Finite Group Databasebeta

← #14736990

Subgroups — #14736990

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079932C212yesmaximal, complemented
2#13077550C211yesmaximal, characteristic, complemented
3#13068107C212yesmaximal, complemented
4#13068097C212yesmaximal, complemented
5#13067961C214yesmaximal, complemented
6C2×#10622095C211yesmaximal, characteristic, complemented
7#13067293C212yesmaximal, complemented
8C11×#3147C211yesmaximal, characteristic
9C2×C11×#135—21no—
10C2×C11×#135—21no—
11C11×#532C2212yes—
12#10623001C2211yescharacteristic
13C11×#495—21no—
14C11×#495—21no—
15C11×#494C2211yescharacteristic
16C11×#493C2211yescharacteristic
17C11×#492C2212yes—
18C2×C4×C8×C11C2211yescharacteristic
19#10622715—21no—
20#10622714—21no—
21#10622707C2214yes—
22#10622688C2214yes—
23#10622654—24no—
24#10622632—22no—
25#10622621—22no—
26#10622537C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2212yes—
28#10622292—21no—
29#10622292C2212yes—
30C8×Dic22—21no—
31C8×Dic22C2212yes—
32#10622185C2214yes—
33#10622182C2214yes—
34#10622095C2212yes—
35#10622095C2212yes—
36C2×C11×#41—22no—
37C11×#135—44no—
38C11×#135—44no—
39C2×C11×Q16—21no—
40C2×C11×Q16—21no—
41C2×C11×SD16—22no—
42C2×C11×SD16—22no—
43C2×C11×D8—21no—
44C2×C11×D8—21no—
45C22×C8×C11D411yescharacteristic
46C22×C8×C11D411yescharacteristic
47C11×C4⋊Q8C2312yes—
48C11×#127C2312yes—
49C11×#124—22no—
50C11×#121—22no—
51C11×#121—22no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C2×C42×C11C2311yescharacteristic
55C2×#4324—24no—
56#66979—21no—
57#66977—21no—
58#66977D412yes—
59C2×#4318—21no—
60C22×C11⋊C8—22no—
61#66923—21no—
62#66922D411yescharacteristic
63#66922D411yescharacteristic
64C4×Dic22—21no—
65C4×Dic22C2312yes—
66C4×C8×C11D411yescharacteristic
67C4×C8×C11D411yescharacteristic
68C4×C8×C11C2311yescharacteristic
69C4×C8×C11C2311yescharacteristic
70#66896—24no—
71#66879—22no—
72Dic11⋊C8—22no—
73Dic11⋊C8—22no—
74C8×Dic11—22no—
75#66874—24no—
76#66872—24no—
77C4⋊(C11⋊C8)—22no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)C2314yes—
80C4⋊(C11⋊C8)C2312yes—
81#19205—111nomaximal, Sylow
82C11×#41—44no—
83C11×#41—44no—
84C2×Q8×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C2×Dic22—21no—
94C2×Dic22C2×D412yes—
95C11×Q16—42no—
96C11×Q16—42no—
97C11×SD16—44no—
98C11×SD16—44no—
99C11×D8—42no—
100C11×D8—42no—
101C2×C8×C11—22no—
102C2×C8×C11SD1614yescomplemented
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C22⋊C4—42no—
110C11×C22⋊C4—42no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114C42×C11C2411yescharacteristic
115C22⋊Dic11—22no—
116#4324—84no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11C2×D412yes—
121Dic11⋊C4—22no—
122Dic11⋊C4—22no—
123C4×Dic11—22no—
124#4318—42no—
125C2×C11⋊C8—24no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—82no—
128#3246—112no—
129#3147D1111yescharacteristic
130#2960—111no—
131#1690—112no—
132#1688—112no—
133#1666—114no—
134C2×#334—111no—
135#1547—112no—
136C23×C11—42no—
137C23×C11#12111yescharacteristic
138Q8×C11—42no—
139Q8×C11—42no—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11—42no—
143D4×C11—42no—
144D4×C11—82no—
145D4×C11—84no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—84no—
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11C2×SD1612yes—
154C2×C4×C11AGL(1,ℤ/8)12yes—
155C2×C4×C11C22×D411yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C2×C4×C11C2×#4111yescharacteristic
158C2×Dic11—22no—
159C2×Dic11—22no—
160Dic22—24no—
161Dic22—42no—
162C8×C11—21no—
163C8×C11—21no—
164C8×C11C2×SD1612yes—
165C8×C11C2×SD1612yes—
166C11⋊C8—42no—
167C11⋊C8—44no—
168C2×#135—21no—
169C2×#135—21no—
170#533—111no—
171#532C2×D1112yes—
172#495—21no—
173#495—21no—
174#494C2×D1111yescharacteristic
175#493C2×D1111yescharacteristic
176#492C2×D1112yes—
177#476—222no—
178#475—114no—
179#465—224no—
180#461—222no—
181#460—114no—
182#446—112no—
183#446—221no—
184C8×Q8—112no—
185C8×Q8—221no—
186#424—221no—
187#423—111no—
188C2×C4⋊C8—112no—
189#405—221no—
190C2×C4×C8C2×D1111yescharacteristic
191#334—112no—
192#334—112no—
193#332—114no—
194#331—114no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—82no—
198C22×C11—82no—
199C22×C11—82no—
200C22×C11#46012yes—
201C22×C11C2×#12111yescharacteristic
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—82no—
206C4×C11#46012yes—
207C4×C11C22×SD1611yescharacteristic
208C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
209C4×C11#57712yes—
210Dic11—42no—
211Dic11—42no—
212C2×#41—22no—
213#135—44no—
214#135—44no—
215C2×Q16—21no—
216C2×Q16—21no—
217C2×SD16—22no—
218C2×SD16—22no—
219C2×SD16—224no—
220C2×D8—21no—
221C2×D8—21no—
222C2×M16—221no—
223C22×C8—222no—
224C22×C8C22⋊D1111yescharacteristic
225C22×C8C22⋊D1111yescharacteristic
226C4⋊Q8—111no—
227C4⋊Q8—111no—
228C4⋊Q8C22×D1112yes—
229#127C22×D1112yes—
230#125—221no—
231#124—22no—
232C22⋊Q8—112no—
233C22⋊Q8—221no—
234#121—22no—
235#121—22no—
236C4×Q8—112no—
237C4×Q8—221no—
238C4×D4—22no—
239C4×D4—22no—
240#117—221no—
241C2×C42C22×D1111yescharacteristic
242#106—224no—
243C4⋊C8—112no—
244C4⋊C8—114no—
245C4⋊C8—222no—
246C4⋊C8—222no—
247C4⋊C8—222no—
248C4⋊C8—221no—
249#103—224no—
250#102—224no—
251#97—222no—
252C4×C8—222no—
253C4×C8C22⋊D1111yescharacteristic
254C4×C8C22⋊D1111yescharacteristic
255C4×C8C22×D1111yescharacteristic
256C4×C8C22×D1111yescharacteristic
257C2×C11—22no—
258C2×C11—162no—
259C2×C11C2×#46011yescharacteristic
260C2×C11#306011yescharacteristic
261C2×C11#306711yescharacteristic
262#41—44no—
263#41—44no—
264C2×Q8—22no—
265C2×Q8—112no—
266C2×Q8—221no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—42no—
271C22×C4—42no—
272C22×C4D4×D1111yescharacteristic
273C22×C4#434111yescharacteristic
274C22×C4C2×C22⋊D1111yescharacteristic
275Q16—42no—
276Q16—42no—
277SD16—44no—
278SD16—44no—
279SD16—884no—
280D8—42no—
281D8—42no—
282M16—442no—
283C2×C8—22no—
284C2×C8—224no—
285C2×C8—222no—
286C2×C8—882no—
287C2×C8#432414yescomplemented
288C2×C8C2×C22⋊D1111yescharacteristic
289C2×C8C2×C22⋊D1111yescharacteristic
290C2×C8C2×C22⋊D1111yescharacteristic
291C2×C8C2×C22⋊D1111yescharacteristic
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—112no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—222no—
298C4⋊C4—221no—
299C4⋊C4—222no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—222no—
303C42—222no—
304C42D4×D1111yescharacteristic
305C42#434111yescharacteristic
306C42C2×C22⋊D1111yescharacteristic
307C42C23×D1111yescharacteristic
308C11#1920511yescharacteristic, complemented, Sylow
309C23—42no—
310C23#6699111yescharacteristic
311Q8—42no—
312Q8—42no—
313Q8—224no—
314Q8—442no—
315D4—42no—
316D4—42no—
317D4—42no—
318D4—42no—
319D4—82no—
320D4—84no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—84no—
325C2×C4—222no—
326C2×C4—222no—
327C2×C4#6698512yes—
328C2×C4C2×#432412yes—
329C2×C4#6699111yescharacteristic
330C2×C4#6699111yescharacteristic
331C2×C4#6699111yescharacteristic
332C2×C4C2×D4×D1111yescharacteristic
333C2×C4C2×#434111yescharacteristic
334C2×C4C22×C22⋊D1111yescharacteristic
335C8—21no—
336C8—21no—
337C8—444no—
338C8—442no—
339C8C2×#432412yes—
340C8C2×#432412yes—
341C22—21no—
342C22—21no—
343C22—82no—
344C22—82no—
345C22—82no—
346C22#1062268812yes—
347C22C2×#6699111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—82no—
352C4—442no—
353C4—442no—
354C4#1062268812yes—
355C4#1062330112yes—
356C4C2×#6698511yescharacteristic
357C4C22×#432411yescharacteristic
358C2—22no—
359C2—162no—
360C2C2×#1062268811yescharacteristic
361C2#1307827411yescharacteristic
362C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3147C2
socleC22×C11C2×#121
hypercenter#3147D11
hypocenterC11#19205
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3147

Complements

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

NH ≅ G/Ntype
1. #13079932C2semidirect
2. #13077550C2semidirect
3. #13068107C2semidirect
4. #13068097C2semidirect
5. #13067961C2semidirect
6. C2×#10622095C2semidirect
7. #13067293C2semidirect
102. C2×C8×C11SD16semidirect
287. C2×C8#4324semidirect
308. C11#19205semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130775502
#130681072
#130680972
#130679612
C2×#106220952
#130672932
C11×#31472
#1920511