Finite Group Databasebeta

← #34079930

Subgroups — #34079930

Order 19328.

410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C22⋊Q8×D151C212yesmaximal
2#23752544C212yesmaximal, complemented
3#23752541C212yesmaximal, complemented
4#23752470C211yesmaximal, characteristic, complemented
5#23752468C212yesmaximal, complemented
6#23752369C212yesmaximal, complemented
7#23752366C212yesmaximal, complemented
8#23752175C211yesmaximal, characteristic
9#470×C151C211yesmaximal, characteristic, complemented
10C2×Q8×D151C2212yes—
11C22×C4×D151C2211yescharacteristic
12C2×Dic604C2211yescharacteristic, complemented
13C2×#14558994C2212yescomplemented
14C2×#14558988C2211yescharacteristic
15#18012719C2212yes—
16#18012718C2212yes—
17#18012717—22no—
18#18012716—22no—
19#18012715C2212yes—
20C4⋊C4×D151—22no—
21C4⋊C4×D151C2212yes—
22C22⋊C4×D151—22no—
23#18012671C2211yescharacteristic, complemented
24#18012670C2212yescomplemented
25#18012664C2212yescomplemented
26#18012663C2212yescomplemented
27#18012662C2212yescomplemented
28(C2×D151)⋊C8C2212yes—
29(C2×D151)⋊C8C2212yes—
30C2×Q16×C151C2211yescharacteristic, complemented
31C2×M16×C151C2211yescharacteristic
32C22⋊Q8×C151C2212yes—
33#106×C151C2211yescharacteristic, complemented
34#103×C151C2212yescomplemented
35C23×D151D411yescharacteristic
36C2×Dic302—22no—
37C2×Dic302C2312yes—
38Q8×D151—42no—
39Q8×D151—42no—
40C22×Dic151D411yescharacteristic
41C2×C4×D151—22no—
42C2×C4×D151—22no—
43C2×C4×D151—41no—
44C2×C4×D151—41no—
45C2×C4×D151D412yes—
46C2×C4×D151C2312yes—
47Dic604—41no—
48#14558994—42no—
49#14558988—41no—
50C2×C151⋊C8C2312yes—
51C4⋊Dic151—22no—
52C4⋊Dic151C2312yes—
53Dic151⋊C4—22no—
54Dic151⋊C4—22no—
55Dic151⋊C4—22no—
56C22⋊Dic151—22no—
57(C2×D151)⋊C4—22no—
58(C2×D151)⋊C4—22no—
59C2×Q8×C151C2312yes—
60C22×C4×C151C2311yescharacteristic
61Q16×C151—41no—
62M16×C151—41no—
63C2×C8×C151C2311yescharacteristic
64C2×C8×C151C2311yescharacteristic
65C4⋊C4×C151—22no—
66C4⋊C4×C151C2312yes—
67C22⋊C4×C151—22no—
68C22×D151—24no—
69C22×D151—41no—
70C22×D151C2×D412yes—
71Dic302—22no—
72Dic302—22no—
73Dic302—44no—
74C2×Dic151—22no—
75C2×Dic151—22no—
76C2×Dic151—41no—
77C2×Dic151C2×D412yes—
78C4×D151—22no—
79C4×D151—22no—
80C4×D151—42no—
81C4×D151—44no—
82C4×D151—44no—
83C151⋊C8—22no—
84C23×C151C2×D411yescharacteristic
85Q8×C151—22no—
86Q8×C151—22no—
87C2×C4×C151—21no—
88C2×C4×C151—21no—
89C2×C4×C151—22no—
90C2×C4×C151—22no—
91C2×C4×C151C2×D411yescharacteristic
92C2×C4×C151C2411yescharacteristic
93C8×C151—21no—
94C8×C151—21no—
95C22×C151—21no—
96C22×C151—22no—
97C22×C151C22×D411yescharacteristic
98C2×D151—22no—
99C2×D151—22no—
100C2×D151—44no—
101C2×D151#13714yes—
102C4×C151—21no—
103C4×C151—42no—
104C4×C151—42no—
105C4×C151H(5,𝔽2)11yescharacteristic
106C4×C151H(5,𝔽2)11yescharacteristic
107Dic151—22no—
108Dic151—42no—
109Dic151—42no—
110C2×C151—41no—
111C2×C151#53411yescharacteristic
112C2×C151C2×#13712yes—
113D151—24no—
114C151#319511yescharacteristic, complemented, Sylow
115#3195—1511nomaximal, Sylow
116C2×C22⋊Q8—1512no—
117#483—1512no—
118#483—1512no—
119#470—1511no—
120#470—1512no—
121#470D15111yescharacteristic, complemented
122#451—1512no—
123#451—1512no—
124#407—1511no—
125C22×Q8—1512no—
126C23×C4—1511no—
127C2×Q16—1512no—
128C2×Q16—1511no—
129C2×Q16C2×D15111yescharacteristic, complemented
130C2×M16—1511no—
131C2×M16C2×D15111yescharacteristic
132C22⋊Q8—3022no—
133C22⋊Q8—3022no—
134C22⋊Q8—1512no—
135C22⋊Q8—1512no—
136C22⋊Q8—1512no—
137C22⋊Q8C2×D15112yes—
138C2×C4⋊C4—3022no—
139C2×C4⋊C4—1512no—
140C2×C22⋊C4—3022no—
141#106—1511no—
142#106—1512no—
143#106C2×D15111yescharacteristic, complemented
144#103—1512no—
145#103—1512no—
146#103—1512no—
147#103C2×D15112yescomplemented
148C22⋊C8—1512no—
149C22⋊C8—1512no—
150C24—1511no—
151C2×Q8—3022no—
152C2×Q8—6042no—
153C2×Q8—6042no—
154C2×Q8—1512no—
155C2×Q8C22×D15112yes—
156C22×C4—3022no—
157C22×C4—3022no—
158C22×C4—6041no—
159C22×C4—6041no—
160C22×C4—1512no—
161C22×C4—1511no—
162C22×C4—1512no—
163C22×C4C22×D15111yescharacteristic
164Q16—41no—
165Q16—6041no—
166Q16—6042no—
167M16—41no—
168M16—6041no—
169C2×C8—1512no—
170C2×C8C22×D15111yescharacteristic
171C2×C8C22×D15111yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—3022no—
174C4⋊C4—3022no—
175C4⋊C4—3022no—
176C4⋊C4—3022no—
177C4⋊C4—1512no—
178C4⋊C4C22×D15112yes—
179C22⋊C4—22no—
180C22⋊C4—3022no—
181C22⋊C4—3022no—
182C22⋊C4—3022no—
183C23—3024no—
184C23—6041no—
185C23—1512no—
186C23D4×D15111yescharacteristic
187Q8—22no—
188Q8—22no—
189Q8—3022no—
190Q8—3022no—
191Q8—6044no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—3022no—
197C2×C4—3022no—
198C2×C4—3022no—
199C2×C4—3022no—
200C2×C4—6042no—
201C2×C4—6044no—
202C2×C4—6044no—
203C2×C4—6041no—
204C2×C4—1512no—
205C2×C4D4×D15111yescharacteristic
206C2×C4C23×D15111yescharacteristic
207C8—21no—
208C8—21no—
209C8—3022no—
210C22—22no—
211C22—21no—
212C22—3022no—
213C22—3022no—
214C22—6044no—
215C22—1514no—
216C22C2×D4×D15111yescharacteristic
217C4—21no—
218C4—42no—
219C4—42no—
220C4—3022no—
221C4—6042no—
222C4—6042no—
223C4#1801278411yescharacteristic
224C4#1801278511yescharacteristic
225C2—41no—
226C2—3024no—
227C2#2375277011yescharacteristic
228C2#137×D15112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#470×C151C2
socleC22×C151C22×D4
prime radicalC23×D151D4
hypercenter#470D151
hypocenterC151#3195
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #23752544C2semidirect
3. #23752541C2semidirect
4. #23752470C2semidirect
5. #23752468C2semidirect
6. #23752369C2semidirect
7. #23752366C2semidirect
9. #470×C151C2semidirect
12. C2×Dic604C22semidirect
13. C2×#14558994C22semidirect
23. #18012671C22semidirect
24. #18012670C22semidirect
25. #18012664C22semidirect
26. #18012663C22semidirect
27. #18012662C22semidirect
30. C2×Q16×C151C22semidirect
33. #106×C151C22semidirect
34. #103×C151C22semidirect
114. C151#3195semidirect
121. #470D151semidirect
129. C2×Q16C2×D151semidirect
143. #106C2×D151semidirect
147. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1512
#237525442
#237525412
#237524702
#237524682
#237523692
#237523662
#237521752
#470×C1512
#3195151