Finite Group Databasebeta

← #28391639

Subgroups — #28391639

Order 14464.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299396C211yesmaximal, characteristic, complemented
2#20299109C211yesmaximal, characteristic, complemented
3#20298616C211yesmaximal, characteristic, complemented
4#20298615C211yesmaximal, characteristic, complemented
5#20298562C211yesmaximal, characteristic, complemented
6#20298354C211yesmaximal, characteristic, complemented
7#525×C113C211yesmaximal, characteristic, complemented
8C2×#14268647C2211yescharacteristic
9#16813653—21no—
10#16813652—21no—
11#16813648—21no—
12#16813647—21no—
13#16813642—22no—
14C2×#14268631C2211yescharacteristic
15C2×#14268631C2211yescharacteristic
16#16813605—21no—
17#16813601—21no—
18#16813596—21no—
19#16813591—21no—
20C4×C22⋊D113—22no—
21#16813581C2211yescharacteristic
22#16813550—22no—
23#16813549—22no—
24C22⋊#11744751—22no—
25C2×#41×C113C2211yescharacteristic
26C23×C4×C113C2211yescharacteristic
27#123×C113—21no—
28C22⋊Q8×C113—21no—
29#121×C113—21no—
30#120×C113—21no—
31C4×D4×C113—22no—
32#117×C113C2211yescharacteristic
33#14268647—21no—
34#14268647—21no—
35#14268647—21no—
36#14268647—21no—
37C2×Dic226D411yescharacteristic, complemented
38C2×D452D411yescharacteristic, complemented
39C2×C22⋊D113—22no—
40C2×C22⋊D113—21no—
41C2×C4×D113—21no—
42#14268637—22no—
43#14268635—22no—
44#14268634—22no—
45#14268632—22no—
46#14268631—21no—
47#14268631—21no—
48#14268631—21no—
49#14268631—21no—
50C2×#11744751—21no—
51C2×#11744751D412yescomplemented
52C4⋊Dic113—21no—
53#14268626—22no—
54C22⋊Dic113—22no—
55C22⋊Dic113—21no—
56#14268624—22no—
57C4×Dic113D412yescomplemented
58C24×C113D411yescharacteristic
59#41×C113—21no—
60#41×C113—21no—
61#41×C113—21no—
62#41×C113—21no—
63C2×Q8×C113D411yescharacteristic, complemented
64C2×D4×C113—22no—
65C2×D4×C113—21no—
66C2×D4×C113D411yescharacteristic, complemented
67C22×C4×C113—21no—
68C22×C4×C113—21no—
69C22×C4×C113—21no—
70C22×C4×C113—21no—
71C22×C4×C113—21no—
72C22×C4×C113—21no—
73C22×C4×C113—21no—
74C22×C4×C113D411yescharacteristic
75C22×C4×C113C2311yescharacteristic
76C4⋊C4×C113—22no—
77C4⋊C4×C113—21no—
78C22⋊C4×C113—22no—
79C22⋊C4×C113—22no—
80C22⋊C4×C113—21no—
81C42×C113D412yescomplemented
82C23×C113—21no—
83C23×C113—21no—
84C23×C113—21no—
85C23×C113—21no—
86C23×C113—42no—
87C23×C113C2×D411yescharacteristic
88C22×D113—21no—
89Q8×C113—21no—
90Q8×C113—21no—
91D4×C113—21no—
92D4×C113—21no—
93D4×C113—44no—
94D4×C113—41no—
95D4×C113—41no—
96C2×C4×C113—22no—
97C2×C4×C113—21no—
98C2×C4×C113—21no—
99C2×C4×C113—21no—
100C2×C4×C113—21no—
101C2×C4×C113—41no—
102C2×C4×C113—41no—
103C2×C4×C113—41no—
104C2×C4×C113—41no—
105C2×C4×C113—41no—
106C2×C4×C113—41no—
107C2×C4×C113C2×D411yescharacteristic
108C2×C4×C113C2×D411yescharacteristic
109C2×C4×C113C2×D411yescharacteristic
110C2×C4×C113C2×D411yescharacteristic
111C2×C4×C113C2×D411yescharacteristic
112C2×C4×C113#4111yescharacteristic
113C22⋊D113—44no—
114C22⋊D113—41no—
115C22⋊D113—41no—
116C2×Dic113—22no—
117C2×Dic113—21no—
118D452—21no—
119D452—21no—
120C4×D113—41no—
121C4×D113—41no—
122Dic226—21no—
123Dic226—21no—
124#11744751—22no—
125#11744751—41no—
126C22×C113—22no—
127C22×C113—22no—
128C22×C113—22no—
129C22×C113—41no—
130C22×C113—41no—
131C22×C113—41no—
132C22×C113—41no—
133C22×C113—42no—
134C22×C113—41no—
135C22×C113—41no—
136C22×C113#12011yescharacteristic
137C22×C113#12011yescharacteristic
138C22×C113#12111yescharacteristic
139C2×D113—42no—
140C2×D113—41no—
141C4×C113—42no—
142C4×C113—41no—
143C4×C113—41no—
144C4×C113#12011yescharacteristic
145C4×C113#12111yescharacteristic
146C4×C113#12111yescharacteristic
147C4×C113#12711yescharacteristic
148Dic113—42no—
149Dic113—41no—
150C2×C113—21no—
151C2×C113—21no—
152C2×C113—21no—
153C2×C113—42no—
154C2×C113—81no—
155C2×C113#39211yescharacteristic
156D113—81no—
157#2010—1131nomaximal, Sylow
158C113#201011yescharacteristic, complemented, Sylow
159#575—1131no—
160#525—1131no—
161#525D11311yescharacteristic, complemented
162#421—1131no—
163#421—1131no—
164#407—1131no—
165H(3,ℤ/4)—1131no—
166C2×#41—1131no—
167C2×#41C2×D11311yescharacteristic
168C23×C4C2×D11311yescharacteristic
169#137—2261no—
170#137—2261no—
171AGL(1,ℤ/8)—2261no—
172AGL(1,ℤ/8)—2261no—
173#135—2262no—
174C2×M16—1131no—
175C2×M16—1131no—
176#123—21no—
177#123—2261no—
178C22⋊Q8—21no—
179C22⋊Q8—2261no—
180#121—21no—
181#121—2261no—
182#120—21no—
183#120—2261no—
184C4×D4—22no—
185C4×D4—2262no—
186#117—1131no—
187#117C2×D11311yescharacteristic
188#104—2262no—
189#104—2262no—
190C22⋊C8—2262no—
191C24C22⋊D11311yescharacteristic
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—2261no—
197#41—2261no—
198#41—2261no—
199#41—2261no—
200C2×Q8—1131no—
201C2×Q8C22⋊D11311yescharacteristic, complemented
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—1131no—
205C2×D4—2262no—
206C2×D4—2261no—
207C2×D4C22⋊D11311yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—2261no—
216C22×C4C22⋊D11311yescharacteristic
217C22×C4C22×D11311yescharacteristic
218Q16—2262no—
219SD16—2262no—
220SD16—2262no—
221D8—2262no—
222M16—2261no—
223M16—2261no—
224M16—2261no—
225M16—2261no—
226C2×C8—1132no—
227C2×C8—2261no—
228C4⋊C4—22no—
229C4⋊C4—21no—
230C4⋊C4—2262no—
231C4⋊C4—2261no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C22⋊C4—21no—
235C22⋊C4—2262no—
236C22⋊C4—2262no—
237C22⋊C4—2261no—
238C42—1132no—
239C42C22⋊D11312yescomplemented
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—42no—
245C23—2261no—
246C23C2×C22⋊D11311yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—2261no—
250Q8—2261no—
251D4—21no—
252D4—21no—
253D4—44no—
254D4—41no—
255D4—41no—
256D4—4524no—
257D4—4521no—
258D4—4521no—
259D4—2261no—
260D4—2261no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—4521no—
273C2×C4—4521no—
274C2×C4—2262no—
275C2×C4—2261no—
276C2×C4D4×D11311yescharacteristic
277C2×C4D4×D11311yescharacteristic
278C2×C4D4×D11311yescharacteristic
279C2×C4C2×C22⋊D11311yescharacteristic
280C2×C4C2×C22⋊D11311yescharacteristic
281C2×C4#1426864611yescharacteristic
282C8—4521no—
283C8—2262no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—4522no—
295C22—4521no—
296C22#1681359011yescharacteristic
297C22#1681359111yescharacteristic
298C22#1681359411yescharacteristic
299C4—42no—
300C4—41no—
301C4—41no—
302C4—4522no—
303C4—4521no—
304C4#1681359011yescharacteristic
305C4#1681359311yescharacteristic
306C4#1681359411yescharacteristic
307C4#1681361811yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—42no—
312C2—81no—
313C2—9041no—
314C2#2029850611yescharacteristic
subgroupG/H
centerC4#16813618
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#525×C113C2
socleC2×C113#392
hypercenter#525D113
hypocenterC113#2010
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #20299396C2semidirect
2. #20299109C2semidirect
3. #20298616C2semidirect
4. #20298615C2semidirect
5. #20298562C2semidirect
6. #20298354C2semidirect
7. #525×C113C2semidirect
37. C2×Dic226D4semidirect
38. C2×D452D4semidirect
51. C2×#11744751D4semidirect
57. C4×Dic113D4semidirect
63. C2×Q8×C113D4semidirect
66. C2×D4×C113D4semidirect
81. C42×C113D4semidirect
158. C113#2010semidirect
161. #525D113semidirect
201. C2×Q8C22⋊D113semidirect
207. C2×D4C22⋊D113semidirect
239. C42C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
#202993962
#202991092
#202986162
#202986152
#202985622
#202983542
#525×C1132
#2010113