Finite Group Databasebeta

← #14681152

Subgroups — #14681152

Order 2816.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66950C211yesmaximal, characteristic
2C2×#10622259C211yesmaximal, characteristic, complemented
3C2×#10622283C211yesmaximal, characteristic
4C2×#10622553C211yesmaximal, characteristic
5C2×#10622277C211yesmaximal, characteristic
6#13066886C211yesmaximal, characteristic, complemented
7#13066883C211yesmaximal, characteristic, complemented
8#13066869C211yesmaximal, characteristic, complemented
9#13066868C211yesmaximal, characteristic, complemented
10#13066864C211yesmaximal, characteristic
11#13066864C211yesmaximal, characteristic
12#13066850C211yesmaximal, characteristic, complemented
13#13066846C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×#66950—24no—
32C2×#66950—24no—
33C2×#66950C418yescomplemented
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
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54#10622553—24no—
55#10622283—24no—
56#10622277—24no—
57#10622259—24no—
58C24×D11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11—41no—
78C22×C4×D11—41no—
79C22×C4×D11C2×C414yes—
80C22×Dic22—22no—
81C22×Dic22—22no—
82C22×Dic22—22no—
83C22×Dic22—22no—
84C22×Dic22—41no—
85C22×Dic22—41no—
86C22×Dic22C2×C414yes—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4C2×C414yes—
90C2×C42×C11—22no—
91C2×C42×C11—22no—
92C2×C42×C11—41no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—41no—
104C2×(C2×D11)⋊C4—41no—
105C2×(C2×D11)⋊C4—41no—
106C2×(C2×D11)⋊C4—41no—
107C2×(C2×D11)⋊C4C2×C414yes—
108C2×(C2×D11)⋊C4C2×C414yes—
109C2×(C2×D11)⋊C4D414yes—
110C2×(C2×D11)⋊C4D414yes—
111C2×C4⋊Dic11—22no—
112C2×C4⋊Dic11—22no—
113C2×C4⋊Dic11—22no—
114C2×C4⋊Dic11—22no—
115C2×C4⋊Dic11—22no—
116C2×C4⋊Dic11—22no—
117C2×C4⋊Dic11—41no—
118C2×C4⋊Dic11C2×C414yes—
119C2×C4⋊Dic11C2×C414yes—
120C2×Dic11⋊C4—22no—
121C2×Dic11⋊C4—22no—
122C2×Dic11⋊C4—41no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—41no—
126#66950—232no—
127C11×#95—22no—
128C11×#95—22no—
129C11×#95—22no—
130C11×#95—41no—
131C11×#95D414yes—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95—41no—
146C11⋊#95—41no—
147#14364—111nomaximal, Sylow
148C24×C11C2411yescharacteristic
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11C22×C412yes—
162C23×D11C2×D412yes—
163C23×D11C2×D412yes—
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×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11C22×C412yes—
204C22×C4×C11C22×C412yes—
205C22×C4×C11C22×C412yes—
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2×D412yes—
208C22×C4×C11C2×D412yes—
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2×D412yes—
211C22×C4×C11#4112yes—
212C22×C4×C11#4112yes—
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×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11C22×C412yes—
257C22×Dic11C22×C412yes—
258C22×Dic11C22×C412yes—
259C22×Dic11C2×D412yes—
260C22×Dic11C2×D412yes—
261C22×Dic11#4112yes—
262C2×C4×D11—28no—
263C2×C4×D11—28no—
264C2×C4×D11—44no—
265C2×C4×D11—44no—
266C2×C4×D11—44no—
267C2×C4×D11—44no—
268C2×C4×D11—44no—
269C2×Dic22—28no—
270C2×Dic22—28no—
271C2×Dic22—44no—
272C2×Dic22—44no—
273C2×Dic22—44no—
274C2×Dic22—44no—
275C2×Dic22—44no—
276C11×C4⋊C4—28no—
277C42×C11—44no—
278(C2×D11)⋊C4—28no—
279(C2×D11)⋊C4—44no—
280(C2×D11)⋊C4—44no—
281(C2×D11)⋊C4—44no—
282(C2×D11)⋊C4—44no—
283(C2×D11)⋊C4C22⋊C4116yes—
284C4⋊Dic11—28no—
285C4⋊Dic11—28no—
286C4⋊Dic11—44no—
287Dic11⋊C4—44no—
288C4×Dic11—44no—
289C22×C22⋊Q8—111no—
290C2×#391—111no—
291C2×#388—111no—
292C2×#388—111no—
293C2×#381—111no—
294#1446—111no—
295#1445—111no—
296#1441—111no—
297#1441—111no—
298#1440—111no—
299#1440—111no—
300#1436—111no—
301#1436D1111yescharacteristic, complemented
302C4⋊#95—111no—
303C22⋊#95—111no—
304C23×C11C23×C411yescharacteristic
305C23×C11C22×D411yescharacteristic
306C23×C11C22×D411yescharacteristic
307C23×C11C22×D411yescharacteristic
308C23×C11C2×#4111yescharacteristic
309C23×C11C2×#4111yescharacteristic
310C23×C11C2×#4111yescharacteristic
311C23×C11H(5,𝔽2)11yescharacteristic
312C23×C11H(5,𝔽2)11yescharacteristic
313C23×C11H(5,𝔽2)11yescharacteristic
314C23×C112−1+411yescharacteristic
315C23×C112−1+411yescharacteristic
316C23×C112−1+411yescharacteristic
317C23×C112−1+411yescharacteristic
318C23×C112−1+411yescharacteristic
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—41no—
349C22×D11—41no—
350C22×D11—41no—
351C22×D11—41no—
352C22×D11—41no—
353C22×D11C2×C22⋊C414yes—
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—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
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×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11C2×C22⋊C414yes—
402C2×C4×C11C4×D414yes—
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—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
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—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11—41no—
450C2×Dic11—41no—
451C2×Dic11C2×C22⋊C414yes—
452C4×D11—416no—
453Dic22—416no—
454C23×Q8—111no—
455C24×C4—111no—
456C2×C22⋊Q8—118no—
457C2×C22⋊Q8—224no—
458C2×C22⋊Q8—224no—
459C22×C4⋊C4—111no—
460C22×C4⋊C4—111no—
461C22×C4⋊C4—111no—
462C22×C4⋊C4—111no—
463C22×C4⋊C4C2×D1111yescharacteristic
464C22×C22⋊C4—111no—
465C22×C22⋊C4—111no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4—111no—
470C22×C42—111no—
471C22×C42C2×D1111yescharacteristic
472#391—224no—
473#388—224no—
474#388—224no—
475#381—224no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95—111no—
480C2×#95—111no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95—111no—
484C2×#95—111no—
485C2×#95—111no—
486C2×#95—111no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95C2×D1111yescharacteristic
492C2×#95C2×D1111yescharacteristic
493C2×#95C2×D1111yescharacteristic
494C2×#95C2×D1111yescharacteristic
495C2×#95C2×D1111yescharacteristic
496C22×C11C22×C22⋊C411yescharacteristic
497C22×C11C2×C4×D411yescharacteristic
498C22×C11C4×#4111yescharacteristic
499C22×C11#51811yescharacteristic
500C22×C11#51911yescharacteristic
501C22×C11#51911yescharacteristic
502C22×C11#52011yescharacteristic
503C22×C11#53611yescharacteristic
504C22×C11#53611yescharacteristic
505C22×C11#53611yescharacteristic
506C22×C11#53611yescharacteristic
507C22×C11#53611yescharacteristic
508C22×C11#53711yescharacteristic
509C22×C11#53911yescharacteristic
510C22×C11#53911yescharacteristic
511C22×C11#54111yescharacteristic
512C22×C11#54211yescharacteristic
513C22×C11#54211yescharacteristic
514C22×C11#54211yescharacteristic
515C22×C11D4211yescharacteristic
516C22×C11D4211yescharacteristic
517C22×C11#54611yescharacteristic
518C22×C11#54611yescharacteristic
519C22×C11#54611yescharacteristic
520C22×C11#54611yescharacteristic
521C22×C11#54711yescharacteristic
522C22×C11#54711yescharacteristic
523C22×C11#54711yescharacteristic
524C22×C11#54811yescharacteristic
525C22×C11#55211yescharacteristic
526C22×C11#55611yescharacteristic
527C22×C11#56211yescharacteristic
528C22×C11#56211yescharacteristic
529C22×C11#56311yescharacteristic
530C22×C11#56311yescharacteristic
531C2×D11—24no—
532C2×D11—24no—
533C2×D11—24no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—42no—
546C4×C11—24no—
547C4×C11—24no—
548C4×C11—42no—
549C4×C11—42no—
550C4×C11—42no—
551C4×C11—42no—
552C4×C11—81no—
553Dic11—24no—
554Dic11—42no—
555Dic11—42no—
556Dic11—42no—
557Dic11—81no—
558Dic11—81no—
559Dic11—81no—
560C25—111no—
561C22×Q8—114no—
562C22×Q8—222no—
563C22×Q8—222no—
564C22×Q8—222no—
565C22×Q8—222no—
566C22×Q8—441no—
567C22×Q8—441no—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4—111no—
571C23×C4—111no—
572C23×C4—114no—
573C23×C4—111no—
574C23×C4—111no—
575C23×C4—111no—
576C23×C4—222no—
577C23×C4—222no—
578C23×C4—222no—
579C23×C4—222no—
580C23×C4—441no—
581C23×C4—441no—
582C23×C4C22×D1111yescharacteristic
583C23×C4C22×D1111yescharacteristic
584C23×C4C22×D1111yescharacteristic
585C23×C4C22×D1111yescharacteristic
586C23×C4C22×D1111yescharacteristic
587C23×C4C22×D1111yescharacteristic
588C23×C4C22×D1111yescharacteristic
589C22⋊Q8—2232no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—114no—
593C2×C4⋊C4—114no—
594C2×C4⋊C4—222no—
595C2×C4⋊C4—222no—
596C2×C4⋊C4—222no—
597C2×C4⋊C4—222no—
598C2×C4⋊C4—222no—
599C2×C4⋊C4—222no—
600C2×C4⋊C4—222no—
601C2×C4⋊C4—222no—
602C2×C4⋊C4—441no—
603C2×C4⋊C4—441no—
604C2×C4⋊C4C4×D1114yes—
605C2×C22⋊C4—114no—
606C2×C22⋊C4—114no—
607C2×C22⋊C4—114no—
608C2×C22⋊C4—114no—
609C2×C22⋊C4—222no—
610C2×C22⋊C4—222no—
611C2×C22⋊C4—222no—
612C2×C22⋊C4—222no—
613C2×C22⋊C4—222no—
614C2×C22⋊C4—222no—
615C2×C22⋊C4—222no—
616C2×C22⋊C4—222no—
617C2×C22⋊C4—222no—
618C2×C22⋊C4—222no—
619C2×C22⋊C4—441no—
620C2×C22⋊C4—441no—
621C2×C22⋊C4—441no—
622C2×C22⋊C4—441no—
623C2×C42—22no—
624C2×C42—22no—
625C2×C42—41no—
626C2×C42—222no—
627C2×C42—222no—
628C2×C42—441no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—41no—
633#95—222no—
634#95—222no—
635#95—222no—
636#95—222no—
637#95—222no—
638#95—222no—
639#95—222no—
640#95—222no—
641#95—222no—
642#95—222no—
643#95—441no—
644#95—441no—
645#95—441no—
646#95—441no—
647#95—441no—
648#95D4414yes—
649C2×C11#231011yescharacteristic
650C2×C11#232311yescharacteristic
651C2×C11#233211yescharacteristic
652C2×C11D4×C22⋊C411yescharacteristic
653C2×C11#233911yescharacteristic
654C2×C11#236211yescharacteristic
655C2×C11#237811yescharacteristic
656C2×C11#267211yescharacteristic
657C2×C11#267411yescharacteristic
658C2×C11#268011yescharacteristic
659C2×C11#268111yescharacteristic
660C2×C11#268711yescharacteristic
661C2×C11#268911yescharacteristic
662C2×C11#269811yescharacteristic
663C2×C11#270011yescharacteristic
664D11—44no—
665C24—112no—
666C24—112no—
667C24—112no—
668C24—221no—
669C24—221no—
670C24—221no—
671C24—221no—
672C24—221no—
673C24—221no—
674C24—221no—
675C24—221no—
676C24—221no—
677C24—221no—
678C24—221no—
679C24—221no—
680C24C23×D1111yescharacteristic
681C2×Q8—228no—
682C2×Q8—228no—
683C2×Q8—444no—
684C2×Q8—444no—
685C2×Q8—444no—
686C2×Q8—444no—
687C2×Q8—444no—
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—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—112no—
731C22×C4—112no—
732C22×C4—112no—
733C22×C4—228no—
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—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—228no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—221no—
761C22×C4—221no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—444no—
779C22×C4—444no—
780C22×C4—444no—
781C22×C4—444no—
782C22×C4—444no—
783C22×C4C2×C4×D1112yes—
784C22×C4C2×C4×D1112yes—
785C22×C4C2×C4×D1112yes—
786C22×C4C2×D4412yes—
787C22×C4C2×D4412yes—
788C22×C4C2×D4412yes—
789C22×C4#433912yes—
790C22×C4D4×D1112yes—
791C22×C4D4×D1112yes—
792C22×C4#434112yes—
793C4⋊C4—28no—
794C4⋊C4—228no—
795C4⋊C4—228no—
796C4⋊C4—444no—
797C4⋊C4—444no—
798C22⋊C4—1116no—
799C22⋊C4—228no—
800C22⋊C4—444no—
801C22⋊C4—444no—
802C22⋊C4—444no—
803C22⋊C4—444no—
804C42—44no—
805C42—444no—
806C11#1436411yescharacteristic, complemented, Sylow
807C23—114no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—222no—
814C23—222no—
815C23—222no—
816C23—222no—
817C23—222no—
818C23—222no—
819C23—222no—
820C23—222no—
821C23—222no—
822C23—222no—
823C23—222no—
824C23—222no—
825C23—222no—
826C23—441no—
827C23—441no—
828C23—441no—
829C23—441no—
830C23—441no—
831C23—441no—
832C23—441no—
833C23—441no—
834C23—441no—
835C23—441no—
836C23—441no—
837C23—441no—
838C23—441no—
839C23—441no—
840C23—441no—
841C23—441no—
842C23C22×C4×D1111yescharacteristic
843C23C22×D4411yescharacteristic
844C23C2×#433911yescharacteristic
845C23C2×D4×D1111yescharacteristic
846C23C2×D4×D1111yescharacteristic
847C23C2×#434111yescharacteristic
848C23#6703711yescharacteristic
849C23#6704011yescharacteristic
850C23#6704011yescharacteristic
851C23#41×D1111yescharacteristic
852C23#6704211yescharacteristic
853C23#6704211yescharacteristic
854C23#6704311yescharacteristic
855C23#6704311yescharacteristic
856C23#6704311yescharacteristic
857Q8—4416no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—114no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—4416no—
922C2×C4—441no—
923C2×C4—441no—
924C2×C4—441no—
925C2×C4—441no—
926C2×C4—441no—
927C2×C4—441no—
928C2×C4—441no—
929C2×C4—441no—
930C2×C4—441no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4—441no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—441no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—441no—
945C2×C4—441no—
946C2×C4—441no—
947C2×C4—441no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—441no—
951C2×C4—441no—
952C2×C4—441no—
953C2×C4—441no—
954C2×C4—441no—
955C2×C4C4×D4414yes—
956C2×C4C22⋊C4×D1114yes—
957C22—224no—
958C22—224no—
959C22—224no—
960C22—442no—
961C22—442no—
962C22—442no—
963C22—442no—
964C22—442no—
965C22—442no—
966C22—442no—
967C22—442no—
968C22—442no—
969C22—442no—
970C22—442no—
971C22—442no—
972C22C2×C4×D4411yescharacteristic
973C22C2×C22⋊C4×D1111yescharacteristic
974C22#1062304111yescharacteristic
975C22#1062304411yescharacteristic
976C22#1062305211yescharacteristic
977C22#1062305711yescharacteristic
978C22#1062306411yescharacteristic
979C22C4×#434111yescharacteristic
980C22#1062307711yescharacteristic
981C22D4×D4411yescharacteristic
982C22D4×D4411yescharacteristic
983C22#1062308111yescharacteristic
984C22#1062308111yescharacteristic
985C22#1062308611yescharacteristic
986C22#1062309211yescharacteristic
987C22#1062310311yescharacteristic
988C22#1062310311yescharacteristic
989C22#1062310711yescharacteristic
990C22#1062311411yescharacteristic
991C22#1062312211yescharacteristic
992C22#1062314111yescharacteristic
993C22#1062314211yescharacteristic
994C22#1062315911yescharacteristic
995C22#1062315911yescharacteristic
996C22#1062317411yescharacteristic
997C22#1062317811yescharacteristic
998C22#1062318611yescharacteristic
999C22#1062319611yescharacteristic
1000C22#1062319811yescharacteristic
1001C22#1062320611yescharacteristic
1002C22#1062322311yescharacteristic
1003C22#1062323011yescharacteristic
1004C22#1062324111yescharacteristic
1005C22#1062324311yescharacteristic
1006C22#1062325511yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—81no—
1014C4—224no—
1015C4—442no—
1016C4—442no—
1017C4—442no—
1018C4—881no—
1019C4—881no—
1020C4—881no—
1021C2—444no—
1022C2#1307119911yescharacteristic
1023C2#1307129911yescharacteristic
1024C2#1307136811yescharacteristic
1025C2C22⋊C4×D4411yescharacteristic
1026C2#1307144211yescharacteristic
1027C2#1307164511yescharacteristic
1028C2#1307178011yescharacteristic
1029C2#1307487011yescharacteristic
1030C2#1307490011yescharacteristic
1031C2#1307495411yescharacteristic
1032C2#1307496311yescharacteristic
1033C2#1307504011yescharacteristic
1034C2#1307507011yescharacteristic
1035C2#1307518511yescharacteristic
1036C2#1307520911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#14364
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#10622259C2semidirect
6. #13066886C2semidirect
7. #13066883C2semidirect
8. #13066869C2semidirect
9. #13066868C2semidirect
12. #13066850C2semidirect
13. #13066846C2semidirect
15. C11×#1436C2semidirect
33. C2×#66950C4semidirect
301. #1436D11semidirect
806. C11#14364semidirect

Maximal subgroups

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

subgroupindex
C22×#669502
C2×#106222592
C2×#106222832
C2×#106225532
C2×#106222772
#130668862
#130668832
#130668692
#130668682
#130668642
#130668502
#130668462
(C2×D11)⋊#952
C11×#14362
#1436411