Finite Group Databasebeta

← #14683796

Subgroups — #14683796

Order 2816.

1390 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×#10622288C211yesmaximal, characteristic
2C2×#10622585C211yesmaximal, characteristic, complemented
3C2×#10622282C211yesmaximal, characteristic
4#13066882C211yesmaximal, characteristic, complemented
5#13066871C211yesmaximal, characteristic, complemented
6#13066860C211yesmaximal, characteristic
7#13066860C211yesmaximal, characteristic
8#13066858C211yesmaximal, characteristic
9#13066854C211yesmaximal, characteristic
10#13066852C211yesmaximal, characteristic
11#13066849C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13#13066847C211yesmaximal, characteristic, complemented
14#13066841C211yesmaximal, 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×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
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#10622585—24no—
52#10622288C418yescomplemented
53#10622282—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—41no—
73C2×C42×C11—41no—
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—41no—
84C2×(C2×D11)⋊C4—41no—
85C2×(C2×D11)⋊C4—41no—
86C2×(C2×D11)⋊C4—41no—
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×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—41no—
102C2×Dic11⋊C4—41no—
103C2×Dic11⋊C4—41no—
104C2×Dic11⋊C4—41no—
105C2×Dic11⋊C4—41no—
106C2×Dic11⋊C4C2×C414yes—
107C2×Dic11⋊C4D414yes—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—41no—
112C2×C4×Dic11—41no—
113C2×C4×Dic11—41no—
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—41no—
127C11⋊#95—41no—
128C11⋊#95—41no—
129C11⋊#95—41no—
130C11⋊#95—41no—
131C11⋊#95—41no—
132C11⋊#95C2×C414yes—
133C11⋊#95C2×C414yes—
134#14569—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×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C22×C412yes—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C2×D412yes—
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×Dic11—21no—
241C22×Dic11C22×C412yes—
242C22×Dic11C22×C412yes—
243C22×Dic11C22×C412yes—
244C22×Dic11C2×D412yes—
245C22×Dic11C2×D412yes—
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—44no—
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—
258Dic11⋊C4—28no—
259Dic11⋊C4—44no—
260Dic11⋊C4—44no—
261Dic11⋊C4—44no—
262C4×Dic11—44no—
263C4×Dic11—44no—
264C2×#397—111no—
265C2×#389—111no—
266C2×#388—111no—
267#1445—111no—
268#1442—111no—
269#1439—111no—
270#1439—111no—
271#1439—111no—
272#1437—111no—
273#1437—111no—
274#1436—111no—
275#1436—111no—
276#1436—111no—
277#1436D1111yescharacteristic, complemented
278#1434—111no—
279C23×C11C23×C411yescharacteristic
280C23×C11C22×D411yescharacteristic
281C23×C11C2×#4111yescharacteristic
282C23×C11C2×#4111yescharacteristic
283C23×C11C2×#4111yescharacteristic
284C23×C11C2×#4111yescharacteristic
285C23×C11C2×#4111yescharacteristic
286C23×C11H(5,𝔽2)11yescharacteristic
287C23×C11H(5,𝔽2)11yescharacteristic
288C23×C11H(5,𝔽2)11yescharacteristic
289C23×C11H(5,𝔽2)11yescharacteristic
290C23×C11H(5,𝔽2)11yescharacteristic
291C23×C112−1+411yescharacteristic
292C23×C112−1+411yescharacteristic
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—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
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—41no—
377C2×C4×C11—41no—
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—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
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×Dic11C4×D414yes—
427C22×C4⋊C4—111no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4—111no—
430C22×C4⋊C4—111no—
431C22×C4⋊C4C2×D1111yescharacteristic
432C22×C22⋊C4—111no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4—111no—
435C22×C22⋊C4—111no—
436C22×C22⋊C4—111no—
437C22×C22⋊C4—111no—
438C22×C22⋊C4—111no—
439C22×C42—111no—
440C22×C42—111no—
441C22×C42C2×D1111yescharacteristic
442#397—118no—
443#389—224no—
444#388—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×C4×D411yescharacteristic
466C22×C11C4×#4111yescharacteristic
467C22×C11C4×#4111yescharacteristic
468C22×C11#51811yescharacteristic
469C22×C11#52011yescharacteristic
470C22×C11#52011yescharacteristic
471C22×C11#52011yescharacteristic
472C22×C11#53411yescharacteristic
473C22×C11#53611yescharacteristic
474C22×C11#53811yescharacteristic
475C22×C11#53811yescharacteristic
476C22×C11#53911yescharacteristic
477C22×C11#53911yescharacteristic
478C22×C11#53911yescharacteristic
479C22×C11#53911yescharacteristic
480C22×C11#54011yescharacteristic
481C22×C11#54111yescharacteristic
482C22×C11#54211yescharacteristic
483C22×C11#54211yescharacteristic
484C22×C11#54611yescharacteristic
485C22×C11#54611yescharacteristic
486C22×C11#54811yescharacteristic
487C22×C11#55011yescharacteristic
488C22×C11#55111yescharacteristic
489C22×C11#55211yescharacteristic
490C22×C11#55311yescharacteristic
491C22×C11#55311yescharacteristic
492C22×C11#55511yescharacteristic
493C22×C11#55611yescharacteristic
494C22×C11#55611yescharacteristic
495C22×C11#55911yescharacteristic
496C22×C11#56011yescharacteristic
497C22×C11#56211yescharacteristic
498C22×C11#56211yescharacteristic
499C22×C11#56311yescharacteristic
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—42no—
516C4×C11—42no—
517C4×C11—42no—
518C4×C11—42no—
519C4×C11—42no—
520C4×C11—42no—
521C4×C11—81no—
522Dic11—24no—
523Dic11—42no—
524Dic11—42no—
525Dic11—42no—
526Dic11—42no—
527Dic11—42no—
528Dic11—81no—
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—114no—
549C2×C4⋊C4—222no—
550C2×C4⋊C4—222no—
551C2×C4⋊C4—222no—
552C2×C4⋊C4—222no—
553C2×C4⋊C4—222no—
554C2×C4⋊C4—441no—
555C2×C4⋊C4—441no—
556C2×C4⋊C4—441no—
557C2×C4⋊C4—441no—
558C2×C4⋊C4—441no—
559C2×C22⋊C4—114no—
560C2×C22⋊C4—114no—
561C2×C22⋊C4—114no—
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—222no—
569C2×C22⋊C4—222no—
570C2×C22⋊C4—441no—
571C2×C22⋊C4—441no—
572C2×C22⋊C4—441no—
573C2×C22⋊C4—441no—
574C2×C22⋊C4—441no—
575C2×C22⋊C4—441no—
576C2×C22⋊C4—441no—
577C2×C22⋊C4—441no—
578C2×C22⋊C4—441no—
579C2×C22⋊C4—441no—
580C2×C42—41no—
581C2×C42—41no—
582C2×C42—41no—
583C2×C42—222no—
584C2×C42—222no—
585C2×C42—222no—
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—441no—
603#95—441no—
604#95—441no—
605#95—441no—
606#95—441no—
607#95—441no—
608#95C4×D1114yes—
609C2×C11#232211yescharacteristic
610C2×C11#233411yescharacteristic
611C2×C11#233511yescharacteristic
612C2×C11#236311yescharacteristic
613C2×C11#236711yescharacteristic
614C2×C11#237311yescharacteristic
615C2×C11#237611yescharacteristic
616C2×C11#268811yescharacteristic
617C2×C11#269411yescharacteristic
618C2×C11#271611yescharacteristic
619C2×C11#273011yescharacteristic
620C2×C11#277711yescharacteristic
621C2×C11#278311yescharacteristic
622C2×C11#279611yescharacteristic
623C2×C11#280811yescharacteristic
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—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—112no—
685C22×C4—112no—
686C22×C4—112no—
687C22×C4—112no—
688C22×C4—112no—
689C22×C4—112no—
690C22×C4—112no—
691C22×C4—112no—
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×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4C2×C4×D1112yes—
734C22×C4C2×C4×D1112yes—
735C22×C4C2×C4×D1112yes—
736C22×C4#433912yes—
737C22×C4#433912yes—
738C22×C4D4×D1112yes—
739C4⋊C4—44no—
740C4⋊C4—228no—
741C4⋊C4—444no—
742C4⋊C4—444no—
743C4⋊C4—444no—
744C22⋊C4—228no—
745C22⋊C4—444no—
746C22⋊C4—444no—
747C22⋊C4—444no—
748C22⋊C4—444no—
749C22⋊C4—444no—
750C22⋊C4—444no—
751C42—44no—
752C42—444no—
753C42—444no—
754C11#1456911yescharacteristic, 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
794C23#6703711yescharacteristic
795C23#6703711yescharacteristic
796C23#6703711yescharacteristic
797C23#6704011yescharacteristic
798C23#6704011yescharacteristic
799C23#41×D1111yescharacteristic
800C23#41×D1111yescharacteristic
801C23#41×D1111yescharacteristic
802C23#6704211yescharacteristic
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—41no—
824C2×C4—41no—
825C2×C4—41no—
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—41no—
853C2×C4—41no—
854C2×C4—114no—
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—441no—
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—441no—
902C2×C4—441no—
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—
918C22C4×#433911yescharacteristic
919C22#1062302111yescharacteristic
920C22#1062303511yescharacteristic
921C22#1062304611yescharacteristic
922C22#1062305311yescharacteristic
923C22#1062306311yescharacteristic
924C22#1062306511yescharacteristic
925C22#1062307111yescharacteristic
926C22#1062307111yescharacteristic
927C22C4×D4×D1111yescharacteristic
928C22#1062307611yescharacteristic
929C22#1062307711yescharacteristic
930C22#1062308411yescharacteristic
931C22#1062308711yescharacteristic
932C22#1062309111yescharacteristic
933C22#1062309911yescharacteristic
934C22#1062310511yescharacteristic
935C22#1062311211yescharacteristic
936C22#1062311411yescharacteristic
937C22#1062312611yescharacteristic
938C22#1062313611yescharacteristic
939C22#1062314111yescharacteristic
940C22#1062316911yescharacteristic
941C22#1062317111yescharacteristic
942C22#1062317711yescharacteristic
943C22#1062317811yescharacteristic
944C22#1062319411yescharacteristic
945C22#1062319511yescharacteristic
946C22#1062319811yescharacteristic
947C22#1062320811yescharacteristic
948C22#1062322311yescharacteristic
949C22#1062322311yescharacteristic
950C22#1062323311yescharacteristic
951C22#1062323511yescharacteristic
952C22#1062325511yescharacteristic
953C4—42no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—81no—
960C4—224no—
961C4—442no—
962C4—442no—
963C4—442no—
964C4—442no—
965C4—442no—
966C4—881no—
967C2—882no—
968C2#1307128011yescharacteristic
969C2#1307138511yescharacteristic
970C2#1307141211yescharacteristic
971C2#1307165511yescharacteristic
972C2#1307168211yescharacteristic
973C2#1307173211yescharacteristic
974C2#1307176511yescharacteristic
975C2#1307504911yescharacteristic
976C2#1307513311yescharacteristic
977C2#1307543711yescharacteristic
978C2#1307561011yescharacteristic
979C2#1307621411yescharacteristic
980C2#1307629811yescharacteristic
981C2#1307645411yescharacteristic
982C2#1307659211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#14569
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#10622585C2semidirect
4. #13066882C2semidirect
5. #13066871C2semidirect
11. #13066849C2semidirect
12. #13066847C2semidirect
13. #13066847C2semidirect
14. #13066841C2semidirect
15. C11×#1436C2semidirect
52. #10622288C4semidirect
277. #1436D11semidirect
754. C11#14569semidirect

Maximal subgroups

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

subgroupindex
C2×#106222882
C2×#106225852
C2×#106222822
#130668822
#130668712
#130668602
#130668582
#130668542
#130668522
#130668492
#130668472
#130668412
C11×#14362
#1456911