Finite Group Databasebeta

← #28401051

Subgroups — #28401051

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×#16813647C211yesmaximal, characteristic, complemented
3C22×#14268636C211yesmaximal, characteristic, complemented
4#20299169C211yesmaximal, characteristic, complemented
5#20299162C211yesmaximal, characteristic, complemented
6#20298991C212yesmaximal, complemented
7#20298986C212yesmaximal, complemented
8#20298979C212yesmaximal, complemented
9#20298969C212yesmaximal, complemented
10#20298553C211yesmaximal, characteristic, complemented
11C2×#135×C113C211yesmaximal, characteristic, complemented
12C22×Dic226C2211yescharacteristic
13C22×D452C2211yescharacteristic
14#16813652—24no—
15#16813647—24no—
16C2×#14268637C2212yescomplemented
17C2×#14268636—24no—
18C2×#14268636C2212yes—
19C2×#14268636C2212yes—
20C2×#14268635C2212yescomplemented
21C2×#14268634C2212yes—
22C2×#14268632C2212yes—
23C2×#14268631C2211yescharacteristic
24#16813620C2212yescomplemented
25#16813618C2212yes—
26#16813611C2212yes—
27#16813609C2212yescomplemented
28#16813603—22no—
29#16813601—22no—
30#16813596—22no—
31#16813590—22no—
32#16813581C2211yescharacteristic
33#16813532C2212yescomplemented
34C8×Dic113C2212yescomplemented
35C2×#41×C113C2211yescharacteristic
36C2×#41×C113C2211yescharacteristic
37#135×C113—24no—
38C2×Q16×C113C2211yescharacteristic, complemented
39C2×SD16×C113C2211yescharacteristic, complemented
40C2×SD16×C113C2211yescharacteristic, complemented
41C2×D8×C113C2211yescharacteristic, complemented
42C22×C8×C113C2211yescharacteristic
43C23×D113—21no—
44C2×Dic226—22no—
45C2×Dic226—22no—
46C2×Dic226—21no—
47C2×Dic226C2312yes—
48C2×D452—22no—
49C2×D452—22no—
50C2×D452—21no—
51C2×D452C2312yes—
52C2×C22⋊D113—24no—
53C22×Dic113—21no—
54#14268637—24no—
55#14268636—24no—
56#14268636—24no—
57#14268635—24no—
58#14268634—24no—
59#14268632—24no—
60#14268631D414yescomplemented
61C2×#11744751C2312yes—
62C4⋊Dic113D412yes—
63#14268626—24no—
64C22⋊Dic113—24no—
65C22⋊Dic113D412yes—
66#14268624—24no—
67C4×Dic113C2312yes—
68#41×C113—22no—
69#41×C113—22no—
70#41×C113—22no—
71#41×C113—22no—
72C2×Q8×C113C2311yescharacteristic
73C2×Q8×C113C2311yescharacteristic
74C2×D4×C113—21no—
75C2×D4×C113—21no—
76C2×D4×C113C2311yescharacteristic
77C2×D4×C113C2311yescharacteristic
78C22×C4×C113—21no—
79C22×C4×C113—21no—
80C22×C4×C113C2311yescharacteristic
81Q16×C113—22no—
82SD16×C113—22no—
83SD16×C113—22no—
84D8×C113—22no—
85C2×C8×C113D414yescomplemented
86C2×C8×C113C2311yescharacteristic
87C2×C8×C113C2311yescharacteristic
88C23×C113—21no—
89C23×C113—21no—
90C23×C113C2×D411yescharacteristic
91C22×D113—22no—
92C22×D113—42no—
93C22×D113—82no—
94Q8×C113—21no—
95Q8×C113—21no—
96Q8×C113—21no—
97Q8×C113—21no—
98D4×C113—21no—
99D4×C113—21no—
100D4×C113—21no—
101D4×C113—21no—
102D4×C113—42no—
103D4×C113—42no—
104C2×C4×C113—21no—
105C2×C4×C113—21no—
106C2×C4×C113—42no—
107C2×C4×C113—42no—
108C2×C4×C113C2×D411yescharacteristic
109C2×C4×C113C2×D412yes—
110C2×C4×C113C2×D412yes—
111C2×C4×C113C2411yescharacteristic
112C22⋊D113—84no—
113C2×Dic113—22no—
114C2×Dic113—42no—
115C2×Dic113C2×D414yes—
116D452—22no—
117D452—22no—
118D452—42no—
119Dic226—22no—
120Dic226—22no—
121Dic226—42no—
122C8×C113C2×D412yes—
123C8×C113C2×D412yes—
124#11744751C2×D414yes—
125C22×C113—22no—
126C22×C113—41no—
127C22×C113—41no—
128C22×C113—42no—
129C22×C113—42no—
130C22×C113#12712yes—
131C22×C113C22×D411yescharacteristic
132C2×D113—42no—
133C2×D113—44no—
134C2×D113—84no—
135C4×C113—41no—
136C4×C113—41no—
137C4×C113#12712yes—
138C4×C113C22×D411yescharacteristic
139C4×C113C22×D411yescharacteristic
140Dic113—24no—
141Dic113—42no—
142C2×C113—22no—
143C2×C113—81no—
144C2×C113—81no—
145C2×C113C2×#12711yescharacteristic
146C2×C113#57712yes—
147D113—82no—
148#3154—1131nomaximal, Sylow
149C113#315411yescharacteristic, complemented, Sylow
150C2×#137—1131no—
151C2×AGL(1,ℤ/8)—1131no—
152C2×#135D11311yescharacteristic, complemented
153C22×SD16—1131no—
154#536—1131no—
155#535—1131no—
156#497—1132no—
157#496—1132no—
158#495—1132no—
159#492—1132no—
160#405—1131no—
161C2×#41C2×D11311yescharacteristic
162C2×#41C2×D11311yescharacteristic
163C22×Q8—1131no—
164C22×D4—1131no—
165#137—2264no—
166AGL(1,ℤ/8)—2264no—
167#135—24no—
168C2×Q16—1132no—
169C2×Q16C2×D11311yescharacteristic, complemented
170C2×SD16—1132no—
171C2×SD16—1132no—
172C2×SD16—1132no—
173C2×SD16—1132no—
174C2×SD16—2264no—
175C2×SD16C2×D11311yescharacteristic, complemented
176C2×SD16C2×D11311yescharacteristic, complemented
177C2×D8—1132no—
178C2×D8C2×D11311yescharacteristic, complemented
179C2×M16—1131no—
180C22×C8C2×D11311yescharacteristic
181C4⋊Q8—1132no—
182#127—1132no—
183#124—1132no—
184#124—1132no—
185#123—2262no—
186C22⋊Q8—2262no—
187#121—2262no—
188#120—2262no—
189#117—1131no—
190#97—1132no—
191C4×C8—1132no—
192C24—2261no—
193#41—22no—
194#41—22no—
195#41—22no—
196#41—22no—
197C2×Q8—1132no—
198C2×Q8—2262no—
199C2×Q8—2262no—
200C2×Q8—2261no—
201C2×Q8C22×D11311yescharacteristic
202C2×Q8C22×D11311yescharacteristic
203C2×D4—21no—
204C2×D4—21no—
205C2×D4—1132no—
206C2×D4—2264no—
207C2×D4—2261no—
208C2×D4—2262no—
209C2×D4—2262no—
210C2×D4C22×D11311yescharacteristic
211C2×D4C22×D11311yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—2261no—
215C22×C4C22×D11311yescharacteristic
216Q16—22no—
217Q16—2264no—
218SD16—22no—
219SD16—22no—
220SD16—2264no—
221SD16—2264no—
222SD16—2264no—
223SD16—2264no—
224D8—22no—
225D8—2264no—
226M16—1134no—
227C2×C8—1132no—
228C2×C8C22⋊D11314yescomplemented
229C2×C8C22×D11311yescharacteristic
230C2×C8C22×D11311yescharacteristic
231C4⋊C4—1132no—
232C4⋊C4—2264no—
233C22⋊C4—1132no—
234C22⋊C4—2264no—
235C22⋊C4—2264no—
236C42—1132no—
237C23—21no—
238C23—21no—
239C23—9042no—
240C23—4522no—
241C23—2262no—
242C23D4×D11311yescharacteristic
243Q8—21no—
244Q8—21no—
245Q8—21no—
246Q8—21no—
247Q8—4522no—
248Q8—2262no—
249Q8—2262no—
250D4—21no—
251D4—21no—
252D4—21no—
253D4—21no—
254D4—42no—
255D4—42no—
256D4—9044no—
257D4—4522no—
258D4—2262no—
259D4—2262no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—1134no—
265C2×C4—4522no—
266C2×C4—2262no—
267C2×C4D4×D11311yescharacteristic
268C2×C4D4×D11312yes—
269C2×C4C2×C22⋊D11312yes—
270C2×C4C23×D11311yescharacteristic
271C8—1134no—
272C8C2×C22⋊D11312yes—
273C8C2×C22⋊D11312yes—
274C22—22no—
275C22—41no—
276C22—41no—
277C22—42no—
278C22—42no—
279C22—9044no—
280C22—4522no—
281C22—4524no—
282C22#1681361812yes—
283C22C2×D4×D11311yescharacteristic
284C4—41no—
285C4—41no—
286C4—4522no—
287C4—2264no—
288C4#1681361812yes—
289C4C2×D4×D11311yescharacteristic
290C4C22×C22⋊D11311yescharacteristic
291C2—22no—
292C2—81no—
293C2—81no—
294C2—9042no—
295C2C2×#1681361811yescharacteristic
296C2#2029940512yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#135×C113C2
socleC22×C113C22×D4
hypercenterC2×#135D113
hypocenterC113#3154
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#16813652C2semidirect
2. C2×#16813647C2semidirect
3. C22×#14268636C2semidirect
4. #20299169C2semidirect
5. #20299162C2semidirect
6. #20298991C2semidirect
7. #20298986C2semidirect
8. #20298979C2semidirect
9. #20298969C2semidirect
10. #20298553C2semidirect
11. C2×#135×C113C2semidirect
16. C2×#14268637C22semidirect
20. C2×#14268635C22semidirect
24. #16813620C22semidirect
27. #16813609C22semidirect
33. #16813532C22semidirect
34. C8×Dic113C22semidirect
38. C2×Q16×C113C22semidirect
39. C2×SD16×C113C22semidirect
40. C2×SD16×C113C22semidirect
41. C2×D8×C113C22semidirect
60. #14268631D4semidirect
85. C2×C8×C113D4semidirect
149. C113#3154semidirect
152. C2×#135D113semidirect
169. C2×Q16C2×D113semidirect
175. C2×SD16C2×D113semidirect
176. C2×SD16C2×D113semidirect
178. C2×D8C2×D113semidirect
228. C2×C8C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136522
C2×#168136472
C22×#142686362
#202991692
#202991622
#202989912
#202989862
#202989792
#202989692
#202985532
C2×#135×C1132
#3154113