Finite Group Databasebeta

← #34080512

Subgroups — #34080512

Order 19328.

354 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 109 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#23752748C212yesmaximal, complemented
2#23752517C212yesmaximal, complemented
3#23752511C212yesmaximal, complemented
4#23752465C211yesmaximal, characteristic
5#23752460C212yesmaximal, complemented
6#23752436C212yesmaximal, complemented
7#23752430C212yesmaximal, complemented
8#23752235C211yesmaximal, characteristic, complemented
9#470×C151C211yesmaximal, characteristic, complemented
10C2×#14558991C2212yes—
11C2×D1208C2211yescharacteristic
12C2×#14558988C2211yescharacteristic
13#18012734—22no—
14#18012730C2212yes—
15#18012728C2212yes—
16#18012723—22no—
17#18012713C2212yes—
18Q8×Dic151C2212yes—
19#18012701C2212yes—
20(C22⋊D151)⋊C4—22no—
21#18012697—22no—
22C2×C4×Dic151C2211yescharacteristic
23#18012672C2212yes—
24#18012671C2211yescharacteristic
25Dic151⋊C8C2212yes—
26Dic151⋊C8C2212yes—
27#18012663C2212yes—
28#18012661C2212yes—
29#18012659C2212yes—
30C2×Q16×C151C2211yescharacteristic
31C2×M16×C151C2211yescharacteristic
32C22⋊Q8×C151C2212yes—
33#106×C151C2211yescharacteristic
34#103×C151C2212yes—
35C2×D604C2312yes—
36C2×C22⋊D151—22no—
37C22×Dic151D412yes—
38C2×C4×D151—22no—
39#14558991—42no—
40D1208—41no—
41#14558988—41no—
42C2×C151⋊C8C2312yes—
43C4⋊Dic151—22no—
44C4⋊Dic151—22no—
45C4⋊Dic151C2312yes—
46Dic151⋊C4—22no—
47(C2×D151)⋊C4—22no—
48(C2×D151)⋊C4—22no—
49(C2×D151)⋊C4—22no—
50(C2×D151)⋊C4—22no—
51C4×Dic151—22no—
52C4×Dic151D411yescharacteristic
53C4×Dic151D411yescharacteristic
54C4×Dic151C2312yes—
55C2×Q8×C151C2312yes—
56C22×C4×C151C2311yescharacteristic
57Q16×C151—41no—
58M16×C151—41no—
59C2×C8×C151C2311yescharacteristic
60C2×C8×C151C2311yescharacteristic
61C4⋊C4×C151—22no—
62C4⋊C4×C151C2312yes—
63C22⋊C4×C151—22no—
64C22×D151—22no—
65D604—22no—
66D604—22no—
67C22⋊D151—44no—
68C2×Dic151—22no—
69C2×Dic151—42no—
70C2×Dic151C2×D412yes—
71C2×Dic151C2×D412yes—
72C4×D151—44no—
73C151⋊C8—22no—
74C23×C151C2×D411yescharacteristic
75Q8×C151—22no—
76Q8×C151—22no—
77C2×C4×C151—21no—
78C2×C4×C151—21no—
79C2×C4×C151—22no—
80C2×C4×C151—22no—
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151C2411yescharacteristic
83C8×C151—21no—
84C8×C151—21no—
85C22×C151—21no—
86C22×C151—22no—
87C22×C151C22×D411yescharacteristic
88C2×D151—42no—
89C2×D151—42no—
90C2×D151—42no—
91C4×C151—21no—
92C4×C151—42no—
93C4×C151—42no—
94C4×C151H(5,𝔽2)11yescharacteristic
95C4×C1512−1+411yescharacteristic
96Dic151—22no—
97Dic151—22no—
98Dic151—42no—
99C2×C151—41no—
100C2×C151#53711yescharacteristic
101C2×C151#57512yes—
102D151—82no—
103C151#325611yescharacteristic, complemented, Sylow
104#3256—1511nomaximal, Sylow
105#529—1512no—
106#479—1512no—
107#478—1512no—
108#470D15111yescharacteristic, complemented
109#469—1511no—
110#468—1512no—
111#464—1512no—
112#463—1512no—
113#423—1511no—
114C2×Q16C2×D15111yescharacteristic
115C2×SD16—1512no—
116C2×D8—1511no—
117C2×M16—1511no—
118C2×M16C2×D15111yescharacteristic
119#126—3022no—
120#125—1512no—
121#124—1512no—
122#123—3022no—
123C22⋊Q8C2×D15112yes—
124#121—1512no—
125C4×Q8—1512no—
126C4×D4—3022no—
127C4×D4—1512no—
128#117—3022no—
129C2×C42—1511no—
130#107—1512no—
131#106—1511no—
132#106C2×D15111yescharacteristic
133C4⋊C8—1512no—
134C4⋊C8—1512no—
135#103—1512no—
136#103C2×D15112yes—
137#102—1512no—
138#102—1512no—
139C2×Q8C22×D15112yes—
140C2×D4—3022no—
141C2×D4—1512no—
142C22×C4—3022no—
143C22×C4—1512no—
144C22×C4C22×D15111yescharacteristic
145Q16—41no—
146SD16—6042no—
147D8—6041no—
148M16—41no—
149M16—6041no—
150C2×C8—1512no—
151C2×C8C22×D15111yescharacteristic
152C2×C8C22×D15111yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—3022no—
155C4⋊C4—3022no—
156C4⋊C4—3022no—
157C4⋊C4—1512no—
158C4⋊C4C22×D15112yes—
159C22⋊C4—22no—
160C22⋊C4—3022no—
161C22⋊C4—3022no—
162C22⋊C4—3022no—
163C22⋊C4—3022no—
164C42—3022no—
165C42—1511no—
166C42—1511no—
167C42—1512no—
168C23—3022no—
169C23D4×D15111yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—3022no—
173D4—3022no—
174D4—6044no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—3022no—
180C2×C4—6044no—
181C2×C4—6042no—
182C2×C4—1512no—
183C2×C4—1512no—
184C2×C4D4×D15111yescharacteristic
185C2×C4C23×D15111yescharacteristic
186C8—21no—
187C8—21no—
188C8—3022no—
189C22—22no—
190C22—21no—
191C22—6042no—
192C22—6042no—
193C22—6042no—
194C22C2×D4×D15111yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—3022no—
199C4—3022no—
200C4—6042no—
201C4#1801278411yescharacteristic
202C4#1801278611yescharacteristic
203C2—41no—
204C2—12082no—
205C2#2375278911yescharacteristic
206C2#2375301112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#470×C151C2
socleC22×C151C22×D4
prime radical#23752465C2
hypercenter#470D151
hypocenterC151#3256
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
1. #23752748C2semidirect
2. #23752517C2semidirect
3. #23752511C2semidirect
5. #23752460C2semidirect
6. #23752436C2semidirect
7. #23752430C2semidirect
8. #23752235C2semidirect
9. #470×C151C2semidirect
103. C151#3256semidirect
108. #470D151semidirect

Maximal subgroups

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

subgroupindex
#237527482
#237525172
#237525112
#237524652
#237524602
#237524362
#237524302
#237522352
#470×C1512
#3256151