Finite Group Databasebeta

← #14769954

Subgroups — #14769954

Order 2816.

1132 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623096C211yesmaximal, characteristic
2D4×#4318C211yesmaximal, characteristic, complemented
3#13069609C211yesmaximal, characteristic, complemented
4#13069608C211yesmaximal, characteristic, complemented
5#13069079C211yesmaximal, characteristic, complemented
6#13069079C211yesmaximal, characteristic, complemented
7#13069077C211yesmaximal, characteristic, complemented
8#13069077C211yesmaximal, characteristic, complemented
9#13068697C211yesmaximal, characteristic, complemented
10#13068694C211yesmaximal, characteristic, complemented
11#13068605C211yesmaximal, characteristic, complemented
12C4×#66887C211yesmaximal, characteristic, complemented
13#13068354C211yesmaximal, characteristic, complemented
14C2×#10622192C211yesmaximal, characteristic, complemented
15D4×C11×M16C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66992C412yes—
20C2×#66983C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26#10623096—21no—
27#10623096—21no—
28#10623096—21no—
29#10623096—21no—
30#10623096—21no—
31#10623096—21no—
32#10623096—21no—
33#10623096—21no—
34C2×#66951C412yes—
35C2×#66936C412yes—
36C2×(C22⋊D11)⋊C4C412yes—
37C2×C4×D44C2211yescharacteristic
38C2×#66923C2211yescharacteristic
39C11×#436—21no—
40C11×#435—21no—
41C11×#435—21no—
42C8×D4×C11—21no—
43C11×#423C2211yescharacteristic
44C11×#407C2211yescharacteristic
45C11×#407C2211yescharacteristic
46C4×C11×M16C2211yescharacteristic
47#10622820C2211yescharacteristic
48#10622820C2211yescharacteristic
49C2×#66887C2211yescharacteristic
50C2×#66887C2211yescharacteristic
51C2×#66887C2211yescharacteristic
52C2×#66887C2211yescharacteristic
53#10622625—21no—
54#10622624—21no—
55#10622624—21no—
56D4×C11⋊C8—21no—
57#10622537C2211yescharacteristic
58C4×#4318C2211yescharacteristic
59#10622192C2211yescharacteristic
60#10622192C2211yescharacteristic
61#10622192C2211yescharacteristic
62#10622192C2211yescharacteristic
63#10622192C2211yescharacteristic
64#10622192C2211yescharacteristic
65#10622192C2211yescharacteristic
66#10622192C2211yescharacteristic
67#10622192C2211yescharacteristic
68#10622192C2211yescharacteristic
69#10622192C2211yescharacteristic
70#10622192C2211yescharacteristic
71C22×D4×C11C2×C411yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C22×C22⋊D11C2×C412yes—
75C22×C22⋊D11C2×C412yes—
76C23×Dic11C2×C412yes—
77C22×D44C2311yescharacteristic
78C22×C4×D11C2×C412yes—
79C2×C11×M16—21no—
80C2×C11×M16—21no—
81C2×C11×M16—22no—
82C2×C11×M16—22no—
83C2×C11×M16—41no—
84C2×C11×M16—41no—
85C2×C11×M16C2311yescharacteristic
86C2×C11×M16C2311yescharacteristic
87C2×C11×M16C2311yescharacteristic
88C2×C11×M16C2311yescharacteristic
89C22×C8×C11—21no—
90C22×C8×C11—21no—
91C4×D4×C11D411yescharacteristic
92C4×D4×C11D411yescharacteristic
93C4×D4×C11D411yescharacteristic
94C4×D4×C11D411yescharacteristic
95C4×D4×C11D411yescharacteristic
96C4×D4×C11D411yescharacteristic
97C4×D4×C11D411yescharacteristic
98C4×D4×C11D411yescharacteristic
99C2×C11×C4⋊C4C2×C411yescharacteristic
100C2×C11×C22⋊C4C2×C411yescharacteristic
101C2×C11×C22⋊C4C2×C411yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×C22⋊Dic11C2×C412yes—
104#66992—22no—
105#66992—22no—
106#66992—22no—
107#66992—22no—
108#66983—21no—
109#66983—21no—
110#66983—21no—
111#66983—21no—
112#66983—21no—
113#66983—21no—
114#66983—21no—
115#66983—21no—
116C2×(C2×D11)⋊C4C2×C412yes—
117C2×(C2×D11)⋊C4C2×C412yes—
118C2×(C2×D11)⋊C4C2×C412yes—
119#66979—21no—
120#66979—21no—
121#66979—21no—
122#66979—21no—
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11—21no—
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11C2×C412yes—
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×Dic11⋊C4C2×C412yes—
132C2×Dic11⋊C4C2×C412yes—
133C2×C4×Dic11C2×C412yes—
134C2×#4318—21no—
135C2×#4318—21no—
136C2×#4318—22no—
137C2×#4318—22no—
138C2×#4318—41no—
139C2×#4318—41no—
140C2×#4318C2311yescharacteristic
141C2×#4318C2311yescharacteristic
142C2×#4318C2311yescharacteristic
143C2×#4318C2311yescharacteristic
144C22×C11⋊C8—21no—
145C22×C11⋊C8—21no—
146#66951—22no—
147#66951—22no—
148#66951—22no—
149#66951—22no—
150#66936—22no—
151#66936—22no—
152#66936—22no—
153#66936—22no—
154(C22⋊D11)⋊C4—22no—
155(C22⋊D11)⋊C4—22no—
156(C22⋊D11)⋊C4—22no—
157(C22⋊D11)⋊C4—22no—
158C4×D44—21no—
159C4×D44—21no—
160C4×D44—21no—
161C4×D44—21no—
162#66923—21no—
163#66923—21no—
164#66923—21no—
165#66923—21no—
166C11×C4⋊C8—21no—
167C11×C4⋊C8—21no—
168C11×C22⋊C8—21no—
169C11×C22⋊C8—21no—
170C11×C22⋊C8—21no—
171C11×C22⋊C8—21no—
172C11×#97—21no—
173C4×C8×C11—21no—
174C22⋊(C11⋊C8)—21no—
175C22⋊(C11⋊C8)—21no—
176C22⋊(C11⋊C8)—21no—
177C22⋊(C11⋊C8)—21no—
178#66887—22no—
179#66887—22no—
180#66887—41no—
181#66887—41no—
182C4⋊(C11⋊C8)—21no—
183C4⋊(C11⋊C8)—21no—
184#66867—21no—
185C4×C11⋊C8—21no—
186#22482—111nomaximal, Sylow
187C24×C11C22×C411yescharacteristic
188C24×C11C22×C411yescharacteristic
189C23×D11C22×C412yes—
190C2×D4×C11—42no—
191C2×D4×C11C22⋊C411yescharacteristic
192C2×D4×C11C22⋊C411yescharacteristic
193C2×D4×C11C22⋊C411yescharacteristic
194C2×D4×C11C22⋊C411yescharacteristic
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×C411yescharacteristic
204C22×C4×C11C22×C411yescharacteristic
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C22×C411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2411yescharacteristic
216C2×C22⋊D11—22no—
217C2×C22⋊D11—22no—
218C2×C22⋊D11—22no—
219C2×C22⋊D11—22no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—82no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—82no—
225C22×Dic11C22×C412yes—
226C22×Dic11C22×C412yes—
227C22×Dic11C22×C412yes—
228C2×D44—21no—
229C2×D44—21no—
230C2×D44—21no—
231C2×D44—21no—
232C2×D44—21no—
233C2×D44—21no—
234C2×C4×D11—22no—
235C2×C4×D11—22no—
236C2×C4×D11—82no—
237C11×M16—21no—
238C11×M16—21no—
239C11×M16—21no—
240C11×M16—21no—
241C11×M16—21no—
242C11×M16—21no—
243C11×M16—21no—
244C11×M16—42no—
245C11×M16—42no—
246C11×M16#4112yes—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—21no—
251C2×C8×C11—42no—
252C2×C8×C11—42no—
253C11×C4⋊C4C22⋊C411yescharacteristic
254C11×C4⋊C4C22⋊C411yescharacteristic
255C11×C4⋊C4C22⋊C411yescharacteristic
256C11×C4⋊C4C22⋊C411yescharacteristic
257C11×C22⋊C4C22⋊C411yescharacteristic
258C11×C22⋊C4C22⋊C411yescharacteristic
259C11×C22⋊C4C22⋊C411yescharacteristic
260C11×C22⋊C4C22⋊C411yescharacteristic
261C11×C22⋊C4C22⋊C411yescharacteristic
262C11×C22⋊C4C22⋊C411yescharacteristic
263C11×C22⋊C4C22⋊C411yescharacteristic
264C11×C22⋊C4C22⋊C411yescharacteristic
265C42×C11C2×D411yescharacteristic
266C42×C11C2×D411yescharacteristic
267C42×C11C2×D411yescharacteristic
268C42×C11C2×D411yescharacteristic
269C22⋊Dic11—22no—
270C22⋊Dic11—22no—
271(C2×D11)⋊C4—22no—
272(C2×D11)⋊C4—22no—
273(C2×D11)⋊C4—22no—
274(C2×D11)⋊C4—22no—
275(C2×D11)⋊C4—22no—
276(C2×D11)⋊C4—22no—
277C4⋊Dic11—22no—
278C4⋊Dic11—22no—
279C4⋊Dic11—21no—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11—21no—
283C4⋊Dic11—21no—
284C4⋊Dic11—21no—
285Dic11⋊C4—22no—
286Dic11⋊C4—22no—
287Dic11⋊C4—22no—
288Dic11⋊C4—22no—
289C4×Dic11—22no—
290C4×Dic11—22no—
291#4318—21no—
292#4318—21no—
293#4318—21no—
294#4318—21no—
295#4318—21no—
296#4318—21no—
297#4318—21no—
298#4318—42no—
299#4318—42no—
300#4318#4112yes—
301C2×C11⋊C8—21no—
302C2×C11⋊C8—21no—
303C2×C11⋊C8—21no—
304C2×C11⋊C8—21no—
305C2×C11⋊C8—42no—
306C2×C11⋊C8—42no—
307C2×#553—111no—
308D4×M16—111no—
309D4×M16D1111yescharacteristic, complemented
310#1998—111no—
311#1998—111no—
312#1900—111no—
313#1900—111no—
314#1900—111no—
315#1900—111no—
316#1822—111no—
317#1821—111no—
318#1800—111no—
319C4×#100—111no—
320#1742—111no—
321C2×#343—111no—
322C23×C11—21no—
323C23×C11—21no—
324C23×C11—22no—
325C23×C11—21no—
326C23×C11—21no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11—41no—
330C23×C11C2×C22⋊C411yescharacteristic
331C23×C11C2×C22⋊C411yescharacteristic
332C23×C11C2×C22⋊C411yescharacteristic
333C23×C11C2×C22⋊C411yescharacteristic
334C23×C11C23×C411yescharacteristic
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—42no—
339C22×D11—42no—
340D4×C11—22no—
341D4×C11—22no—
342D4×C11—41no—
343D4×C11—41no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—21no—
359C2×C4×C11—21no—
360C2×C4×C11—21no—
361C2×C4×C11—21no—
362C2×C4×C11—21no—
363C2×C4×C11—21no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11C2×C22⋊C411yescharacteristic
367C2×C4×C11C2×C22⋊C411yescharacteristic
368C2×C4×C11C2×C22⋊C411yescharacteristic
369C2×C4×C11C2×C22⋊C411yescharacteristic
370C2×C4×C11C2×C22⋊C411yescharacteristic
371C2×C4×C11C2×C22⋊C411yescharacteristic
372C2×C4×C11C2×C22⋊C411yescharacteristic
373C2×C4×C11C2×C22⋊C411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C2×#4111yescharacteristic
377C2×C4×C11C2×#4111yescharacteristic
378C2×C4×C11H(5,𝔽2)11yescharacteristic
379C2×C4×C112−1+411yescharacteristic
380C22⋊D11—44no—
381C22⋊D11—44no—
382C22⋊D11—82no—
383C22⋊D11—82no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—42no—
388C2×Dic11—42no—
389C2×Dic11—42no—
390C2×Dic11—82no—
391C2×Dic11—82no—
392D44—41no—
393D44—41no—
394D44—41no—
395D44—41no—
396C4×D11—82no—
397C4×D11—82no—
398C8×C11—22no—
399C8×C11—41no—
400C8×C11—41no—
401C8×C11—41no—
402C11⋊C8—22no—
403C11⋊C8—41no—
404C11⋊C8—41no—
405C11⋊C8—41no—
406C22×M16—111no—
407C22×M16—111no—
408C22×M16C2×D1111yescharacteristic
409C22×M16C2×D1111yescharacteristic
410#553—221no—
411#553—221no—
412#553—221no—
413#553—221no—
414#553—221no—
415#553—221no—
416#553—221no—
417#553—221no—
418C2×#126—112no—
419C2×#125—111no—
420C2×#123—112no—
421C2×#121—112no—
422C2×#121—111no—
423C2×#121—111no—
424C2×C4×D4—112no—
425C2×C4×D4—111no—
426C2×C4×D4C2×D1111yescharacteristic
427C2×#117—111no—
428C22×C4⋊C4—111no—
429#436—21no—
430#436—221no—
431#435—21no—
432#435—21no—
433#435—221no—
434#435—221no—
435C8×D4—21no—
436C8×D4—221no—
437#423—111no—
438#423C2×D1111yescharacteristic
439C2×#100—111no—
440C2×#100—111no—
441C2×#100—111no—
442C2×#100—111no—
443#407—111no—
444#407—111no—
445#407C2×D1111yescharacteristic
446#407C2×D1111yescharacteristic
447C4×M16—111no—
448C4×M16C2×D1111yescharacteristic
449#343—111no—
450#343—111no—
451#343—111no—
452#343—111no—
453#343—111no—
454#343—111no—
455#343—111no—
456#343—111no—
457#343—111no—
458#343—111no—
459#343—111no—
460#343—111no—
461C22×C11—21no—
462C22×C11—21no—
463C22×C11—21no—
464C22×C11—21no—
465C22×C11—21no—
466C22×C11—21no—
467C22×C11—21no—
468C22×C11—21no—
469C22×C11—21no—
470C22×C11—21no—
471C22×C11—21no—
472C22×C11—21no—
473C22×C11—21no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—81no—
477C22×C11—81no—
478C22×C11#41312yes—
479C22×C11C22×C22⋊C411yescharacteristic
480C22×C11C4×#4111yescharacteristic
481C22×C11#52011yescharacteristic
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—82no—
486C2×D11—82no—
487C4×C11—21no—
488C4×C11—21no—
489C4×C11—21no—
490C4×C11—21no—
491C4×C11—21no—
492C4×C11—21no—
493C4×C11—21no—
494C4×C11—21no—
495C4×C11#54611yescharacteristic
496C4×C11#54611yescharacteristic
497C4×C11#54711yescharacteristic
498C4×C11#54711yescharacteristic
499Dic11—42no—
500Dic11—42no—
501Dic11—42no—
502C22×D4—112no—
503C22×D4—112no—
504C22×D4—111no—
505C22×D4C4×D1111yescharacteristic
506C23×C4—112no—
507C23×C4—112no—
508C23×C4C22×D1111yescharacteristic
509C23×C4C22×D1111yescharacteristic
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—41no—
515C2×M16—41no—
516C2×M16—111no—
517C2×M16—111no—
518C2×M16—111no—
519C2×M16—111no—
520C2×M16—221no—
521C2×M16—221no—
522C2×M16—222no—
523C2×M16—222no—
524C2×M16—441no—
525C2×M16—441no—
526C2×M16C22×D1111yescharacteristic
527C2×M16C22×D1111yescharacteristic
528C2×M16C22×D1111yescharacteristic
529C2×M16C22×D1111yescharacteristic
530C22×C8—21no—
531C22×C8—21no—
532C22×C8—221no—
533C22×C8—221no—
534#126—222no—
535#126—222no—
536#126—222no—
537#126—222no—
538#125—221no—
539#125—221no—
540#125—221no—
541#125—221no—
542#123—222no—
543#123—222no—
544#123—222no—
545#123—222no—
546#121—222no—
547#121—222no—
548#121—222no—
549#121—222no—
550#121—221no—
551#121—221no—
552#121—221no—
553#121—221no—
554#121—221no—
555#121—221no—
556#121—221no—
557#121—221no—
558C4×D4—222no—
559C4×D4—222no—
560C4×D4—222no—
561C4×D4—222no—
562C4×D4—221no—
563C4×D4—221no—
564C4×D4—221no—
565C4×D4—221no—
566C4×D4D4411yescharacteristic
567C4×D4D4411yescharacteristic
568C4×D4D4411yescharacteristic
569C4×D4D4411yescharacteristic
570C4×D4C22⋊D1111yescharacteristic
571C4×D4C22⋊D1111yescharacteristic
572C4×D4C22⋊D1111yescharacteristic
573C4×D4C22⋊D1111yescharacteristic
574#117—221no—
575#117—221no—
576#117—221no—
577#117—221no—
578C2×C4⋊C4—112no—
579C2×C4⋊C4—112no—
580C2×C4⋊C4—112no—
581C2×C4⋊C4—111no—
582C2×C4⋊C4—111no—
583C2×C4⋊C4—111no—
584C2×C4⋊C4—221no—
585C2×C4⋊C4—221no—
586C2×C4⋊C4—221no—
587C2×C4⋊C4—221no—
588C2×C4⋊C4C4×D1111yescharacteristic
589C2×C22⋊C4—112no—
590C2×C22⋊C4—112no—
591C2×C22⋊C4—112no—
592C2×C22⋊C4—112no—
593C2×C22⋊C4C4×D1111yescharacteristic
594C2×C22⋊C4C4×D1111yescharacteristic
595C2×C42—112no—
596C2×C42C22×D1111yescharacteristic
597C4⋊C8—21no—
598C4⋊C8—21no—
599C4⋊C8—221no—
600C4⋊C8—221no—
601#100—222no—
602#100—222no—
603#100—441no—
604#100—441no—
605C22⋊C8—21no—
606C22⋊C8—21no—
607C22⋊C8—21no—
608C22⋊C8—21no—
609C22⋊C8—221no—
610C22⋊C8—221no—
611C22⋊C8—221no—
612C22⋊C8—221no—
613#97—21no—
614#97—221no—
615C4×C8—21no—
616C4×C8—221no—
617C2×C11—21no—
618C2×C11—21no—
619C2×C11—22no—
620C2×C11—41no—
621C2×C11—41no—
622C2×C11—41no—
623C2×C11#233911yescharacteristic
624C2×C11C2×#41311yescharacteristic
625C2×C11#288811yescharacteristic
626D11—82no—
627C24—112no—
628C24C2×C4×D1111yescharacteristic
629C24C2×C4×D1111yescharacteristic
630C2×D4—42no—
631C2×D4—222no—
632C2×D4—222no—
633C2×D4—222no—
634C2×D4—222no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—444no—
642C2×D4—882no—
643C2×D4(C2×D11)⋊C411yescharacteristic
644C2×D4(C2×D11)⋊C411yescharacteristic
645C2×D4(C2×D11)⋊C411yescharacteristic
646C2×D4(C2×D11)⋊C411yescharacteristic
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—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—222no—
659C22×C4—222no—
660C22×C4—222no—
661C22×C4—222no—
662C22×C4—882no—
663C22×C4—882no—
664C22×C4C2×C4×D1111yescharacteristic
665C22×C4C2×C4×D1111yescharacteristic
666C22×C4C2×C4×D1111yescharacteristic
667C22×C4C2×C4×D1111yescharacteristic
668C22×C4C2×D4411yescharacteristic
669C22×C4C2×D4411yescharacteristic
670C22×C4C2×D4411yescharacteristic
671C22×C4C2×D4411yescharacteristic
672C22×C4C2×C22⋊D1111yescharacteristic
673C22×C4C2×C22⋊D1111yescharacteristic
674C22×C4C2×C22⋊D1111yescharacteristic
675C22×C4C2×C22⋊D1111yescharacteristic
676C22×C4C23×D1111yescharacteristic
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—42no—
685M16—42no—
686M16—112no—
687M16—221no—
688M16—221no—
689M16—221no—
690M16—221no—
691M16—221no—
692M16—221no—
693M16—221no—
694M16—442no—
695M16—442no—
696M16#434112yes—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—42no—
702C2×C8—42no—
703C2×C8—221no—
704C2×C8—221no—
705C2×C8—221no—
706C2×C8—221no—
707C2×C8—442no—
708C2×C8—442no—
709C4⋊C4—222no—
710C4⋊C4—222no—
711C4⋊C4—222no—
712C4⋊C4—222no—
713C4⋊C4—222no—
714C4⋊C4—222no—
715C4⋊C4—221no—
716C4⋊C4—221no—
717C4⋊C4—221no—
718C4⋊C4—221no—
719C4⋊C4—221no—
720C4⋊C4—221no—
721C4⋊C4(C2×D11)⋊C411yescharacteristic
722C4⋊C4(C2×D11)⋊C411yescharacteristic
723C4⋊C4(C2×D11)⋊C411yescharacteristic
724C4⋊C4(C2×D11)⋊C411yescharacteristic
725C22⋊C4—222no—
726C22⋊C4—222no—
727C22⋊C4—222no—
728C22⋊C4—222no—
729C22⋊C4—222no—
730C22⋊C4—222no—
731C22⋊C4—222no—
732C22⋊C4—222no—
733C22⋊C4(C2×D11)⋊C411yescharacteristic
734C22⋊C4(C2×D11)⋊C411yescharacteristic
735C22⋊C4(C2×D11)⋊C411yescharacteristic
736C22⋊C4(C2×D11)⋊C411yescharacteristic
737C22⋊C4(C2×D11)⋊C411yescharacteristic
738C22⋊C4(C2×D11)⋊C411yescharacteristic
739C22⋊C4(C2×D11)⋊C411yescharacteristic
740C22⋊C4(C2×D11)⋊C411yescharacteristic
741C42—222no—
742C42—222no—
743C42C2×D4411yescharacteristic
744C42C2×D4411yescharacteristic
745C42C2×C22⋊D1111yescharacteristic
746C42C2×C22⋊D1111yescharacteristic
747C11#2248211yescharacteristic, complemented, Sylow
748C23—22no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—222no—
757C23—222no—
758C23—222no—
759C23—442no—
760C23—442no—
761C23C2×(C2×D11)⋊C411yescharacteristic
762C23C2×(C2×D11)⋊C411yescharacteristic
763C23C2×(C2×D11)⋊C411yescharacteristic
764C23C2×(C2×D11)⋊C411yescharacteristic
765C23C22×C4×D1111yescharacteristic
766D4—22no—
767D4—22no—
768D4—41no—
769D4—41no—
770D4—444no—
771D4—444no—
772D4—441no—
773D4—441no—
774D4—441no—
775D4—441no—
776D4—882no—
777D4—882no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—442no—
804C2×C4—442no—
805C2×C4—442no—
806C2×C4—882no—
807C2×C4—882no—
808C2×C4—882no—
809C2×C4—882no—
810C2×C4C2×(C2×D11)⋊C411yescharacteristic
811C2×C4C2×(C2×D11)⋊C411yescharacteristic
812C2×C4C2×(C2×D11)⋊C411yescharacteristic
813C2×C4C2×(C2×D11)⋊C411yescharacteristic
814C2×C4C2×(C2×D11)⋊C411yescharacteristic
815C2×C4C2×(C2×D11)⋊C411yescharacteristic
816C2×C4C2×(C2×D11)⋊C411yescharacteristic
817C2×C4C2×(C2×D11)⋊C411yescharacteristic
818C2×C4C22×D4411yescharacteristic
819C2×C4C2×#434111yescharacteristic
820C2×C4#6703711yescharacteristic
821C2×C4#41×D1111yescharacteristic
822C2×C4#6704311yescharacteristic
823C2×C4C22×C22⋊D1111yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C8—222no—
829C8—441no—
830C8—441no—
831C8—441no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—42no—
846C22—42no—
847C22—81no—
848C22—81no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—882no—
853C22—882no—
854C22#1062274512yes—
855C22C4×#434111yescharacteristic
856C22#1062307711yescharacteristic
857C22C22×(C2×D11)⋊C411yescharacteristic
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—442no—
867C4—442no—
868C4—442no—
869C4#1062308511yescharacteristic
870C4#1062308611yescharacteristic
871C4#1062333711yescharacteristic
872C4#1062335511yescharacteristic
873C2—21no—
874C2—21no—
875C2—22no—
876C2—41no—
877C2—41no—
878C2—41no—
879C2—882no—
880C2#1307144111yescharacteristic
881C2C2×#1062274511yescharacteristic
882C2#1307709411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×M16C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623096C2
cosocleC22×C4×C11C24
hypercenterD4×M16D11
hypocenterC11#22482
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. D4×#4318C2semidirect
3. #13069609C2semidirect
4. #13069608C2semidirect
5. #13069079C2semidirect
6. #13069079C2semidirect
7. #13069077C2semidirect
8. #13069077C2semidirect
9. #13068697C2semidirect
10. #13068694C2semidirect
11. #13068605C2semidirect
12. C4×#66887C2semidirect
13. #13068354C2semidirect
14. C2×#10622192C2semidirect
15. D4×C11×M16C2semidirect
309. D4×M16D11semidirect
747. C11#22482semidirect

Maximal subgroups

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

subgroupindex
C2×#106230962
D4×#43182
#130696092
#130696082
#130690792
#130690772
#130686972
#130686942
#130686052
C4×#668872
#130683542
C2×#106221922
D4×C11×M162
#2248211