Finite Group Databasebeta

← #14681790

Subgroups — #14681790

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622598C211yesmaximal, characteristic, complemented
2C2×#10622564C211yesmaximal, characteristic
3C2×#10622564C211yesmaximal, characteristic
4C2×#10622825C211yesmaximal, characteristic
5#13066881C211yesmaximal, characteristic, complemented
6#13066873C211yesmaximal, characteristic, complemented
7#13066869C211yesmaximal, characteristic, complemented
8#13066869C211yesmaximal, characteristic, complemented
9#13066861C211yesmaximal, characteristic
10#13066861C211yesmaximal, characteristic
11#13066850C211yesmaximal, characteristic, complemented
12#13066850C211yesmaximal, characteristic, complemented
13#13066845C211yesmaximal, characteristic, complemented
14#13066839C211yesmaximal, characteristic
15C2×C11×#385C211yesmaximal, 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×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C11×#385C418yescomplemented
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36#10622825—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
53#10622598—24no—
54#10622564—24no—
55#10622564—24no—
56C25×C11C2311yescharacteristic
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—41no—
60C23×C4×C11—41no—
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—41no—
81C2×C11×C4⋊C4—41no—
82C2×C11×C4⋊C4C2×C414yes—
83C2×C11×C4⋊C4C2×C414yes—
84C2×C11×C22⋊C4—41no—
85C2×C11×C22⋊C4—41no—
86C2×C11×C22⋊C4C2×C414yes—
87C2×C11×C22⋊C4C2×C414yes—
88C2×C11×C22⋊C4D414yes—
89C2×C11×C22⋊C4Q814yes—
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—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—41no—
99C2×C22⋊Dic11—41no—
100C2×C22⋊Dic11—41no—
101C2×C22⋊Dic11—41no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11—22no—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—41no—
110C2×C4⋊Dic11—41no—
111C2×C4⋊Dic11—41no—
112C2×C4⋊Dic11—41no—
113C2×C4⋊Dic11—41no—
114C2×C4⋊Dic11—41no—
115C2×C4⋊Dic11—41no—
116C2×C4⋊Dic11—41no—
117C2×C4⋊Dic11—41no—
118C2×C4⋊Dic11—41no—
119C2×C4⋊Dic11D414yes—
120C2×C4×Dic11—22no—
121C2×C4×Dic11—22no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—41no—
125C2×C4×Dic11—41no—
126C11×#95C2×C414yes—
127C11×#95C2×C414yes—
128C11⋊#95—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144#14408—111nomaximal, Sylow
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×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11C22×C412yes—
158C24×C11C2×D412yes—
159C24×C11C2×Q812yes—
160C24×C11C2411yescharacteristic
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—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—28no—
192C22×C4×C11—44no—
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×C11C22×C412yes—
201C22×C4×C11C22×C412yes—
202C22×C4×C11C22×C412yes—
203C22×C4×C11C22×C412yes—
204C22×C4×C11C2×D412yes—
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2×Q812yes—
208C22×C4×C11C2×Q812yes—
209C22×C4×C11#4112yes—
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×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11C2×D412yes—
263C22×Dic11C2×D412yes—
264C22×Dic11#4112yes—
265C22×Dic11#4112yes—
266C11×C4⋊C4—28no—
267C11×C4⋊C4—44no—
268C11×C22⋊C4—44no—
269C11×C22⋊C4C4⋊C4116yescomplemented
270C22⋊Dic11—44no—
271C22⋊Dic11—44no—
272C22⋊Dic11—44no—
273C22⋊Dic11—44no—
274C4⋊Dic11—44no—
275C4⋊Dic11—44no—
276C4⋊Dic11—44no—
277C4⋊Dic11—44no—
278C4⋊Dic11—44no—
279C4⋊Dic11—44no—
280C4×Dic11—44no—
281C4×Dic11—44no—
282C2×#389—111no—
283C2×#388—111no—
284C2×#388—111no—
285C2×#385D1111yescharacteristic
286C2×#380—111no—
287#1444—111no—
288#1442—111no—
289#1441—111no—
290#1441—111no—
291#1439—111no—
292#1439—111no—
293#1436—111no—
294#1436—111no—
295C4⋊#95—111no—
296C22⋊#95—111no—
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—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
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—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11C2×C4⋊C414yes—
332C23×C11C23×C411yescharacteristic
333C23×C11C22×D411yescharacteristic
334C23×C11C22×D411yescharacteristic
335C23×C11C22×Q811yescharacteristic
336C23×C11C2×#4111yescharacteristic
337C23×C11C2×#4111yescharacteristic
338C23×C11C2×#4111yescharacteristic
339C23×C11H(5,𝔽2)11yescharacteristic
340C23×C11H(5,𝔽2)11yescharacteristic
341C23×C11H(5,𝔽2)11yescharacteristic
342C23×C11H(5,𝔽2)11yescharacteristic
343C23×C11H(5,𝔽2)11yescharacteristic
344C23×C112−1+411yescharacteristic
345C23×C112−1+411yescharacteristic
346C23×C112−1+411yescharacteristic
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—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—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—416no—
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×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11C2×C4⋊C414yes—
388C2×C4×C11C2×C4⋊C414yes—
389C2×C4×C11C4×D414yes—
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—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C24×C4C2×D1111yescharacteristic
447C22×C4⋊C4—111no—
448C22×C4⋊C4—111no—
449C22×C4⋊C4—111no—
450C22×C4⋊C4—111no—
451C22×C4⋊C4—111no—
452C22×C4⋊C4—111no—
453C22×C4⋊C4C2×D1111yescharacteristic
454C22×C4⋊C4C2×D1111yescharacteristic
455C22×C22⋊C4—111no—
456C22×C22⋊C4—111no—
457C22×C22⋊C4—111no—
458C22×C22⋊C4—111no—
459C22×C22⋊C4C2×D1111yescharacteristic
460C22×C22⋊C4C2×D1111yescharacteristic
461C22×C42—111no—
462C22×C42—111no—
463#389—224no—
464#388—224no—
465#388—224no—
466#385Dic1118yescomplemented
467#380—224no—
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×#95—111no—
479C2×#95—111no—
480C2×#95—111no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95—111no—
484C2×#95C2×D1111yescharacteristic
485C2×#95C2×D1111yescharacteristic
486C22×C11—24no—
487C22×C11—24no—
488C22×C11—24no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11C22×C4⋊C411yescharacteristic
502C22×C11C2×C4×D411yescharacteristic
503C22×C11C4×#4111yescharacteristic
504C22×C11#51811yescharacteristic
505C22×C11#51811yescharacteristic
506C22×C11#51911yescharacteristic
507C22×C11#52011yescharacteristic
508C22×C11#53411yescharacteristic
509C22×C11#53511yescharacteristic
510C22×C11#53711yescharacteristic
511C22×C11#53711yescharacteristic
512C22×C11#53811yescharacteristic
513C22×C11#53811yescharacteristic
514C22×C11#53811yescharacteristic
515C22×C11#53911yescharacteristic
516C22×C11#54011yescharacteristic
517C22×C11#54211yescharacteristic
518C22×C11#54411yescharacteristic
519C22×C11#54411yescharacteristic
520C22×C11D4211yescharacteristic
521C22×C11#54611yescharacteristic
522C22×C11#54611yescharacteristic
523C22×C11#54711yescharacteristic
524C22×C11#54711yescharacteristic
525C22×C11#54811yescharacteristic
526C22×C11D4×Q811yescharacteristic
527C22×C11#55211yescharacteristic
528C22×C11#55411yescharacteristic
529C22×C11#55411yescharacteristic
530C22×C11#55411yescharacteristic
531C22×C11#55611yescharacteristic
532C22×C11#56211yescharacteristic
533C22×C11#56211yescharacteristic
534C22×C11#56311yescharacteristic
535C22×C11#56311yescharacteristic
536C4×C11—24no—
537C4×C11—24no—
538C4×C11—24no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11—42no—
542Dic11—42no—
543Dic11—42no—
544Dic11—42no—
545Dic11—42no—
546Dic11—81no—
547Dic11—81no—
548Dic11—81no—
549Dic11—81no—
550C25C22×D1111yescharacteristic
551C23×C4—22no—
552C23×C4—22no—
553C23×C4—41no—
554C23×C4—41no—
555C23×C4—41no—
556C23×C4—41no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—111no—
560C23×C4—111no—
561C23×C4—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4C2×Dic1114yes—
566C23×C4C22×D1111yescharacteristic
567C23×C4C22×D1111yescharacteristic
568C23×C4C22×D1111yescharacteristic
569C23×C4C22×D1111yescharacteristic
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—41no—
576C2×C4⋊C4—114no—
577C2×C4⋊C4—222no—
578C2×C4⋊C4—222no—
579C2×C4⋊C4—222no—
580C2×C4⋊C4—222no—
581C2×C4⋊C4—222no—
582C2×C4⋊C4—222no—
583C2×C4⋊C4—222no—
584C2×C4⋊C4—441no—
585C2×C4⋊C4—441no—
586C2×C4⋊C4—441no—
587C2×C4⋊C4—441no—
588C2×C4⋊C4—441no—
589C2×C4⋊C4—441no—
590C2×C4⋊C4—441no—
591C2×C4⋊C4—441no—
592C2×C4⋊C4—441no—
593C2×C4⋊C4—441no—
594C2×C4⋊C4C2×Dic1114yes—
595C2×C4⋊C4C2×Dic1114yes—
596C2×C22⋊C4—41no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—222no—
599C2×C22⋊C4—222no—
600C2×C22⋊C4—222no—
601C2×C22⋊C4—222no—
602C2×C22⋊C4—222no—
603C2×C22⋊C4—222no—
604C2×C22⋊C4—222no—
605C2×C22⋊C4—222no—
606C2×C22⋊C4—441no—
607C2×C22⋊C4—441no—
608C2×C22⋊C4—441no—
609C2×C22⋊C4—441no—
610C2×C22⋊C4Dic2214yes—
611C2×C22⋊C4D4414yes—
612C2×C22⋊C4C2×Dic1114yes—
613C2×C22⋊C4C2×Dic1114yes—
614C2×C42—222no—
615C2×C42—222no—
616C2×C42—222no—
617C2×C42—222no—
618C2×C42—441no—
619C2×C42—441no—
620#95—222no—
621#95—222no—
622#95—222no—
623#95—222no—
624#95—222no—
625#95—222no—
626#95—222no—
627#95—222no—
628#95—222no—
629#95—222no—
630#95—441no—
631#95—441no—
632#95—441no—
633#95—441no—
634#95—441no—
635#95—441no—
636#95C2×Dic1114yes—
637#95C2×Dic1114yes—
638C2×C11—44no—
639C2×C11#231611yescharacteristic
640C2×C11#232111yescharacteristic
641C2×C11#233511yescharacteristic
642C2×C11D4×C4⋊C411yescharacteristic
643C2×C11#234911yescharacteristic
644C2×C11#236211yescharacteristic
645C2×C11#237811yescharacteristic
646C2×C11#267111yescharacteristic
647C2×C11#267611yescharacteristic
648C2×C11#269511yescharacteristic
649C2×C11#271511yescharacteristic
650C2×C11#272011yescharacteristic
651C2×C11#272911yescharacteristic
652C2×C11#276811yescharacteristic
653C2×C11#278811yescharacteristic
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24C2×Dic2212yes—
667C24C2×D4412yes—
668C24C22×Dic1112yes—
669C24C23×D1111yescharacteristic
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—21no—
681C22×C4—21no—
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—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—28no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—112no—
708C22×C4—112no—
709C22×C4—112no—
710C22×C4—112no—
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×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—221no—
761C22×C4—221no—
762C22×C4—221no—
763C22×C4C2×Dic2212yes—
764C22×C4C2×Dic2212yes—
765C22×C4C2×D4412yes—
766C22×C4C2×D4412yes—
767C22×C4D4×D1112yes—
768C22×C4#434112yes—
769C22×C4C22×Dic1112yes—
770C22×C4C22×Dic1112yes—
771C22×C4C22×Dic1112yes—
772C22×C4C22×Dic1112yes—
773C22×C4C22×Dic1112yes—
774C22×C4C22×Dic1112yes—
775C4⋊C4—28no—
776C4⋊C4—44no—
777C4⋊C4—444no—
778C4⋊C4—444no—
779C4⋊C4—444no—
780C4⋊C4—444no—
781C4⋊C4—444no—
782C4⋊C4—444no—
783C22⋊C4—44no—
784C22⋊C4—444no—
785C22⋊C4—444no—
786C22⋊C4—444no—
787C22⋊C4—444no—
788C22⋊C4C4⋊Dic11116yescomplemented
789C42—444no—
790C42—444no—
791C11#1440811yescharacteristic, complemented, Sylow
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊Dic1114yes—
827C23C22×Dic2211yescharacteristic
828C23C22×D4411yescharacteristic
829C23C2×D4×D1111yescharacteristic
830C23C2×#434111yescharacteristic
831C23#6703711yescharacteristic
832C23#6703711yescharacteristic
833C23#6703711yescharacteristic
834C23#6703711yescharacteristic
835C23#6704011yescharacteristic
836C23#6704011yescharacteristic
837C23#41×D1111yescharacteristic
838C23#41×D1111yescharacteristic
839C23#6704211yescharacteristic
840C23#6704311yescharacteristic
841C23C23×Dic1111yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—416no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—222no—
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—441no—
928C2×C4—441no—
929C2×C4—441no—
930C2×C4—441no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4—441no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4C2×C4⋊Dic1114yes—
939C2×C4C2×C4⋊Dic1114yes—
940C2×C4D4×Dic1114yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22#1062303111yescharacteristic
957C22#1062303111yescharacteristic
958C22#1062304111yescharacteristic
959C22#1062304111yescharacteristic
960C22D4×Dic2211yescharacteristic
961C22#1062307011yescharacteristic
962C22#1062307011yescharacteristic
963C22#1062307411yescharacteristic
964C22D4×D4411yescharacteristic
965C22#1062308511yescharacteristic
966C22#1062308511yescharacteristic
967C22#1062308611yescharacteristic
968C22#1062312011yescharacteristic
969C22#1062312311yescharacteristic
970C22#1062312411yescharacteristic
971C22#1062312411yescharacteristic
972C22#1062316211yescharacteristic
973C22#1062316411yescharacteristic
974C22#1062317011yescharacteristic
975C22#1062317211yescharacteristic
976C22#1062317711yescharacteristic
977C22#1062317711yescharacteristic
978C22#1062317811yescharacteristic
979C22#1062317811yescharacteristic
980C22#1062318811yescharacteristic
981C22#1062319111yescharacteristic
982C22#1062319311yescharacteristic
983C22#1062319411yescharacteristic
984C22C22×C4⋊Dic1111yescharacteristic
985C22C2×D4×Dic1111yescharacteristic
986C22#1062332911yescharacteristic
987C22#1062332911yescharacteristic
988C22#1062334311yescharacteristic
989C22#41×Dic1111yescharacteristic
990C22#1062335811yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—442no—
998C4—442no—
999C4—442no—
1000C4—442no—
1001C4—881no—
1002C4—881no—
1003C4—881no—
1004C4—881no—
1005C2—44no—
1006C2#1307123411yescharacteristic
1007C2#1307127711yescharacteristic
1008C2#1307141011yescharacteristic
1009C2D4×C4⋊Dic1111yescharacteristic
1010C2#1307152611yescharacteristic
1011C2#1307164711yescharacteristic
1012C2#1307178211yescharacteristic
1013C2#1307485511yescharacteristic
1014C2#1307492011yescharacteristic
1015C2#1307514911yescharacteristic
1016C2#1307542511yescharacteristic
1017C2#1307549711yescharacteristic
1018C2#1307560211yescharacteristic
1019C2#1307609311yescharacteristic
1020C2#1307636611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#385C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#385D11
hypocenterC11#14408
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#10622598C2semidirect
5. #13066881C2semidirect
6. #13066873C2semidirect
7. #13066869C2semidirect
8. #13066869C2semidirect
11. #13066850C2semidirect
12. #13066850C2semidirect
13. #13066845C2semidirect
33. C11×#385C4semidirect
269. C11×C22⋊C4C4⋊C4semidirect
466. #385Dic11semidirect
788. C22⋊C4C4⋊Dic11semidirect
791. C11#14408semidirect

Maximal subgroups

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

subgroupindex
C2×#106225982
C2×#106225642
C2×#106228252
#130668812
#130668732
#130668692
#130668612
#130668502
#130668452
#130668392
C2×C11×#3852
#1440811