Finite Group Databasebeta

← #14679149

Subgroups — #14679149

Order 2816.

1738 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×#10622594C211yesmaximal, characteristic, complemented
2C2×#10622563C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic11C211yesmaximal, characteristic
5#13066884C211yesmaximal, characteristic, complemented
6#13066869C211yesmaximal, characteristic, complemented
7#13066861C211yesmaximal, characteristic
8#13066853C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic
10#13066850C211yesmaximal, characteristic, complemented
11#13066850C211yesmaximal, characteristic, complemented
12#13066848C211yesmaximal, characteristic, complemented
13#13066845C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic
15C2×C11×#399C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C11×#399C418yescomplemented
34C2×C11×#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
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
52#10622594—24no—
53C4⋊C4×Dic11—24no—
54#10622563—24no—
55C22⋊C4×Dic11—24no—
56C25×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—22no—
68C23×Dic11—41no—
69C23×Dic11—41no—
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×C4⋊C4C2×C414yescomplemented
85C2×C11×C4⋊C4C2×C414yescomplemented
86C2×C11×C4⋊C4C2×C414yescomplemented
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⋊C4C2×C414yes—
94C2×C11×C22⋊C4C2×C414yes—
95C2×C11×C22⋊C4C2×C414yes—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—41no—
103C2×C22⋊Dic11—41no—
104C2×C22⋊Dic11Q814yes—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11—22no—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—22no—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11—41no—
112C2×C4⋊Dic11—41no—
113C2×C4⋊Dic11D414yes—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11—22no—
120C2×C4×Dic11—22no—
121C2×C4×Dic11—22no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—41no—
124C2×C4×Dic11—41no—
125C2×C4×Dic11—41no—
126C11×#95C2×C414yescomplemented
127C11⋊#95—22no—
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⋊#95D414yes—
144#14178—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×Q812yes—
159C24×C11#4112yes—
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—21no—
192C22×C4×C11—21no—
193C22×C4×C11C22×C412yes—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C22×C412yes—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11#4112yes—
202C22×C4×C11#4112yes—
203C22×Dic11—28no—
204C22×Dic11—21no—
205C22×Dic11—21no—
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—44no—
251C22×Dic11—44no—
252C22×Dic11—44no—
253C22×Dic11—44no—
254C22×Dic11—44no—
255C22×Dic11—44no—
256C22×Dic11C2×D412yes—
257C22×Dic11C2×D412yes—
258C22×Dic11C2×D412yes—
259C22×Dic11C2×D412yes—
260C22×Dic11C2×Q812yes—
261C22×Dic11C2×Q812yes—
262C22×Dic11#4112yes—
263C22×Dic11#4112yes—
264C22×Dic11#4112yes—
265C22×Dic11#4112yes—
266C11×C4⋊C4—28no—
267C11×C4⋊C4—28no—
268C11×C4⋊C4—44no—
269C11×C22⋊C4—28no—
270C11×C22⋊C4—28no—
271C11×C22⋊C4—44no—
272C22⋊Dic11—28no—
273C22⋊Dic11—44no—
274C22⋊Dic11—44no—
275C4⋊Dic11—28no—
276C4⋊Dic11—44no—
277C4⋊Dic11—44no—
278C4×Dic11—28no—
279C4×Dic11—44no—
280C4×Dic11—44no—
281C4×Dic11—44no—
282C2×#399D1111yescharacteristic
283C2×#387—111no—
284C2×#385—111no—
285C2×C4×C4⋊C4—111no—
286C2×C4×C22⋊C4—111no—
287#1445—111no—
288#1441—111no—
289#1439—111no—
290#1437—111no—
291#1437—111no—
292#1436—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×C11C4×Q814yes—
332C23×C11C23×C411yescharacteristic
333C23×C11C22×D411yescharacteristic
334C23×C11C22×D411yescharacteristic
335C23×C11C22×Q811yescharacteristic
336C23×C11C2×#4111yescharacteristic
337C23×C11C2×#4111yescharacteristic
338C23×C11C2×#4111yescharacteristic
339C23×C11C2×#4111yescharacteristic
340C23×C11C2×#4111yescharacteristic
341C23×C11C2×#4111yescharacteristic
342C23×C11C2×#4111yescharacteristic
343C23×C11H(5,𝔽2)11yescharacteristic
344C23×C11H(5,𝔽2)11yescharacteristic
345C23×C11H(5,𝔽2)11yescharacteristic
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—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×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11C4×D414yes—
388C2×C4×C11C4×D414yes—
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—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—416no—
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×Dic11C22⋊Q814yes—
445C2×Dic11#12314yes—
446C24×C4—111no—
447C22×C4⋊C4—111no—
448C22×C4⋊C4—111no—
449C22×C4⋊C4—111no—
450C22×C4⋊C4C2×D1111yescharacteristic
451C22×C4⋊C4C2×D1111yescharacteristic
452C22×C4⋊C4C2×D1111yescharacteristic
453C22×C22⋊C4—111no—
454C22×C22⋊C4—111no—
455C22×C22⋊C4—111no—
456C22×C22⋊C4C2×D1111yescharacteristic
457C22×C22⋊C4C2×D1111yescharacteristic
458C22×C22⋊C4C2×D1111yescharacteristic
459C22×C42—111no—
460C22×C42—111no—
461C22×C42—111no—
462C22×C42—111no—
463#399Dic1118yescomplemented
464#387—224no—
465#385—224no—
466C4×C4⋊C4—224no—
467C4×C22⋊C4—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×#95—111no—
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×C11C2×C4×D411yescharacteristic
502C22×C11C2×C4×D411yescharacteristic
503C22×C11C2×C4×Q811yescharacteristic
504C22×C11C4×#4111yescharacteristic
505C22×C11C4×#4111yescharacteristic
506C22×C11#51811yescharacteristic
507C22×C11#52011yescharacteristic
508C22×C11C2×C22⋊Q811yescharacteristic
509C22×C11C2×#12311yescharacteristic
510C22×C11#52511yescharacteristic
511C22×C11#52511yescharacteristic
512C22×C11#52911yescharacteristic
513C22×C11#52911yescharacteristic
514C22×C11#52911yescharacteristic
515C22×C11#53311yescharacteristic
516C22×C11#53811yescharacteristic
517C22×C11#53911yescharacteristic
518C22×C11#54011yescharacteristic
519C22×C11#54211yescharacteristic
520C22×C11D4211yescharacteristic
521C22×C11#54611yescharacteristic
522C22×C11#54611yescharacteristic
523C22×C11#54711yescharacteristic
524C22×C11D4×Q811yescharacteristic
525C22×C11#55011yescharacteristic
526C22×C11#55011yescharacteristic
527C22×C11#55111yescharacteristic
528C22×C11#55111yescharacteristic
529C22×C11#55111yescharacteristic
530C22×C11#55211yescharacteristic
531C22×C11#55211yescharacteristic
532C22×C11#55411yescharacteristic
533C22×C11#55411yescharacteristic
534C22×C11#55411yescharacteristic
535C22×C11#55911yescharacteristic
536C4×C11—24no—
537C4×C11—24no—
538C4×C11—42no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11—42no—
542Dic11—24no—
543Dic11—24no—
544Dic11—42no—
545Dic11—42no—
546Dic11—42no—
547Dic11—42no—
548Dic11—81no—
549Dic11—81no—
550C25C22×D1111yescharacteristic
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×C4—222no—
560C23×C4—222no—
561C23×C4—222no—
562C23×C4—222no—
563C23×C4—222no—
564C23×C4—441no—
565C23×C4—441no—
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—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—114no—
579C2×C4⋊C4—222no—
580C2×C4⋊C4—222no—
581C2×C4⋊C4—222no—
582C2×C4⋊C4—222no—
583C2×C4⋊C4—222no—
584C2×C4⋊C4—222no—
585C2×C4⋊C4—441no—
586C2×C4⋊C4—441no—
587C2×C4⋊C4C2×Dic1114yescomplemented
588C2×C4⋊C4C2×Dic1114yescomplemented
589C2×C4⋊C4C2×Dic1114yescomplemented
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—41no—
596C2×C22⋊C4—114no—
597C2×C22⋊C4—222no—
598C2×C22⋊C4—222no—
599C2×C22⋊C4—222no—
600C2×C22⋊C4—222no—
601C2×C22⋊C4—222no—
602C2×C22⋊C4—222no—
603C2×C22⋊C4—441no—
604C2×C22⋊C4—441no—
605C2×C22⋊C4C2×Dic1114yes—
606C2×C22⋊C4C2×Dic1114yes—
607C2×C22⋊C4C2×Dic1114yes—
608C2×C42—222no—
609C2×C42—222no—
610C2×C42—222no—
611C2×C42—222no—
612C2×C42—222no—
613C2×C42—222no—
614C2×C42—222no—
615C2×C42—222no—
616C2×C42—222no—
617C2×C42—441no—
618C2×C42—441no—
619C2×C42—441no—
620#95—114no—
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—222no—
631#95—222no—
632#95—441no—
633#95—441no—
634#95—441no—
635#95—441no—
636#95—441no—
637#95C2×Dic1114yescomplemented
638C2×C11—44no—
639C2×C11C4×#12311yescharacteristic
640C2×C11C4×C22⋊Q811yescharacteristic
641C2×C11#233511yescharacteristic
642C2×C11#235911yescharacteristic
643C2×C11#236011yescharacteristic
644C2×C11#236611yescharacteristic
645C2×C11#236811yescharacteristic
646C2×C11#241811yescharacteristic
647C2×C11#242311yescharacteristic
648C2×C11#244911yescharacteristic
649C2×C11#245411yescharacteristic
650C2×C11#247111yescharacteristic
651C2×C11#247911yescharacteristic
652C2×C11#257511yescharacteristic
653C2×C11#258911yescharacteristic
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24Q8×D1112yes—
667C24#434312yes—
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—21no—
701C22×C4—21no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—112no—
709C22×C4—112no—
710C22×C4—112no—
711C22×C4—112no—
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—228no—
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—444no—
760C22×C4—444no—
761C22×C4—444no—
762C22×C4—444no—
763C22×C4—444no—
764C22×C4—444no—
765C22×C4D4×D1112yes—
766C22×C4D4×D1112yes—
767C22×C4#434112yes—
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—28no—
777C4⋊C4—44no—
778C4⋊C4—228no—
779C4⋊C4—444no—
780C4⋊C4—444no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—44no—
784C22⋊C4—228no—
785C22⋊C4—444no—
786C22⋊C4—444no—
787C42—228no—
788C42—444no—
789C42—444no—
790C42—444no—
791C11#1417811yescharacteristic, 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—
826C23Q8×Dic1114yes—
827C23C2×D4×D1111yescharacteristic
828C23C2×D4×D1111yescharacteristic
829C23C2×#434111yescharacteristic
830C23C2×#434111yescharacteristic
831C23#6703711yescharacteristic
832C23#6703711yescharacteristic
833C23C2×Q8×D1111yescharacteristic
834C23C2×#434311yescharacteristic
835C23#41×D1111yescharacteristic
836C23#41×D1111yescharacteristic
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—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
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—114no—
883C2×C4—114no—
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—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—4416no—
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×C4—441no—
939C2×C4D4×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#1062315311yescharacteristic
957C22#1062315511yescharacteristic
958C22D11×C22⋊Q811yescharacteristic
959C22#1062315811yescharacteristic
960C22#1062316111yescharacteristic
961C22#1062316311yescharacteristic
962C22#1062316611yescharacteristic
963C22#1062316711yescharacteristic
964C22#1062316711yescharacteristic
965C22#1062316811yescharacteristic
966C22#1062316811yescharacteristic
967C22#1062317311yescharacteristic
968C22#1062318011yescharacteristic
969C22#1062318011yescharacteristic
970C22#1062318111yescharacteristic
971C22D11×#12311yescharacteristic
972C22#1062318511yescharacteristic
973C22#1062318611yescharacteristic
974C22#1062318711yescharacteristic
975C22#1062318811yescharacteristic
976C22#1062318911yescharacteristic
977C22#1062319111yescharacteristic
978C22#1062319311yescharacteristic
979C22#1062319411yescharacteristic
980C22#1062324411yescharacteristic
981C22#1062324811yescharacteristic
982C22#1062324911yescharacteristic
983C22#1062324911yescharacteristic
984C22C2×D4×Dic1111yescharacteristic
985C22C2×D4×Dic1111yescharacteristic
986C22#1062332911yescharacteristic
987C22C2×Q8×Dic1111yescharacteristic
988C22#41×Dic1111yescharacteristic
989C22#41×Dic1111yescharacteristic
990C22#1062335811yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—224no—
998C4—224no—
999C4—442no—
1000C4—442no—
1001C4—442no—
1002C4—442no—
1003C4—881no—
1004C4—881no—
1005C2—44no—
1006C2#123×Dic1111yescharacteristic
1007C2C22⋊Q8×Dic1111yescharacteristic
1008C2#1307141011yescharacteristic
1009C2#1307161211yescharacteristic
1010C2#1307162511yescharacteristic
1011C2#1307168111yescharacteristic
1012C2#1307170111yescharacteristic
1013C2#1307208111yescharacteristic
1014C2#1307213411yescharacteristic
1015C2#1307242811yescharacteristic
1016C2#1307248311yescharacteristic
1017C2#1307272011yescharacteristic
1018C2#1307285011yescharacteristic
1019C2#1307390611yescharacteristic
1020C2#1307406011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#399C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#399D11
hypocenterC11#14178
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C2×#10622594C2semidirect
3. C2×C4⋊C4×Dic11C2semidirect
5. #13066884C2semidirect
6. #13066869C2semidirect
10. #13066850C2semidirect
11. #13066850C2semidirect
12. #13066848C2semidirect
13. #13066845C2semidirect
33. C11×#399C4semidirect
84. C2×C11×C4⋊C4C2×C4semidirect
85. C2×C11×C4⋊C4C2×C4semidirect
86. C2×C11×C4⋊C4C2×C4semidirect
126. C11×#95C2×C4semidirect
463. #399Dic11semidirect
587. C2×C4⋊C4C2×Dic11semidirect
588. C2×C4⋊C4C2×Dic11semidirect
589. C2×C4⋊C4C2×Dic11semidirect
637. #95C2×Dic11semidirect
791. C11#14178semidirect

Maximal subgroups

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

subgroupindex
C2×#106225942
C2×#106225632
C2×C4⋊C4×Dic112
C2×C22⋊C4×Dic112
#130668842
#130668692
#130668612
#130668532
#130668502
#130668482
#130668452
#130668382
C2×C11×#3992
#1417811