Finite Group Databasebeta

← #14677916

Subgroups — #14677916

Order 2816.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622267C211yesmaximal, characteristic, complemented
2C2×#10622281C211yesmaximal, characteristic
3C2×#10622279C211yesmaximal, characteristic
4#13066878C211yesmaximal, characteristic, complemented
5#13066867C211yesmaximal, characteristic, complemented
6#13066860C211yesmaximal, characteristic
7#13066860C211yesmaximal, characteristic
8#13066854C211yesmaximal, characteristic
9#13066852C211yesmaximal, characteristic
10#13066851C211yesmaximal, characteristic, complemented
11#13066850C211yesmaximal, characteristic, complemented
12Dic11⋊#95C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic
14C4×C11⋊#95C211yesmaximal, characteristic, complemented
15C11×#1434C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
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#10622281C418yescomplemented
52#10622279—24no—
53#10622267—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
69C22×C4×D11—22no—
70C22×C4×D11—22no—
71C22×C4×D11—41no—
72C22×C4×D11—41no—
73C22×C4×D11—41no—
74C22×C4×D11—41no—
75C22×C4×D11C2×C414yes—
76C2×C42×C11—22no—
77C2×C42×C11—22no—
78C2×C42×C11—41no—
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—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—41no—
91C2×(C2×D11)⋊C4—41no—
92C2×(C2×D11)⋊C4—41no—
93C2×(C2×D11)⋊C4—41no—
94C2×(C2×D11)⋊C4C2×C414yes—
95C2×(C2×D11)⋊C4C2×C414yes—
96C2×(C2×D11)⋊C4Q814yes—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11C2×C414yes—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—41no—
104C2×Dic11⋊C4—41no—
105C2×Dic11⋊C4—41no—
106C2×Dic11⋊C4—41no—
107C2×Dic11⋊C4—41no—
108C2×Dic11⋊C4C2×C414yes—
109C2×C4×Dic11—22no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—22no—
112C2×C4×Dic11—41no—
113C2×C4×Dic11—41no—
114C2×C4×Dic11—41no—
115C2×C4×Dic11—41no—
116C2×C4×Dic11—41no—
117C2×C4×Dic11D414yes—
118C11×#95—22no—
119C11×#95—22no—
120C11×#95—22no—
121C11×#95—22no—
122C11×#95—41no—
123C11×#95C2×C414yes—
124C11⋊#95—22no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—41no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95C2×C414yes—
138#14075—111nomaximal, Sylow
139C24×C11C2411yescharacteristic
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×D11—21no—
151C23×D11—21no—
152C23×D11C22×C412yes—
153C23×D11C2×Q812yes—
154C23×D11#4112yes—
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×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2×Q812yes—
201C22×C4×C11#4112yes—
202C22×C4×C11#4112yes—
203C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
244C22×Dic11C22×C412yes—
245C22×Dic11C22×C412yes—
246C22×Dic11C2×D412yes—
247C22×Dic11C2×D412yes—
248C22×Dic11C2×Q812yes—
249C22×Dic11#4112yes—
250C22×Dic11#4112yes—
251C22×Dic11#4112yes—
252C22×Dic11#4112yes—
253C2×C4×D11—28no—
254C2×C4×D11—44no—
255C2×C4×D11—44no—
256C2×C4×D11—44no—
257C2×C4×D11—44no—
258C2×C4×D11—44no—
259C2×C4×D11—44no—
260C42×C11—44no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—28no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267C4⋊Dic11—28no—
268Dic11⋊C4—44no—
269Dic11⋊C4—44no—
270Dic11⋊C4—44no—
271C4×Dic11—44no—
272C4×Dic11—44no—
273C4×Dic11—44no—
274C2×#387—111no—
275C2×#385—111no—
276C2×C4×C22⋊C4—111no—
277#1443—111no—
278#1441—111no—
279#1439—111no—
280#1439—111no—
281#1437—111no—
282#1437—111no—
283#1436—111no—
284#1436—111no—
285C4⋊#95—111no—
286#1434D1111yescharacteristic, complemented
287C22⋊#95—111no—
288C4×#95—111no—
289C23×C11C23×C411yescharacteristic
290C23×C11C22×D411yescharacteristic
291C23×C11C22×Q811yescharacteristic
292C23×C11C2×#4111yescharacteristic
293C23×C11C2×#4111yescharacteristic
294C23×C11C2×#4111yescharacteristic
295C23×C11C2×#4111yescharacteristic
296C23×C11C2×#4111yescharacteristic
297C23×C11C2×#4111yescharacteristic
298C23×C11C2×#4111yescharacteristic
299C23×C11C2×#4111yescharacteristic
300C23×C11H(5,𝔽2)11yescharacteristic
301C23×C11H(5,𝔽2)11yescharacteristic
302C23×C11H(5,𝔽2)11yescharacteristic
303C23×C11H(5,𝔽2)11yescharacteristic
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
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—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
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×D11C4×Q814yes—
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—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
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×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×C11C22⋊Q814yes—
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—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—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—
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#11714yes—
436C2×Dic11C4×D414yes—
437C4×D11—416no—
438C24×C4—111no—
439C22×C4⋊C4—111no—
440C22×C4⋊C4—111no—
441C22×C4⋊C4—111no—
442C22×C4⋊C4—111no—
443C22×C22⋊C4—111no—
444C22×C22⋊C4—111no—
445C22×C22⋊C4—111no—
446C22×C22⋊C4—111no—
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C42—111no—
450C22×C42—111no—
451C22×C42—111no—
452C22×C42C2×D1111yescharacteristic
453#387—224no—
454#385—118no—
455C4×C22⋊C4—224no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95—111no—
463C2×#95—111no—
464C2×#95—111no—
465C2×#95—111no—
466C2×#95—111no—
467C2×#95—111no—
468C2×#95—111no—
469C2×#95—111no—
470C2×#95C2×D1111yescharacteristic
471C2×#95C2×D1111yescharacteristic
472C2×#95C2×D1111yescharacteristic
473C2×#95C2×D1111yescharacteristic
474C2×#95C2×D1111yescharacteristic
475C2×#95C2×D1111yescharacteristic
476C22×C11C2×#11711yescharacteristic
477C22×C11C2×C4×D411yescharacteristic
478C22×C11C2×C4×Q811yescharacteristic
479C22×C11C4×#4111yescharacteristic
480C22×C11C4×#4111yescharacteristic
481C22×C11#51811yescharacteristic
482C22×C11#51811yescharacteristic
483C22×C11C2×C22⋊Q811yescharacteristic
484C22×C11#52511yescharacteristic
485C22×C11#52911yescharacteristic
486C22×C11#52911yescharacteristic
487C22×C11#52911yescharacteristic
488C22×C11#53211yescharacteristic
489C22×C11#53211yescharacteristic
490C22×C11#53311yescharacteristic
491C22×C11#53411yescharacteristic
492C22×C11#53511yescharacteristic
493C22×C11#53811yescharacteristic
494C22×C11#53811yescharacteristic
495C22×C11#55111yescharacteristic
496C22×C11#55111yescharacteristic
497C22×C11#55111yescharacteristic
498C22×C11#55111yescharacteristic
499C22×C11#55111yescharacteristic
500C22×C11#55311yescharacteristic
501C22×C11#55311yescharacteristic
502C22×C11#55311yescharacteristic
503C22×C11#55311yescharacteristic
504C22×C11#55311yescharacteristic
505C22×C11#55311yescharacteristic
506C22×C11#55411yescharacteristic
507C22×C11#55411yescharacteristic
508C22×C11#55411yescharacteristic
509C22×C11#55411yescharacteristic
510C22×C11#55911yescharacteristic
511C2×D11—24no—
512C2×D11—24no—
513C2×D11—24no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—42no—
526C4×C11—24no—
527C4×C11—42no—
528C4×C11—42no—
529C4×C11—42no—
530C4×C11—42no—
531C4×C11—42no—
532C4×C11—81no—
533Dic11—24no—
534Dic11—24no—
535Dic11—42no—
536Dic11—42no—
537Dic11—42no—
538Dic11—42no—
539Dic11—81no—
540C25—111no—
541C23×C4—111no—
542C23×C4—111no—
543C23×C4—111no—
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—114no—
548C23×C4—111no—
549C23×C4—222no—
550C23×C4—222no—
551C23×C4—441no—
552C23×C4—441no—
553C23×C4—441no—
554C23×C4—441no—
555C23×C4C22×D1111yescharacteristic
556C23×C4C22×D1111yescharacteristic
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1111yescharacteristic
559C23×C4C22×D1111yescharacteristic
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C2×C4⋊C4—114no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—222no—
565C2×C4⋊C4—222no—
566C2×C4⋊C4—222no—
567C2×C4⋊C4—222no—
568C2×C4⋊C4—222no—
569C2×C4⋊C4—441no—
570C2×C4⋊C4—441no—
571C2×C4⋊C4—441no—
572C2×C4⋊C4—441no—
573C2×C4⋊C4—441no—
574C2×C22⋊C4—114no—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—114no—
577C2×C22⋊C4—222no—
578C2×C22⋊C4—222no—
579C2×C22⋊C4—222no—
580C2×C22⋊C4—222no—
581C2×C22⋊C4—222no—
582C2×C22⋊C4—222no—
583C2×C22⋊C4—222no—
584C2×C22⋊C4—222no—
585C2×C22⋊C4—222no—
586C2×C22⋊C4—222no—
587C2×C22⋊C4—222no—
588C2×C22⋊C4—441no—
589C2×C22⋊C4—441no—
590C2×C22⋊C4—441no—
591C2×C22⋊C4—441no—
592C2×C42—22no—
593C2×C42—22no—
594C2×C42—41no—
595C2×C42—114no—
596C2×C42—222no—
597C2×C42—222no—
598C2×C42—222no—
599C2×C42—441no—
600C2×C42—441no—
601C2×C42—441no—
602C2×C42—441no—
603C2×C42—441no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—41no—
609#95—114no—
610#95—222no—
611#95—222no—
612#95—222no—
613#95—222no—
614#95—222no—
615#95—222no—
616#95—222no—
617#95—222no—
618#95—222no—
619#95—441no—
620#95—441no—
621#95—441no—
622#95—441no—
623#95C4×D1114yes—
624C2×C11#229311yescharacteristic
625C2×C11C4×C22⋊Q811yescharacteristic
626C2×C11#232111yescharacteristic
627C2×C11#234511yescharacteristic
628C2×C11#235311yescharacteristic
629C2×C11#236811yescharacteristic
630C2×C11#237411yescharacteristic
631C2×C11#256411yescharacteristic
632C2×C11#256611yescharacteristic
633C2×C11#257611yescharacteristic
634C2×C11#257811yescharacteristic
635C2×C11#258711yescharacteristic
636C2×C11#258911yescharacteristic
637C2×C11#260211yescharacteristic
638C2×C11#260311yescharacteristic
639D11—44no—
640C24—112no—
641C24—112no—
642C24—112no—
643C24—221no—
644C24—221no—
645C24—221no—
646C24—221no—
647C24—221no—
648C24—221no—
649C24—221no—
650C24—221no—
651C24—221no—
652C24—221no—
653C24—221no—
654C24—221no—
655C24C23×D1111yescharacteristic
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—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—112no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—228no—
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×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—444no—
748C22×C4—444no—
749C22×C4—444no—
750C22×C4—444no—
751C22×C4—444no—
752C22×C4—444no—
753C22×C4C2×C4×D1112yes—
754C22×C4C2×C4×D1112yes—
755C22×C4C2×C4×D1112yes—
756C22×C4#433912yes—
757C22×C4#433912yes—
758C22×C4D4×D1112yes—
759C22×C4#434112yes—
760C22×C4Q8×D1112yes—
761C4⋊C4—228no—
762C4⋊C4—444no—
763C4⋊C4—444no—
764C4⋊C4—444no—
765C22⋊C4—228no—
766C22⋊C4—228no—
767C22⋊C4—228no—
768C22⋊C4—444no—
769C22⋊C4—444no—
770C22⋊C4—444no—
771C42—44no—
772C42—444no—
773C42—444no—
774C42—444no—
775C11#1407511yescharacteristic, complemented, Sylow
776C23—114no—
777C23—222no—
778C23—222no—
779C23—222no—
780C23—222no—
781C23—222no—
782C23—222no—
783C23—222no—
784C23—222no—
785C23—222no—
786C23—222no—
787C23—222no—
788C23—222no—
789C23—222no—
790C23—222no—
791C23—222no—
792C23—222no—
793C23—222no—
794C23—222no—
795C23—441no—
796C23—441no—
797C23—441no—
798C23—441no—
799C23—441no—
800C23—441no—
801C23—441no—
802C23—441no—
803C23—441no—
804C23—441no—
805C23—441no—
806C23—441no—
807C23—441no—
808C23—441no—
809C23—441no—
810C23—441no—
811C23C22×C4×D1111yescharacteristic
812C23C2×#433911yescharacteristic
813C23C2×#433911yescharacteristic
814C23C2×D4×D1111yescharacteristic
815C23C2×#434111yescharacteristic
816C23#6703711yescharacteristic
817C23C2×Q8×D1111yescharacteristic
818C23#41×D1111yescharacteristic
819C23#41×D1111yescharacteristic
820C23#41×D1111yescharacteristic
821C23#41×D1111yescharacteristic
822C23#41×D1111yescharacteristic
823C23#6704211yescharacteristic
824C23#6704211yescharacteristic
825C23#6704211yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
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—114no—
875C2×C4—114no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
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—4416no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—441no—
904C2×C4—441no—
905C2×C4—441no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—441no—
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#6694914yes—
925C22—224no—
926C22—224no—
927C22—224no—
928C22—442no—
929C22—442no—
930C22—442no—
931C22—442no—
932C22—442no—
933C22—442no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22C4×#433911yescharacteristic
941C22#1062302611yescharacteristic
942C22C2×#6694911yescharacteristic
943C22D11×#11711yescharacteristic
944C22#1062305211yescharacteristic
945C22#1062305811yescharacteristic
946C22#1062305811yescharacteristic
947C22#1062305911yescharacteristic
948C22#1062306111yescharacteristic
949C22#1062306111yescharacteristic
950C22#1062306111yescharacteristic
951C22C4×#434111yescharacteristic
952C22C4×D4×D1111yescharacteristic
953C22#1062307611yescharacteristic
954C22#1062307811yescharacteristic
955C22#1062309011yescharacteristic
956C22#1062309611yescharacteristic
957C22C4×Q8×D1111yescharacteristic
958C22#1062310911yescharacteristic
959C22#1062312711yescharacteristic
960C22#1062313611yescharacteristic
961C22#1062316611yescharacteristic
962C22#1062316711yescharacteristic
963C22#1062318011yescharacteristic
964C22#1062318811yescharacteristic
965C22#1062318911yescharacteristic
966C22#1062319211yescharacteristic
967C22#1062319911yescharacteristic
968C22#1062320511yescharacteristic
969C22#1062322111yescharacteristic
970C22#1062322111yescharacteristic
971C22#1062323511yescharacteristic
972C22#1062323611yescharacteristic
973C22#1062323711yescharacteristic
974C22#1062324011yescharacteristic
975C4—24no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—81no—
982C4—224no—
983C4—224no—
984C4—442no—
985C4—442no—
986C4—442no—
987C4—442no—
988C4—881no—
989C2—444no—
990C2#1307107611yescharacteristic
991C2C4×#6694911yescharacteristic
992C2#1307126911yescharacteristic
993C2#1307149011yescharacteristic
994C2#1307155711yescharacteristic
995C2#1307169811yescharacteristic
996C2#1307175011yescharacteristic
997C2#1307379411yescharacteristic
998C2#1307381511yescharacteristic
999C2#1307391611yescharacteristic
1000C2#1307394811yescharacteristic
1001C2#1307404111yescharacteristic
1002C2#1307407311yescharacteristic
1003C2#1307423511yescharacteristic
1004C2#1307424111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1434D11
hypocenterC11#14075
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×#10622267C2semidirect
4. #13066878C2semidirect
5. #13066867C2semidirect
10. #13066851C2semidirect
11. #13066850C2semidirect
12. Dic11⋊#95C2semidirect
14. C4×C11⋊#95C2semidirect
15. C11×#1434C2semidirect
51. #10622281C4semidirect
286. #1434D11semidirect
775. C11#14075semidirect

Maximal subgroups

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

subgroupindex
C2×#106222672
C2×#106222812
C2×#106222792
#130668782
#130668672
#130668602
#130668542
#130668522
#130668512
#130668502
Dic11⋊#952
(C2×D11)⋊#952
C4×C11⋊#952
C11×#14342
#1407511