Finite Group Databasebeta

← #14683079

Subgroups — #14683079

Order 2816.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622564C211yesmaximal, characteristic, complemented
2C2×#10622833C211yesmaximal, characteristic
3C2×#10622833C211yesmaximal, characteristic
4C2×#10622563C211yesmaximal, characteristic, complemented
5#13066884C211yesmaximal, characteristic, complemented
6#13066878C211yesmaximal, characteristic, complemented
7#13066869C211yesmaximal, characteristic, complemented
8#13066865C211yesmaximal, characteristic, complemented
9#13066861C211yesmaximal, characteristic, complemented
10#13066853C211yesmaximal, characteristic, complemented
11#13066850C211yesmaximal, characteristic, complemented
12#13066838C211yesmaximal, characteristic, complemented
13#13066838C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C2×C11×#394C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C11×#394C418yescomplemented
34C2×C11×#95C2211yescharacteristic
35#10622833—24no—
36#10622833—24no—
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#10622564—24no—
55#10622563—24no—
56C25×C11C2311yescharacteristic
57C25×C11C2311yescharacteristic
58C22×D4×C11—22no—
59C22×D4×C11—22no—
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11—41no—
63C22×D4×C11—41no—
64C22×D4×C11C2×C414yes—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×Dic11—22no—
71C23×Dic11—22no—
72C23×Dic11—22no—
73C23×Dic11—22no—
74C23×Dic11—22no—
75C23×Dic11—22no—
76C23×Dic11—41no—
77C23×Dic11—41no—
78C23×Dic11—41no—
79C23×Dic11—41no—
80C23×Dic11—41no—
81C23×Dic11—41no—
82C23×Dic11—41no—
83C23×Dic11—41no—
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C2×C11×C4⋊C4—41no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4C2×C414yescomplemented
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—41no—
100C2×C11×C22⋊C4—41no—
101C2×C11×C22⋊C4—41no—
102C2×C11×C22⋊C4—41no—
103C2×C11×C22⋊C4C2×C414yescomplemented
104C2×C11×C22⋊C4C2×C414yescomplemented
105C2×C11×C22⋊C4C2×C414yescomplemented
106C2×C11×C22⋊C4C2×C414yescomplemented
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11—22no—
111C2×C22⋊Dic11—22no—
112C2×C22⋊Dic11—22no—
113C2×C22⋊Dic11—22no—
114C2×C22⋊Dic11—22no—
115C2×C22⋊Dic11—41no—
116C2×C22⋊Dic11—41no—
117C2×C22⋊Dic11—41no—
118C2×C22⋊Dic11—41no—
119C2×C22⋊Dic11—41no—
120C2×C22⋊Dic11—41no—
121C2×C22⋊Dic11—41no—
122C2×C22⋊Dic11—41no—
123C2×C22⋊Dic11D414yes—
124C2×C22⋊Dic11D414yes—
125C2×C4⋊Dic11—22no—
126C2×C4⋊Dic11—22no—
127C2×C4⋊Dic11—22no—
128C2×C4⋊Dic11—22no—
129C2×C4⋊Dic11—41no—
130C2×C4⋊Dic11—41no—
131C2×C4×Dic11—22no—
132C2×C4×Dic11—41no—
133C2×C4×Dic11—41no—
134C11×#95C2×C414yescomplemented
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—41no—
145C11⋊#95—41no—
146C11⋊#95—41no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95—41no—
152#14517—111nomaximal, Sylow
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11C22×C412yes—
178C24×C11C22×C412yes—
179C24×C11C2×D412yes—
180C24×C11C2×D412yes—
181C24×C11#4112yes—
182C24×C11#4112yes—
183C24×C11C2411yescharacteristic
184C2×D4×C11—28no—
185C2×D4×C11—28no—
186C2×D4×C11—44no—
187C2×D4×C11—44no—
188C2×D4×C11—44no—
189C2×D4×C11—44no—
190C2×D4×C11—44no—
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×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11C22×C412yes—
222C22×C4×C11C22×C412yes—
223C22×C4×C11C22×C412yes—
224C22×C4×C11C22×C412yes—
225C22×C4×C11C22×C412yes—
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—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—44no—
277C22×Dic11—44no—
278C22×Dic11—44no—
279C22×Dic11—44no—
280C22×Dic11—44no—
281C22×Dic11—44no—
282C22×Dic11—44no—
283C22×Dic11—44no—
284C22×Dic11—44no—
285C22×Dic11—44no—
286C22×Dic11—44no—
287C22×Dic11—44no—
288C22×Dic11—44no—
289C22×Dic11—44no—
290C22×Dic11C2×D412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11C2×D412yes—
294C22×Dic11#4112yes—
295C22×Dic11#4112yes—
296C11×C4⋊C4—44no—
297C11×C22⋊C4—28no—
298C11×C22⋊C4—28no—
299C11×C22⋊C4—44no—
300C11×C22⋊C4—44no—
301C22⋊Dic11—44no—
302C22⋊Dic11—44no—
303C22⋊Dic11—44no—
304C22⋊Dic11—44no—
305C22⋊Dic11—44no—
306C22⋊Dic11—44no—
307C4⋊Dic11—44no—
308C4⋊Dic11—44no—
309C4×Dic11—44no—
310C2×#394D1111yescharacteristic
311C2×#388—111no—
312C2×#386—111no—
313C2×#386—111no—
314C2×#385—111no—
315#1445—111no—
316#1443—111no—
317#1441—111no—
318#1440—111no—
319#1439—111no—
320#1437—111no—
321#1436—111no—
322C22⋊#95—111no—
323C22⋊#95—111no—
324C22⋊#95—111no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11C4×D414yes—
394C23×C11C4×D414yes—
395C23×C11C23×C411yescharacteristic
396C23×C11C22×D411yescharacteristic
397C23×C11C22×D411yescharacteristic
398C23×C11C2×#4111yescharacteristic
399C23×C11C2×#4111yescharacteristic
400C23×C11C2×#4111yescharacteristic
401C23×C11C2×#4111yescharacteristic
402C23×C11H(5,𝔽2)11yescharacteristic
403C23×C11H(5,𝔽2)11yescharacteristic
404C23×C11H(5,𝔽2)11yescharacteristic
405C23×C11H(5,𝔽2)11yescharacteristic
406C23×C11H(5,𝔽2)11yescharacteristic
407C23×C11H(5,𝔽2)11yescharacteristic
408C23×C112−1+411yescharacteristic
409C23×C112−1+411yescharacteristic
410D4×C11—416no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—416no—
465C2×Dic11—416no—
466C2×Dic11—41no—
467C2×Dic11—41no—
468C2×Dic11—41no—
469C2×Dic11—41no—
470C2×Dic11—41no—
471C2×Dic11—41no—
472C2×Dic11—41no—
473C2×Dic11—41no—
474C2×Dic11—41no—
475C2×Dic11—41no—
476C2×Dic11—41no—
477C2×Dic11—41no—
478C2×Dic11—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C2×Dic11—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C2×Dic11—41no—
500C2×Dic11—41no—
501C2×Dic11—41no—
502C2×Dic11—41no—
503C2×Dic11—41no—
504C23×D4C2×D1111yescharacteristic
505C24×C4—111no—
506C24×C4—111no—
507C22×C4⋊C4—111no—
508C22×C4⋊C4—111no—
509C22×C4⋊C4C2×D1111yescharacteristic
510C22×C22⋊C4—111no—
511C22×C22⋊C4—111no—
512C22×C22⋊C4—111no—
513C22×C22⋊C4—111no—
514C22×C22⋊C4—111no—
515C22×C22⋊C4—111no—
516C22×C22⋊C4C2×D1111yescharacteristic
517C22×C22⋊C4C2×D1111yescharacteristic
518C22×C22⋊C4C2×D1111yescharacteristic
519C22×C22⋊C4C2×D1111yescharacteristic
520C22×C42—111no—
521#394Dic1118yescomplemented
522#388—224no—
523#386—224no—
524#386—224no—
525#385—224no—
526C2×#95—111no—
527C2×#95—111no—
528C2×#95—111no—
529C2×#95—111no—
530C2×#95—111no—
531C2×#95—111no—
532C2×#95—111no—
533C2×#95—111no—
534C2×#95—111no—
535C2×#95—111no—
536C2×#95—111no—
537C2×#95—111no—
538C2×#95—111no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95—111no—
543C2×#95C2×D1111yescharacteristic
544C22×C11—24no—
545C22×C11—24no—
546C22×C11—24no—
547C22×C11—24no—
548C22×C11—24no—
549C22×C11—24no—
550C22×C11—42no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—42no—
572C22×C11—42no—
573C22×C11—42no—
574C22×C11C2×C4×D411yescharacteristic
575C22×C11C2×C4×D411yescharacteristic
576C22×C11C4×#4111yescharacteristic
577C22×C11#51811yescharacteristic
578C22×C11#51811yescharacteristic
579C22×C11#52011yescharacteristic
580C22×C11#52011yescharacteristic
581C22×C11#53411yescharacteristic
582C22×C11#53411yescharacteristic
583C22×C11#53611yescharacteristic
584C22×C11#53711yescharacteristic
585C22×C11#53811yescharacteristic
586C22×C11#53811yescharacteristic
587C22×C11#53811yescharacteristic
588C22×C11#53911yescharacteristic
589C22×C11#53911yescharacteristic
590C22×C11#53911yescharacteristic
591C22×C11#54211yescharacteristic
592C22×C11#54211yescharacteristic
593C22×C11D4211yescharacteristic
594C22×C11#54611yescharacteristic
595C22×C11#54611yescharacteristic
596C22×C11#54611yescharacteristic
597C22×C11#54611yescharacteristic
598C22×C11#54611yescharacteristic
599C22×C11#54711yescharacteristic
600C22×C11#55111yescharacteristic
601C22×C11#55111yescharacteristic
602C22×C11#55211yescharacteristic
603C22×C11#55311yescharacteristic
604C22×C11#55311yescharacteristic
605C22×C11#56011yescharacteristic
606C22×C11#56011yescharacteristic
607C22×C11#56211yescharacteristic
608C22×C11#56211yescharacteristic
609C4×C11—42no—
610C4×C11—42no—
611C4×C11—42no—
612C4×C11—42no—
613C4×C11—42no—
614Dic11—42no—
615Dic11—42no—
616Dic11—42no—
617Dic11—42no—
618Dic11—42no—
619Dic11—42no—
620Dic11—81no—
621Dic11—81no—
622C25C22×D1111yescharacteristic
623C25C22×D1111yescharacteristic
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—41no—
629C22×D4—41no—
630C22×D4C2×Dic1114yes—
631C23×C4—111no—
632C23×C4—111no—
633C23×C4—111no—
634C23×C4—111no—
635C23×C4—111no—
636C23×C4—111no—
637C23×C4—111no—
638C23×C4—111no—
639C23×C4—222no—
640C23×C4—222no—
641C23×C4—222no—
642C23×C4—222no—
643C23×C4—222no—
644C23×C4—222no—
645C23×C4—441no—
646C23×C4—441no—
647C23×C4—441no—
648C23×C4—441no—
649C23×C4—441no—
650C23×C4—441no—
651C23×C4—441no—
652C23×C4—441no—
653C23×C4C22×D1111yescharacteristic
654C23×C4C22×D1111yescharacteristic
655C23×C4C22×D1111yescharacteristic
656C23×C4C22×D1111yescharacteristic
657C23×C4C22×D1111yescharacteristic
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—222no—
661C2×C4⋊C4—222no—
662C2×C4⋊C4—222no—
663C2×C4⋊C4—222no—
664C2×C4⋊C4—441no—
665C2×C4⋊C4—441no—
666C2×C4⋊C4C2×Dic1114yescomplemented
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—41no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4—114no—
676C2×C22⋊C4—114no—
677C2×C22⋊C4—222no—
678C2×C22⋊C4—222no—
679C2×C22⋊C4—222no—
680C2×C22⋊C4—222no—
681C2×C22⋊C4—222no—
682C2×C22⋊C4—222no—
683C2×C22⋊C4—222no—
684C2×C22⋊C4—222no—
685C2×C22⋊C4—441no—
686C2×C22⋊C4—441no—
687C2×C22⋊C4—441no—
688C2×C22⋊C4—441no—
689C2×C22⋊C4—441no—
690C2×C22⋊C4—441no—
691C2×C22⋊C4—441no—
692C2×C22⋊C4—441no—
693C2×C22⋊C4C2×Dic1114yescomplemented
694C2×C22⋊C4C2×Dic1114yescomplemented
695C2×C22⋊C4C2×Dic1114yescomplemented
696C2×C22⋊C4C2×Dic1114yescomplemented
697C2×C42—222no—
698C2×C42—441no—
699C2×C42—441no—
700#95—222no—
701#95—222no—
702#95—222no—
703#95—222no—
704#95—222no—
705#95—222no—
706#95—222no—
707#95—222no—
708#95—222no—
709#95—441no—
710#95—441no—
711#95—441no—
712#95—441no—
713#95—441no—
714#95—441no—
715#95—441no—
716#95—441no—
717#95C2×Dic1114yescomplemented
718C2×C11—44no—
719C2×C11—44no—
720C2×C11#232211yescharacteristic
721C2×C11#232511yescharacteristic
722C2×C11#233711yescharacteristic
723C2×C11#235811yescharacteristic
724C2×C11#235911yescharacteristic
725C2×C11#236411yescharacteristic
726C2×C11#237711yescharacteristic
727C2×C11#266811yescharacteristic
728C2×C11#267211yescharacteristic
729C2×C11#268711yescharacteristic
730C2×C11#269111yescharacteristic
731C2×C11#269711yescharacteristic
732C2×C11#270811yescharacteristic
733C2×C11#274611yescharacteristic
734C2×C11#275011yescharacteristic
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24D4×D1112yes—
760C24D4×D1112yes—
761C24#434112yes—
762C24#434112yes—
763C24C22×Dic1112yes—
764C24C22×Dic1112yes—
765C24C23×D1111yescharacteristic
766C2×D4—28no—
767C2×D4—28no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—44no—
771C2×D4—44no—
772C2×D4—44no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—112no—
804C22×C4—112no—
805C22×C4—112no—
806C22×C4—112no—
807C22×C4—112no—
808C22×C4—112no—
809C22×C4—221no—
810C22×C4—221no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—221no—
815C22×C4—221no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—444no—
860C22×C4—444no—
861C22×C4—444no—
862C22×C4—444no—
863C22×C4—444no—
864C22×C4—444no—
865C22×C4—444no—
866C22×C4—444no—
867C22×C4—444no—
868C22×C4—444no—
869C22×C4—444no—
870C22×C4—444no—
871C22×C4—444no—
872C22×C4—444no—
873C22×C4C22×Dic1112yes—
874C22×C4C22×Dic1112yes—
875C22×C4C22×Dic1112yes—
876C22×C4C22×Dic1112yes—
877C22×C4C22×Dic1112yes—
878C4⋊C4—44no—
879C4⋊C4—444no—
880C4⋊C4—444no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—444no—
886C22⋊C4—444no—
887C22⋊C4—444no—
888C22⋊C4—444no—
889C22⋊C4—444no—
890C22⋊C4—444no—
891C42—444no—
892C11#1451711yescharacteristic, complemented, Sylow
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23D4×Dic1114yes—
962C23D4×Dic1114yes—
963C23C2×D4×D1111yescharacteristic
964C23C2×D4×D1111yescharacteristic
965C23C2×#434111yescharacteristic
966C23C2×#434111yescharacteristic
967C23#6703711yescharacteristic
968C23#6703711yescharacteristic
969C23#6703711yescharacteristic
970C23#6703711yescharacteristic
971C23#41×D1111yescharacteristic
972C23#41×D1111yescharacteristic
973C23#6704211yescharacteristic
974C23#6704211yescharacteristic
975C23#6704311yescharacteristic
976C23#6704311yescharacteristic
977C23C23×Dic1111yescharacteristic
978D4—416no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—222no—
1032C2×C4—4416no—
1033C2×C4—4416no—
1034C2×C4—441no—
1035C2×C4—441no—
1036C2×C4—441no—
1037C2×C4—441no—
1038C2×C4—441no—
1039C2×C4—441no—
1040C2×C4—441no—
1041C2×C4—441no—
1042C2×C4—441no—
1043C2×C4—441no—
1044C2×C4—441no—
1045C2×C4—441no—
1046C2×C4—441no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C2×C4—441no—
1053C2×C4—441no—
1054C2×C4—441no—
1055C2×C4—441no—
1056C2×C4—441no—
1057C2×C4—441no—
1058C2×C4—441no—
1059C2×C4—441no—
1060C2×C4—441no—
1061C2×C4—441no—
1062C2×C4—441no—
1063C2×C4—441no—
1064C2×C4—441no—
1065C2×C4—441no—
1066C2×C4—441no—
1067C2×C4—441no—
1068C2×C4—441no—
1069C2×C4—441no—
1070C2×C4—441no—
1071C2×C4—441no—
1072C22—24no—
1073C22—24no—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22#1062311811yescharacteristic
1103C22#1062312111yescharacteristic
1104C22#1062312211yescharacteristic
1105C22#1062312211yescharacteristic
1106C22#1062312811yescharacteristic
1107C22#1062313211yescharacteristic
1108C22#1062313211yescharacteristic
1109C22#1062313311yescharacteristic
1110C22#1062313611yescharacteristic
1111C22#1062314111yescharacteristic
1112C22#1062314111yescharacteristic
1113C22#1062314811yescharacteristic
1114C22#1062315111yescharacteristic
1115C22#1062315111yescharacteristic
1116C22#1062315211yescharacteristic
1117C22#1062315211yescharacteristic
1118C22#1062317911yescharacteristic
1119C22#1062318111yescharacteristic
1120C22#1062318411yescharacteristic
1121C22#1062318511yescharacteristic
1122C22#1062318611yescharacteristic
1123C22#1062318911yescharacteristic
1124C22#1062319611yescharacteristic
1125C22#1062319611yescharacteristic
1126C22#1062320011yescharacteristic
1127C22#1062320011yescharacteristic
1128C22#1062320911yescharacteristic
1129C22#1062320911yescharacteristic
1130C22C2×D4×Dic1111yescharacteristic
1131C22C2×D4×Dic1111yescharacteristic
1132C22#1062332911yescharacteristic
1133C22#1062332911yescharacteristic
1134C22#41×Dic1111yescharacteristic
1135C22#1062335811yescharacteristic
1136C22#1062335811yescharacteristic
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—442no—
1143C4—442no—
1144C4—442no—
1145C4—442no—
1146C4—442no—
1147C4—442no—
1148C4—881no—
1149C4—881no—
1150C2—44no—
1151C2—44no—
1152C2#1307128811yescharacteristic
1153C2#1307132111yescharacteristic
1154C2#1307143111yescharacteristic
1155C2#1307160011yescharacteristic
1156C2#1307161211yescharacteristic
1157C2#1307166811yescharacteristic
1158C2#1307177311yescharacteristic
1159C2#1307482311yescharacteristic
1160C2#1307486911yescharacteristic
1161C2#1307504311yescharacteristic
1162C2#1307509011yescharacteristic
1163C2#1307518211yescharacteristic
1164C2#1307532711yescharacteristic
1165C2#1307580211yescharacteristic
1166C2#1307585611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#394C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#394D11
hypocenterC11#14517
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C2×#10622564C2semidirect
4. C2×#10622563C2semidirect
5. #13066884C2semidirect
6. #13066878C2semidirect
7. #13066869C2semidirect
8. #13066865C2semidirect
9. #13066861C2semidirect
10. #13066853C2semidirect
11. #13066850C2semidirect
12. #13066838C2semidirect
13. #13066838C2semidirect
14. #13066838C2semidirect
33. C11×#394C4semidirect
94. C2×C11×C4⋊C4C2×C4semidirect
103. C2×C11×C22⋊C4C2×C4semidirect
104. C2×C11×C22⋊C4C2×C4semidirect
105. C2×C11×C22⋊C4C2×C4semidirect
106. C2×C11×C22⋊C4C2×C4semidirect
134. C11×#95C2×C4semidirect
521. #394Dic11semidirect
666. C2×C4⋊C4C2×Dic11semidirect
693. C2×C22⋊C4C2×Dic11semidirect
694. C2×C22⋊C4C2×Dic11semidirect
695. C2×C22⋊C4C2×Dic11semidirect
696. C2×C22⋊C4C2×Dic11semidirect
717. #95C2×Dic11semidirect
892. C11#14517semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
C2×#106228332
C2×#106225632
#130668842
#130668782
#130668692
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