Finite Group Databasebeta

← #34080239

Subgroups — #34080239

Order 19328.

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

normal subgroups only

This group has 404 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#23752763C211yesmaximal, characteristic
2C4⋊Q8×D151C211yesmaximal, characteristic, complemented
3#23752608C211yesmaximal, characteristic, complemented
4#23752560C211yesmaximal, characteristic, complemented
5#23752559C211yesmaximal, characteristic, complemented
6#23752532C214yesmaximal, complemented
7#23752501C214yesmaximal, complemented
8#23752263C211yesmaximal, characteristic, complemented
9#498×C151C211yesmaximal, characteristic, complemented
10C2×#14559005—21no—
11C2×Q8×D151—21no—
12#18012739C2211yescharacteristic
13#18012738—21no—
14#18012738C2212yes—
15#18012737—21no—
16#18012736C2211yescharacteristic
17#18012728—21no—
18#18012714—21no—
19#18012714C2212yes—
20#18012701—21no—
21#18012701C2212yes—
22C4⋊C4×D151—21no—
23C4⋊C4×D151C2212yes—
24C42×D151C2211yescharacteristic
25#18012670C2214yes—
26Dic151⋊C8C2212yes—
27#18012661C2214yes—
28#18012659C2214yes—
29(C2×D151)⋊C8C2212yes—
30C4×C151⋊C8C2211yescharacteristic
31C4⋊Q8×C151C2211yescharacteristic
32C4⋊Q8×C151C2211yescharacteristic
33#106×C151C2214yes—
34C4×C8×C151C2211yescharacteristic
35#14559005—44no—
36C2×Dic302—22no—
37C2×Dic302—21no—
38Q8×D151—44no—
39C2×D604—22no—
40C2×D604—21no—
41C2×D604—21no—
42C2×D604C2312yes—
43C2×C4×D151—22no—
44C2×C4×D151—22no—
45C2×C4×D151D411yescharacteristic
46C2×C4×D151D411yescharacteristic
47C2×C4×D151C2311yescharacteristic
48C2×C151⋊C8C2312yes—
49C4⋊Dic151—21no—
50C4⋊Dic151C2312yes—
51Dic151⋊C4—22no—
52Dic151⋊C4—22no—
53(C2×D151)⋊C4—22no—
54(C2×D151)⋊C4—22no—
55C4×Dic151D411yescharacteristic
56C4×Dic151D411yescharacteristic
57C4×Dic151C2311yescharacteristic
58C2×Q8×C151—21no—
59C2×Q8×C151—21no—
60C2×C8×C151C2312yes—
61C4⋊C4×C151—21no—
62C4⋊C4×C151—21no—
63C4⋊C4×C151C2312yes—
64C4⋊C4×C151C2312yes—
65C42×C151C2311yescharacteristic
66C22×D151—22no—
67C22×D151C2×D411yescharacteristic
68Dic302—44no—
69Dic302—42no—
70D604—24no—
71D604—44no—
72D604—42no—
73D604—42no—
74C2×Dic151—22no—
75C2×Dic151C2×D411yescharacteristic
76C2×Dic151C2×D411yescharacteristic
77C2×Dic151C2×D411yescharacteristic
78C4×D151—22no—
79C4×D151—22no—
80C4×D151—44no—
81C4×D151—44no—
82C4×D151SD1614yes—
83C151⋊C8—22no—
84Q8×C151—42no—
85Q8×C151—42no—
86C2×C4×C151—22no—
87C2×C4×C151—22no—
88C2×C4×C151C2×D411yescharacteristic
89C2×C4×C151C2×D411yescharacteristic
90C2×C4×C151C2411yescharacteristic
91C8×C151—22no—
92C22×C151C22×D411yescharacteristic
93C2×D151—21no—
94C2×D151—21no—
95C2×D151—42no—
96C2×D151—42no—
97C2×D151—42no—
98C2×D151C2×SD1612yes—
99C4×C151—42no—
100C4×C151—42no—
101C4×C151C2×SD1612yes—
102C4×C151AGL(1,ℤ/8)12yes—
103C4×C1512−1+412yes—
104Dic151—21no—
105Dic151—21no—
106Dic151—42no—
107Dic151C2×SD1612yes—
108C2×C151#53611yescharacteristic
109C2×C151C22×SD1611yescharacteristic
110C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
111D151—22no—
112D151—82no—
113C151#322711yescharacteristic, complemented, Sylow
114#3227—1511nomaximal, Sylow
115#532—1511no—
116C2×C4⋊Q8—1511no—
117#498—1511no—
118#498D15111yescharacteristic, complemented
119#486—1511no—
120#486—1511no—
121#481—1514no—
122#476—1514no—
123#431—1511no—
124C2×#41—3021no—
125C22×Q8—3021no—
126C4⋊Q8—3021no—
127C4⋊Q8—3021no—
128C4⋊Q8—1512no—
129C4⋊Q8—1511no—
130C4⋊Q8C2×D15111yescharacteristic
131C4⋊Q8C2×D15111yescharacteristic
132#127—1511no—
133#124—3021no—
134#121—3021no—
135#121—1512no—
136C4×D4—3021no—
137C4×D4—1512no—
138C2×C4⋊C4—3021no—
139C2×C4⋊C4—1512no—
140C2×C42—1511no—
141#106—1514no—
142#106C2×D15114yes—
143C4⋊C8—1512no—
144#102—1514no—
145#102—1514no—
146C22⋊C8—1512no—
147C4×C8—1511no—
148C4×C8C2×D15111yescharacteristic
149#41—6044no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—3022no—
153C2×Q8—3021no—
154C2×Q8—6044no—
155C2×D4—3022no—
156C2×D4—3021no—
157C2×D4—3021no—
158C2×D4—1512no—
159C22×C4—3022no—
160C22×C4—3022no—
161C22×C4—1511no—
162C22×C4—1511no—
163C22×C4—1511no—
164C2×C8—1512no—
165C2×C8C22×D15112yes—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—3022no—
169C4⋊C4—3022no—
170C4⋊C4—3021no—
171C4⋊C4—1512no—
172C4⋊C4C22×D15112yes—
173C4⋊C4C22×D15112yes—
174C22⋊C4—3022no—
175C22⋊C4—3022no—
176C42—1511no—
177C42—1511no—
178C42—1511no—
179C42C22×D15111yescharacteristic
180C23—3022no—
181C23—1511no—
182Q8—42no—
183Q8—42no—
184Q8—6044no—
185Q8—6042no—
186D4—3024no—
187D4—6044no—
188D4—6042no—
189D4—6042no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—3022no—
193C2×C4—3022no—
194C2×C4—3022no—
195C2×C4—6044no—
196C2×C4—6044no—
197C2×C4—1511no—
198C2×C4—1511no—
199C2×C4—1511no—
200C2×C4—1514no—
201C2×C4D4×D15111yescharacteristic
202C2×C4D4×D15111yescharacteristic
203C2×C4C23×D15111yescharacteristic
204C8—22no—
205C8—3022no—
206C22—3021no—
207C22—3021no—
208C22—6042no—
209C22—6042no—
210C22—6042no—
211C22—1512no—
212C22C2×D4×D15111yescharacteristic
213C4—42no—
214C4—42no—
215C4—3021no—
216C4—3021no—
217C4—6042no—
218C4—1512no—
219C4SD16×D15112yes—
220C4#1801276612yes—
221C4#1801278712yes—
222C2—3022no—
223C2—12082no—
224C2#2375278711yescharacteristic
225C2C2×SD16×D15111yescharacteristic
226C2C2×#1801276611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#498×C151C2
socleC22×C151C22×D4
prime radical#23752763C2
hypercenter#498D151
hypocenterC151#3227
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D151C2semidirect
3. #23752608C2semidirect
4. #23752560C2semidirect
5. #23752559C2semidirect
6. #23752532C2semidirect
7. #23752501C2semidirect
8. #23752263C2semidirect
9. #498×C151C2semidirect
113. C151#3227semidirect
118. #498D151semidirect

Maximal subgroups

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

subgroupindex
#237527632
C4⋊Q8×D1512
#237526082
#237525602
#237525592
#237525322
#237525012
#237522632
#498×C1512
#3227151