Finite Group Databasebeta

← #34080248

Subgroups — #34080248

Order 19328.

370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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#23752769C211yesmaximal, characteristic, complemented
2#23752762C211yesmaximal, characteristic
3#23752617C211yesmaximal, characteristic, complemented
4#23752610C211yesmaximal, characteristic, complemented
5#23752559C211yesmaximal, characteristic, complemented
6#23752559C211yesmaximal, characteristic, complemented
7#23752537C214yesmaximal, complemented
8#23752513C214yesmaximal, complemented
9#431×C151C211yesmaximal, characteristic, complemented
10C2×#14559004—21no—
11#18012739C2211yescharacteristic
12#18012739C2211yescharacteristic
13#18012739C2211yescharacteristic
14#18012736C2211yescharacteristic
15#18012731C2212yes—
16#18012727—21no—
17#18012718—21no—
18#18012718—21no—
19#18012713—21no—
20#18012713C2212yes—
21C4×Dic302—21no—
22C4×Dic302—21no—
23C4×D604—21no—
24C4×D604C2212yes—
25#18012698C2212yes—
26#18012673C2214yes—
27#18012671C2214yes—
28#18012661C2214yes—
29#18012661C2214yes—
30C2×C42×C151C2211yescharacteristic
31C4⋊C8×C151C2212yes—
32C22⋊C8×C151C2212yes—
33C4×C8×C151C2211yescharacteristic
34C4×C8×C151C2211yescharacteristic
35#14559004—44no—
36C2×Dic302—21no—
37C2×Dic302—21no—
38C2×Dic302—21no—
39C2×D604—21no—
40C2×D604—21no—
41C2×D604C2312yes—
42C2×C22⋊D151—22no—
43C2×C4×D151—22no—
44C4⋊Dic151—21no—
45C4⋊Dic151—21no—
46C4⋊Dic151—21no—
47C4⋊Dic151C2312yes—
48C4⋊Dic151C2312yes—
49C4⋊Dic151C2312yes—
50Dic151⋊C4—22no—
51Dic151⋊C4—22no—
52C22⋊Dic151—22no—
53(C2×D151)⋊C4—22no—
54(C2×D151)⋊C4—22no—
55C4×Dic151—22no—
56C22×C4×C151D411yescharacteristic
57C22×C4×C151D411yescharacteristic
58C22×C4×C151C2311yescharacteristic
59C2×C8×C151C2312yes—
60C2×C8×C151C2312yes—
61C42×C151D411yescharacteristic
62C42×C151D411yescharacteristic
63C42×C151C2311yescharacteristic
64C42×C151C2311yescharacteristic
65C22×D151—22no—
66Dic302—42no—
67Dic302—42no—
68Dic302—42no—
69D604—24no—
70D604—42no—
71D604—42no—
72C22⋊D151—44no—
73C2×Dic151—22no—
74C2×Dic151—22no—
75C2×Dic151—22no—
76C4×D151—44no—
77C23×C151C2×D411yescharacteristic
78C2×C4×C151—22no—
79C2×C4×C151—22no—
80C2×C4×C151—22no—
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151C2×D411yescharacteristic
83C2×C4×C151C2×D411yescharacteristic
84C2×C4×C151C2×D411yescharacteristic
85C2×C4×C151C2×D411yescharacteristic
86C2×C4×C151C2411yescharacteristic
87C8×C151—22no—
88C8×C151—22no—
89C22×C151—21no—
90C22×C151—21no—
91C22×C151—21no—
92C22×C151C22×D411yescharacteristic
93C2×D151—42no—
94C2×D151—42no—
95C2×D151—42no—
96C4×C151—21no—
97C4×C151—21no—
98C4×C151—21no—
99C4×C151#13512yes—
100C4×C151AGL(1,ℤ/8)12yes—
101C4×C1512−1+412yes—
102Dic151—42no—
103Dic151—42no—
104Dic151—42no—
105C2×C151—41no—
106C2×C151#53611yescharacteristic
107C2×C151C2×#13511yescharacteristic
108C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
109D151—82no—
110C151#322811yescharacteristic, complemented, Sylow
111#3228—1511nomaximal, Sylow
112#533—1511no—
113#532—1511no—
114#500—1511no—
115#498—1511no—
116#486—1511no—
117#486—1511no—
118#482—1514no—
119#478—1514no—
120#431D15111yescharacteristic, complemented
121C2×#41—3021no—
122C4⋊Q8—1511no—
123C4⋊Q8—1511no—
124C4⋊Q8—1511no—
125#127—1511no—
126#125—1512no—
127#124—3021no—
128C22⋊Q8—3021no—
129C22⋊Q8—3021no—
130#121—3021no—
131#121—1512no—
132C4×Q8—3021no—
133C4×Q8—3021no—
134C4×D4—3021no—
135C4×D4—1512no—
136#117—1512no—
137C2×C42C2×D15111yescharacteristic
138#107—1514no—
139#106—1514no—
140C4⋊C8C2×D15112yes—
141#102—1514no—
142#102—1514no—
143C22⋊C8C2×D15112yes—
144C4×C8C2×D15111yescharacteristic
145C4×C8C2×D15111yescharacteristic
146#41—6044no—
147C2×Q8—3021no—
148C2×Q8—3021no—
149C2×Q8—3021no—
150C2×D4—3022no—
151C2×D4—3021no—
152C2×D4—3021no—
153C2×D4—1512no—
154C22×C4—3022no—
155C22×C4D60411yescharacteristic
156C22×C4D60411yescharacteristic
157C22×C4C22×D15111yescharacteristic
158C2×C8C22×D15112yes—
159C2×C8C22×D15112yes—
160C4⋊C4—3022no—
161C4⋊C4—3022no—
162C4⋊C4—3021no—
163C4⋊C4—3021no—
164C4⋊C4—3021no—
165C4⋊C4—1512no—
166C4⋊C4—1512no—
167C4⋊C4—1512no—
168C22⋊C4—3022no—
169C22⋊C4—3022no—
170C22⋊C4—3022no—
171C42—3022no—
172C42D60411yescharacteristic
173C42D60411yescharacteristic
174C42C22×D15111yescharacteristic
175C42C22×D15111yescharacteristic
176C23—3022no—
177C23C2×D60411yescharacteristic
178Q8—6042no—
179Q8—6042no—
180Q8—6042no—
181D4—3024no—
182D4—6044no—
183D4—6042no—
184D4—6042no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—3022no—
189C2×C4—3022no—
190C2×C4—3022no—
191C2×C4—6044no—
192C2×C4C2×D60411yescharacteristic
193C2×C4C2×D60411yescharacteristic
194C2×C4C2×D60411yescharacteristic
195C2×C4C2×D60411yescharacteristic
196C2×C4C2×D60411yescharacteristic
197C2×C4C23×D15111yescharacteristic
198C8—22no—
199C8—22no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—6042no—
204C22—6042no—
205C22—6042no—
206C22C22×D60411yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—6042no—
211C4—6042no—
212C4—6042no—
213C4#1801276112yes—
214C4#1801276712yes—
215C4#1801278612yes—
216C2—41no—
217C2—12082no—
218C2#2375278811yescharacteristic
219C2C2×#1801276111yescharacteristic
220C2C2×#1801276711yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#431×C151C2
socleC22×C151C22×D4
prime radical#23752762C2
hypercenter#431D151
hypocenterC151#3228
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #23752769C2semidirect
3. #23752617C2semidirect
4. #23752610C2semidirect
5. #23752559C2semidirect
6. #23752559C2semidirect
7. #23752537C2semidirect
8. #23752513C2semidirect
9. #431×C151C2semidirect
110. C151#3228semidirect
120. #431D151semidirect

Maximal subgroups

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

subgroupindex
#237527692
#237527622
#237526172
#237526102
#237525592
#237525372
#237525132
#431×C1512
#3228151