Finite Group Databasebeta

← #14816628

Subgroups — #14816628

Order 2816.

812 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622635C211yesmaximal, characteristic, complemented
2C2×#10622577C211yesmaximal, characteristic
3#13072329C211yesmaximal, characteristic
4#13070154C211yesmaximal, characteristic, complemented
5#13070107C211yesmaximal, characteristic, complemented
6#13069997C211yesmaximal, characteristic, complemented
7#13069954C211yesmaximal, characteristic, complemented
8#13069374C211yesmaximal, characteristic, complemented
9#13069194C211yesmaximal, characteristic, complemented
10#13069050C211yesmaximal, characteristic
11#13068929C211yesmaximal, characteristic
12#13068870C211yesmaximal, characteristic, complemented
13#13068804C211yesmaximal, characteristic
14#13068801C211yesmaximal, characteristic
15C11×#2360C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C11×#391C2211yescharacteristic
23C11×#389—21no—
24C11×#389C2211yescharacteristic
25C11×#387—21no—
26C11×#385—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C22⋊C4—21no—
29C4×C11×C22⋊C4C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622825C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622635—24no—
37#10622577—24no—
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622562—21no—
45#10622561—21no—
46#10622548C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622267—21no—
52#10622260—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8Q814yes—
66C4×Q8×C11—22no—
67C4×Q8×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86#66979—22no—
87#66979—41no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×#4318—22no—
100C2×#4318—22no—
101C2×#4318—22no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66923—22no—
107#66923—41no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95D411yescharacteristic
113C11×#95D411yescharacteristic
114#66899—22no—
115#66899—22no—
116#66899—22no—
117#66899—41no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C22⋊(C11⋊C8)—22no—
122#66872—22no—
123#66872D414yes—
124#66871—22no—
125#66871—22no—
126#66871—22no—
127#66871—41no—
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—22no—
130#26362—111nomaximal, Sylow
131C24×C11C2×D411yescharacteristic
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11C2×Q812yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—81no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×Q812yes—
155C22×C4×C11#4112yes—
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—81no—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×Q812yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—41no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—42no—
179C42×C11—81no—
180C22⋊Dic11—42no—
181C22⋊Dic11—81no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—42no—
190C4⋊Dic11—81no—
191C4⋊Dic11C2×D412yes—
192Dic11⋊C4—42no—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195Dic11⋊C4—81no—
196C4×Dic11—42no—
197#4318—28no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8C2×D412yes—
209C2×C11⋊C8#4112yes—
210C2×#479—111no—
211C2×#428—111no—
212#2441—111no—
213#2360D1111yescharacteristic
214#2095—111no—
215#2086—111no—
216#2066—111no—
217#2059—111no—
218#1947—111no—
219#1919—111no—
220#1894—111no—
221#1873—111no—
222#1863—111no—
223#1852—111no—
224#1851—111no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11C22⋊Q812yes—
232C23×C11C22×D411yescharacteristic
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11—41no—
236Q8×C11—41no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—84no—
267C2×C4×C11C22⋊Q812yes—
268C2×C4×C11#13712yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×Q811yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×C4×C112−1+411yescharacteristic
275C2×Dic11—22no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C11⋊C8—22no—
288C11⋊C8—22no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C22×M16—111no—
292C2×#125—111no—
293C2×C22⋊Q8C2×D1111yescharacteristic
294C2×C4×Q8C2×D1111yescharacteristic
295C2×#117—111no—
296C22×C4⋊C4C2×D1111yescharacteristic
297#479—224no—
298#428—224no—
299C2×#107—111no—
300C2×#107—111no—
301C2×#107—111no—
302C2×#107—111no—
303C2×#106—111no—
304C2×#106—111no—
305C2×C4⋊C8—111no—
306C2×C4⋊C8—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×C22⋊C8—111no—
312#399—221no—
313#396—221no—
314#391C2×D1111yescharacteristic
315#389—21no—
316#389—111no—
317#389—111no—
318#389—221no—
319#389C2×D1111yescharacteristic
320#387—21no—
321#387—221no—
322#385—21no—
323#384—111no—
324#380—111no—
325C4×C4⋊C4C2×D1111yescharacteristic
326C4×C22⋊C4—21no—
327C4×C22⋊C4C2×D1111yescharacteristic
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#336—111no—
335#336—111no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—22no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11C2×C22⋊Q811yescharacteristic
344C22×C11D4211yescharacteristic
345C22×C11#54711yescharacteristic
346C22×C11C2×#13711yescharacteristic
347C22×C11#57511yescharacteristic
348C22×C11#57611yescharacteristic
349C22×C11#57811yescharacteristic
350C4×C11—22no—
351C4×C11—22no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—41no—
358C4×C11—81no—
359C4×C11#52511yescharacteristic
360C4×C11#53911yescharacteristic
361C4×C11D4×Q811yescharacteristic
362C4×C11#55411yescharacteristic
363Dic11—42no—
364Dic11—81no—
365Dic11—81no—
366Dic11—81no—
367C22×Q8C22×D1111yescharacteristic
368C23×C4—21no—
369C23×C4C22×D1111yescharacteristic
370C2×M16—222no—
371C2×M16—222no—
372C2×M16—222no—
373C22×C8—111no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8—111no—
377#125—222no—
378#125—441no—
379C22⋊Q8—22no—
380C22⋊Q8Dic2214yes—
381C4×Q8—22no—
382C4×Q8—41no—
383#117—222no—
384#117—441no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—41no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4C22⋊D1111yescharacteristic
408C2×C22⋊C4C22⋊D1111yescharacteristic
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—221no—
412C2×C42C22×D1111yescharacteristic
413C2×C42C22×D1111yescharacteristic
414#107—222no—
415#107—222no—
416#107—222no—
417#107—441no—
418#106—114no—
419#106—222no—
420C4⋊C8—222no—
421C4⋊C8—222no—
422#103—222no—
423#103—222no—
424#103—222no—
425#103—441no—
426C22⋊C8—222no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95C22⋊D1111yescharacteristic
435#95C22⋊D1111yescharacteristic
436C2×C11—42no—
437C2×C11#244911yescharacteristic
438C2×C11#307811yescharacteristic
439C2×C11#308311yescharacteristic
440C2×C11#326811yescharacteristic
441C2×C11#327611yescharacteristic
442C2×C11#334611yescharacteristic
443C2×C11#335211yescharacteristic
444C24C2×C22⋊D1111yescharacteristic
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×Dic2212yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—81no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4C2×Dic2212yes—
467C22×C4#433912yes—
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C23×D1111yescharacteristic
474M16—228no—
475C2×C8—112no—
476C2×C8—112no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C4⋊C4—24no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—81no—
495C4⋊C4—112no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4—442no—
507C4⋊C4—881no—
508C4⋊C4—881no—
509C4⋊C4C2×Dic2212yes—
510C4⋊C4D4×D1112yes—
511C22⋊C4—24no—
512C22⋊C4—22no—
513C22⋊C4—41no—
514C22⋊C4—442no—
515C22⋊C4—881no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—42no—
521C42—81no—
522C42—442no—
523C11#2636211yescharacteristic, complemented, Sylow
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23#6697712yes—
531C23C22×C22⋊D1111yescharacteristic
532Q8—22no—
533Q8—22no—
534Q8—41no—
535Q8—41no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—84no—
566C2×C4—222no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4#6697712yes—
579C2×C4#6699512yes—
580C2×C4C22×Dic2211yescharacteristic
581C2×C4C2×#433911yescharacteristic
582C2×C4C2×D4×D1111yescharacteristic
583C2×C4#6703711yescharacteristic
584C2×C4#41×D1111yescharacteristic
585C2×C4#6704311yescharacteristic
586C8—222no—
587C8—222no—
588C8—441no—
589C8—441no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22C2×#6697711yescharacteristic
598C22D4×C22⋊D1111yescharacteristic
599C22C2×#6699511yescharacteristic
600C22#1062335311yescharacteristic
601C22#1062335511yescharacteristic
602C22#1062336611yescharacteristic
603C22#1062336911yescharacteristic
604C4—22no—
605C4—22no—
606C4—42no—
607C4—41no—
608C4—42no—
609C4—41no—
610C4—42no—
611C4—41no—
612C4—81no—
613C4—442no—
614C4—881no—
615C4—881no—
616C4—881no—
617C4D4×Dic2211yescharacteristic
618C4#1062307011yescharacteristic
619C4#1062307811yescharacteristic
620C4#1062309511yescharacteristic
621C2—42no—
622C2#1307241911yescharacteristic
623C2#1307842111yescharacteristic
624C2#1307846711yescharacteristic
625C2#1308015211yescharacteristic
626C2#1308026211yescharacteristic
627C2#1308109511yescharacteristic
628C2#1308118511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2360C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2360D11
hypocenterC11#26362
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
1. C2×#10622635C2semidirect
4. #13070154C2semidirect
5. #13070107C2semidirect
6. #13069997C2semidirect
7. #13069954C2semidirect
8. #13069374C2semidirect
9. #13069194C2semidirect
12. #13068870C2semidirect
523. C11#26362semidirect

Maximal subgroups

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

subgroupindex
C2×#106226352
C2×#106225772
#130723292
#130701542
#130701072
#130699972
#130699542
#130693742
#130691942
#130690502
#130689292
#130688702
#130688042
#130688012
C11×#23602
#2636211