Finite Group Databasebeta

← #14675835

Subgroups — #14675835

Order 2816.

1602 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622590C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×Dic11C211yesmaximal, characteristic
3C2×C22⋊C4×Dic11C211yesmaximal, characteristic
4#13066863C211yesmaximal, characteristic
5#13066863C211yesmaximal, characteristic
6#13066861C211yesmaximal, characteristic
7#13066850C211yesmaximal, characteristic, complemented
8#13066848C211yesmaximal, characteristic, complemented
9#13066842C211yesmaximal, characteristic, complemented
10#13066842C211yesmaximal, characteristic, complemented
11#13066841C211yesmaximal, characteristic, complemented
12#13066840C211yesmaximal, characteristic, complemented
13#13066840C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic
15C11×#1439C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
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#10622590—24no—
52C22⋊C4×Dic11—24no—
53C22⋊C4×Dic11C418yescomplemented
54C25×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11—22no—
62C23×Dic11—22no—
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—41no—
66C23×Dic11—41no—
67C23×Dic11C2×C414yes—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—41no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—41no—
86C2×C11×C22⋊C4—41no—
87C2×C11×C22⋊C4C2×C414yes—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—41no—
95C2×C22⋊Dic11—41no—
96C2×C22⋊Dic11C2×C414yes—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11—41no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—41no—
107C2×C4×Dic11—41no—
108C2×C4×Dic11—41no—
109C2×C4×Dic11—41no—
110C2×C4×Dic11C2×C414yes—
111C2×C4×Dic11C2×C414yes—
112C11×#95—22no—
113C11×#95—22no—
114C11×#95—41no—
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⋊#95C2×C414yes—
132C11⋊#95C2×C414yes—
133C11⋊#95D414yes—
134#13888—111nomaximal, Sylow
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—21no—
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—21no—
145C24×C11—21no—
146C24×C11—21no—
147C24×C11C22×C412yes—
148C24×C11#4112yes—
149C24×C11#4112yes—
150C24×C11C2411yescharacteristic
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×C11C22×C412yes—
188C22×C4×C11C22×C412yes—
189C22×C4×C11C2×D412yes—
190C22×C4×C11#4112yes—
191C22×C4×C11#4112yes—
192C22×C4×C11#4112yes—
193C22×Dic11—28no—
194C22×Dic11—28no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
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—44no—
242C22×Dic11—44no—
243C22×Dic11—44no—
244C22×Dic11—44no—
245C22×Dic11—44no—
246C22×Dic11C22×C412yes—
247C22×Dic11C22×C412yes—
248C22×Dic11C22×C412yes—
249C22×Dic11C22×C412yes—
250C22×Dic11C2×D412yes—
251C22×Dic11C2×D412yes—
252C22×Dic11#4112yes—
253C22×Dic11#4112yes—
254C22×Dic11#4112yes—
255C22×Dic11#4112yes—
256C11×C4⋊C4—44no—
257C11×C22⋊C4—28no—
258C11×C22⋊C4—28no—
259C11×C22⋊C4—44no—
260C22⋊Dic11—28no—
261C22⋊Dic11—28no—
262C22⋊Dic11—44no—
263C4⋊Dic11—44no—
264C4×Dic11—28no—
265C4×Dic11—44no—
266C4×Dic11—44no—
267C4×Dic11—44no—
268C2×#382—111no—
269C2×C4×C22⋊C4—111no—
270C2×C4×C22⋊C4—111no—
271#1440—111no—
272#1440—111no—
273#1439—111no—
274#1439D1111yescharacteristic
275#1436—111no—
276#1436—111no—
277#1434—111no—
278#1434—111no—
279#1434—111no—
280#1434—111no—
281#1434—111no—
282C22⋊#95—111no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11#11714yes—
318C23×C11C23×C411yescharacteristic
319C23×C11C22×D411yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11C2×#4111yescharacteristic
322C23×C11C2×#4111yescharacteristic
323C23×C11C2×#4111yescharacteristic
324C23×C11C2×#4111yescharacteristic
325C23×C11C2×#4111yescharacteristic
326C23×C11C2×#4111yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11H(5,𝔽2)11yescharacteristic
330C23×C11H(5,𝔽2)11yescharacteristic
331C23×C11H(5,𝔽2)11yescharacteristic
332C23×C112−1+411yescharacteristic
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—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#11714yes—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
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—416no—
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—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11#11714yes—
431C2×Dic11C4×D414yes—
432C24×C4—111no—
433C22×C4⋊C4—111no—
434C22×C4⋊C4C2×D1111yescharacteristic
435C22×C22⋊C4—111no—
436C22×C22⋊C4—111no—
437C22×C22⋊C4—111no—
438C22×C22⋊C4C2×D1111yescharacteristic
439C22×C22⋊C4C2×D1111yescharacteristic
440C22×C22⋊C4C2×D1111yescharacteristic
441C22×C42—111no—
442C22×C42—111no—
443C22×C42—111no—
444C22×C42—111no—
445#382—224no—
446C4×C22⋊C4—118no—
447C4×C22⋊C4—224no—
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×#95—111no—
462C2×#95—111no—
463C2×#95—111no—
464C2×#95—111no—
465C2×#95—111no—
466C2×#95—111no—
467C2×#95C2×D1111yescharacteristic
468C2×#95C2×D1111yescharacteristic
469C2×#95C2×D1111yescharacteristic
470C22×C11—24no—
471C22×C11—24no—
472C22×C11—24no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11C2×#11711yescharacteristic
486C22×C11C2×#11711yescharacteristic
487C22×C11C2×#11711yescharacteristic
488C22×C11C2×C4×D411yescharacteristic
489C22×C11C4×#4111yescharacteristic
490C22×C11#51811yescharacteristic
491C22×C11#52011yescharacteristic
492C22×C11#52511yescharacteristic
493C22×C11#52511yescharacteristic
494C22×C11#52911yescharacteristic
495C22×C11#52911yescharacteristic
496C22×C11#52911yescharacteristic
497C22×C11#52911yescharacteristic
498C22×C11#52911yescharacteristic
499C22×C11#52911yescharacteristic
500C22×C11#53811yescharacteristic
501C22×C11#53811yescharacteristic
502C22×C11#53911yescharacteristic
503C22×C11#53911yescharacteristic
504C22×C11#54611yescharacteristic
505C22×C11#54611yescharacteristic
506C22×C11#54611yescharacteristic
507C22×C11#54811yescharacteristic
508C22×C11#55111yescharacteristic
509C22×C11#55111yescharacteristic
510C22×C11#55211yescharacteristic
511C22×C11#55211yescharacteristic
512C22×C11#55211yescharacteristic
513C22×C11#55311yescharacteristic
514C22×C11#55311yescharacteristic
515C22×C11#55311yescharacteristic
516C22×C11#55511yescharacteristic
517C22×C11#55511yescharacteristic
518C22×C11#55911yescharacteristic
519C22×C11#55911yescharacteristic
520C4×C11—24no—
521C4×C11—42no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11—81no—
525C4×C11—81no—
526Dic11—24no—
527Dic11—24no—
528Dic11—42no—
529Dic11—42no—
530Dic11—42no—
531Dic11—42no—
532Dic11—81no—
533Dic11—81no—
534C25C22×D1111yescharacteristic
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—111no—
539C23×C4—111no—
540C23×C4—111no—
541C23×C4—114no—
542C23×C4—111no—
543C23×C4—111no—
544C23×C4—222no—
545C23×C4—222no—
546C23×C4—222no—
547C23×C4—222no—
548C23×C4—441no—
549C23×C4—441no—
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—222no—
560C2×C4⋊C4—222no—
561C2×C4⋊C4—441no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—114no—
571C2×C22⋊C4—222no—
572C2×C22⋊C4—222no—
573C2×C22⋊C4—222no—
574C2×C22⋊C4—222no—
575C2×C22⋊C4—222no—
576C2×C22⋊C4—222no—
577C2×C22⋊C4—441no—
578C2×C22⋊C4—441no—
579C2×C22⋊C4C4×D1114yes—
580C2×C42—114no—
581C2×C42—114no—
582C2×C42—222no—
583C2×C42—222no—
584C2×C42—222no—
585C2×C42—222no—
586C2×C42—222no—
587C2×C42—222no—
588C2×C42—441no—
589C2×C42—441no—
590C2×C42—441no—
591C2×C42—441no—
592#95—22no—
593#95—22no—
594#95—41no—
595#95—114no—
596#95—114no—
597#95—114no—
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—222no—
608#95—222no—
609#95—441no—
610#95—441no—
611#95—441no—
612#95—441no—
613#95—441no—
614C2×C11—44no—
615C2×C11#228311yescharacteristic
616C2×C11#229011yescharacteristic
617C2×C11#231811yescharacteristic
618C2×C11#234211yescharacteristic
619C2×C11#234611yescharacteristic
620C2×C11#235211yescharacteristic
621C2×C11#235711yescharacteristic
622C2×C11#245911yescharacteristic
623C2×C11#245911yescharacteristic
624C2×C11#246011yescharacteristic
625C2×C11#246011yescharacteristic
626C2×C11#251711yescharacteristic
627C2×C11#251711yescharacteristic
628C2×C11#251811yescharacteristic
629C2×C11#251811yescharacteristic
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24C2×C4×D1112yes—
643C24#434112yes—
644C24#434312yes—
645C24C23×D1111yescharacteristic
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—112no—
683C22×C4—112no—
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—228no—
693C22×C4—228no—
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×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—444no—
741C22×C4—444no—
742C22×C4—444no—
743C22×C4—444no—
744C22×C4—444no—
745C22×C4C2×C4×D1112yes—
746C22×C4C2×C4×D1112yes—
747C22×C4D4×D1112yes—
748C22×C4#434112yes—
749C22×C4#434112yes—
750C22×C4#434112yes—
751C4⋊C4—44no—
752C4⋊C4—444no—
753C22⋊C4—28no—
754C22⋊C4—28no—
755C22⋊C4—44no—
756C22⋊C4—228no—
757C22⋊C4—228no—
758C22⋊C4—444no—
759C42—228no—
760C42—444no—
761C42—444no—
762C42—444no—
763C11#1388811yescharacteristic, complemented, Sylow
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23#6694514yes—
799C23C22×C4×D1111yescharacteristic
800C23C2×D4×D1111yescharacteristic
801C23C2×#434111yescharacteristic
802C23C2×#434111yescharacteristic
803C23C2×#434111yescharacteristic
804C23C2×#434111yescharacteristic
805C23#6703711yescharacteristic
806C23#6703711yescharacteristic
807C23C2×#434311yescharacteristic
808C23#41×D1111yescharacteristic
809C23#41×D1111yescharacteristic
810C23#41×D1111yescharacteristic
811C23#41×D1111yescharacteristic
812C23#6704211yescharacteristic
813C23#6704311yescharacteristic
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—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—41no—
855C2×C4—114no—
856C2×C4—114no—
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—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—4416no—
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—
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#6693014yes—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22C2×#6693011yescharacteristic
929C22C2×#6694511yescharacteristic
930C22D11×#11711yescharacteristic
931C22C4×#434111yescharacteristic
932C22C4×D4×D1111yescharacteristic
933C22#1062307611yescharacteristic
934C22#1062307711yescharacteristic
935C22#1062311711yescharacteristic
936C22#1062312211yescharacteristic
937C22#1062312411yescharacteristic
938C22#1062312911yescharacteristic
939C22#1062313111yescharacteristic
940C22#1062313111yescharacteristic
941C22#1062313211yescharacteristic
942C22#1062314111yescharacteristic
943C22#1062314511yescharacteristic
944C22#1062314711yescharacteristic
945C22#1062314911yescharacteristic
946C22#1062315511yescharacteristic
947C22#1062315511yescharacteristic
948C22#1062315511yescharacteristic
949C22#1062315811yescharacteristic
950C22#1062317511yescharacteristic
951C22#1062317611yescharacteristic
952C22#1062318011yescharacteristic
953C22#1062318111yescharacteristic
954C22#1062318111yescharacteristic
955C22#1062319011yescharacteristic
956C22#1062319611yescharacteristic
957C22#1062320111yescharacteristic
958C22#1062320711yescharacteristic
959C22#1062321211yescharacteristic
960C22#1062323611yescharacteristic
961C22#1062323911yescharacteristic
962C22#1062324411yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—81no—
968C4—81no—
969C4—224no—
970C4—224no—
971C4—442no—
972C4—442no—
973C4—442no—
974C4—442no—
975C4—881no—
976C4—881no—
977C2—44no—
978C2#1307101111yescharacteristic
979C2#1307105211yescharacteristic
980C2#1307124411yescharacteristic
981C2#1307146411yescharacteristic
982C2#1307149811yescharacteristic
983C2#1307154311yescharacteristic
984C2#1307158811yescharacteristic
985C2#1307254811yescharacteristic
986C2#1307255611yescharacteristic
987C2#1307256311yescharacteristic
988C2#1307257111yescharacteristic
989C2#1307326011yescharacteristic
990C2#1307326511yescharacteristic
991C2#1307326911yescharacteristic
992C2#1307327711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1439D11
hypocenterC11#13888
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#10622590C2semidirect
7. #13066850C2semidirect
8. #13066848C2semidirect
9. #13066842C2semidirect
10. #13066842C2semidirect
11. #13066841C2semidirect
12. #13066840C2semidirect
13. #13066840C2semidirect
53. C22⋊C4×Dic11C4semidirect
763. C11#13888semidirect

Maximal subgroups

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

subgroupindex
C2×#106225902
C2×C22⋊C4×Dic112
#130668632
#130668612
#130668502
#130668482
#130668422
#130668412
#130668402
#130668382
C11×#14392
#1388811