Finite Group Databasebeta

← #14681157

Subgroups — #14681157

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×#66931C211yesmaximal, characteristic
2C2×#10622542C211yesmaximal, characteristic, complemented
3C2×#10622564C211yesmaximal, characteristic
4C2×#10622556C211yesmaximal, characteristic
5#13066886C211yesmaximal, characteristic, complemented
6#13066883C211yesmaximal, characteristic, complemented
7#13066870C211yesmaximal, characteristic, complemented
8#13066866C211yesmaximal, characteristic, complemented
9#13066863C211yesmaximal, characteristic
10#13066863C211yesmaximal, characteristic
11#13066851C211yesmaximal, characteristic, complemented
12#13066849C211yesmaximal, characteristic, complemented
13#13066845C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic
15C2×C11×#388C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×#66931—24no—
32C2×#66931—24no—
33C2×#66931C418yescomplemented
34C11×#388—24no—
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
54C2×C11⋊#95C2211yescharacteristic
55#10622564—24no—
56#10622556—24no—
57#10622542—24no—
58C25×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—41no—
70C23×Dic11—41no—
71C23×Dic11C2×C414yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
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⋊C4—41no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—41no—
95C2×C11×C22⋊C4—41no—
96C2×C11×C22⋊C4C2×C414yes—
97C2×C11×C22⋊C4D414yes—
98C2×C11×C22⋊C4D414yes—
99C2×C42×C11—22no—
100C2×C42×C11—22no—
101C2×C42×C11—41no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—22no—
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—41no—
109C2×C22⋊Dic11—41no—
110C2×C22⋊Dic11C2×C414yes—
111C2×C4⋊Dic11—22no—
112C2×C4⋊Dic11—22no—
113C2×C4⋊Dic11—22no—
114C2×C4⋊Dic11—22no—
115C2×C4⋊Dic11—41no—
116C2×C4⋊Dic11C2×C414yes—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—22no—
121C2×Dic11⋊C4C2×C414yes—
122C2×Dic11⋊C4C2×C414yes—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—41no—
126#66931—232no—
127C11×#95—22no—
128C11×#95—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
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—41no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95—41no—
146C11⋊#95D414yes—
147#14364—111nomaximal, Sylow
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11C22×C412yes—
161C24×C11C2×D412yes—
162C24×C11C2×D412yes—
163C24×C11C2411yescharacteristic
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×C11C22×C412yes—
199C22×C4×C11C22×C412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2×D412yes—
204C22×C4×C11C2×D412yes—
205C22×C4×C11#4112yes—
206C22×Dic11—28no—
207C22×Dic11—28no—
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×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×Dic11—44no—
257C22×Dic11—44no—
258C22×Dic11—44no—
259C22×Dic11—44no—
260C22×Dic11—44no—
261C22×Dic11C22×C412yes—
262C22×Dic11C22×C412yes—
263C22×Dic11C22×C412yes—
264C22×Dic11C22×C412yes—
265C22×Dic11C2×D412yes—
266C22×Dic11C2×D412yes—
267C22×Dic11#4112yes—
268C22×Dic11#4112yes—
269C2×Dic22—28no—
270C2×Dic22—28no—
271C2×Dic22—44no—
272C2×Dic22—44no—
273C2×Dic22—44no—
274C2×Dic22—44no—
275C2×Dic22—44no—
276C11×C4⋊C4—44no—
277C11×C22⋊C4—44no—
278C11×C22⋊C4—44no—
279C11×C22⋊C4C22⋊C4116yes—
280C42×C11—44no—
281C22⋊Dic11—28no—
282C22⋊Dic11—44no—
283C22⋊Dic11—44no—
284C4⋊Dic11—28no—
285C4⋊Dic11—44no—
286Dic11⋊C4—28no—
287Dic11⋊C4—28no—
288C4×Dic11—44no—
289C22×C22⋊Q8—111no—
290C2×#391—111no—
291C2×#388—111no—
292C2×#388D1111yescharacteristic
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#1436—111no—
302C4⋊#95—111no—
303C22⋊#95—111no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—41no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—41no—
338C23×C11C2×C22⋊C414yes—
339C23×C11C23×C411yescharacteristic
340C23×C11C22×D411yescharacteristic
341C23×C11C22×D411yescharacteristic
342C23×C11C22×D411yescharacteristic
343C23×C11C2×#4111yescharacteristic
344C23×C11C2×#4111yescharacteristic
345C23×C11C2×#4111yescharacteristic
346C23×C11H(5,𝔽2)11yescharacteristic
347C23×C11H(5,𝔽2)11yescharacteristic
348C23×C11H(5,𝔽2)11yescharacteristic
349C23×C112−1+411yescharacteristic
350C23×C112−1+411yescharacteristic
351C23×C112−1+411yescharacteristic
352C23×C112−1+411yescharacteristic
353C23×C112−1+411yescharacteristic
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—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×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×C11C2×C22⋊C414yes—
395C2×C4×C11C2×C22⋊C414yes—
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—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—416no—
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×Dic11—41no—
452C2×Dic11C4×D414yes—
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⋊C4C2×D1111yescharacteristic
468C22×C22⋊C4C2×D1111yescharacteristic
469C22×C22⋊C4C2×D1111yescharacteristic
470C22×C42—111no—
471C22×C42C2×D1111yescharacteristic
472#391—224no—
473#388—24no—
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×#95—111no—
492C2×#95—111no—
493C2×#95—111no—
494C2×#95C2×D1111yescharacteristic
495C2×#95C2×D1111yescharacteristic
496C22×C11—24no—
497C22×C11—24no—
498C22×C11—24no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11C22×C22⋊C411yescharacteristic
512C22×C11C2×C4×D411yescharacteristic
513C22×C11C4×#4111yescharacteristic
514C22×C11#51811yescharacteristic
515C22×C11#51911yescharacteristic
516C22×C11#51911yescharacteristic
517C22×C11#52011yescharacteristic
518C22×C11#53611yescharacteristic
519C22×C11#53611yescharacteristic
520C22×C11#53611yescharacteristic
521C22×C11#53611yescharacteristic
522C22×C11#53611yescharacteristic
523C22×C11#53711yescharacteristic
524C22×C11#53911yescharacteristic
525C22×C11#53911yescharacteristic
526C22×C11#54111yescharacteristic
527C22×C11#54211yescharacteristic
528C22×C11#54211yescharacteristic
529C22×C11#54211yescharacteristic
530C22×C11D4211yescharacteristic
531C22×C11D4211yescharacteristic
532C22×C11#54611yescharacteristic
533C22×C11#54611yescharacteristic
534C22×C11#54611yescharacteristic
535C22×C11#54611yescharacteristic
536C22×C11#54711yescharacteristic
537C22×C11#54711yescharacteristic
538C22×C11#54711yescharacteristic
539C22×C11#54811yescharacteristic
540C22×C11#55211yescharacteristic
541C22×C11#55611yescharacteristic
542C22×C11#56211yescharacteristic
543C22×C11#56211yescharacteristic
544C22×C11#56311yescharacteristic
545C22×C11#56311yescharacteristic
546C4×C11—24no—
547C4×C11—24no—
548C4×C11—42no—
549C4×C11—42no—
550C4×C11—81no—
551C4×C11—81no—
552Dic11—24no—
553Dic11—42no—
554Dic11—42no—
555Dic11—42no—
556Dic11—42no—
557Dic11—42no—
558Dic11—81no—
559Dic11—81no—
560C25C22×D1111yescharacteristic
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—111no—
573C23×C4—111no—
574C23×C4—114no—
575C23×C4—111no—
576C23×C4—111no—
577C23×C4—222no—
578C23×C4—222no—
579C23×C4—222no—
580C23×C4—222no—
581C23×C4—441no—
582C23×C4—441no—
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—41no—
593C2×C4⋊C4—114no—
594C2×C4⋊C4—114no—
595C2×C4⋊C4—114no—
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—222no—
603C2×C4⋊C4—222no—
604C2×C4⋊C4—441no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4—41no—
611C2×C22⋊C4—114no—
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—441no—
619C2×C22⋊C4—441no—
620C2×C22⋊C4C4×D1114yes—
621C2×C22⋊C4D4414yes—
622C2×C22⋊C4C22⋊D1114yes—
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—114no—
632#95—222no—
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#95—441no—
649C2×C11—44no—
650C2×C11#231011yescharacteristic
651C2×C11#232311yescharacteristic
652C2×C11#233211yescharacteristic
653C2×C11D4×C22⋊C411yescharacteristic
654C2×C11#233911yescharacteristic
655C2×C11#236211yescharacteristic
656C2×C11#237811yescharacteristic
657C2×C11#267211yescharacteristic
658C2×C11#267411yescharacteristic
659C2×C11#268011yescharacteristic
660C2×C11#268111yescharacteristic
661C2×C11#268711yescharacteristic
662C2×C11#268911yescharacteristic
663C2×C11#269811yescharacteristic
664C2×C11#270011yescharacteristic
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24C2×C4×D1112yes—
678C24C2×D4412yes—
679C24C2×C22⋊D1112yes—
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—112no—
723C22×C4—112no—
724C22×C4—112no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—228no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—228no—
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—221no—
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—221no—
779C22×C4—221no—
780C22×C4—444no—
781C22×C4—444no—
782C22×C4—444no—
783C22×C4—444no—
784C22×C4—444no—
785C22×C4C2×C4×D1112yes—
786C22×C4C2×C4×D1112yes—
787C22×C4C2×D4412yes—
788C22×C4C2×D4412yes—
789C22×C4D4×D1112yes—
790C22×C4#434112yes—
791C22×C4C2×C22⋊D1112yes—
792C22×C4C2×C22⋊D1112yes—
793C4⋊C4—44no—
794C4⋊C4—228no—
795C4⋊C4—228no—
796C4⋊C4—228no—
797C4⋊C4—444no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—228no—
801C22⋊C4—444no—
802C22⋊C4—444no—
803C22⋊C4(C2×D11)⋊C4116yes—
804C42—44no—
805C42—444no—
806C11#1436411yescharacteristic, complemented, Sylow
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23C2×(C2×D11)⋊C414yes—
842C23C22×C4×D1111yescharacteristic
843C23C22×D4411yescharacteristic
844C23C2×D4×D1111yescharacteristic
845C23C2×#434111yescharacteristic
846C23#6703711yescharacteristic
847C23#6703711yescharacteristic
848C23#41×D1111yescharacteristic
849C23#41×D1111yescharacteristic
850C23#6704211yescharacteristic
851C23#6704311yescharacteristic
852C23#6704311yescharacteristic
853C23#6704311yescharacteristic
854C23#6704311yescharacteristic
855C23#6704311yescharacteristic
856C23C22×C22⋊D1111yescharacteristic
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—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
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—114no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
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—4416no—
921C2×C4—441no—
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×C4C2×(C2×D11)⋊C414yes—
956C2×C4C2×(C2×D11)⋊C414yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22#1062304711yescharacteristic
973C22#1062304711yescharacteristic
974C22#1062305711yescharacteristic
975C22#1062305711yescharacteristic
976C22C4×#434111yescharacteristic
977C22C4×D4×D1111yescharacteristic
978C22#1062307611yescharacteristic
979C22#1062307711yescharacteristic
980C22D4×D4411yescharacteristic
981C22#1062308511yescharacteristic
982C22#1062308511yescharacteristic
983C22#1062308611yescharacteristic
984C22#1062312911yescharacteristic
985C22#1062313311yescharacteristic
986C22#1062313911yescharacteristic
987C22#1062315211yescharacteristic
988C22#1062317911yescharacteristic
989C22#1062318211yescharacteristic
990C22#1062318611yescharacteristic
991C22#1062319111yescharacteristic
992C22#1062320011yescharacteristic
993C22#1062320211yescharacteristic
994C22#1062321311yescharacteristic
995C22#1062321511yescharacteristic
996C22#1062323211yescharacteristic
997C22#1062323911yescharacteristic
998C22#1062324111yescharacteristic
999C22#1062324311yescharacteristic
1000C22C22×(C2×D11)⋊C411yescharacteristic
1001C22D4×C22⋊D1111yescharacteristic
1002C22#1062333711yescharacteristic
1003C22#1062335511yescharacteristic
1004C22#1062335611yescharacteristic
1005C22#1062335611yescharacteristic
1006C22#1062336011yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—224no—
1014C4—442no—
1015C4—442no—
1016C4—442no—
1017C4—442no—
1018C4—442no—
1019C4—881no—
1020C4—881no—
1021C2—44no—
1022C2#1307120011yescharacteristic
1023C2#1307129511yescharacteristic
1024C2#1307136611yescharacteristic
1025C2D4×(C2×D11)⋊C411yescharacteristic
1026C2#1307144111yescharacteristic
1027C2#1307164611yescharacteristic
1028C2#1307178311yescharacteristic
1029C2#1307486511yescharacteristic
1030C2#1307489511yescharacteristic
1031C2#1307495311yescharacteristic
1032C2#1307496211yescharacteristic
1033C2#1307503511yescharacteristic
1034C2#1307506511yescharacteristic
1035C2#1307518411yescharacteristic
1036C2#1307520811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#388D11
hypocenterC11#14364
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#10622542C2semidirect
5. #13066886C2semidirect
6. #13066883C2semidirect
7. #13066870C2semidirect
8. #13066866C2semidirect
11. #13066851C2semidirect
12. #13066849C2semidirect
13. #13066845C2semidirect
33. C2×#66931C4semidirect
806. C11#14364semidirect

Maximal subgroups

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

subgroupindex
C22×#669312
C2×#106225422
C2×#106225642
C2×#106225562
#130668862
#130668832
#130668702
#130668662
#130668632
#130668512
#130668492
#130668452
#130668382
C2×C11×#3882
#1436411