Finite Group Databasebeta

← #14680340

Subgroups — #14680340

Order 2816.

1398 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×#10622553C211yesmaximal, characteristic
2C2×#10622553C211yesmaximal, characteristic
3C2×#10622546C211yesmaximal, characteristic, complemented
4#13066880C211yesmaximal, characteristic, complemented
5#13066876C211yesmaximal, characteristic, complemented
6#13066872C211yesmaximal, characteristic, complemented
7#13066871C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic
9#13066862C211yesmaximal, characteristic
10#13066862C211yesmaximal, characteristic
11#13066860C211yesmaximal, characteristic
12#13066854C211yesmaximal, characteristic
13#13066849C211yesmaximal, characteristic, complemented
14#13066846C211yesmaximal, characteristic, complemented
15C4×C11×#95C211yesmaximal, characteristic, complemented
16C22×C42×C11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
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#10622553C418yescomplemented
53#10622546—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×C42×C11—22no—
70C2×C42×C11—41no—
71C2×C42×C11—41no—
72C2×C42×C11—41no—
73C2×C42×C11—41no—
74C2×C42×C11—41no—
75C2×C42×C11—41no—
76C2×C42×C11C2×C414yes—
77C2×C42×C11D414yes—
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—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)⋊C4—41no—
94C2×(C2×D11)⋊C4—41no—
95C2×(C2×D11)⋊C4—41no—
96C2×(C2×D11)⋊C4C2×C414yes—
97C2×(C2×D11)⋊C4C2×C414yes—
98C2×(C2×D11)⋊C4C2×C414yes—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11—41no—
102C2×C4⋊Dic11—41no—
103C2×C4⋊Dic11—41no—
104C2×C4⋊Dic11—41no—
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⋊C4—41no—
113C2×Dic11⋊C4C2×C414yes—
114C11×#95—22no—
115C11×#95—22no—
116C11×#95—22no—
117C11×#95—22no—
118C11⋊#95—22no—
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#14279—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×C11C22×C412yes—
190C22×C4×C11C22×C412yes—
191C22×C4×C11C22×C412yes—
192C22×C4×C11C2×D412yes—
193C22×C4×C11C2×D412yes—
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×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—
249C42×C11—44no—
250C42×C11—44no—
251C42×C11—44no—
252(C2×D11)⋊C4—28no—
253(C2×D11)⋊C4—28no—
254(C2×D11)⋊C4—44no—
255(C2×D11)⋊C4—44no—
256(C2×D11)⋊C4—44no—
257(C2×D11)⋊C4—44no—
258(C2×D11)⋊C4—44no—
259C4⋊Dic11—44no—
260C4⋊Dic11—44no—
261Dic11⋊C4—28no—
262Dic11⋊C4—44no—
263Dic11⋊C4—44no—
264C2×#388—111no—
265C2×#388—111no—
266C2×#387—111no—
267#1444—111no—
268#1443—111no—
269#1442—111no—
270#1442—111no—
271#1440—111no—
272#1439—111no—
273#1439—111no—
274#1439—111no—
275#1437—111no—
276#1436—111no—
277C4⋊#95—111no—
278C4×#95D1111yescharacteristic, complemented
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—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—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—41no—
388C2×Dic11—41no—
389C2×Dic11—41no—
390C2×Dic11—41no—
391C2×Dic11—41no—
392C2×Dic11—41no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—41no—
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×Dic11—41no—
427C22×C4⋊C4—111no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4—111no—
430C22×C4⋊C4—111no—
431C22×C4⋊C4—111no—
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×C42C2×D1111yescharacteristic
440C22×C42C2×D1111yescharacteristic
441C22×C42C2×D1111yescharacteristic
442#388—118no—
443#388—224no—
444#387—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×#95—111no—
461C2×#95C2×D1111yescharacteristic
462C2×#95C2×D1111yescharacteristic
463C2×#95C2×D1111yescharacteristic
464C2×#95C2×D1111yescharacteristic
465C22×C11C2×#11711yescharacteristic
466C22×C11C2×C4×D411yescharacteristic
467C22×C11C4×#4111yescharacteristic
468C22×C11#51811yescharacteristic
469C22×C11#52011yescharacteristic
470C22×C11#52011yescharacteristic
471C22×C11#52011yescharacteristic
472C22×C11#52911yescharacteristic
473C22×C11#52911yescharacteristic
474C22×C11#53211yescharacteristic
475C22×C11#53211yescharacteristic
476C22×C11#53411yescharacteristic
477C22×C11#53511yescharacteristic
478C22×C11#53611yescharacteristic
479C22×C11#53711yescharacteristic
480C22×C11#53811yescharacteristic
481C22×C11#53811yescharacteristic
482C22×C11#53811yescharacteristic
483C22×C11#53811yescharacteristic
484C22×C11#53811yescharacteristic
485C22×C11#53911yescharacteristic
486C22×C11#53911yescharacteristic
487C22×C11#53911yescharacteristic
488C22×C11#53911yescharacteristic
489C22×C11#53911yescharacteristic
490C22×C11#54011yescharacteristic
491C22×C11#54011yescharacteristic
492C22×C11#54111yescharacteristic
493C22×C11#54111yescharacteristic
494C22×C11#54211yescharacteristic
495C22×C11#54211yescharacteristic
496C22×C11#54211yescharacteristic
497C22×C11#54211yescharacteristic
498C22×C11#54211yescharacteristic
499C22×C11#54211yescharacteristic
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—42no—
521C4×C11—42no—
522Dic11—42no—
523Dic11—42no—
524Dic11—42no—
525Dic11—81no—
526Dic11—81no—
527Dic11—81no—
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—114no—
545C2×C4⋊C4—222no—
546C2×C4⋊C4—222no—
547C2×C4⋊C4—222no—
548C2×C4⋊C4—222no—
549C2×C4⋊C4—222no—
550C2×C4⋊C4—222no—
551C2×C4⋊C4—441no—
552C2×C4⋊C4—441no—
553C2×C4⋊C4—441no—
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—22no—
581C2×C42—41no—
582C2×C42—41no—
583C2×C42—41no—
584C2×C42—41no—
585C2×C42—41no—
586C2×C42—41no—
587C2×C42C4×D1114yes—
588C2×C42D4414yes—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—22no—
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—441no—
604#95—441no—
605#95—441no—
606#95—441no—
607#95—441no—
608#95—441no—
609C2×C11#229311yescharacteristic
610C2×C11#231411yescharacteristic
611C2×C11#231811yescharacteristic
612C2×C11#232511yescharacteristic
613C2×C11#232611yescharacteristic
614C2×C11#233411yescharacteristic
615C2×C11#233511yescharacteristic
616C2×C11#264911yescharacteristic
617C2×C11#265011yescharacteristic
618C2×C11#265311yescharacteristic
619C2×C11#265411yescharacteristic
620C2×C11#266111yescharacteristic
621C2×C11#266211yescharacteristic
622C2×C11#266311yescharacteristic
623C2×C11#266411yescharacteristic
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—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—221no—
683C22×C4—221no—
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—221no—
689C22×C4—221no—
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×C4C2×C4×D1112yes—
729C22×C4C2×C4×D1112yes—
730C22×C4C2×C4×D1112yes—
731C22×C4C2×D4412yes—
732C22×C4C2×D4412yes—
733C22×C4C2×D4412yes—
734C22×C4#433912yes—
735C22×C4#433912yes—
736C22×C4#433912yes—
737C22×C4#433912yes—
738C22×C4#433912yes—
739C4⋊C4—228no—
740C4⋊C4—444no—
741C4⋊C4—444no—
742C4⋊C4—444no—
743C4⋊C4—444no—
744C22⋊C4—228no—
745C22⋊C4—228no—
746C22⋊C4—444no—
747C22⋊C4—444no—
748C22⋊C4—444no—
749C22⋊C4—444no—
750C22⋊C4—444no—
751C42—44no—
752C42—44no—
753C42—44no—
754C11#1427911yescharacteristic, 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
791C23C22×D4411yescharacteristic
792C23C2×#433911yescharacteristic
793C23C2×#433911yescharacteristic
794C23C2×#433911yescharacteristic
795C23C2×#433911yescharacteristic
796C23C2×#433911yescharacteristic
797C23#6703711yescharacteristic
798C23#6703711yescharacteristic
799C23#6703711yescharacteristic
800C23#6704011yescharacteristic
801C23#6704211yescharacteristic
802C23#6704211yescharacteristic
803C23#6704311yescharacteristic
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—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
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—222no—
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—441no—
862C2×C4—441no—
863C2×C4—441no—
864C2×C4—441no—
865C2×C4—441no—
866C2×C4—441no—
867C2×C4—441no—
868C2×C4—441no—
869C2×C4—441no—
870C2×C4—441no—
871C2×C4—441no—
872C2×C4—441no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—441no—
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#6692514yes—
902C2×C4C4×D4414yes—
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
919C22C2×C4×D4411yescharacteristic
920C22C4×#433911yescharacteristic
921C22#1062300811yescharacteristic
922C22#1062300811yescharacteristic
923C22#1062301011yescharacteristic
924C22#1062301011yescharacteristic
925C22#1062301711yescharacteristic
926C22#1062302411yescharacteristic
927C22#1062302511yescharacteristic
928C22#1062303511yescharacteristic
929C22#1062304111yescharacteristic
930C22#1062304611yescharacteristic
931C22#1062305411yescharacteristic
932C22#1062305411yescharacteristic
933C22#1062305611yescharacteristic
934C22#1062305711yescharacteristic
935C22#1062306511yescharacteristic
936C22#1062306511yescharacteristic
937C22#1062309111yescharacteristic
938C22#1062309111yescharacteristic
939C22#1062309111yescharacteristic
940C22#1062309111yescharacteristic
941C22#1062309211yescharacteristic
942C22#1062309211yescharacteristic
943C22#1062309311yescharacteristic
944C22#1062309311yescharacteristic
945C22#1062309511yescharacteristic
946C22#1062309511yescharacteristic
947C22#1062309511yescharacteristic
948C22#1062309511yescharacteristic
949C22#1062311311yescharacteristic
950C22#1062311311yescharacteristic
951C22#1062311411yescharacteristic
952C22#1062311411yescharacteristic
953C4—24no—
954C4—24no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—442no—
961C4—442no—
962C4—442no—
963C4—881no—
964C4—881no—
965C4—881no—
966C4—881no—
967C2—882no—
968C2#1307108011yescharacteristic
969C2#1307122111yescharacteristic
970C2#1307124311yescharacteristic
971C2#1307131911yescharacteristic
972C2#1307132711yescharacteristic
973C2#1307139111yescharacteristic
974C2#1307140611yescharacteristic
975C2#1307461311yescharacteristic
976C2#1307462811yescharacteristic
977C2#1307467311yescharacteristic
978C2#1307468811yescharacteristic
979C2#1307474211yescharacteristic
980C2#1307475311yescharacteristic
981C2#1307476411yescharacteristic
982C2#1307477511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC4×C11×#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4×#95D11
hypocenterC11#14279
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
3. C2×#10622546C2semidirect
4. #13066880C2semidirect
5. #13066876C2semidirect
6. #13066872C2semidirect
7. #13066871C2semidirect
13. #13066849C2semidirect
14. #13066846C2semidirect
15. C4×C11×#95C2semidirect
52. #10622553C4semidirect
278. C4×#95D11semidirect
754. C11#14279semidirect

Maximal subgroups

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

subgroupindex
C2×#106225532
C2×#106225462
#130668802
#130668762
#130668722
#130668712
#130668642
#130668622
#130668602
#130668542
#130668492
#130668462
C4×C11×#952
#1427911