Finite Group Databasebeta

← #34080924

Subgroups — #34080924

Order 19328.

494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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#23752866C211yesmaximal, characteristic, complemented
2D4×D604C211yesmaximal, characteristic, complemented
3#23752559C211yesmaximal, characteristic, complemented
4#23752526C212yesmaximal, complemented
5#23752493C211yesmaximal, characteristic, complemented
6#23752448C212yesmaximal, complemented
7#23752408C211yesmaximal, characteristic, complemented
8#23752348C212yesmaximal, complemented
9C4×D1208C211yesmaximal, characteristic, complemented
10C2×#18012661C212yesmaximal, complemented
11C8×D4×C151C211yesmaximal, characteristic, complemented
12C2×#14559003—21no—
13C22×D604C2212yes—
14C2×D4×D151—21no—
15C2×D1208C2211yescharacteristic
16C2×D1208C2212yescomplemented
17#18012739C2211yescharacteristic, complemented
18#18012736C2211yescharacteristic
19#18012723—22no—
20#18012719—21no—
21#18012714—21no—
22#18012713C2212yes—
23#18012713C2212yescomplemented
24#18012709—22no—
25C4×D604C2211yescharacteristic
26C4×D604C2211yescharacteristic, complemented
27C2×C4⋊Dic151C2212yescomplemented
28#18012673C2212yescomplemented
29#18012673C2211yescharacteristic, complemented
30#18012661C2211yescharacteristic
31#18012661C2212yes—
32#18012661C2211yescharacteristic, complemented
33#18012661C2212yescomplemented
34#18012661C2212yescomplemented
35#18012661C2212yescomplemented
36C22×C8×C151C2212yescomplemented
37C4×D4×C151C2211yescharacteristic
38C4⋊C8×C151C2211yescharacteristic, complemented
39C22⋊C8×C151C2212yescomplemented
40C4×C8×C151C2211yescharacteristic, complemented
41C23×D151—22no—
42#14559003—44no—
43C2×Dic302—21no—
44C2×D604—24no—
45C2×D604—22no—
46C2×D604—21no—
47C2×D604—21no—
48C2×D604—42no—
49C2×D604C2311yescharacteristic
50C2×D604C2312yes—
51C2×D604C2311yescharacteristic
52C2×C22⋊D151—22no—
53C2×C22⋊D151—22no—
54D4×D151—44no—
55C22×Dic151—22no—
56C2×C4×D151—21no—
57C2×C4×D151—21no—
58D1208—22no—
59D1208—42no—
60C4⋊Dic151—22no—
61C4⋊Dic151—21no—
62C4⋊Dic151C2311yescharacteristic
63C4⋊Dic151C2311yescharacteristic
64C4⋊Dic151C2312yes—
65(C2×D151)⋊C4—21no—
66(C2×D151)⋊C4—21no—
67(C2×D151)⋊C4—22no—
68(C2×D151)⋊C4—22no—
69C2×D4×C151D411yescharacteristic
70C22×C4×C151C2312yes—
71C2×C8×C151—42no—
72C2×C8×C151C2311yescharacteristic
73C2×C8×C151C2312yes—
74C2×C8×C151C2311yescharacteristic
75C4⋊C4×C151D411yescharacteristic
76C22⋊C4×C151D412yes—
77C42×C151C2311yescharacteristic
78C22×D151—21no—
79C22×D151—21no—
80C22×D151—22no—
81C22×D151—44no—
82C22×D151—44no—
83C22×D151—82no—
84Dic302—42no—
85D604—21no—
86D604—22no—
87D604—21no—
88D604—21no—
89D604—22no—
90D604—44no—
91D604—42no—
92D604—81no—
93D604#4112yescomplemented
94C22⋊D151—44no—
95C22⋊D151—44no—
96C2×Dic151—21no—
97C2×Dic151—21no—
98C2×Dic151—22no—
99C2×Dic151—44no—
100C4×D151—42no—
101C4×D151—42no—
102C23×C151C2×D412yes—
103D4×C151D814yescomplemented
104C2×C4×C151—22no—
105C2×C4×C151—22no—
106C2×C4×C151C2×D411yescharacteristic
107C2×C4×C151C2×D412yes—
108C2×C4×C151C2×D411yescharacteristic
109C2×C4×C151C2411yescharacteristic
110C8×C151—21no—
111C8×C151—22no—
112C8×C151—21no—
113C22×C151—22no—
114C22×C151—22no—
115C22×C151C2×D814yes—
116C22×C151C22×D411yescharacteristic
117C2×D151—22no—
118C2×D151—41no—
119C2×D151—41no—
120C2×D151—42no—
121C2×D151—41no—
122C2×D151—41no—
123C2×D151—42no—
124C2×D151—42no—
125C2×D151—41no—
126C2×D151—88no—
127C4×C151—22no—
128C4×C151—21no—
129C4×C151C2×D812yes—
130C4×C151C2×#4111yescharacteristic
131C4×C151H(5,𝔽2)11yescharacteristic
132Dic151—41no—
133Dic151—41no—
134Dic151—42no—
135C2×C151—24no—
136C2×C151#54611yescharacteristic
137C2×C151C22×D811yescharacteristic
138C2×C151#57711yescharacteristic
139D151—42no—
140D151—81no—
141D151—82no—
142C151#329411yescharacteristic, complemented, Sylow
143#3294—1511nomaximal, Sylow
144#547—1511no—
145D42—1511no—
146#486—1511no—
147#480—1512no—
148#474—1511no—
149#466—1512no—
150#459—1511no—
151#447—1512no—
152C4×D8—1511no—
153C8×D4D15111yescharacteristic, complemented
154C2×#102—1512no—
155C2×#41—3021no—
156C22×D4—3021no—
157C22×D4—1512no—
158C2×D8—1511no—
159C2×D8—1512no—
160C22×C8C2×D15112yescomplemented
161C4⋊Q8—1511no—
162#127—1511no—
163#123—3022no—
164C22⋊Q8—3021no—
165#121—3021no—
166#121—1512no—
167#121—1512no—
168#120—3022no—
169C4×D4—1511no—
170C4×D4—1511no—
171C4×D4C2×D15111yescharacteristic
172C2×C4⋊C4—1512no—
173#107—1511no—
174#107—1512no—
175C4⋊C8C2×D15111yescharacteristic, complemented
176#102—1511no—
177#102—1512no—
178#102—1512no—
179#102—1512no—
180#102—1511no—
181#102—1512no—
182C22⋊C8C2×D15112yescomplemented
183C4×C8C2×D15111yescharacteristic, complemented
184C24—3022no—
185#41—6044no—
186C2×Q8—3021no—
187C2×D4—3024no—
188C2×D4—3022no—
189C2×D4—3022no—
190C2×D4—3022no—
191C2×D4—3021no—
192C2×D4—3021no—
193C2×D4—6042no—
194C2×D4—6044no—
195C2×D4—1512no—
196C2×D4—1511no—
197C2×D4—1511no—
198C2×D4D60411yescharacteristic
199C22×C4—3022no—
200C22×C4—3021no—
201C22×C4—3021no—
202C22×C4C22×D15112yes—
203D8—3022no—
204D8—6042no—
205C2×C8—42no—
206C2×C8C22×D15111yescharacteristic
207C2×C8C22×D15111yescharacteristic
208C2×C8C22×D15112yes—
209C4⋊C4—3022no—
210C4⋊C4—3021no—
211C4⋊C4—1511no—
212C4⋊C4—1512no—
213C4⋊C4—1511no—
214C4⋊C4D60411yescharacteristic
215C22⋊C4—3021no—
216C22⋊C4—3021no—
217C22⋊C4—3022no—
218C22⋊C4—3022no—
219C22⋊C4D60412yes—
220C42C22×D15111yescharacteristic
221C23—3021no—
222C23—3021no—
223C23—3022no—
224C23—6044no—
225C23—6044no—
226C23—12082no—
227C23C2×D60412yes—
228Q8—6042no—
229D4—3021no—
230D4—3022no—
231D4—3021no—
232D4—3021no—
233D4—3022no—
234D4—6044no—
235D4—6044no—
236D4—6044no—
237D4—6042no—
238D4—1512no—
239D4—12081no—
240D4D120814yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—3021no—
244C2×C4—3021no—
245C2×C4—3022no—
246C2×C4—6044no—
247C2×C4—6042no—
248C2×C4—6042no—
249C2×C4C2×D60411yescharacteristic
250C2×C4C2×D60412yes—
251C2×C4C2×D60411yescharacteristic
252C2×C4C23×D15111yescharacteristic
253C8—21no—
254C8—21no—
255C8—22no—
256C22—22no—
257C22—22no—
258C22—3022no—
259C22—6041no—
260C22—6041no—
261C22—6041no—
262C22—6042no—
263C22—6042no—
264C22—6041no—
265C22—6042no—
266C22—6041no—
267C22—12088no—
268C22C2×D120814yes—
269C22C22×D60411yescharacteristic
270C4—21no—
271C4—22no—
272C4—6041no—
273C4—6041no—
274C4—6042no—
275C4C2×D120812yes—
276C4#41×D15111yescharacteristic
277C4#1801278411yescharacteristic
278C2—24no—
279C2—6042no—
280C2—12082no—
281C2—12081no—
282C2#2375285711yescharacteristic
283C2C22×D120811yescharacteristic
284C2#2375302411yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC8×D4×C151C2
socleC22×C151C22×D4
hypercenterC8×D4D151
hypocenterC151#3294
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #23752866C2semidirect
2. D4×D604C2semidirect
3. #23752559C2semidirect
4. #23752526C2semidirect
5. #23752493C2semidirect
6. #23752448C2semidirect
7. #23752408C2semidirect
8. #23752348C2semidirect
9. C4×D1208C2semidirect
10. C2×#18012661C2semidirect
11. C8×D4×C151C2semidirect
16. C2×D1208C22semidirect
17. #18012739C22semidirect
23. #18012713C22semidirect
26. C4×D604C22semidirect
27. C2×C4⋊Dic151C22semidirect
28. #18012673C22semidirect
29. #18012673C22semidirect
32. #18012661C22semidirect
33. #18012661C22semidirect
34. #18012661C22semidirect
35. #18012661C22semidirect
36. C22×C8×C151C22semidirect
38. C4⋊C8×C151C22semidirect
39. C22⋊C8×C151C22semidirect
40. C4×C8×C151C22semidirect
93. D604#41semidirect
103. D4×C151D8semidirect
142. C151#3294semidirect
153. C8×D4D151semidirect
160. C22×C8C2×D151semidirect
175. C4⋊C8C2×D151semidirect
182. C22⋊C8C2×D151semidirect
183. C4×C8C2×D151semidirect
240. D4D1208semidirect

Maximal subgroups

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

subgroupindex
#237528662
D4×D6042
#237525592
#237525262
#237524932
#237524482
#237524082
#237523482
C4×D12082
C2×#180126612
C8×D4×C1512
#3294151