Finite Group Databasebeta

← #14681712

Subgroups — #14681712

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×#10622553C211yesmaximal, characteristic
2C2×#10622603C211yesmaximal, characteristic
3C2×#10622281C211yesmaximal, characteristic
4C2×#10622602C211yesmaximal, characteristic
5C2×#10622263C211yesmaximal, characteristic, complemented
6#13066880C211yesmaximal, characteristic, complemented
7#13066879C211yesmaximal, characteristic, complemented
8#13066874C211yesmaximal, characteristic, complemented
9#13066869C211yesmaximal, characteristic, complemented
10#13066860C211yesmaximal, characteristic
11#13066860C211yesmaximal, characteristic
12#13066849C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
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#10622603C418yescomplemented
52#10622602—24no—
53#10622553—24no—
54#10622281—24no—
55#10622263—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—41no—
75C22×C4×D11—41no—
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×C42×C11—22no—
85C2×C42×C11—22no—
86C2×C42×C11—41no—
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)⋊C4—41no—
99C2×(C2×D11)⋊C4—41no—
100C2×(C2×D11)⋊C4C2×C414yes—
101C2×(C2×D11)⋊C4C2×C414yes—
102C2×(C2×D11)⋊C4C2×C414yes—
103C2×(C2×D11)⋊C4D414yes—
104C2×(C2×D11)⋊C4Q814yes—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—41no—
107C2×C4⋊Dic11—41no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—22no—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—41no—
117C2×Dic11⋊C4—41no—
118C2×Dic11⋊C4—41no—
119C2×Dic11⋊C4—41no—
120C2×Dic11⋊C4—41no—
121C2×Dic11⋊C4—41no—
122C2×Dic11⋊C4—41no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11C2×C414yescomplemented
126C11×#95—22no—
127C11×#95—22no—
128C11×#95—41no—
129C11×#95—41no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—41no—
137C11⋊#95—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95C2×C414yescomplemented
142C11⋊#95C2×C414yescomplemented
143C11⋊#95D414yes—
144#14403—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×D412yes—
160C23×D11C2×Q812yes—
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×C11C22×C412yes—
203C22×C4×C11C22×C412yes—
204C22×C4×C11C22×C412yes—
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2×Q812yes—
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×Dic11C22×C412yes—
252C22×Dic11C22×C412yes—
253C22×Dic11C22×C412yes—
254C22×Dic11C2×D412yes—
255C22×Dic11C2×D412yes—
256C22×Dic11C2×D412yes—
257C22×Dic11C2×Q812yes—
258C22×Dic11#4112yes—
259C2×C4×D11—44no—
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—
268C42×C11—44no—
269(C2×D11)⋊C4—28no—
270(C2×D11)⋊C4—44no—
271(C2×D11)⋊C4—44no—
272(C2×D11)⋊C4—44no—
273(C2×D11)⋊C4—44no—
274(C2×D11)⋊C4C4⋊C4116yescomplemented
275C4⋊Dic11—44no—
276Dic11⋊C4—44no—
277Dic11⋊C4—44no—
278Dic11⋊C4—44no—
279Dic11⋊C4—44no—
280Dic11⋊C4—44no—
281C4×Dic11—28no—
282C2×#388—111no—
283C2×#388—111no—
284C2×#385—111no—
285C2×#385—111no—
286C2×#382—111no—
287#1444—111no—
288#1444—111no—
289#1442—111no—
290#1441—111no—
291#1439—111no—
292#1439—111no—
293#1436—111no—
294C4⋊#95—111no—
295C4⋊#95D1111yescharacteristic, complemented
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×C11H(5,𝔽2)11yescharacteristic
305C23×C11H(5,𝔽2)11yescharacteristic
306C23×C11H(5,𝔽2)11yescharacteristic
307C23×C11H(5,𝔽2)11yescharacteristic
308C23×C11H(5,𝔽2)11yescharacteristic
309C23×C112−1+411yescharacteristic
310C23×C112−1+411yescharacteristic
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×D11C2×C4⋊C414yes—
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×C11C2×C4⋊C414yes—
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—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×Dic11C2×C4⋊C414yes—
444C2×Dic11C4×D414yes—
445C4×D11—416no—
446C24×C4—111no—
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⋊C4—111no—
460C22×C22⋊C4—111no—
461C22×C42—111no—
462C22×C42C2×D1111yescharacteristic
463#388—118no—
464#388—224no—
465#385—224no—
466#385—224no—
467#382—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×#95C2×D1111yescharacteristic
483C2×#95C2×D1111yescharacteristic
484C2×#95C2×D1111yescharacteristic
485C2×#95C2×D1111yescharacteristic
486C22×C11C22×C4⋊C411yescharacteristic
487C22×C11C2×C4×D411yescharacteristic
488C22×C11C4×#4111yescharacteristic
489C22×C11#51811yescharacteristic
490C22×C11#52011yescharacteristic
491C22×C11#52011yescharacteristic
492C22×C11#52011yescharacteristic
493C22×C11#53511yescharacteristic
494C22×C11#53511yescharacteristic
495C22×C11#53611yescharacteristic
496C22×C11#53711yescharacteristic
497C22×C11#53811yescharacteristic
498C22×C11#53911yescharacteristic
499C22×C11#54011yescharacteristic
500C22×C11#54111yescharacteristic
501C22×C11#54211yescharacteristic
502C22×C11#54211yescharacteristic
503C22×C11#54411yescharacteristic
504C22×C11#54411yescharacteristic
505C22×C11D4211yescharacteristic
506C22×C11#54611yescharacteristic
507C22×C11#54611yescharacteristic
508C22×C11#54611yescharacteristic
509C22×C11#54711yescharacteristic
510C22×C11#54711yescharacteristic
511C22×C11D4×Q811yescharacteristic
512C22×C11#55111yescharacteristic
513C22×C11#55211yescharacteristic
514C22×C11#55411yescharacteristic
515C22×C11#55411yescharacteristic
516C22×C11#55411yescharacteristic
517C22×C11H(3,𝔽4)11yescharacteristic
518C22×C11#56211yescharacteristic
519C22×C11#56211yescharacteristic
520C22×C11#56311yescharacteristic
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—24no—
537C4×C11—42no—
538C4×C11—42no—
539C4×C11—42no—
540C4×C11—42no—
541C4×C11—42no—
542C4×C11—81no—
543Dic11—24no—
544Dic11—24no—
545Dic11—42no—
546Dic11—42no—
547Dic11—81no—
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—441no—
562C23×C4—441no—
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—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—222no—
585C2×C4⋊C4—222no—
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⋊C4—441no—
595C2×C4⋊C4C4×D1114yescomplemented
596C2×C22⋊C4—114no—
597C2×C22⋊C4—114no—
598C2×C22⋊C4—114no—
599C2×C22⋊C4—114no—
600C2×C22⋊C4—114no—
601C2×C22⋊C4—222no—
602C2×C22⋊C4—222no—
603C2×C22⋊C4—222no—
604C2×C22⋊C4—222no—
605C2×C22⋊C4—222no—
606C2×C22⋊C4—222no—
607C2×C22⋊C4—222no—
608C2×C22⋊C4—441no—
609C2×C22⋊C4—441no—
610C2×C22⋊C4—441no—
611C2×C22⋊C4—441no—
612C2×C22⋊C4—441no—
613C2×C22⋊C4—441no—
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—41no—
617C2×C42—114no—
618C2×C42—222no—
619C2×C42—222no—
620#95—22no—
621#95—22no—
622#95—41no—
623#95—41no—
624#95—114no—
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—441no—
634#95—441no—
635#95—441no—
636#95—441no—
637#95—441no—
638C2×C11#231711yescharacteristic
639C2×C11#232411yescharacteristic
640C2×C11#233411yescharacteristic
641C2×C11D4×C4⋊C411yescharacteristic
642C2×C11#234911yescharacteristic
643C2×C11#235911yescharacteristic
644C2×C11#237911yescharacteristic
645C2×C11#267011yescharacteristic
646C2×C11#267211yescharacteristic
647C2×C11#269811yescharacteristic
648C2×C11#270411yescharacteristic
649C2×C11#270611yescharacteristic
650C2×C11#272011yescharacteristic
651C2×C11#276311yescharacteristic
652C2×C11#276811yescharacteristic
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—112no—
712C22×C4—112no—
713C22×C4—112no—
714C22×C4—112no—
715C22×C4—112no—
716C22×C4—112no—
717C22×C4—112no—
718C22×C4—112no—
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—444no—
761C22×C4—444no—
762C22×C4—444no—
763C22×C4—444no—
764C22×C4—444no—
765C22×C4—444no—
766C22×C4—444no—
767C22×C4C2×C4×D1112yes—
768C22×C4C2×C4×D1112yes—
769C22×C4C2×C4×D1112yes—
770C22×C4#433912yes—
771C22×C4#433912yes—
772C22×C4D4×D1112yes—
773C22×C4D4×D1112yes—
774C22×C4Q8×D1112yes—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—444no—
778C4⋊C4—444no—
779C4⋊C4—444no—
780C4⋊C4—444no—
781C4⋊C4—444no—
782C4⋊C4—444no—
783C22⋊C4—1116no—
784C22⋊C4—228no—
785C22⋊C4—444no—
786C22⋊C4—444no—
787C22⋊C4—444no—
788C22⋊C4—444no—
789C42—44no—
790C42—228no—
791C11#1440311yescharacteristic, 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×#433911yescharacteristic
829C23C2×#433911yescharacteristic
830C23C2×D4×D1111yescharacteristic
831C23C2×D4×D1111yescharacteristic
832C23#6703711yescharacteristic
833C23#6703711yescharacteristic
834C23#6703711yescharacteristic
835C23C2×Q8×D1111yescharacteristic
836C23#6704011yescharacteristic
837C23#6704011yescharacteristic
838C23#41×D1111yescharacteristic
839C23#6704211yescharacteristic
840C23#6704211yescharacteristic
841C23#6704311yescharacteristic
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—114no—
891C2×C4—114no—
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—4416no—
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×C4—441no—
940C2×C4C4⋊C4×D1114yes—
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—
956C22C4×#433911yescharacteristic
957C22#1062301711yescharacteristic
958C22#1062302111yescharacteristic
959C22#1062302111yescharacteristic
960C22C2×C4⋊C4×D1111yescharacteristic
961C22#1062303811yescharacteristic
962C22#1062304211yescharacteristic
963C22#1062304211yescharacteristic
964C22#1062304611yescharacteristic
965C22#1062305811yescharacteristic
966C22#1062306511yescharacteristic
967C22C4×D4×D1111yescharacteristic
968C22#1062307711yescharacteristic
969C22#1062308111yescharacteristic
970C22#1062309111yescharacteristic
971C22#1062310511yescharacteristic
972C22#1062310511yescharacteristic
973C22#1062311211yescharacteristic
974C22#1062311411yescharacteristic
975C22#1062312811yescharacteristic
976C22#1062313811yescharacteristic
977C22#1062314011yescharacteristic
978C22#1062314611yescharacteristic
979C22#1062315911yescharacteristic
980C22#1062316211yescharacteristic
981C22#1062317811yescharacteristic
982C22#1062317811yescharacteristic
983C22#1062320011yescharacteristic
984C22#1062321411yescharacteristic
985C22#1062322011yescharacteristic
986C22#1062322111yescharacteristic
987C22#1062324611yescharacteristic
988C22#1062325811yescharacteristic
989C22#1062326011yescharacteristic
990C22#1062326611yescharacteristic
991C4—24no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—81no—
998C4—224no—
999C4—224no—
1000C4—442no—
1001C4—442no—
1002C4—881no—
1003C4—881no—
1004C4—881no—
1005C2—444no—
1006C2#1307123811yescharacteristic
1007C2#1307130211yescharacteristic
1008C2#1307138511yescharacteristic
1009C2#1307151711yescharacteristic
1010C2#1307152311yescharacteristic
1011C2#1307161311yescharacteristic
1012C2#1307178811yescharacteristic
1013C2#1307483911yescharacteristic
1014C2#1307486811yescharacteristic
1015C2#1307519311yescharacteristic
1016C2#1307526911yescharacteristic
1017C2#1307530411yescharacteristic
1018C2#1307549111yescharacteristic
1019C2#1307602911yescharacteristic
1020C2#1307609911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4⋊#95D11
hypocenterC11#14403
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
5. C2×#10622263C2semidirect
6. #13066880C2semidirect
7. #13066879C2semidirect
8. #13066874C2semidirect
9. #13066869C2semidirect
12. #13066849C2semidirect
13. Dic11⋊#95C2semidirect
15. C11×C4⋊#95C2semidirect
51. #10622603C4semidirect
83. C2×C11×C4⋊C4C2×C4semidirect
125. C2×C4×Dic11C2×C4semidirect
141. C11⋊#95C2×C4semidirect
142. C11⋊#95C2×C4semidirect
274. (C2×D11)⋊C4C4⋊C4semidirect
295. C4⋊#95D11semidirect
595. C2×C4⋊C4C4×D11semidirect
791. C11#14403semidirect

Maximal subgroups

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

subgroupindex
C2×#106225532
C2×#106226032
C2×#106222812
C2×#106226022
C2×#106222632
#130668802
#130668792
#130668742
#130668692
#130668602
#130668492
Dic11⋊#952
(C2×D11)⋊#952
C11×C4⋊#952
#1440311