Finite Group Databasebeta

← #14677113

Subgroups — #14677113

Order 2816.

1462 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622283C211yesmaximal, characteristic
2C2×#10622553C211yesmaximal, characteristic
3C2×#10622264C211yesmaximal, characteristic, complemented
4#13066877C211yesmaximal, characteristic, complemented
5#13066868C211yesmaximal, characteristic, complemented
6#13066864C211yesmaximal, characteristic
7#13066858C211yesmaximal, characteristic
8#13066852C211yesmaximal, characteristic
9#13066852C211yesmaximal, characteristic
10#13066852C211yesmaximal, characteristic
11#13066847C211yesmaximal, characteristic, complemented
12#13066845C211yesmaximal, characteristic, complemented
13C4×C11⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×(C2×D11)⋊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×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
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#10622553—24no—
52#10622283C418yescomplemented
53#10622264—24no—
54C24×D11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—41no—
72C2×C42×C11—22no—
73C2×C42×C11—22no—
74C2×C42×C11—41no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—41no—
88C2×(C2×D11)⋊C4—41no—
89C2×(C2×D11)⋊C4—41no—
90C2×(C2×D11)⋊C4—41no—
91C2×(C2×D11)⋊C4—41no—
92C2×(C2×D11)⋊C4—41no—
93C2×(C2×D11)⋊C4C2×C414yes—
94C2×(C2×D11)⋊C4C2×C414yes—
95C2×(C2×D11)⋊C4C2×C414yes—
96C2×C4⋊Dic11—41no—
97C2×C4⋊Dic11—41no—
98C2×C4⋊Dic11C2×C414yes—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—41no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—41no—
110C2×C4×Dic11—41no—
111C2×C4×Dic11—41no—
112C2×C4×Dic11—41no—
113C2×C4×Dic11C2×C414yes—
114C11×#95—22no—
115C11×#95—22no—
116C11×#95—41no—
117C11×#95—41no—
118C11×#95C2×C414yes—
119C11⋊#95—22no—
120C11⋊#95—22no—
121C11⋊#95—22no—
122C11⋊#95—22no—
123C11⋊#95—22no—
124C11⋊#95—22no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—41no—
132C11⋊#95C2×C414yes—
133C11⋊#95D414yes—
134#14013—111nomaximal, Sylow
135C24×C11C2411yescharacteristic
136C23×D11—21no—
137C23×D11—21no—
138C23×D11—21no—
139C23×D11—21no—
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—21no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11C22×C412yes—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
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×C11C22×C412yes—
192C22×C4×C11C22×C412yes—
193C22×C4×C11C22×C412yes—
194C22×C4×C11C2×D412yes—
195C22×C4×C11#4112yes—
196C22×C4×C11#4112yes—
197C22×C4×C11#4112yes—
198C22×C4×C11#4112yes—
199C22×C4×C11#4112yes—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
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×Dic11C22×C412yes—
241C22×Dic11C22×C412yes—
242C22×Dic11C22×C412yes—
243C22×Dic11C2×D412yes—
244C22×Dic11C2×D412yes—
245C22×Dic11#4112yes—
246C22×Dic11#4112yes—
247C22×Dic11#4112yes—
248C22×Dic11#4112yes—
249C11×C4⋊C4—44no—
250C42×C11—44no—
251(C2×D11)⋊C4—28no—
252(C2×D11)⋊C4—28no—
253(C2×D11)⋊C4—44no—
254(C2×D11)⋊C4—44no—
255(C2×D11)⋊C4—44no—
256(C2×D11)⋊C4—44no—
257(C2×D11)⋊C4—44no—
258C4⋊Dic11—44no—
259Dic11⋊C4—44no—
260C4×Dic11—28no—
261C4×Dic11—44no—
262C4×Dic11—44no—
263C4×Dic11—44no—
264C2×#388—111no—
265C2×#388—111no—
266C2×#383—111no—
267#1443—111no—
268#1441—111no—
269#1440—111no—
270#1439—111no—
271#1437—111no—
272#1437—111no—
273#1437—111no—
274#1436—111no—
275#1436D1111yescharacteristic, complemented
276C4⋊#95—111no—
277C4×#95—111no—
278C4×#95—111no—
279C23×C11C23×C411yescharacteristic
280C23×C11C22×D411yescharacteristic
281C23×C11C2×#4111yescharacteristic
282C23×C11C2×#4111yescharacteristic
283C23×C11C2×#4111yescharacteristic
284C23×C11C2×#4111yescharacteristic
285C23×C11C2×#4111yescharacteristic
286C23×C11C2×#4111yescharacteristic
287C23×C11C2×#4111yescharacteristic
288C23×C11C2×#4111yescharacteristic
289C23×C11C2×#4111yescharacteristic
290C23×C11H(5,𝔽2)11yescharacteristic
291C23×C11H(5,𝔽2)11yescharacteristic
292C23×C11H(5,𝔽2)11yescharacteristic
293C23×C112−1+411yescharacteristic
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—41no—
302C22×D11—41no—
303C22×D11—41no—
304C22×D11—41no—
305C22×D11—41no—
306C22×D11—41no—
307C22×D11—41no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
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#11714yes—
377C2×C4×C11C4×D414yes—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
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—41no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11#12614yes—
427C22×C4⋊C4—111no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4C2×D1111yescharacteristic
430C22×C22⋊C4—111no—
431C22×C22⋊C4—111no—
432C22×C22⋊C4—111no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4—111no—
435C22×C22⋊C4—111no—
436C22×C22⋊C4—111no—
437C22×C42—111no—
438C22×C42—111no—
439C22×C42—111no—
440C22×C42—111no—
441C22×C42C2×D1111yescharacteristic
442#388—118no—
443#388—224no—
444#383—224no—
445C2×#95—111no—
446C2×#95—111no—
447C2×#95—111no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95C2×D1111yescharacteristic
461C2×#95C2×D1111yescharacteristic
462C2×#95C2×D1111yescharacteristic
463C2×#95C2×D1111yescharacteristic
464C2×#95C2×D1111yescharacteristic
465C22×C11C2×#11711yescharacteristic
466C22×C11C2×C4×D411yescharacteristic
467C22×C11C4×#4111yescharacteristic
468C22×C11C4×#4111yescharacteristic
469C22×C11C4×#4111yescharacteristic
470C22×C11#51811yescharacteristic
471C22×C11#52011yescharacteristic
472C22×C11C2×#12611yescharacteristic
473C22×C11#52911yescharacteristic
474C22×C11#52911yescharacteristic
475C22×C11#52911yescharacteristic
476C22×C11#52911yescharacteristic
477C22×C11#52911yescharacteristic
478C22×C11#53211yescharacteristic
479C22×C11#53211yescharacteristic
480C22×C11#53811yescharacteristic
481C22×C11#53811yescharacteristic
482C22×C11#54211yescharacteristic
483C22×C11#54211yescharacteristic
484C22×C11#54611yescharacteristic
485C22×C11#54611yescharacteristic
486C22×C11#54711yescharacteristic
487C22×C11#55011yescharacteristic
488C22×C11#55111yescharacteristic
489C22×C11#55111yescharacteristic
490C22×C11#55111yescharacteristic
491C22×C11#55211yescharacteristic
492C22×C11#55311yescharacteristic
493C22×C11#55311yescharacteristic
494C22×C11#55311yescharacteristic
495C22×C11#55311yescharacteristic
496C22×C11#55311yescharacteristic
497C22×C11#55511yescharacteristic
498C22×C11#55611yescharacteristic
499C22×C11#55611yescharacteristic
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—42no—
506C2×D11—42no—
507C2×D11—81no—
508C2×D11—81no—
509C2×D11—81no—
510C2×D11—81no—
511C2×D11—81no—
512C2×D11—81no—
513C2×D11—81no—
514C2×D11—81no—
515C4×C11—24no—
516C4×C11—24no—
517C4×C11—42no—
518C4×C11—42no—
519C4×C11—42no—
520C4×C11—81no—
521C4×C11—81no—
522Dic11—24no—
523Dic11—42no—
524Dic11—42no—
525Dic11—42no—
526Dic11—42no—
527Dic11—42no—
528Dic11—42no—
529C25—111no—
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4C22×D1111yescharacteristic
538C23×C4C22×D1111yescharacteristic
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543C23×C4C22×D1111yescharacteristic
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—114no—
548C2×C4⋊C4—222no—
549C2×C4⋊C4—222no—
550C2×C4⋊C4—441no—
551C2×C4⋊C4—441no—
552C2×C4⋊C4—441no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—222no—
557C2×C22⋊C4—222no—
558C2×C22⋊C4—222no—
559C2×C22⋊C4—222no—
560C2×C22⋊C4—222no—
561C2×C22⋊C4—222no—
562C2×C22⋊C4—222no—
563C2×C22⋊C4—222no—
564C2×C22⋊C4—222no—
565C2×C22⋊C4—222no—
566C2×C22⋊C4—222no—
567C2×C22⋊C4—222no—
568C2×C22⋊C4—441no—
569C2×C22⋊C4—441no—
570C2×C22⋊C4—441no—
571C2×C22⋊C4—441no—
572C2×C22⋊C4—441no—
573C2×C22⋊C4—441no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—41no—
577C2×C42—114no—
578C2×C42—222no—
579C2×C42—222no—
580C2×C42—222no—
581C2×C42—222no—
582C2×C42—222no—
583C2×C42—222no—
584C2×C42—222no—
585C2×C42—441no—
586C2×C42—441no—
587C2×C42—441no—
588C2×C42—441no—
589#95—22no—
590#95—22no—
591#95—41no—
592#95—41no—
593#95—114no—
594#95—114no—
595#95—222no—
596#95—222no—
597#95—222no—
598#95—222no—
599#95—222no—
600#95—222no—
601#95—222no—
602#95—222no—
603#95—222no—
604#95—222no—
605#95—222no—
606#95—222no—
607#95—441no—
608#95C4×D1114yes—
609C2×C11#229311yescharacteristic
610C2×C11C4×#12611yescharacteristic
611C2×C11#233711yescharacteristic
612C2×C11#234711yescharacteristic
613C2×C11#235311yescharacteristic
614C2×C11#235911yescharacteristic
615C2×C11#236311yescharacteristic
616C2×C11#251011yescharacteristic
617C2×C11#251211yescharacteristic
618C2×C11#251811yescharacteristic
619C2×C11#252111yescharacteristic
620C2×C11#252511yescharacteristic
621C2×C11#253211yescharacteristic
622C2×C11#255411yescharacteristic
623C2×C11#255911yescharacteristic
624D11—82no—
625C24—112no—
626C24—221no—
627C24—221no—
628C24—221no—
629C24—221no—
630C24—221no—
631C24—221no—
632C24—221no—
633C24—221no—
634C24—221no—
635C24—221no—
636C24—221no—
637C24—221no—
638C24—221no—
639C24—221no—
640C24C23×D1111yescharacteristic
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
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—112no—
682C22×C4—112no—
683C22×C4—112no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—112no—
687C22×C4—112no—
688C22×C4—112no—
689C22×C4—112no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4C2×C4×D1112yes—
731C22×C4C2×C4×D1112yes—
732C22×C4C2×C4×D1112yes—
733C22×C4#433912yes—
734C22×C4#433912yes—
735C22×C4D4×D1112yes—
736C22×C4#434112yes—
737C22×C4#434312yes—
738C22×C4#434312yes—
739C4⋊C4—44no—
740C4⋊C4—444no—
741C4⋊C4—444no—
742C22⋊C4—228no—
743C22⋊C4—228no—
744C22⋊C4—444no—
745C22⋊C4—444no—
746C22⋊C4—444no—
747C22⋊C4—444no—
748C22⋊C4—444no—
749C42—44no—
750C42—228no—
751C42—444no—
752C42—444no—
753C42—444no—
754C11#1401311yescharacteristic, complemented, Sylow
755C23—222no—
756C23—222no—
757C23—222no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23—222no—
762C23—441no—
763C23—441no—
764C23—441no—
765C23—441no—
766C23—441no—
767C23—441no—
768C23—441no—
769C23—441no—
770C23—441no—
771C23—441no—
772C23—441no—
773C23—441no—
774C23—441no—
775C23—441no—
776C23—441no—
777C23—441no—
778C23—441no—
779C23—441no—
780C23—441no—
781C23—441no—
782C23—441no—
783C23—441no—
784C23—441no—
785C23—441no—
786C23—441no—
787C23—441no—
788C23—441no—
789C23—441no—
790C23C22×C4×D1111yescharacteristic
791C23C2×#433911yescharacteristic
792C23C2×#433911yescharacteristic
793C23C2×D4×D1111yescharacteristic
794C23C2×#434111yescharacteristic
795C23#6703711yescharacteristic
796C23#6703711yescharacteristic
797C23C2×#434311yescharacteristic
798C23C2×#434311yescharacteristic
799C23#41×D1111yescharacteristic
800C23#41×D1111yescharacteristic
801C23#41×D1111yescharacteristic
802C23#41×D1111yescharacteristic
803C23#6704211yescharacteristic
804C23#6704311yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—114no—
853C2×C4—222no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—441no—
878C2×C4—441no—
879C2×C4—441no—
880C2×C4—441no—
881C2×C4—441no—
882C2×C4—441no—
883C2×C4—441no—
884C2×C4—441no—
885C2×C4—441no—
886C2×C4—441no—
887C2×C4—441no—
888C2×C4—441no—
889C2×C4—441no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4#6692514yes—
902C2×C4#6694614yes—
903C22—442no—
904C22—442no—
905C22—442no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22—442no—
910C22—881no—
911C22—881no—
912C22—881no—
913C22—881no—
914C22—881no—
915C22—881no—
916C22—881no—
917C22—881no—
918C22C2×#6692511yescharacteristic
919C22#1062302611yescharacteristic
920C22C2×#6694611yescharacteristic
921C22#1062304511yescharacteristic
922C22#1062305311yescharacteristic
923C22#1062305811yescharacteristic
924C22#1062306411yescharacteristic
925C22C4×#434111yescharacteristic
926C22#1062307111yescharacteristic
927C22#1062307611yescharacteristic
928C22#1062307711yescharacteristic
929C22#1062307911yescharacteristic
930C22#1062307911yescharacteristic
931C22#1062308911yescharacteristic
932C22#1062309611yescharacteristic
933C22C4×#434311yescharacteristic
934C22#1062311111yescharacteristic
935C22#1062311111yescharacteristic
936C22#1062311511yescharacteristic
937C22#1062312211yescharacteristic
938C22#1062313011yescharacteristic
939C22#1062314411yescharacteristic
940C22#1062315511yescharacteristic
941C22#1062316111yescharacteristic
942C22#1062316811yescharacteristic
943C22#1062317311yescharacteristic
944C22#1062318011yescharacteristic
945C22#1062318611yescharacteristic
946C22#1062318811yescharacteristic
947C22#1062320011yescharacteristic
948C22#1062322211yescharacteristic
949C22#1062322611yescharacteristic
950C22D11×#12611yescharacteristic
951C22#1062324111yescharacteristic
952C22#1062326511yescharacteristic
953C4—24no—
954C4—24no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—81no—
959C4—81no—
960C4—224no—
961C4—442no—
962C4—442no—
963C4—442no—
964C4—442no—
965C4—442no—
966C4—442no—
967C2—882no—
968C2#1307107711yescharacteristic
969C2#1307116611yescharacteristic
970C2#1307142711yescharacteristic
971C2#1307150511yescharacteristic
972C2#1307155011yescharacteristic
973C2#1307160611yescharacteristic
974C2#1307165311yescharacteristic
975C2#1307317311yescharacteristic
976C2#1307319911yescharacteristic
977C2#1307327311yescharacteristic
978C2#1307331811yescharacteristic
979C2#1307337911yescharacteristic
980C2#1307348411yescharacteristic
981C2#1307368011yescharacteristic
982C2#1307374911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#14013
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×#10622264C2semidirect
4. #13066877C2semidirect
5. #13066868C2semidirect
11. #13066847C2semidirect
12. #13066845C2semidirect
13. C4×C11⋊#95C2semidirect
14. #95×Dic11C2semidirect
15. C11×#1436C2semidirect
52. #10622283C4semidirect
275. #1436D11semidirect
754. C11#14013semidirect

Maximal subgroups

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

subgroupindex
C2×#106222832
C2×#106225532
C2×#106222642
#130668772
#130668682
#130668642
#130668582
#130668522
#130668472
#130668452
C4×C11⋊#952
#95×Dic112
C11×#14362
#1401311