Finite Group Databasebeta

← #14731026

Subgroups — #14731026

Order 2816.

918 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079561C211yesmaximal, characteristic, complemented
2C2×#10622694C211yesmaximal, characteristic, complemented
3#13078431C211yesmaximal, characteristic
4#13067837C214yesmaximal, complemented
5#13067830C214yesmaximal, complemented
6#13067297C211yesmaximal, characteristic, complemented
7#13067071C211yesmaximal, characteristic, complemented
8#13066998C211yesmaximal, characteristic
9C11×#3503C211yesmaximal, characteristic
10Q82×C11C2212yes—
11C11×#557—21no—
12C11×#554—22no—
13C11×#554C2212yes—
14D4×Q8×C11—22no—
15D4×Q8×C11—21no—
16C11×#544—22no—
17C11×#544—21no—
18C11×#533—21no—
19C11×#533C2211yescharacteristic
20C2×C11×C4⋊Q8—21no—
21C2×C11×C4⋊Q8C2211yescharacteristic
22C11×#520—21no—
23C4×C11×#41C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25#10622845—21no—
26C2×#66899—22no—
27#10622706—21no—
28#10622705—21no—
29#10622694—22no—
30#10622694C2214yes—
31#10622663—22no—
32#10622644C2214yes—
33#10622634—21no—
34#10622633C2212yes—
35#10622621—21no—
36#10622620C2212yes—
37#10622608—21no—
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622184C2214yes—
42Q8⋊(C11⋊C8)C2214yes—
43Q8⋊(C11⋊C8)C2212yes—
44D4⋊(C11⋊C8)C2212yes—
45C2×C11×#41D411yescharacteristic
46C22×Q8×C11—22no—
47C22×Q8×C11D412yes—
48C22×Dic22—21no—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—24no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8D412yes—
57C11×C4⋊Q8D411yescharacteristic
58C11×C4⋊Q8D411yescharacteristic
59C11×C4⋊Q8C2312yes—
60C11×#125—22no—
61C11×#125—24no—
62C11×#125—22no—
63C11×#125—21no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—24no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8D412yes—
71C4×Q8×C11—22no—
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C4×Q8×C11—21no—
75C4×Q8×C11D411yescharacteristic
76C4×Q8×C11C2311yescharacteristic
77C4×Q8×C11C2312yes—
78C4×D4×C11—24no—
79C4×D4×C11—22no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11D411yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C11×#117—22no—
85C11×#117—21no—
86C11×#117—21no—
87C11×#117D411yescharacteristic
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—22no—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C2×#4326—24no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×#4318—21no—
98C22×C11⋊C8—21no—
99#66922—21no—
100#66922—21no—
101#66922—21no—
102#66922C2312yes—
103#66899—28no—
104#66899—22no—
105#66896—22no—
106C22⋊(C11⋊C8)—21no—
107#66874—24no—
108#66872—22no—
109#66871—22no—
110C4⋊(C11⋊C8)—21no—
111C4⋊(C11⋊C8)C2312yes—
112C4⋊(C11⋊C8)C2312yes—
113C4×C11⋊C8—21no—
114C4×C11⋊C8—21no—
115C4×C11⋊C8C2312yes—
116#18633—111nomaximal, Sylow
117C11×#41—22no—
118C11×#41Q1614yescomplemented
119C2×Q8×C11—24no—
120C2×Q8×C11—22no—
121C2×Q8×C11—21no—
122C2×Q8×C11—44no—
123C2×Q8×C11—84no—
124C2×Q8×C11C2×D412yes—
125C2×Q8×C11C2×D411yescharacteristic
126C2×Q8×C11C2×D414yes—
127C2×D4×C11—21no—
128C2×D4×C11C2×D411yescharacteristic
129C22×C4×C11—21no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×Dic11—41no—
138C2×Dic22—22no—
139C2×Dic22—41no—
140C2×Dic22—82no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4C2×D411yescharacteristic
157C11×C4⋊C4C2×D411yescharacteristic
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—21no—
162C11×C22⋊C4—21no—
163C11×C22⋊C4—21no—
164C42×C11—24no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—22no—
169C42×C11C2×D411yescharacteristic
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11C2411yescharacteristic
173#4326—84no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—41no—
177C4⋊Dic11—41no—
178#4318—42no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—42no—
183#3503D1111yescharacteristic
184#3209—111no—
185C2×#487—111no—
186#3079—111no—
187#1645—114no—
188#1644—114no—
189#1548—111no—
190#1493—111no—
191#1476—111no—
192C23×C11—21no—
193C23×C11#12011yescharacteristic
194Q8×C11—21no—
195Q8×C11—24no—
196Q8×C11—44no—
197Q8×C11—44no—
198Q8×C11—42no—
199Q8×C11—84no—
200Q8×C11C2×Q1612yes—
201D4×C11—24no—
202D4×C11—21no—
203D4×C11C2×Q1612yes—
204C2×C4×C11—21no—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—82no—
216C2×C4×C11—84no—
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11#12011yescharacteristic
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11C2×Q1612yes—
221C2×C4×C11#13712yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×Dic11—42no—
226C2×Dic11—82no—
227Dic22—44no—
228Dic22—82no—
229C11⋊C8—42no—
230C11⋊C8—42no—
231C11⋊C8—42no—
232Q82C2×D1112yes—
233#557—21no—
234#554—22no—
235#554C2×D1112yes—
236D4×Q8—22no—
237D4×Q8—21no—
238#544—22no—
239#544—21no—
240#533—21no—
241#533C2×D1111yescharacteristic
242C2×C4⋊Q8—21no—
243C2×C4⋊Q8—111no—
244C2×C4⋊Q8C2×D1111yescharacteristic
245#520—21no—
246C4×#41C2×D1111yescharacteristic
247#494—221no—
248#487—114no—
249#487—222no—
250#487—221no—
251#477—221no—
252#476—221no—
253#475—112no—
254#474—112no—
255#462—114no—
256#451—222no—
257#431—111no—
258#428—221no—
259#423—111no—
260#417—221no—
261C2×#103—222no—
262C2×C4×C8—111no—
263#333—114no—
264Q8⋊C8—114no—
265Q8⋊C8—112no—
266D4⋊C8—112no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—22no—
270C22×C11—41no—
271C22×C11—41no—
272C22×C11#45112yes—
273C22×C11C2×#12011yescharacteristic
274C4×C11—22no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—41no—
278C4×C11—42no—
279C4×C11—41no—
280C4×C11—44no—
281C4×C11—42no—
282C4×C11#45112yes—
283C4×C11#45512yes—
284C4×C11C22×Q1611yescharacteristic
285C4×C11C2×#13711yescharacteristic
286C4×C11#57712yes—
287Dic11—82no—
288C2×#41C22⋊D1111yescharacteristic
289C22×Q8—22no—
290C22×Q8—221no—
291C22×Q8C22⋊D1112yes—
292C2×Q16—224no—
293C2×M16—221no—
294C22×C8—221no—
295C4⋊Q8—22no—
296C4⋊Q8—22no—
297C4⋊Q8—24no—
298C4⋊Q8—22no—
299C4⋊Q8—22no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—112no—
303C4⋊Q8—221no—
304C4⋊Q8—221no—
305C4⋊Q8—221no—
306C4⋊Q8C22⋊D1112yes—
307C4⋊Q8C22⋊D1111yescharacteristic
308C4⋊Q8C22⋊D1111yescharacteristic
309C4⋊Q8C22×D1112yes—
310#125—22no—
311#125—24no—
312#125—22no—
313#125—21no—
314C22⋊Q8—22no—
315C22⋊Q8—24no—
316C22⋊Q8—24no—
317C22⋊Q8—22no—
318C22⋊Q8—24no—
319C22⋊Q8—21no—
320C22⋊Q8C22⋊D1112yes—
321C4×Q8—22no—
322C4×Q8—22no—
323C4×Q8—22no—
324C4×Q8—21no—
325C4×Q8C22⋊D1111yescharacteristic
326C4×Q8C22×D1111yescharacteristic
327C4×Q8C22×D1112yes—
328C4×D4—24no—
329C4×D4—22no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4C22⋊D1111yescharacteristic
333C4×D4C22×D1111yescharacteristic
334#117—22no—
335#117—21no—
336#117—21no—
337#117C22⋊D1111yescharacteristic
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4—221no—
344C2×C42—21no—
345C2×C42C22×D1111yescharacteristic
346#107—222no—
347#106—222no—
348C4⋊C8—112no—
349C4⋊C8—112no—
350C4⋊C8—221no—
351#103—228no—
352#103—222no—
353#103—224no—
354#102—222no—
355C22⋊C8—221no—
356C4×C8—112no—
357C4×C8—221no—
358C4×C8—221no—
359C2×C11—22no—
360C2×C11—42no—
361C2×C11C2×#45111yescharacteristic
362C2×C11#301011yescharacteristic
363C2×C11C2×#45511yescharacteristic
364#41—22no—
365#41#432614yescomplemented
366C2×Q8—24no—
367C2×Q8—22no—
368C2×Q8—21no—
369C2×Q8—44no—
370C2×Q8—84no—
371C2×Q8—222no—
372C2×Q8—441no—
373C2×Q8—882no—
374C2×Q8C2×C22⋊D1112yes—
375C2×Q8C2×C22⋊D1111yescharacteristic
376C2×Q8C2×C22⋊D1114yes—
377C2×D4—21no—
378C2×D4C2×C22⋊D1111yescharacteristic
379C22×C4—21no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—441no—
385C22×C4C2×C22⋊D1111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387C22×C4C2×C22⋊D1111yescharacteristic
388Q16—884no—
389M16—442no—
390C2×C8—222no—
391C2×C8—222no—
392C2×C8—222no—
393C2×C8—442no—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—222no—
410C4⋊C4—222no—
411C4⋊C4—441no—
412C4⋊C4—441no—
413C4⋊C4C2×C22⋊D1112yes—
414C4⋊C4C2×C22⋊D1111yescharacteristic
415C4⋊C4C2×C22⋊D1111yescharacteristic
416C22⋊C4—24no—
417C22⋊C4—22no—
418C22⋊C4—21no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C42—24no—
422C42—21no—
423C42—21no—
424C42—21no—
425C42—22no—
426C42C2×C22⋊D1111yescharacteristic
427C42C2×C22⋊D1111yescharacteristic
428C42C2×C22⋊D1111yescharacteristic
429C42C23×D1111yescharacteristic
430C11#1863311yescharacteristic, complemented, Sylow
431C23—21no—
432C23#6700611yescharacteristic
433Q8—21no—
434Q8—24no—
435Q8—44no—
436Q8—44no—
437Q8—42no—
438Q8—84no—
439Q8—444no—
440Q8—882no—
441Q8C2×#432612yes—
442D4—24no—
443D4—21no—
444D4C2×#432612yes—
445C2×C4—21no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—82no—
457C2×C4—84no—
458C2×C4—442no—
459C2×C4—882no—
460C2×C4#6699512yes—
461C2×C4C2×#432612yes—
462C2×C4#6700611yescharacteristic
463C2×C4#6700611yescharacteristic
464C2×C4#6700611yescharacteristic
465C2×C4C22×C22⋊D1111yescharacteristic
466C2×C4C22×C22⋊D1111yescharacteristic
467C2×C4C22×C22⋊D1111yescharacteristic
468C8—442no—
469C8—442no—
470C8—442no—
471C22—21no—
472C22—21no—
473C22—22no—
474C22—41no—
475C22—41no—
476C22#1062284112yes—
477C22C2×#6700611yescharacteristic
478C4—22no—
479C4—21no—
480C4—21no—
481C4—41no—
482C4—42no—
483C4—41no—
484C4—44no—
485C4—42no—
486C4—882no—
487C4#1062284112yes—
488C4#1062285512yes—
489C4C2×#6699511yescharacteristic
490C4C22×#432611yescharacteristic
491C4#1062336812yes—
492C2—22no—
493C2—42no—
494C2C2×#1062284111yescharacteristic
495C2#1307790211yescharacteristic
496C2C2×#1062285511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3503C2
socleC22×C11C2×#120
prime radicalC2×C11×#41D4
hypercenter#3503D11
hypocenterC11#18633
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #13079561C2semidirect
2. C2×#10622694C2semidirect
4. #13067837C2semidirect
5. #13067830C2semidirect
6. #13067297C2semidirect
7. #13067071C2semidirect
118. C11×#41Q16semidirect
365. #41#4326semidirect
430. C11#18633semidirect

Maximal subgroups

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

subgroupindex
#130795612
C2×#106226942
#130784312
#130678372
#130678302
#130672972
#130670712
#130669982
C11×#35032
#1863311