Finite Group Databasebeta

← #14679144

Subgroups — #14679144

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×#10622562C211yesmaximal, characteristic
2C2×#10622591C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic11C211yesmaximal, characteristic
5#13066883C211yesmaximal, characteristic, complemented
6#13066866C211yesmaximal, characteristic, complemented
7#13066859C211yesmaximal, characteristic
8#13066853C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic
10#13066848C211yesmaximal, characteristic, complemented
11#13066847C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, 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×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C11×#385—24no—
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C4×C22⋊Dic11—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#10622591—24no—
54C4⋊C4×Dic11—24no—
55#10622562C418yescomplemented
56C25×C11C2311yescharacteristic
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—22no—
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—41no—
63C23×C4×C11—41no—
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⋊C4D414yes—
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⋊C4C2×C414yes—
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⋊Dic11C2×C414yes—
100C2×C22⋊Dic11C2×C414yes—
101C2×C22⋊Dic11Q814yes—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11C2×C414yescomplemented
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—41no—
110C2×Dic11⋊C4—41no—
111C2×Dic11⋊C4—41no—
112C2×Dic11⋊C4C2×C414yescomplemented
113C2×Dic11⋊C4C2×C414yescomplemented
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×#95—22no—
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—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95C2×C414yescomplemented
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—28no—
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—44no—
196C22×C4×C11—44no—
197C22×C4×C11—44no—
198C22×C4×C11—44no—
199C22×C4×C11—44no—
200C22×C4×C11—44no—
201C22×C4×C11C22×C412yes—
202C22×C4×C11C22×C412yes—
203C22×C4×C11C2×D412yes—
204C22×C4×C11C2×D412yes—
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2×D412yes—
207C22×C4×C11#4112yes—
208C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
256C22×Dic11C22×C412yes—
257C22×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C2×D412yes—
260C22×Dic11C2×D412yes—
261C22×Dic11C2×Q812yes—
262C22×Dic11C2×Q812yes—
263C22×Dic11#4112yes—
264C22×Dic11#4112yes—
265C22×Dic11#4112yes—
266C11×C4⋊C4—28no—
267C11×C4⋊C4—44no—
268C11×C22⋊C4—28no—
269C11×C22⋊C4—44no—
270C22⋊Dic11—28no—
271C22⋊Dic11—28no—
272C22⋊Dic11—44no—
273C22⋊Dic11—44no—
274C4⋊Dic11—28no—
275Dic11⋊C4—28no—
276Dic11⋊C4—44no—
277Dic11⋊C4—44no—
278C4×Dic11—28no—
279C4×Dic11—44no—
280C4×Dic11—44no—
281C4×Dic11—44no—
282C2×#399—111no—
283C2×#387—111no—
284C2×#385D1111yescharacteristic
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—416no—
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×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11C4×D414yes—
389C2×C4×C11#12314yes—
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—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
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×Dic11C4×D414yes—
445C2×Dic11C22⋊Q814yes—
446C24×C4C2×D1111yescharacteristic
447C22×C4⋊C4—111no—
448C22×C4⋊C4—111no—
449C22×C4⋊C4—111no—
450C22×C4⋊C4—111no—
451C22×C4⋊C4C2×D1111yescharacteristic
452C22×C4⋊C4C2×D1111yescharacteristic
453C22×C22⋊C4—111no—
454C22×C22⋊C4—111no—
455C22×C22⋊C4—111no—
456C22×C22⋊C4—111no—
457C22×C22⋊C4C2×D1111yescharacteristic
458C22×C22⋊C4C2×D1111yescharacteristic
459C22×C42—111no—
460C22×C42—111no—
461C22×C42—111no—
462C22×C42—111no—
463#399—118no—
464#387—224no—
465#385—24no—
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×#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×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—81no—
542Dic11—24no—
543Dic11—24no—
544Dic11—42no—
545Dic11—42no—
546Dic11—42no—
547Dic11—42no—
548Dic11—42no—
549Dic11—81no—
550C25C22×D1111yescharacteristic
551C23×C4—22no—
552C23×C4—22no—
553C23×C4—22no—
554C23×C4—22no—
555C23×C4—22no—
556C23×C4—41no—
557C23×C4—41no—
558C23×C4—111no—
559C23×C4—111no—
560C23×C4—111no—
561C23×C4—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4—111no—
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—114no—
578C2×C4⋊C4—114no—
579C2×C4⋊C4—114no—
580C2×C4⋊C4—222no—
581C2×C4⋊C4—222no—
582C2×C4⋊C4—222no—
583C2×C4⋊C4—222no—
584C2×C4⋊C4—222no—
585C2×C4⋊C4—222no—
586C2×C4⋊C4—441no—
587C2×C4⋊C4—441no—
588C2×C4⋊C4—441no—
589C2×C4⋊C4C22⋊D1114yes—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—114no—
596C2×C22⋊C4—114no—
597C2×C22⋊C4—114no—
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—441no—
605C2×C22⋊C4—441no—
606C2×C22⋊C4—441no—
607C2×C22⋊C4C4×D1114yes—
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—22no—
621#95—22no—
622#95—114no—
623#95—114no—
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—222no—
633#95—441no—
634#95—441no—
635#95—441no—
636#95—441no—
637#95—441no—
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—
666C24C2×C4×D1112yes—
667C24#434112yes—
668C24Q8×D1112yes—
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—28no—
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—21no—
703C22×C4—21no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—112no—
714C22×C4—112no—
715C22×C4—112no—
716C22×C4—112no—
717C22×C4—112no—
718C22×C4—112no—
719C22×C4—112no—
720C22×C4—112no—
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×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4C2×C4×D1112yes—
767C22×C4C2×C4×D1112yes—
768C22×C4#433912yes—
769C22×C4D4×D1112yes—
770C22×C4#434112yes—
771C22×C4#434112yes—
772C22×C4C2×C22⋊D1112yes—
773C22×C4C2×C22⋊D1112yes—
774C22×C4C2×C22⋊D1112yes—
775C4⋊C4—28no—
776C4⋊C4—44no—
777C4⋊C4—228no—
778C4⋊C4—228no—
779C4⋊C4—444no—
780C4⋊C4—444no—
781C22⋊C4—28no—
782C22⋊C4—44no—
783C22⋊C4—228no—
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—
826C23#6694014yes—
827C23C22×C4×D1111yescharacteristic
828C23C2×#433911yescharacteristic
829C23C2×D4×D1111yescharacteristic
830C23C2×#434111yescharacteristic
831C23C2×#434111yescharacteristic
832C23C2×#434111yescharacteristic
833C23#6703711yescharacteristic
834C23#6703711yescharacteristic
835C23C2×Q8×D1111yescharacteristic
836C23#6704011yescharacteristic
837C23#41×D1111yescharacteristic
838C23#41×D1111yescharacteristic
839C23#41×D1111yescharacteristic
840C23#6704211yescharacteristic
841C23C22×C22⋊D1111yescharacteristic
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—416no—
864C2×C4—41no—
865C2×C4—41no—
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—41no—
883C2×C4—114no—
884C2×C4—114no—
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—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
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×C4C4×C22⋊D1114yes—
940C2×C4#6698814yes—
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—
956C22C2×#6694011yescharacteristic
957C22#1062303511yescharacteristic
958C22#1062304211yescharacteristic
959C22#1062304411yescharacteristic
960C22C4×#434111yescharacteristic
961C22C4×#434111yescharacteristic
962C22#1062306911yescharacteristic
963C22#1062306911yescharacteristic
964C22C4×D4×D1111yescharacteristic
965C22#1062307611yescharacteristic
966C22#1062308411yescharacteristic
967C22#1062309011yescharacteristic
968C22#1062311711yescharacteristic
969C22#1062311811yescharacteristic
970C22#1062312211yescharacteristic
971C22#1062312411yescharacteristic
972C22#1062315311yescharacteristic
973C22D11×C22⋊Q811yescharacteristic
974C22#1062316211yescharacteristic
975C22#1062316611yescharacteristic
976C22#1062316711yescharacteristic
977C22#1062316911yescharacteristic
978C22#1062317011yescharacteristic
979C22#1062317411yescharacteristic
980C22#1062318011yescharacteristic
981C22#1062318911yescharacteristic
982C22#1062319011yescharacteristic
983C22#1062319411yescharacteristic
984C22C2×C4×C22⋊D1111yescharacteristic
985C22C2×#6698811yescharacteristic
986C22D4×C22⋊D1111yescharacteristic
987C22#1062333711yescharacteristic
988C22Q8×C22⋊D1111yescharacteristic
989C22#1062335911yescharacteristic
990C22#1062336511yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—81no—
997C4—224no—
998C4—224no—
999C4—442no—
1000C4—442no—
1001C4—442no—
1002C4—442no—
1003C4—442no—
1004C4—881no—
1005C2—44no—
1006C2C4×#6698811yescharacteristic
1007C2#1307114811yescharacteristic
1008C2#1307140111yescharacteristic
1009C2#1307161111yescharacteristic
1010C2#1307162111yescharacteristic
1011C2#1307167811yescharacteristic
1012C2#1307169711yescharacteristic
1013C2#1307207411yescharacteristic
1014C2#1307213711yescharacteristic
1015C2#1307242211yescharacteristic
1016C2#1307248511yescharacteristic
1017C2#1307272311yescharacteristic
1018C2#1307284411yescharacteristic
1019C2#1307390911yescharacteristic
1020C2#1307406411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#385C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#385D11
hypocenterC11#14178
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#10622591C2semidirect
3. C2×C4⋊C4×Dic11C2semidirect
5. #13066883C2semidirect
6. #13066866C2semidirect
10. #13066848C2semidirect
11. #13066847C2semidirect
12. #13066847C2semidirect
13. Dic11⋊#95C2semidirect
55. #10622562C4semidirect
104. C2×C4⋊Dic11C2×C4semidirect
112. C2×Dic11⋊C4C2×C4semidirect
113. C2×Dic11⋊C4C2×C4semidirect
142. C11⋊#95C2×C4semidirect
791. C11#14178semidirect

Maximal subgroups

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

subgroupindex
C2×#106225622
C2×#106225912
C2×C4⋊C4×Dic112
C2×C4×C22⋊Dic112
#130668832
#130668662
#130668592
#130668532
#130668482
#130668472
Dic11⋊#952
#130668392
C2×C11×#3852
#1417811