Finite Group Databasebeta

← #14772149

Subgroups — #14772149

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622643C211yesmaximal, characteristic
2C2×#10622643C211yesmaximal, characteristic
3C2×C4×#4326C211yesmaximal, characteristic
4#13071536C211yesmaximal, characteristic
5#13069356C211yesmaximal, characteristic
6#13069341C211yesmaximal, characteristic
7#13068884C211yesmaximal, characteristic
8#13068883C211yesmaximal, characteristic
9#13068870C211yesmaximal, characteristic
10#13068869C211yesmaximal, characteristic
11#13068782C211yesmaximal, characteristic
12#13068631C211yesmaximal, characteristic
13#13068618C211yesmaximal, characteristic
14#13068491C211yesmaximal, characteristic
15Q8×C11×C4⋊C4C211yesmaximal, characteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#389—21no—
24C11×#389—21no—
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#384—21no—
28C11×#384C2211yescharacteristic
29C4×C11×C4⋊C4—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622643—24no—
35#10622643C418yescomplemented
36C4×#4326—24no—
37#10622585—21no—
38#10622585—21no—
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622549C2211yescharacteristic
48#10622541C2211yescharacteristic
49#10622541C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×#66867C2211yescharacteristic
53C2×C4×C11⋊C8C2211yescharacteristic
54#10622263—21no—
55#10622262—21no—
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—41no—
68C4×Q8×C11—41no—
69C4×Q8×C11C2×C414yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×#4326C2×C414yes—
89C2×#4326D414yes—
90C2×#4326Q814yes—
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×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C4×Dic22—22no—
107C4×Dic22—22no—
108C4×Dic22—22no—
109C4×Dic22—41no—
110C4×Dic22—41no—
111C4×Dic22C2×C414yes—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95D411yescharacteristic
115C11×#95D411yescharacteristic
116#66899—22no—
117#66899—22no—
118#66899C2×C414yes—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123#66874—22no—
124#66874—22no—
125#66874C2×C414yes—
126#66872—22no—
127#66872—41no—
128#66872C2×C414yes—
129#66871—22no—
130#66871—41no—
131C4⋊(C11⋊C8)—22no—
132#66867—22no—
133#66867C2×C414yes—
134C4×C11⋊C8—22no—
135#22679—111nomaximal, Sylow
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C22×C412yes—
140C2×Q8×C11C2×D412yes—
141C2×Q8×C11C2×Q812yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22C22×C412yes—
161C2×Dic22C2×D412yes—
162C2×Dic22C2×Q812yes—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—41no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—81no—
175C11×C4⋊C4—81no—
176C11×C4⋊C4—81no—
177C11×C4⋊C4C22×C412yes—
178C42×C11—24no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—42no—
184C42×C11—42no—
185C42×C11C22×C412yes—
186C42×C11#4112yes—
187#4326C4⋊C4116yescomplemented
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11C22×C412yes—
194Dic11⋊C4—24no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199C4×Dic11—24no—
200C4×Dic11—42no—
201C4×Dic11—42no—
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⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8C22×C412yes—
211C2×C11⋊C8C22×C412yes—
212C2×C11⋊C8C2×D412yes—
213C2×C11⋊C8C2×Q812yes—
214C2×#441—111no—
215C2×#441—111no—
216C2×C4×Q16—111no—
217#2351—111no—
218Q8×C4⋊C4D1111yescharacteristic
219#1944—111no—
220#1941—111no—
221#1865—111no—
222#1865—111no—
223#1863—111no—
224#1863—111no—
225#1847—111no—
226#1805—111no—
227#1803—111no—
228#1771—111no—
229C23×C11C22×D411yescharacteristic
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11—22no—
233Q8×C11C2×C4⋊C414yes—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11C4×D412yes—
262C2×C4×C11C4×D412yes—
263C2×C4×C11#13712yes—
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×Q811yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×C4×C112−1+411yescharacteristic
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282Dic22—22no—
283Dic22—22no—
284Dic22—22no—
285Dic22C2×C4⋊C414yes—
286C11⋊C8—22no—
287C11⋊C8—41no—
288C11⋊C8—41no—
289C11⋊C8C2×C4⋊C414yes—
290C22×Q16—111no—
291C2×C4×Q8—111no—
292C2×C4×Q8—111no—
293C2×C4×Q8—111no—
294C2×C4×Q8C2×D1111yescharacteristic
295C2×C4×Q8C2×D1111yescharacteristic
296C2×C4×Q8C2×D1111yescharacteristic
297#441—118no—
298#441—224no—
299C4×Q16—224no—
300C2×#107—111no—
301C2×#107—111no—
302C2×#106—111no—
303C2×#106—111no—
304C2×#106—111no—
305C2×C4⋊C8—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#97—111no—
313C2×#97—111no—
314C2×C4×C8—111no—
315#389—21no—
316#389—21no—
317#389—111no—
318#389—111no—
319#389—221no—
320#389—221no—
321#389C2×D1111yescharacteristic
322#389C2×D1111yescharacteristic
323#384—21no—
324#384C2×D1111yescharacteristic
325#382—111no—
326#382—221no—
327C4×C4⋊C4—21no—
328C4×C4⋊C4—221no—
329C4×C4⋊C4C2×D1111yescharacteristic
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#336—111no—
335#336—111no—
336C22×C11C2×C4×D411yescharacteristic
337C22×C11D4211yescharacteristic
338C22×C11D4×Q811yescharacteristic
339C22×C11C2×#13711yescharacteristic
340C22×C11#57511yescharacteristic
341C22×C11#57711yescharacteristic
342C22×C11#57811yescharacteristic
343C4×C11—24no—
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—42no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11C22×C4⋊C411yescharacteristic
354C4×C11#52011yescharacteristic
355C4×C11#54711yescharacteristic
356C4×C11#55411yescharacteristic
357Dic11—24no—
358Dic11—42no—
359Dic11—81no—
360Dic11—81no—
361C22×Q8—111no—
362C22×Q8C22×D1111yescharacteristic
363C2×Q16—114no—
364C2×Q16—114no—
365C2×Q16—114no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8—111no—
370C4×Q8—22no—
371C4×Q8—22no—
372C4×Q8—22no—
373C4×Q8—41no—
374C4×Q8—41no—
375C4×Q8—114no—
376C4×Q8—222no—
377C4×Q8—222no—
378C4×Q8—222no—
379C4×Q8—441no—
380C4×Q8—441no—
381C4×Q8C4×D1114yes—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4C22⋊D1111yescharacteristic
398C2×C4⋊C4C22⋊D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—221no—
406C2×C42—221no—
407C2×C42—221no—
408C2×C42C22×D1111yescharacteristic
409C2×C42C22×D1111yescharacteristic
410C2×C42C22×D1111yescharacteristic
411#107—222no—
412#107—441no—
413#106—114no—
414#106—222no—
415#106—441no—
416C4⋊C8—222no—
417#103—114no—
418#103—114no—
419#103—222no—
420#103—222no—
421#103—222no—
422#103—222no—
423#97—114no—
424#97—222no—
425C4×C8—222no—
426#95—21no—
427#95—21no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95C22⋊D1111yescharacteristic
433#95C22⋊D1111yescharacteristic
434C2×C11D4×C4⋊C411yescharacteristic
435C2×C11C4×#13711yescharacteristic
436C2×C11#294711yescharacteristic
437C2×C11#327011yescharacteristic
438C2×C11#327111yescharacteristic
439C2×C11#338711yescharacteristic
440C2×C11#339011yescharacteristic
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—112no—
445C2×Q8—112no—
446C2×Q8—112no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8C2×C4×D1112yes—
451C2×Q8D4×D1112yes—
452C2×Q8Q8×D1112yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C2×C22⋊D1111yescharacteristic
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C2×C22⋊D1111yescharacteristic
465C22×C4C2×C22⋊D1111yescharacteristic
466C22×C4C2×C22⋊D1111yescharacteristic
467C22×C4C23×D1111yescharacteristic
468Q16—1116no—
469C2×C8—112no—
470C2×C8—112no—
471C2×C8—112no—
472C2×C8—112no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C4⋊C4—24no—
482C4⋊C4—22no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4—81no—
495C4⋊C4—112no—
496C4⋊C4—224no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4C2×C4×D1112yes—
507C42—24no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—42no—
513C42—42no—
514C42—224no—
515C42—442no—
516C42—442no—
517C42C2×C4×D1112yes—
518C42#433912yes—
519C11#2267911yescharacteristic, complemented, Sylow
520C23C22×C22⋊D1111yescharacteristic
521Q8—22no—
522Q8—22no—
523Q8—22no—
524Q8—114no—
525Q8—222no—
526Q8—222no—
527Q8—222no—
528Q8C4⋊C4×D1114yes—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4C4×C22⋊D1112yes—
569C2×C4C4×C22⋊D1112yes—
570C2×C4#6699512yes—
571C2×C4C22×C4×D1111yescharacteristic
572C2×C4C2×#433911yescharacteristic
573C2×C4C2×D4×D1111yescharacteristic
574C2×C4#6703711yescharacteristic
575C2×C4C2×Q8×D1111yescharacteristic
576C2×C4#6704011yescharacteristic
577C8—114no—
578C8—222no—
579C8—441no—
580C8—441no—
581C22C2×C4×C22⋊D1111yescharacteristic
582C22D4×C22⋊D1111yescharacteristic
583C22C2×#6699511yescharacteristic
584C22Q8×C22⋊D1111yescharacteristic
585C22#1062335311yescharacteristic
586C22#1062336711yescharacteristic
587C22#1062336911yescharacteristic
588C4—22no—
589C4—24no—
590C4—22no—
591C4—22no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—42no—
596C4—81no—
597C4—81no—
598C4—224no—
599C4—442no—
600C4—881no—
601C4—881no—
602C4C2×C4⋊C4×D1111yescharacteristic
603C4#1062303511yescharacteristic
604C4#1062303811yescharacteristic
605C4#1062304211yescharacteristic
606C2C4⋊C4×C22⋊D1111yescharacteristic
607C2C4×#6699511yescharacteristic
608C2#1307745511yescharacteristic
609C2#1308018711yescharacteristic
610C2#1308019711yescharacteristic
611C2#1308154411yescharacteristic
612C2#1308157911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingQ8×C11×C4⋊C4C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterQ8×C4⋊C4D11
hypocenterC11#22679
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
35. #10622643C4semidirect
187. #4326C4⋊C4semidirect
519. C11#22679semidirect

Maximal subgroups

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

subgroupindex
C2×#106226432
C2×C4×#43262
#130715362
#130693562
#130693412
#130688842
#130688832
#130688702
#130688692
#130687822
#130686312
#130686182
#130684912
Q8×C11×C4⋊C42
#2267911