Finite Group Databasebeta

← #34080917

Subgroups — #34080917

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
1D4×D604C211yesmaximal, characteristic, complemented
2#23752560C211yesmaximal, characteristic, complemented
3#23752525C212yesmaximal, complemented
4#23752489C211yesmaximal, characteristic, complemented
5#23752446C212yesmaximal, complemented
6#23752407C211yesmaximal, characteristic, complemented
7#23752345C212yesmaximal, complemented
8C4×#14558989C211yesmaximal, characteristic, complemented
9D4×C151⋊C8C211yesmaximal, characteristic, complemented
10C2×#18012659C212yesmaximal, complemented
11#547×C151C211yesmaximal, characteristic, complemented
12C22×D604C2212yes—
13C2×D4×D151—21no—
14C2×#14558989C2211yescharacteristic
15C2×#14558989C2212yescomplemented
16C22×C151⋊C8C2212yescomplemented
17#18012736C2211yescharacteristic
18#18012714—21no—
19#18012713C2212yes—
20#18012709—22no—
21C4×D604C2211yescharacteristic
22#18012672C2212yescomplemented
23#18012672C2211yescharacteristic, complemented
24C4⋊(C151⋊C8)C2211yescharacteristic, complemented
25#18012660C2211yescharacteristic, complemented
26#18012659C2211yescharacteristic
27#18012659C2212yes—
28#18012659C2212yescomplemented
29#18012659C2212yescomplemented
30#18012659C2212yescomplemented
31C22⋊(C151⋊C8)C2212yescomplemented
32C4×C151⋊C8C2211yescharacteristic, complemented
33C2×#41×C151—21no—
34C4⋊Q8×C151C2211yescharacteristic, complemented
35#123×C151—22no—
36C22⋊Q8×C151—21no—
37#121×C151C2212yescomplemented
38C4×D4×C151C2211yescharacteristic
39C4×D4×C151C2211yescharacteristic, complemented
40C2×C4⋊C4×C151C2212yescomplemented
41C23×D151—22no—
42C2×D604—24no—
43C2×D604—22no—
44C2×D604—21no—
45C2×D604—21no—
46C2×D604—42no—
47C2×D604C2312yes—
48C2×D604C2311yescharacteristic
49C2×C22⋊D151—22no—
50D4×D151—44no—
51C2×C4×D151—21no—
52#14558989—22no—
53#14558989—42no—
54C2×C151⋊C8—42no—
55C2×C151⋊C8C2312yes—
56C2×C151⋊C8C2311yescharacteristic
57C2×C151⋊C8C2311yescharacteristic
58C4⋊Dic151C2311yescharacteristic
59(C2×D151)⋊C4—21no—
60(C2×D151)⋊C4—22no—
61#41×C151—44no—
62C2×Q8×C151—21no—
63C2×D4×C151—22no—
64C2×D4×C151D411yescharacteristic
65C2×D4×C151C2311yescharacteristic
66C22×C4×C151—22no—
67C22×C4×C151—21no—
68C22×C4×C151C2312yes—
69C4⋊C4×C151—22no—
70C4⋊C4×C151—21no—
71C4⋊C4×C151D411yescharacteristic
72C4⋊C4×C151C2311yescharacteristic
73C4⋊C4×C151C2312yes—
74C22⋊C4×C151—21no—
75C22⋊C4×C151—22no—
76C22⋊C4×C151D412yes—
77C42×C151C2311yescharacteristic
78C22×D151—21no—
79C22×D151—22no—
80C22×D151—44no—
81C22×D151—44no—
82C22×D151—82no—
83D604—22no—
84D604—21no—
85D604—22no—
86D604—44no—
87D604—42no—
88D604—81no—
89D604#4112yescomplemented
90C22⋊D151—44no—
91C2×Dic151—21no—
92C4×D151—42no—
93C151⋊C8—21no—
94C151⋊C8—21no—
95C151⋊C8—22no—
96C23×C151—21no—
97C23×C151C2×D412yes—
98Q8×C151—42no—
99D4×C151—21no—
100D4×C151—21no—
101D4×C151—44no—
102D4×C151D814yescomplemented
103C2×C4×C151—22no—
104C2×C4×C151—22no—
105C2×C4×C151—22no—
106C2×C4×C151—21no—
107C2×C4×C151—44no—
108C2×C4×C151—42no—
109C2×C4×C151C2×D411yescharacteristic
110C2×C4×C151C2×D412yes—
111C2×C4×C151C2×D411yescharacteristic
112C2×C4×C151C2411yescharacteristic
113C22×C151—22no—
114C22×C151—22no—
115C22×C151—41no—
116C22×C151—41no—
117C22×C151—41no—
118C22×C151C2×D814yes—
119C22×C151C22×D411yescharacteristic
120C2×D151—22no—
121C2×D151—41no—
122C2×D151—41no—
123C2×D151—42no—
124C2×D151—42no—
125C2×D151—42no—
126C2×D151—88no—
127C4×C151—22no—
128C4×C151—21no—
129C4×C151—41no—
130C4×C151—42no—
131C4×C151C2×D812yes—
132C4×C151C2×#4111yescharacteristic
133C4×C151H(5,𝔽2)11yescharacteristic
134Dic151—41no—
135C2×C151—24no—
136C2×C151—81no—
137C2×C151#54611yescharacteristic
138C2×C151C22×D811yescharacteristic
139C2×C151#57711yescharacteristic
140D151—42no—
141D151—82no—
142C151#329411yescharacteristic, complemented, Sylow
143#3294—1511nomaximal, Sylow
144#547D15111yescharacteristic, complemented
145D42—1511no—
146#486—1511no—
147#480—1512no—
148#474—1511no—
149#466—1512no—
150#459—1511no—
151#447—1512no—
152C4×D8—1511no—
153C8×D4—1511no—
154C2×#102—1512no—
155C2×#41—21no—
156C22×D4—3021no—
157C22×D4—1512no—
158C2×D8—1511no—
159C2×D8—1512no—
160C22×C8—1512no—
161C4⋊Q8C2×D15111yescharacteristic, complemented
162#127—1511no—
163#123—22no—
164C22⋊Q8—21no—
165#121—3021no—
166#121—1512no—
167#121C2×D15112yescomplemented
168#120—3022no—
169C4×D4—1511no—
170C4×D4C2×D15111yescharacteristic
171C4×D4C2×D15111yescharacteristic, complemented
172C2×C4⋊C4C2×D15112yescomplemented
173#107—1511no—
174#107—1512no—
175C4⋊C8—1511no—
176#102—1511no—
177#102—1511no—
178#102—1512no—
179#102—1512no—
180#102—1512no—
181#102—1512no—
182C22⋊C8—1512no—
183C4×C8—1511no—
184C24—3022no—
185#41—44no—
186C2×Q8—21no—
187C2×D4—22no—
188C2×D4—3024no—
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×D4C22⋊D15111yescharacteristic
198C2×D4C22×D15111yescharacteristic
199C22×C4—22no—
200C22×C4—21no—
201C22×C4—3021no—
202C22×C4C22×D15112yes—
203D8—3022no—
204D8—6042no—
205C2×C8—6042no—
206C2×C8—1511no—
207C2×C8—1511no—
208C2×C8—1512no—
209C4⋊C4—22no—
210C4⋊C4—21no—
211C4⋊C4—1511no—
212C4⋊C4C22⋊D15111yescharacteristic
213C4⋊C4C22×D15111yescharacteristic
214C4⋊C4C22×D15112yes—
215C22⋊C4—21no—
216C22⋊C4—22no—
217C22⋊C4—3021no—
218C22⋊C4—3022no—
219C22⋊C4C22⋊D15112yes—
220C42C22×D15111yescharacteristic
221C23—21no—
222C23—3021no—
223C23—3022no—
224C23—6044no—
225C23—6044no—
226C23—12082no—
227C23C2×C22⋊D15112yes—
228Q8—42no—
229D4—21no—
230D4—21no—
231D4—44no—
232D4—3022no—
233D4—3021no—
234D4—3022no—
235D4—6044no—
236D4—6044no—
237D4—6042no—
238D4—1512no—
239D4—12081no—
240D4#1455898914yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—44no—
246C2×C4—42no—
247C2×C4—3021no—
248C2×C4—6042no—
249C2×C4C2×C22⋊D15111yescharacteristic
250C2×C4C2×C22⋊D15112yes—
251C2×C4C2×C22⋊D15111yescharacteristic
252C2×C4C23×D15111yescharacteristic
253C8—3021no—
254C8—3021no—
255C8—3022no—
256C22—22no—
257C22—22no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—3022no—
262C22—6041no—
263C22—6041no—
264C22—6042no—
265C22—6042no—
266C22—6042no—
267C22—12088no—
268C22C2×#1455898914yes—
269C22C22×C22⋊D15111yescharacteristic
270C4—21no—
271C4—22no—
272C4—41no—
273C4—42no—
274C4—6041no—
275C4C2×#1455898912yes—
276C4#41×D15111yescharacteristic
277C4#1801278511yescharacteristic
278C2—24no—
279C2—81no—
280C2—6042no—
281C2—12082no—
282C2#2375285011yescharacteristic
283C2C22×#1455898911yescharacteristic
284C2#2375302011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#547×C151C2
socleC22×C151C22×D4
hypercenter#547D151
hypocenterC151#3294
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. D4×D604C2semidirect
2. #23752560C2semidirect
3. #23752525C2semidirect
4. #23752489C2semidirect
5. #23752446C2semidirect
6. #23752407C2semidirect
7. #23752345C2semidirect
8. C4×#14558989C2semidirect
9. D4×C151⋊C8C2semidirect
10. C2×#18012659C2semidirect
11. #547×C151C2semidirect
15. C2×#14558989C22semidirect
16. C22×C151⋊C8C22semidirect
22. #18012672C22semidirect
23. #18012672C22semidirect
24. C4⋊(C151⋊C8)C22semidirect
25. #18012660C22semidirect
28. #18012659C22semidirect
29. #18012659C22semidirect
30. #18012659C22semidirect
31. C22⋊(C151⋊C8)C22semidirect
32. C4×C151⋊C8C22semidirect
34. C4⋊Q8×C151C22semidirect
37. #121×C151C22semidirect
39. C4×D4×C151C22semidirect
40. C2×C4⋊C4×C151C22semidirect
89. D604#41semidirect
102. D4×C151D8semidirect
142. C151#3294semidirect
144. #547D151semidirect
161. C4⋊Q8C2×D151semidirect
167. #121C2×D151semidirect
171. C4×D4C2×D151semidirect
172. C2×C4⋊C4C2×D151semidirect
240. D4#14558989semidirect

Maximal subgroups

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

subgroupindex
D4×D6042
#237525602
#237525252
#237524892
#237524462
#237524072
#237523452
C4×#145589892
D4×C151⋊C82
C2×#180126592
#547×C1512
#3294151