Finite Group Databasebeta

← #34077180

Subgroups — #34077180

Order 19328.

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

normal subgroups only

This group has 380 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
1C2×#18012730C211yesmaximal, characteristic
2C2×#18012729C211yesmaximal, characteristic
3#23752154C212yesmaximal
4#23752152C211yesmaximal, characteristic
5#23752151C211yesmaximal, characteristic
6#23752146C212yesmaximal
7#23752145C212yesmaximal
8#23752143C212yesmaximal
9#23752143C211yesmaximal, characteristic
10#23752076C211yesmaximal, characteristic
11#398×C151C211yesmaximal, characteristic
12#18012730—24no—
13#18012729—24no—
14C2×C4⋊Dic151C2211yescharacteristic
15C2×C4⋊Dic151C2212yes—
16C2×C4⋊Dic151C2211yescharacteristic
17C2×Dic151⋊C4C2211yescharacteristic
18C2×Dic151⋊C4C2211yescharacteristic
19C2×Dic151⋊C4C2211yescharacteristic
20C2×Dic151⋊C4C2211yescharacteristic
21C2×Dic151⋊C4C2212yes—
22C2×Dic151⋊C4C2212yes—
23C2×Dic151⋊C4C2212yes—
24C2×C4×Dic151C2211yescharacteristic
25C151⋊#95C2211yescharacteristic
26C151⋊#95C2212yes—
27C151⋊#95C2212yes—
28C151⋊#95C2212yes—
29C151⋊#95C2212yes—
30C151⋊#95C2212yes—
31C151⋊#95C2212yes—
32C2×C4⋊C4×C151C2211yescharacteristic
33C2×C4⋊C4×C151C2211yescharacteristic
34C2×C4⋊C4×C151C2212yes—
35#95×C151C2211yescharacteristic
36#95×C151C2212yes—
37C22×Dic151C2311yescharacteristic
38C22×Dic151C2311yescharacteristic
39C22×Dic151C2312yes—
40C22×Dic151C2312yes—
41C22×Dic151C2311yescharacteristic
42C22×Dic151C2311yescharacteristic
43C4⋊Dic151—22no—
44C4⋊Dic151—24no—
45C4⋊Dic151—22no—
46Dic151⋊C4—22no—
47Dic151⋊C4—22no—
48Dic151⋊C4—22no—
49Dic151⋊C4—24no—
50Dic151⋊C4—22no—
51Dic151⋊C4—42no—
52Dic151⋊C4—42no—
53C4×Dic151D414yes—
54C22×C4×C151C2312yes—
55C22×C4×C151C2311yescharacteristic
56C22×C4×C151C2311yescharacteristic
57C22×C4×C151C2312yes—
58C22×C4×C151C2311yescharacteristic
59C4⋊C4×C151—22no—
60C4⋊C4×C151—22no—
61C4⋊C4×C151—42no—
62C2×Dic151—21no—
63C2×Dic151—21no—
64C2×Dic151—22no—
65C2×Dic151—21no—
66C2×Dic151—21no—
67C2×Dic151—22no—
68C2×Dic151—21no—
69C2×Dic151—22no—
70C2×Dic151—22no—
71C2×Dic151—21no—
72C2×Dic151—22no—
73C2×Dic151—24no—
74C2×Dic151—22no—
75C2×Dic151C2×D412yes—
76C2×Dic151C2×D412yes—
77C23×C151C2411yescharacteristic
78C2×C4×C151—22no—
79C2×C4×C151—21no—
80C2×C4×C151—21no—
81C2×C4×C151—22no—
82C2×C4×C151—22no—
83C2×C4×C151—22no—
84C2×C4×C151—21no—
85C2×C4×C151—22no—
86C2×C4×C151—22no—
87C2×C4×C151—21no—
88C2×C4×C151—22no—
89C2×C4×C151—22no—
90C2×C4×C151C2×D412yes—
91C22×C151C22×D411yescharacteristic
92C22×C151H(5,𝔽2)11yescharacteristic
93C22×C1512−1+412yes—
94C22×C1512−1+411yescharacteristic
95C22×C1512−1+412yes—
96C4×C151—22no—
97C4×C151—41no—
98C4×C151—41no—
99C4×C151—42no—
100C4×C151—42no—
101Dic151—22no—
102Dic151—22no—
103Dic151—41no—
104Dic151—42no—
105Dic151—41no—
106Dic151—42no—
107C2×C151#53611yescharacteristic
108C2×C151#53611yescharacteristic
109C2×C151#53711yescharacteristic
110C2×C151#56312yes—
111C2×C151#56412yes—
112C151#282211yescharacteristic, complemented, Sylow
113#2822—1511nomaximal, Sylow
114C2×#125—1511no—
115C2×#125—1511no—
116#400—1511no—
117#400—1511no—
118#400—1512no—
119#398—1511no—
120#398—1512no—
121#398—1512no—
122#398—1512no—
123#398D15111yescharacteristic
124#382—1511no—
125#125—3024no—
126#125—3024no—
127C2×C4⋊C4—1511no—
128C2×C4⋊C4—1512no—
129C2×C4⋊C4—1511no—
130C2×C4⋊C4—1511no—
131C2×C4⋊C4—1511no—
132C2×C4⋊C4—1511no—
133C2×C4⋊C4—1512no—
134C2×C4⋊C4—1511no—
135C2×C4⋊C4—1512no—
136C2×C4⋊C4—1512no—
137C2×C4⋊C4C2×D15111yescharacteristic
138C2×C4⋊C4C2×D15111yescharacteristic
139C2×C4⋊C4C2×D15112yes—
140C2×C42—1511no—
141#95—1511no—
142#95—1512no—
143#95—1512no—
144#95—1512no—
145#95—1512no—
146#95—1512no—
147#95—1512no—
148#95C2×D15111yescharacteristic
149#95C2×D15112yes—
150C22×C4—1512no—
151C22×C4—1511no—
152C22×C4—1512no—
153C22×C4—1511no—
154C22×C4—1511no—
155C22×C4—1511no—
156C22×C4C22×D15112yes—
157C22×C4C22×D15111yescharacteristic
158C22×C4C22×D15111yescharacteristic
159C22×C4C22×D15112yes—
160C22×C4C22×D15111yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—42no—
164C4⋊C4—3022no—
165C4⋊C4—3022no—
166C4⋊C4—3022no—
167C4⋊C4—3024no—
168C4⋊C4—3022no—
169C4⋊C4—3024no—
170C4⋊C4—3022no—
171C4⋊C4—3022no—
172C4⋊C4—6042no—
173C4⋊C4—6042no—
174C42—1514no—
175C23C23×D15111yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—3021no—
189C2×C4—3021no—
190C2×C4—3022no—
191C2×C4—3021no—
192C2×C4—3022no—
193C2×C4—3021no—
194C2×C4—3022no—
195C2×C4—3021no—
196C2×C4—3022no—
197C2×C4—3022no—
198C2×C4—3021no—
199C2×C4—3022no—
200C2×C4—3024no—
201C2×C4—1512no—
202C2×C4—1512no—
203C2×C4D4×D15112yes—
204C22C2×D4×D15111yescharacteristic
205C22#1801278411yescharacteristic
206C22#1801278612yes—
207C22#1801278611yescharacteristic
208C22#1801278712yes—
209C4—22no—
210C4—42no—
211C4—41no—
212C4—41no—
213C4—42no—
214C4—3022no—
215C4—3022no—
216C4—6042no—
217C4—6041no—
218C4—6042no—
219C4—6041no—
220C2#2375278411yescharacteristic
221C2#2375278711yescharacteristic
222C2#2375279111yescharacteristic
223C2#2375296312yes—
224C2C151⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, prime radical, cosocleC23×C151C24
Fitting#398×C151C2
hypercenter#398D151
hypocenterC151#2822
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
112. C151#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#180127302
C2×#180127292
#237521542
#237521522
#237521512
#237521462
#237521452
#237521432
#237520762
#398×C1512
#2822151