111no—
282#1442—111no—
283#1441—111no—
284#1441—111no—
285#1440—111no—
286#1440—111no—
287#1437—111no—
288#1437—111no—
289#1436—111no—
290#1436—111no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
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#11714yes—
326C23×C11C23×C411yescharacteristic
327C23×C11C22×D411yescharacteristic
328C23×C11C22×D411yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11C2×#4111yescharacteristic
333C23×C11H(5,𝔽2)11yescharacteristic
334C23×C11H(5,𝔽2)11yescharacteristic
335C23×C11H(5,𝔽2)11yescharacteristic
336C23×C11H(5,𝔽2)11yescharacteristic
337C23×C112−1+411yescharacteristic
338C23×C112−1+411yescharacteristic
339C23×C112−1+411yescharacteristic
340C23×C112−1+411yescharacteristic
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—416no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11C4×D414yes—
383C2×C4×C11C4×D414yes—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
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—
440C24×C4C2×D1111yescharacteristic
441C22×C4⋊C4—111no—
442C22×C4⋊C4—111no—
443C22×C4⋊C4—111no—
444C22×C4⋊C4—111no—
445C22×C4⋊C4C2×D1111yescharacteristic
446C22×C4⋊C4C2×D1111yescharacteristic
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4C2×D1111yescharacteristic
452C22×C22⋊C4C2×D1111yescharacteristic
453C22×C42—111no—
454C22×C42—111no—
455#387—224no—
456#387—224no—
457#385—118no—
458#380—24no—
459#380—224no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95—111no—
463C2×#95—111no—
464C2×#95—111no—
465C2×#95—111no—
466C2×#95—111no—
467C2×#95—111no—
468C2×#95—111no—
469C2×#95—111no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95C2×D1111yescharacteristic
479C2×#95C2×D1111yescharacteristic
480C22×C11—24no—
481C22×C11—24no—
482C22×C11—24no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11C2×#11711yescharacteristic
496C22×C11C2×C4×D411yescharacteristic
497C22×C11C2×C4×D411yescharacteristic
498C22×C11#51811yescharacteristic
499C22×C11#51911yescharacteristic
500C22×C11#52011yescharacteristic
501C22×C11#52011yescharacteristic
502C22×C11#53611yescharacteristic
503C22×C11#53611yescharacteristic
504C22×C11#53711yescharacteristic
505C22×C11#53711yescharacteristic
506C22×C11#53911yescharacteristic
507C22×C11#53911yescharacteristic
508C22×C11#53911yescharacteristic
509C22×C11#53911yescharacteristic
510C22×C11#54111yescharacteristic
511C22×C11#54111yescharacteristic
512C22×C11#54211yescharacteristic
513C22×C11#54211yescharacteristic
514C22×C11D4211yescharacteristic
515C22×C11#54611yescharacteristic
516C22×C11#54611yescharacteristic
517C22×C11#54611yescharacteristic
518C22×C11#54611yescharacteristic
519C22×C11#54811yescharacteristic
520C22×C11#54811yescharacteristic
521C22×C11#55111yescharacteristic
522C22×C11#55211yescharacteristic
523C22×C11#55211yescharacteristic
524C22×C11#55311yescharacteristic
525C22×C11#55311yescharacteristic
526C22×C11#56011yescharacteristic
527C22×C11#56211yescharacteristic
528C22×C11#56211yescharacteristic
529C22×C11#56311yescharacteristic
530C4×C11—24no—
531C4×C11—24no—
532C4×C11—42no—
533C4×C11—42no—
534C4×C11—81no—
535C4×C11—81no—
536Dic11—42no—
537Dic11—42no—
538Dic11—42no—
539Dic11—42no—
540Dic11—42no—
541Dic11—42no—
542Dic11—81no—
543Dic11—81no—
544C25C22×D1111yescharacteristic
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—22no—
549C23×C4—41no—
550C23×C4—41no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4—111no—
556C23×C4—111no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4C4×D1114yes—
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C23×C4C22×D1111yescharacteristic
563C23×C4C22×D1111yescharacteristic
564C23×C4C22×D1111yescharacteristic
565C23×C4C22×D1111yescharacteristic
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—41no—
571C2×C4⋊C4—41no—
572C2×C4⋊C4—114no—
573C2×C4⋊C4—114no—
574C2×C4⋊C4—222no—
575C2×C4⋊C4—222no—
576C2×C4⋊C4—222no—
577C2×C4⋊C4—222no—
578C2×C4⋊C4—222no—
579C2×C4⋊C4—222no—
580C2×C4⋊C4—222no—
581C2×C4⋊C4—222no—
582C2×C4⋊C4—441no—
583C2×C4⋊C4—441no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—41no—
589C2×C22⋊C4—41no—
590C2×C22⋊C4—114no—
591C2×C22⋊C4—114no—
592C2×C22⋊C4—222no—
593C2×C22⋊C4—222no—
594C2×C22⋊C4—222no—
595C2×C22⋊C4—222no—
596C2×C22⋊C4—222no—
597C2×C22⋊C4—222no—
598C2×C22⋊C4—441no—
599C2×C22⋊C4—441no—
600C2×C22⋊C4—441no—
601C2×C22⋊C4—441no—
602C2×C42—222no—
603C2×C42—222no—
604C2×C42—441no—
605C2×C42—441no—
606C2×C42—441no—
607C2×C42—441no—
608#95—22no—
609#95—114no—
610#95—114no—
611#95—114no—
612#95—222no—
613#95—222no—
614#95—222no—
615#95—222no—
616#95—222no—
617#95—222no—
618#95—222no—
619#95—441no—
620#95—441no—
621#95—441no—
622#95—441no—
623#95—441no—
624#95—441no—
625#95—441no—
626#95—441no—
627#95C22⋊D1114yes—
628C2×C11—44no—
629C2×C11#231311yescharacteristic
630C2×C11#232311yescharacteristic
631C2×C11#232311yescharacteristic
632C2×C11#235211yescharacteristic
633C2×C11#235211yescharacteristic
634C2×C11#235811yescharacteristic
635C2×C11#237611yescharacteristic
636C2×C11#268111yescharacteristic
637C2×C11#268111yescharacteristic
638C2×C11#269011yescharacteristic
639C2×C11#269011yescharacteristic
640C2×C11#269111yescharacteristic
641C2×C11#269111yescharacteristic
642C2×C11#274711yescharacteristic
643C2×C11#274711yescharacteristic
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24C2×C4×D1112yes—
657C24#434112yes—
658C24#434312yes—
659C24C23×D1111yescharacteristic
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—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
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×C4C2×C4×D1112yes—
758C22×C4C2×C4×D1112yes—
759C22×C4#433912yes—
760C22×C4D4×D1112yes—
761C22×C4#434112yes—
762C22×C4C2×C22⋊D1112yes—
763C22×C4C2×C22⋊D1112yes—
764C22×C4C2×C22⋊D1112yes—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—228no—
768C4⋊C4—228no—
769C4⋊C4—444no—
770C4⋊C4—444no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4—228no—
774C22⋊C4—444no—
775C22⋊C4—444no—
776C22⋊C4—444no—
777C42—444no—
778C42—444no—
779C11#1440911yescharacteristic, complemented, Sylow
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23#6694514yes—
815C23C22×C4×D1111yescharacteristic
816C23C2×#433911yescharacteristic
817C23C2×D4×D1111yescharacteristic
818C23C2×#434111yescharacteristic
819C23C2×#434111yescharacteristic
820C23#6703711yescharacteristic
821C23#6703711yescharacteristic
822C23#6703711yescharacteristic
823C23C2×#434311yescharacteristic
824C23#6704011yescharacteristic
825C23#6704211yescharacteristic
826C23#6704311yescharacteristic
827C23#6704311yescharacteristic
828C23#6704311yescharacteristic
829C23C22×C22⋊D1111yescharacteristic
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—416no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—441no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—441no—
904C2×C4—441no—
905C2×C4—441no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—441no—
911C2×C4—441no—
912C2×C4—441no—
913C2×C4—441no—
914C2×C4—441no—
915C2×C4—441no—
916C2×C4—441no—
917C2×C4—441no—
918C2×C4—441no—
919C2×C4—441no—
920C2×C4—441no—
921C2×C4—441no—
922C2×C4—441no—
923C2×C4—441no—
924C2×C4—441no—
925C2×C4—441no—
926C2×C4—441no—
927C2×C4(C22⋊D11)⋊C414yes—
928C2×C4C4×C22⋊D1114yes—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22C2×(C22⋊D11)⋊C411yescharacteristic
945C22#1062301711yescharacteristic
946C22#1062302111yescharacteristic
947C22#1062302611yescharacteristic
948C22C2×#6694511yescharacteristic
949C22#1062303511yescharacteristic
950C22#1062304411yescharacteristic
951C22#1062304511yescharacteristic
952C22#1062304711yescharacteristic
953C22#1062304911yescharacteristic
954C22#1062305411yescharacteristic
955C22#1062306511yescharacteristic
956C22#1062312911yescharacteristic
957C22#1062313311yescharacteristic
958C22#1062313311yescharacteristic
959C22#1062313411yescharacteristic
960C22#1062313911yescharacteristic
961C22#1062314911yescharacteristic
962C22#1062315111yescharacteristic
963C22#1062315211yescharacteristic
964C22#1062315611yescharacteristic
965C22#1062315911yescharacteristic
966C22#1062316111yescharacteristic
967C22#1062317311yescharacteristic
968C22#1062317611yescharacteristic
969C22#1062317611yescharacteristic
970C22#1062317711yescharacteristic
971C22#1062317811yescharacteristic
972C22C2×C4×C22⋊D1111yescharacteristic
973C22D4×C22⋊D1111yescharacteristic
974C22#1062333711yescharacteristic
975C22#1062333711yescharacteristic
976C22#1062334811yescharacteristic
977C22#1062335611yescharacteristic
978C22#1062336411yescharacteristic
979C4—24no—
980C4—24no—
981C4—42no—
982C4—42no—
983C4—81no—
984C4—81no—
985C4—442no—
986C4—442no—
987C4—442no—
988C4—442no—
989C4—442no—
990C4—442no—
991C4—881no—
992C4—881no—
993C2—44no—
994C2#1307121811yescharacteristic
995C2#1307129411yescharacteristic
996C2#1307129811yescharacteristic
997C2#1307154111yescharacteristic
998C2#1307154711yescharacteristic
999C2#1307159511yescharacteristic
1000C2#1307176011yescharacteristic
1001C2#1307496211yescharacteristic
1002C2#1307497111yescharacteristic
1003C2#1307507811yescharacteristic
1004C2#1307508211yescharacteristic
1005C2#1307509311yescharacteristic
1006C2#1307509711yescharacteristic
1007C2#1307581111yescharacteristic
1008C2#1307581511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11#14409
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×#10622268C2semidirect
2. C2×#10622591C2semidirect
5. #13066875C2semidirect
6. #13066872C2semidirect
7. #13066870C2semidirect
8. #13066866C2semidirect
13. #13066850C2semidirect
14. #13066848C2semidirect
35. #10622823C4semidirect
779. C11#14409semidirect

Maximal subgroups

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

subgroupindex
C2×#106222682
C2×#106225912
C2×#106228232
C2×#106228252
#130668752
#130668722
#130668702
#130668662
#130668632
#130668532
#130668502
#130668482
C2×C11×#3802
#1440911