Finite Group Databasebeta

← #14679143

Subgroups — #14679143

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×#10622605C211yesmaximal, characteristic
2C2×#10622591C211yesmaximal, characteristic, complemented
3C2×#10622602C211yesmaximal, characteristic
4C2×#10622262C211yesmaximal, characteristic, complemented
5C2×#10622279C211yesmaximal, characteristic
6#13066882C211yesmaximal, characteristic, complemented
7#13066860C211yesmaximal, characteristic
8#13066852C211yesmaximal, characteristic
9#13066852C211yesmaximal, characteristic
10#13066851C211yesmaximal, characteristic, complemented
11#13066848C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×#1441C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
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
51#10622605C418yescomplemented
52#10622602—24no—
53#10622591—24no—
54#10622279—24no—
55#10622262—24no—
56C24×D11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11—41no—
77C22×C4×D11—41no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C4⋊C4—41no—
82C2×C11×C4⋊C4—41no—
83C2×C11×C4⋊C4C2×C414yescomplemented
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—41no—
95C2×(C2×D11)⋊C4—41no—
96C2×(C2×D11)⋊C4—41no—
97C2×(C2×D11)⋊C4—41no—
98C2×(C2×D11)⋊C4C2×C414yes—
99C2×(C2×D11)⋊C4C2×C414yes—
100C2×(C2×D11)⋊C4C2×C414yes—
101C2×(C2×D11)⋊C4Q814yes—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—41no—
111C2×Dic11⋊C4C2×C414yescomplemented
112C2×Dic11⋊C4C2×C414yescomplemented
113C2×Dic11⋊C4D414yes—
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—41no—
129C11×#95—41no—
130C11×#95—41no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95C2×C414yescomplemented
143C11⋊#95D414yes—
144#14178—111nomaximal, Sylow
145C24×C11C2411yescharacteristic
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11C22×C412yes—
159C23×D11C2×Q812yes—
160C23×D11#4112yes—
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×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11C22×C412yes—
204C22×C4×C11C22×C412yes—
205C22×C4×C11C22×C412yes—
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2×D412yes—
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×Dic11C22×C412yes—
247C22×Dic11C22×C412yes—
248C22×Dic11C22×C412yes—
249C22×Dic11C2×D412yes—
250C22×Dic11C2×D412yes—
251C22×Dic11C2×D412yes—
252C22×Dic11C2×D412yes—
253C22×Dic11C2×Q812yes—
254C22×Dic11#4112yes—
255C22×Dic11#4112yes—
256C22×Dic11#4112yes—
257C22×Dic11#4112yes—
258C22×Dic11#4112yes—
259C2×C4×D11—28no—
260C2×C4×D11—44no—
261C2×C4×D11—44no—
262C2×C4×D11—44no—
263C2×C4×D11—44no—
264C2×C4×D11—44no—
265C2×C4×D11—44no—
266C11×C4⋊C4—44no—
267C11×C4⋊C4—44no—
268(C2×D11)⋊C4—28no—
269(C2×D11)⋊C4—28no—
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—44no—
272(C2×D11)⋊C4—44no—
273(C2×D11)⋊C4—44no—
274Dic11⋊C4—28no—
275Dic11⋊C4—28no—
276Dic11⋊C4—28no—
277Dic11⋊C4—44no—
278C4×Dic11—28no—
279C4×Dic11—44no—
280C4×Dic11—44no—
281C4×Dic11—44no—
282C2×#399—111no—
283C2×#387—111no—
284C2×#385—111no—
285C2×C4×C4⋊C4—111no—
286C2×C4×C22⋊C4—111no—
287#1445—111no—
288#1441D1111yescharacteristic, complemented
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×C11C23×C411yescharacteristic
298C23×C11C22×D411yescharacteristic
299C23×C11C22×D411yescharacteristic
300C23×C11C22×Q811yescharacteristic
301C23×C11C2×#4111yescharacteristic
302C23×C11C2×#4111yescharacteristic
303C23×C11C2×#4111yescharacteristic
304C23×C11C2×#4111yescharacteristic
305C23×C11C2×#4111yescharacteristic
306C23×C11C2×#4111yescharacteristic
307C23×C11C2×#4111yescharacteristic
308C23×C11H(5,𝔽2)11yescharacteristic
309C23×C11H(5,𝔽2)11yescharacteristic
310C23×C11H(5,𝔽2)11yescharacteristic
311C23×C112−1+411yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11C4×Q814yes—
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—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×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×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—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
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×Dic11C4×D414yes—
442C2×Dic11C4×D414yes—
443C2×Dic11C22⋊Q814yes—
444C2×Dic11#12314yes—
445C4×D11—416no—
446C24×C4—111no—
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⋊C4—111no—
458C22×C22⋊C4—111no—
459C22×C42—111no—
460C22×C42—111no—
461C22×C42—111no—
462C22×C42—111no—
463#399—118no—
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×#95C2×D1111yescharacteristic
482C2×#95C2×D1111yescharacteristic
483C2×#95C2×D1111yescharacteristic
484C2×#95C2×D1111yescharacteristic
485C2×#95C2×D1111yescharacteristic
486C22×C11C2×C4×D411yescharacteristic
487C22×C11C2×C4×D411yescharacteristic
488C22×C11C2×C4×Q811yescharacteristic
489C22×C11C4×#4111yescharacteristic
490C22×C11C4×#4111yescharacteristic
491C22×C11#51811yescharacteristic
492C22×C11#52011yescharacteristic
493C22×C11C2×C22⋊Q811yescharacteristic
494C22×C11C2×#12311yescharacteristic
495C22×C11#52511yescharacteristic
496C22×C11#52511yescharacteristic
497C22×C11#52911yescharacteristic
498C22×C11#52911yescharacteristic
499C22×C11#52911yescharacteristic
500C22×C11#53311yescharacteristic
501C22×C11#53811yescharacteristic
502C22×C11#53911yescharacteristic
503C22×C11#54011yescharacteristic
504C22×C11#54211yescharacteristic
505C22×C11D4211yescharacteristic
506C22×C11#54611yescharacteristic
507C22×C11#54611yescharacteristic
508C22×C11#54711yescharacteristic
509C22×C11D4×Q811yescharacteristic
510C22×C11#55011yescharacteristic
511C22×C11#55011yescharacteristic
512C22×C11#55111yescharacteristic
513C22×C11#55111yescharacteristic
514C22×C11#55111yescharacteristic
515C22×C11#55211yescharacteristic
516C22×C11#55211yescharacteristic
517C22×C11#55411yescharacteristic
518C22×C11#55411yescharacteristic
519C22×C11#55411yescharacteristic
520C22×C11#55911yescharacteristic
521C2×D11—24no—
522C2×D11—24no—
523C2×D11—24no—
524C2×D11—42no—
525C2×D11—42no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C4×C11—42no—
537C4×C11—42no—
538C4×C11—42no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11—42no—
542C4×C11—42no—
543Dic11—24no—
544Dic11—24no—
545Dic11—24no—
546Dic11—24no—
547Dic11—42no—
548Dic11—81no—
549Dic11—81no—
550C25—111no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4—111no—
556C23×C4—111no—
557C23×C4—111no—
558C23×C4—222no—
559C23×C4—222no—
560C23×C4—222no—
561C23×C4—222no—
562C23×C4—222no—
563C23×C4—441no—
564C23×C4—441no—
565C23×C4C22×D1111yescharacteristic
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—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—222no—
587C2×C4⋊C4—222no—
588C2×C4⋊C4—441no—
589C2×C4⋊C4C4×D1114yescomplemented
590C2×C22⋊C4—114no—
591C2×C22⋊C4—114no—
592C2×C22⋊C4—114no—
593C2×C22⋊C4—114no—
594C2×C22⋊C4—222no—
595C2×C22⋊C4—222no—
596C2×C22⋊C4—222no—
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—222no—
604C2×C22⋊C4—441no—
605C2×C22⋊C4—441no—
606C2×C22⋊C4—441no—
607C2×C22⋊C4—441no—
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—41no—
623#95—41no—
624#95—41no—
625#95—114no—
626#95—114no—
627#95—222no—
628#95—222no—
629#95—222no—
630#95—222no—
631#95—222no—
632#95—222no—
633#95—222no—
634#95—222no—
635#95—222no—
636#95—441no—
637#95—441no—
638C2×C11C4×#12311yescharacteristic
639C2×C11C4×C22⋊Q811yescharacteristic
640C2×C11#233511yescharacteristic
641C2×C11#235911yescharacteristic
642C2×C11#236011yescharacteristic
643C2×C11#236611yescharacteristic
644C2×C11#236811yescharacteristic
645C2×C11#241811yescharacteristic
646C2×C11#242311yescharacteristic
647C2×C11#244911yescharacteristic
648C2×C11#245411yescharacteristic
649C2×C11#247111yescharacteristic
650C2×C11#247911yescharacteristic
651C2×C11#257511yescharacteristic
652C2×C11#258911yescharacteristic
653D11—44no—
654C24—112no—
655C24—112no—
656C24—112no—
657C24—221no—
658C24—221no—
659C24—221no—
660C24—221no—
661C24—221no—
662C24—221no—
663C24—221no—
664C24—221no—
665C24—221no—
666C24—221no—
667C24—221no—
668C24—221no—
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—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—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—112no—
722C22×C4—112no—
723C22×C4—112no—
724C22×C4—112no—
725C22×C4—228no—
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—444no—
763C22×C4—444no—
764C22×C4—444no—
765C22×C4—444no—
766C22×C4—444no—
767C22×C4—444no—
768C22×C4C2×C4×D1112yes—
769C22×C4C2×C4×D1112yes—
770C22×C4C2×C4×D1112yes—
771C22×C4D4×D1112yes—
772C22×C4D4×D1112yes—
773C22×C4Q8×D1112yes—
774C22×C4#434312yes—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—228no—
778C4⋊C4—228no—
779C4⋊C4—228no—
780C4⋊C4—444no—
781C22⋊C4—228no—
782C22⋊C4—228no—
783C22⋊C4—228no—
784C22⋊C4—444no—
785C22⋊C4—444no—
786C22⋊C4—444no—
787C42—228no—
788C42—444no—
789C42—444no—
790C42—444no—
791C11#1417811yescharacteristic, complemented, Sylow
792C23—114no—
793C23—222no—
794C23—222no—
795C23—222no—
796C23—222no—
797C23—222no—
798C23—222no—
799C23—222no—
800C23—222no—
801C23—222no—
802C23—222no—
803C23—222no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—441no—
812C23—441no—
813C23—441no—
814C23—441no—
815C23—441no—
816C23—441no—
817C23—441no—
818C23—441no—
819C23—441no—
820C23—441no—
821C23—441no—
822C23—441no—
823C23—441no—
824C23—441no—
825C23—441no—
826C23—441no—
827C23C22×C4×D1111yescharacteristic
828C23C2×D4×D1111yescharacteristic
829C23C2×D4×D1111yescharacteristic
830C23#6703711yescharacteristic
831C23#6703711yescharacteristic
832C23#6703711yescharacteristic
833C23C2×Q8×D1111yescharacteristic
834C23C2×#434311yescharacteristic
835C23#6704011yescharacteristic
836C23#41×D1111yescharacteristic
837C23#41×D1111yescharacteristic
838C23#41×D1111yescharacteristic
839C23#41×D1111yescharacteristic
840C23#41×D1111yescharacteristic
841C23#41×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—41no—
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—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—114no—
892C2×C4—114no—
893C2×C4—114no—
894C2×C4—114no—
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—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—4416no—
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×C4—441no—
940C2×C4—441no—
941C22—224no—
942C22—224no—
943C22—224no—
944C22—442no—
945C22—442no—
946C22—442no—
947C22—442no—
948C22—442no—
949C22—442no—
950C22—442no—
951C22—442no—
952C22—442no—
953C22—442no—
954C22—442no—
955C22—442no—
956C22#1062301711yescharacteristic
957C22#1062303511yescharacteristic
958C22#1062305311yescharacteristic
959C22C4×D4×D1111yescharacteristic
960C22C4×D4×D1111yescharacteristic
961C22C4×Q8×D1111yescharacteristic
962C22C4×#434311yescharacteristic
963C22#1062312111yescharacteristic
964C22#1062313011yescharacteristic
965C22#1062313011yescharacteristic
966C22#1062314111yescharacteristic
967C22#1062314111yescharacteristic
968C22#1062314411yescharacteristic
969C22#1062314611yescharacteristic
970C22D11×C22⋊Q811yescharacteristic
971C22#1062315811yescharacteristic
972C22#1062316711yescharacteristic
973C22#1062316711yescharacteristic
974C22#1062316811yescharacteristic
975C22#1062316811yescharacteristic
976C22#1062316911yescharacteristic
977C22#1062317111yescharacteristic
978C22D11×#12311yescharacteristic
979C22#1062318711yescharacteristic
980C22#1062319511yescharacteristic
981C22#1062321011yescharacteristic
982C22#1062321911yescharacteristic
983C22#1062322211yescharacteristic
984C22#1062322411yescharacteristic
985C22#1062322411yescharacteristic
986C22#1062323711yescharacteristic
987C22#1062323711yescharacteristic
988C22#1062325711yescharacteristic
989C22#1062325811yescharacteristic
990C22#1062326111yescharacteristic
991C4—42no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—224no—
999C4—224no—
1000C4—224no—
1001C4—224no—
1002C4—442no—
1003C4—881no—
1004C4—881no—
1005C2—444no—
1006C2#1307113711yescharacteristic
1007C2#1307115011yescharacteristic
1008C2#1307140211yescharacteristic
1009C2#1307160311yescharacteristic
1010C2#1307161811yescharacteristic
1011C2#1307167911yescharacteristic
1012C2#1307169511yescharacteristic
1013C2#1307207111yescharacteristic
1014C2#1307213611yescharacteristic
1015C2#1307241811yescharacteristic
1016C2#1307248111yescharacteristic
1017C2#1307273011yescharacteristic
1018C2#1307284011yescharacteristic
1019C2#1307390011yescharacteristic
1020C2#1307407011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1441D11
hypocenterC11#14178
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×#10622591C2semidirect
4. C2×#10622262C2semidirect
6. #13066882C2semidirect
10. #13066851C2semidirect
11. #13066848C2semidirect
12. #13066847C2semidirect
13. Dic11⋊#95C2semidirect
15. C11×#1441C2semidirect
51. #10622605C4semidirect
83. C2×C11×C4⋊C4C2×C4semidirect
111. C2×Dic11⋊C4C2×C4semidirect
112. C2×Dic11⋊C4C2×C4semidirect
142. C11⋊#95C2×C4semidirect
288. #1441D11semidirect
589. C2×C4⋊C4C4×D11semidirect
791. C11#14178semidirect

Maximal subgroups

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

subgroupindex
C2×#106226052
C2×#106225912
C2×#106226022
C2×#106222622
C2×#106222792
#130668822
#130668602
#130668522
#130668512
#130668482
#130668472
Dic11⋊#952
(C2×D11)⋊#952
C11×#14412
#1417811