Finite Group Databasebeta

← #28401046

Subgroups — #28401046

Order 14464.

564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#16813652C211yesmaximal, characteristic, complemented
2C2×#16813648C211yesmaximal, characteristic, complemented
3C2×#16813642C211yesmaximal, characteristic, complemented
4C22×#14268635C211yesmaximal, characteristic, complemented
5#20299174C211yesmaximal, characteristic, complemented
6#20298993C212yesmaximal, complemented
7#20298985C212yesmaximal, complemented
8#20298980C212yesmaximal, complemented
9#20298970C212yesmaximal, complemented
10#20298554C211yesmaximal, characteristic, complemented
11#535×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C22×Dic226C2211yescharacteristic
14#16813652—24no—
15#16813648—24no—
16#16813642—24no—
17C2×#14268637C2211yescharacteristic, complemented
18C2×#14268637C2212yescomplemented
19C2×#14268635—24no—
20C2×#14268635C2212yes—
21C2×#14268635C2212yes—
22C2×#14268635C2212yes—
23C2×#14268635C2211yescharacteristic, complemented
24C2×#14268635C2212yescomplemented
25C2×#14268634C2211yescharacteristic, complemented
26C2×#14268632C2212yes—
27C2×#14268632C2211yescharacteristic, complemented
28C2×#14268631C2211yescharacteristic
29C22×#11744751C2211yescharacteristic
30#16813622C2212yescomplemented
31#16813610C2212yescomplemented
32#16813606—22no—
33#16813602—22no—
34#16813533C2212yescomplemented
35C4×#11744751C2212yescomplemented
36C2×#41×C113C2211yescharacteristic
37C22×D4×C113C2211yescharacteristic
38#127×C113C2212yes—
39#124×C113C2212yes—
40#121×C113—22no—
41#120×C113—22no—
42#117×C113C2211yescharacteristic
43#14268647—22no—
44#14268647—22no—
45C2×Dic226—22no—
46C2×Dic226—22no—
47C2×Dic226—21no—
48C2×Dic226C2312yes—
49C2×Dic226C2311yescharacteristic
50C2×D452C2311yescharacteristic
51C2×C22⋊D113—21no—
52C22×Dic113—21no—
53C2×C4×D113—21no—
54#14268637—22no—
55#14268637—24no—
56#14268635—24no—
57#14268635—24no—
58#14268635—24no—
59#14268635—22no—
60#14268635—24no—
61#14268634—22no—
62#14268632—24no—
63#14268632—22no—
64#14268631D414yescomplemented
65C2×#11744751D414yescomplemented
66C2×#11744751C2311yescharacteristic
67C2×#11744751C2311yescharacteristic
68C2×#11744751C2312yes—
69C4⋊Dic113—24no—
70#14268624—24no—
71C24×C113—21no—
72#41×C113—22no—
73#41×C113—22no—
74C2×Q8×C113C2311yescharacteristic
75C2×D4×C113—21no—
76C2×D4×C113—22no—
77C2×D4×C113—22no—
78C2×D4×C113—21no—
79C2×D4×C113—24no—
80C2×D4×C113C2312yes—
81C2×D4×C113C2311yescharacteristic
82C22×C4×C113—21no—
83C22×C4×C113C2311yescharacteristic
84C4⋊C4×C113D412yes—
85C22⋊C4×C113—24no—
86C22⋊C4×C113D412yes—
87C42×C113C2312yes—
88C23×C113—22no—
89C23×C113—21no—
90C23×C113—42no—
91C23×C113—82no—
92C23×C113C2×D411yescharacteristic
93C22×D113—21no—
94Q8×C113—21no—
95Q8×C113—21no—
96D4×C113—22no—
97D4×C113—22no—
98D4×C113—21no—
99D4×C113—21no—
100D4×C113—42no—
101D4×C113—42no—
102D4×C113—84no—
103C2×C4×C113—21no—
104C2×C4×C113—42no—
105C2×C4×C113C2×D412yes—
106C2×C4×C113C2×D412yes—
107C2×C4×C113C2×D414yes—
108C2×C4×C113C2×D411yescharacteristic
109C2×C4×C113C2411yescharacteristic
110C22⋊D113—42no—
111C2×Dic113—22no—
112C2×Dic113—21no—
113C2×Dic113—42no—
114D452—21no—
115D452—21no—
116C4×D113—42no—
117Dic226—22no—
118Dic226—21no—
119Dic226—22no—
120Dic226—21no—
121Dic226—42no—
122#11744751C2×D412yes—
123#11744751C2×D412yes—
124#11744751C2×D414yes—
125C22×C113—22no—
126C22×C113—41no—
127C22×C113—42no—
128C22×C113—42no—
129C22×C113—44no—
130C22×C113—84no—
131C22×C113#12712yes—
132C22×C113C22×D411yescharacteristic
133C2×D113—41no—
134C2×D113—42no—
135C4×C113—24no—
136C4×C113—41no—
137C4×C113#12712yes—
138C4×C113C22×D411yescharacteristic
139C4×C113C22×D411yescharacteristic
140Dic113—42no—
141Dic113—41no—
142C2×C113—22no—
143C2×C113—81no—
144C2×C113—82no—
145C2×C113C2×#12711yescharacteristic
146C2×C113#57712yes—
147D113—81no—
148#3154—1131nomaximal, Sylow
149C113#315411yescharacteristic, complemented, Sylow
150C2×#137—1131no—
151C2×AGL(1,ℤ/8)—1131no—
152C2×#135—1131no—
153C22×SD16—1131no—
154#536—1131no—
155#535D11311yescharacteristic, complemented
156#497—1132no—
157#496—1132no—
158#495—1132no—
159#492—1132no—
160#405—1131no—
161C2×#41—1131no—
162C2×#41C2×D11311yescharacteristic
163C22×Q8—1131no—
164C22×D4C2×D11311yescharacteristic
165#137—2264no—
166AGL(1,ℤ/8)—2264no—
167#135—2264no—
168C2×Q16—1131no—
169C2×Q16—1132no—
170C2×SD16—1131no—
171C2×SD16—1132no—
172C2×SD16—1132no—
173C2×SD16—1131no—
174C2×SD16—1132no—
175C2×SD16—1132no—
176C2×SD16—2264no—
177C2×D8—1131no—
178C2×D8—1132no—
179C2×M16—1131no—
180C22×C8—1131no—
181C4⋊Q8—1132no—
182#127C2×D11312yes—
183#124—1132no—
184#124C2×D11312yes—
185#123—2262no—
186C22⋊Q8—2262no—
187#121—22no—
188#120—22no—
189#117C2×D11311yescharacteristic
190#97—1132no—
191C4×C8—1132no—
192C24—21no—
193#41—22no—
194#41—22no—
195#41—2262no—
196#41—2262no—
197C2×Q8—1132no—
198C2×Q8—1131no—
199C2×Q8—2262no—
200C2×Q8—2262no—
201C2×Q8—2261no—
202C2×Q8C22×D11311yescharacteristic
203C2×D4—21no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—24no—
208C2×D4—1131no—
209C2×D4—2261no—
210C2×D4C22×D11312yes—
211C2×D4C22×D11311yescharacteristic
212C22×C4—21no—
213C22×C4—2261no—
214C22×C4—2261no—
215C22×C4C22×D11311yescharacteristic
216Q16—2262no—
217Q16—2264no—
218SD16—2264no—
219SD16—2264no—
220SD16—2262no—
221SD16—2264no—
222SD16—2264no—
223SD16—2262no—
224D8—2262no—
225D8—2264no—
226M16—1134no—
227C2×C8—1134no—
228C2×C8—1131no—
229C2×C8—1132no—
230C2×C8—1131no—
231C4⋊C4—2264no—
232C4⋊C4C22⋊D11312yes—
233C22⋊C4—24no—
234C22⋊C4—2264no—
235C22⋊C4C22⋊D11312yes—
236C42C22×D11312yes—
237C23—22no—
238C23—21no—
239C23—42no—
240C23—82no—
241C23—2261no—
242C23C2×C22⋊D11311yescharacteristic
243Q8—21no—
244Q8—21no—
245Q8—4522no—
246Q8—2262no—
247Q8—2261no—
248Q8—2262no—
249Q8—2261no—
250D4—22no—
251D4—21no—
252D4—22no—
253D4—21no—
254D4—42no—
255D4—42no—
256D4—84no—
257D4—4522no—
258D4—2261no—
259D4—2261no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—4522no—
263C2×C4—4522no—
264C2×C4—2262no—
265C2×C4—2261no—
266C2×C4D4×D11312yes—
267C2×C4D4×D11312yes—
268C2×C4C2×C22⋊D11314yes—
269C2×C4C2×C22⋊D11311yescharacteristic
270C2×C4C23×D11311yescharacteristic
271C8—1132no—
272C8—1132no—
273C8—1134no—
274C22—22no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—44no—
279C22—84no—
280C22—4521no—
281C22—4522no—
282C22#1681361812yes—
283C22C22×C22⋊D11311yescharacteristic
284C4—24no—
285C4—41no—
286C4—4521no—
287C4—4522no—
288C4#1681361812yes—
289C4C2×D4×D11311yescharacteristic
290C4C2×D4×D11311yescharacteristic
291C2—22no—
292C2—82no—
293C2—81no—
294C2—9041no—
295C2C2×#1681361811yescharacteristic
296C2#2029940912yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#535×C113C2
socleC22×C113C22×D4
hypercenter#535D113
hypocenterC113#3154
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#16813652C2semidirect
2. C2×#16813648C2semidirect
3. C2×#16813642C2semidirect
4. C22×#14268635C2semidirect
5. #20299174C2semidirect
6. #20298993C2semidirect
7. #20298985C2semidirect
8. #20298980C2semidirect
9. #20298970C2semidirect
10. #20298554C2semidirect
11. #535×C113C2semidirect
17. C2×#14268637C22semidirect
18. C2×#14268637C22semidirect
23. C2×#14268635C22semidirect
24. C2×#14268635C22semidirect
25. C2×#14268634C22semidirect
27. C2×#14268632C22semidirect
30. #16813622C22semidirect
31. #16813610C22semidirect
34. #16813533C22semidirect
35. C4×#11744751C22semidirect
64. #14268631D4semidirect
65. C2×#11744751D4semidirect
149. C113#3154semidirect
155. #535D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136522
C2×#168136482
C2×#168136422
C22×#142686352
#202991742
#202989932
#202989852
#202989802
#202989702
#202985542
#535×C1132
#3154113