Finite Group Databasebeta

← #14767718

Subgroups — #14767718

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071890C211yesmaximal, characteristic
2#13069552C211yesmaximal, characteristic, complemented
3#13069550C211yesmaximal, characteristic, complemented
4#13069334C211yesmaximal, characteristic, complemented
5#13069333C211yesmaximal, characteristic, complemented
6#13069176C211yesmaximal, characteristic, complemented
7#13069173C211yesmaximal, characteristic, complemented
8#13069173C211yesmaximal, characteristic, complemented
9#13069172C211yesmaximal, characteristic, complemented
10#13068801C211yesmaximal, characteristic
11#13068798C211yesmaximal, characteristic
12#13068598C211yesmaximal, characteristic
13C8×C22⋊Dic11C211yesmaximal, characteristic
14#13068312C211yesmaximal, characteristic
15C8×C11×C22⋊C4C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C4×C11×C22⋊C4C2211yescharacteristic
24C4×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622562C411yescharacteristic
33#10622561C411yescharacteristic
34#10622561C411yescharacteristic
35#10622560C411yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C4×Dic11⋊C4C2211yescharacteristic
38C4×Dic11⋊C4C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41#10622274C411yescharacteristic
42#10622273C411yescharacteristic
43#10622270C411yescharacteristic
44#10622269C411yescharacteristic
45C11×#336C2211yescharacteristic
46C11×#336C2211yescharacteristic
47#10622188C2211yescharacteristic
48#10622188C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×Dic22C2×C411yescharacteristic
61C22×C8×C11—41no—
62C22×C8×C11—41no—
63C22×C8×C11Q814yescomplemented
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C22⋊C4C2×C411yescharacteristic
69C2×C11×C22⋊C4C2×C411yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11C2×C411yescharacteristic
73C2×C22⋊Dic11C2×C411yescharacteristic
74C2×C22⋊Dic11C2×C411yescharacteristic
75C2×C22⋊Dic11C2×C411yescharacteristic
76#66979—41no—
77#66979—41no—
78C2×C4⋊Dic11C2×C411yescharacteristic
79C2×C4⋊Dic11C2×C411yescharacteristic
80C2×C4⋊Dic11C2×C411yescharacteristic
81C2×C4⋊Dic11C2×C411yescharacteristic
82C2×C4⋊Dic11C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×Dic11⋊C4C2×C411yescharacteristic
88C2×Dic11⋊C4C2×C411yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C2×#4318—22no—
94C2×#4318—41no—
95C2×#4318—41no—
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C4×Dic22—41no—
101C4×Dic22—41no—
102C11×C22⋊C8—22no—
103C4×C8×C11—41no—
104C4×C8×C11—41no—
105C11×#95C2×C411yescharacteristic
106C11×#95C2×C411yescharacteristic
107C11⋊#95C2×C411yescharacteristic
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110C11⋊#95C2×C411yescharacteristic
111C11⋊#95C2×C411yescharacteristic
112C11⋊#95C2×C411yescharacteristic
113C11⋊#95C2×C411yescharacteristic
114C11⋊#95C2×C411yescharacteristic
115C22⋊(C11⋊C8)—22no—
116Dic11⋊C8—41no—
117Dic11⋊C8—41no—
118Dic11⋊C8—41no—
119Dic11⋊C8—41no—
120C8×Dic11—41no—
121C8×Dic11—41no—
122C4⋊(C11⋊C8)—41no—
123C4⋊(C11⋊C8)—41no—
124#22288—111nomaximal, Sylow
125C24×C11C22×C411yescharacteristic
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C2×Q812yes—
136C22×C4×C11#4112yes—
137C22×C4×C11C2411yescharacteristic
138C22×Dic11C22×C411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142C22×Dic11C22×C411yescharacteristic
143C22×Dic11C22×C411yescharacteristic
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C2×Dic22—22no—
147C2×Dic22—22no—
148C2×Dic22—41no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—44no—
160C2×C8×C11C2×Q812yes—
161C2×C8×C11C2×Q812yes—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C22⋊Dic11—22no—
169C22⋊Dic11—22no—
170C22⋊Dic11—41no—
171C22⋊Dic11—41no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—41no—
175C4⋊Dic11—41no—
176C4⋊Dic11—41no—
177Dic11⋊C4—22no—
178Dic11⋊C4—22no—
179Dic11⋊C4—22no—
180Dic11⋊C4—22no—
181Dic11⋊C4—41no—
182Dic11⋊C4—41no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—21no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191#4318—44no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204#2396—111no—
205#1984—111no—
206#1984—111no—
207#1939—111no—
208#1939—111no—
209#1916—111no—
210#1916—111no—
211#1916—111no—
212#1916—111no—
213#1851—111no—
214#1851—111no—
215#1798—111no—
216C8×C22⋊C4—111no—
217C8×C22⋊C4D1111yescharacteristic
218#1729—111no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11C4×Q812yes—
226C23×C11C23×C411yescharacteristic
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11C4×Q812yes—
244C2×C4×C11#13112yes—
245C2×C4×C11#13112yes—
246C2×C4×C11C22×Q811yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×C4×C11H(5,𝔽2)11yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11#13112yes—
275C2×Dic11#13112yes—
276Dic22—44no—
277C8×C11—22no—
278C8×C11—22no—
279C8×C11—41no—
280C8×C11—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C22×M16—111no—
286C23×C8C2×D1111yescharacteristic
287C2×C4×Q8—111no—
288C2×#117—111no—
289C2×C4⋊C8—111no—
290C2×C4⋊C8—111no—
291C2×C4⋊C8—111no—
292C2×C4⋊C8—111no—
293C2×C4⋊C8—111no—
294C2×C4⋊C8—111no—
295C2×C22⋊C8—111no—
296C2×C22⋊C8C2×D1111yescharacteristic
297C2×C4×C8—111no—
298C2×C4×C8—111no—
299C2×C4×C8C2×D1111yescharacteristic
300C2×C4×C8C2×D1111yescharacteristic
301#400—111no—
302#399—111no—
303#398—111no—
304#398—111no—
305#396—111no—
306#396—111no—
307#395—111no—
308#393—111no—
309C4×C4⋊C4—111no—
310C4×C4⋊C4—111no—
311C4×C4⋊C4—111no—
312C4×C22⋊C4—111no—
313C4×C22⋊C4C2×D1111yescharacteristic
314#336—111no—
315#336—111no—
316#336—111no—
317#336—111no—
318#336—111no—
319#336—111no—
320#336—111no—
321#336—111no—
322#336—111no—
323#336—111no—
324#336—111no—
325#336—111no—
326#336C2×D1111yescharacteristic
327#336C2×D1111yescharacteristic
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11C2×C4×Q811yescharacteristic
336C22×C11#51811yescharacteristic
337C22×C11#52011yescharacteristic
338C22×C11C2×#13111yescharacteristic
339C22×C11C2×#13111yescharacteristic
340C22×C11C2×#13111yescharacteristic
341C22×C11C2×#13111yescharacteristic
342C4×C11—22no—
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11#53811yescharacteristic
348C4×C11#53911yescharacteristic
349C4×C11#54311yescharacteristic
350C4×C11#54411yescharacteristic
351Dic11—22no—
352Dic11—22no—
353Dic11—41no—
354Dic11—41no—
355Dic11—41no—
356Dic11—41no—
357Dic11—41no—
358Dic11—41no—
359C22×Q8—111no—
360C23×C4C22×D1111yescharacteristic
361C2×M16—222no—
362C2×M16—441no—
363C2×M16—441no—
364C22×C8—41no—
365C22×C8—41no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8Dic2214yescomplemented
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1111yescharacteristic
373C22×C8C22×D1111yescharacteristic
374C22×C8C22×D1111yescharacteristic
375C4×Q8—441no—
376C4×Q8—441no—
377#117—441no—
378#117—441no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C22⋊C4—111no—
391C2×C22⋊C4—111no—
392C2×C22⋊C4—111no—
393C2×C22⋊C4—111no—
394C2×C22⋊C4C4×D1111yescharacteristic
395C2×C22⋊C4C4×D1111yescharacteristic
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42C22×D1111yescharacteristic
401C2×C42C22×D1111yescharacteristic
402C4⋊C8—441no—
403C4⋊C8—441no—
404C4⋊C8—441no—
405C4⋊C8—441no—
406C4⋊C8—441no—
407C4⋊C8—441no—
408C22⋊C8—22no—
409C22⋊C8—222no—
410C4×C8—41no—
411C4×C8—41no—
412C4×C8—441no—
413C4×C8—441no—
414#95—111no—
415#95—111no—
416#95—111no—
417#95—111no—
418#95—111no—
419#95—111no—
420#95—111no—
421#95—111no—
422#95C4×D1111yescharacteristic
423#95C4×D1111yescharacteristic
424C2×C11—42no—
425C2×C11#232911yescharacteristic
426C2×C11#296011yescharacteristic
427C2×C11#296011yescharacteristic
428C2×C11#297711yescharacteristic
429C2×C11#297911yescharacteristic
430C2×C11#299411yescharacteristic
431C2×C11#299411yescharacteristic
432C24C2×C4×D1111yescharacteristic
433C2×Q8—222no—
434C2×Q8—222no—
435C2×Q8—441no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4C2×Dic2212yes—
449C22×C4C2×C4×D1111yescharacteristic
450C22×C4C2×C4×D1111yescharacteristic
451C22×C4C2×C4×D1111yescharacteristic
452C22×C4C2×C4×D1111yescharacteristic
453C22×C4C2×C4×D1111yescharacteristic
454C22×C4#433912yes—
455C22×C4C23×D1111yescharacteristic
456M16—444no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—44no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8C2×Dic2212yes—
481C2×C8C2×Dic2212yes—
482C4⋊C4—222no—
483C4⋊C4—222no—
484C4⋊C4—222no—
485C4⋊C4—222no—
486C4⋊C4—222no—
487C4⋊C4—222no—
488C4⋊C4—441no—
489C4⋊C4—441no—
490C4⋊C4—441no—
491C4⋊C4—441no—
492C4⋊C4—441no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—222no—
496C22⋊C4—222no—
497C22⋊C4—441no—
498C22⋊C4—441no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—221no—
504C42—221no—
505C42—221no—
506C42—221no—
507C42—221no—
508C42—221no—
509C42—221no—
510C42—221no—
511C11#2228811yescharacteristic, complemented, Sylow
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23C4×Dic2212yes—
519C23C22×C4×D1111yescharacteristic
520Q8—444no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—112no—
538C2×C4—112no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4C4×Dic2212yes—
562C2×C4#6695412yes—
563C2×C4#6695412yes—
564C2×C4C22×Dic2211yescharacteristic
565C2×C4C2×#433911yescharacteristic
566C2×C4#6703711yescharacteristic
567C2×C4#6703711yescharacteristic
568C2×C4#6704211yescharacteristic
569C2×C4#6704311yescharacteristic
570C8—22no—
571C8—22no—
572C8—41no—
573C8—41no—
574C8—441no—
575C8—441no—
576C8—441no—
577C8—441no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22C2×C4×Dic2211yescharacteristic
586C22#1062307611yescharacteristic
587C22#1062307711yescharacteristic
588C22C2×#6695411yescharacteristic
589C22C2×#6695411yescharacteristic
590C22D11×#13111yescharacteristic
591C22D11×#13111yescharacteristic
592C4—22no—
593C4—22no—
594C4—22no—
595C4—41no—
596C4—41no—
597C4—222no—
598C4—222no—
599C4—441no—
600C4—441no—
601C4—441no—
602C4—441no—
603C4—441no—
604C4—441no—
605C4#1062301411yescharacteristic
606C4#1062305011yescharacteristic
607C4#1062309111yescharacteristic
608C4#1062309511yescharacteristic
609C2—42no—
610C2#1307134411yescharacteristic
611C2#1307754811yescharacteristic
612C2#1307755011yescharacteristic
613C2#1307766911yescharacteristic
614C2#1307767911yescharacteristic
615C2#1307777111yescharacteristic
616C2#1307777311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC8×C11×C22⋊C4C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC8×C22⋊C4D11
hypocenterC11#22288
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13069552C2semidirect
3. #13069550C2semidirect
4. #13069334C2semidirect
5. #13069333C2semidirect
6. #13069176C2semidirect
7. #13069173C2semidirect
8. #13069173C2semidirect
9. #13069172C2semidirect
63. C22×C8×C11Q8semidirect
370. C22×C8Dic22semidirect
511. C11#22288semidirect

Maximal subgroups

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

subgroupindex
#130718902
#130695522
#130695502
#130693342
#130693332
#130691762
#130691732
#130691722
#130688012
#130687982
#130685982
C8×C22⋊Dic112
#130683122
C8×C11×C22⋊C42
#2228811