Finite Group Databasebeta

← #34077298

Subgroups — #34077298

Order 19328.

380 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752154C212yesmaximal, complemented
2#23752153C212yesmaximal, complemented
3#23752150C212yesmaximal, complemented
4#23752140C212yesmaximal
5#23752137C211yesmaximal, characteristic
6#23752132C212yesmaximal, complemented
7#23752124C211yesmaximal, characteristic
8#23752085C212yesmaximal
9#385×C151C211yesmaximal, characteristic
10C22×Dic302C2211yescharacteristic
11C2×C4⋊Dic151C2211yescharacteristic
12C2×Dic151⋊C4C2212yes—
13C2×Dic151⋊C4C2212yes—
14C2×Dic151⋊C4C2212yes—
15C2×C22⋊Dic151C2212yes—
16C2×C22⋊Dic151C2212yes—
17C151⋊#95C2212yes—
18C151⋊#95C2212yes—
19C151⋊#95C2211yescharacteristic
20C151⋊#95C2212yes—
21C151⋊#95C2212yes—
22C151⋊#95C2212yes—
23C151⋊#95C2212yes—
24C151⋊#95C2211yescharacteristic
25C151⋊#95C2212yes—
26C23×C4×C151C2211yescharacteristic
27C2×C4⋊C4×C151C2212yes—
28C2×C22⋊C4×C151C2211yescharacteristic
29C2×C22⋊C4×C151C2211yescharacteristic
30#95×C151C2212yes—
31C2×Dic302—41no—
32C2×Dic302—42no—
33C22×Dic151C2312yes—
34C22×Dic151C2312yes—
35C22×Dic151C2312yes—
36C22×Dic151C2312yes—
37C4⋊Dic151—41no—
38Dic151⋊C4—42no—
39Dic151⋊C4—42no—
40Dic151⋊C4—42no—
41C22⋊Dic151—24no—
42C22⋊Dic151—42no—
43C24×C151C2311yescharacteristic
44C22×C4×C151—41no—
45C22×C4×C151—42no—
46C22×C4×C151C2312yes—
47C22×C4×C151C2312yes—
48C22×C4×C151C2311yescharacteristic
49C22×C4×C151C2311yescharacteristic
50C4⋊C4×C151—42no—
51C22⋊C4×C151—22no—
52C22⋊C4×C151—41no—
53Dic302—44no—
54C2×Dic151—22no—
55C2×Dic151—22no—
56C2×Dic151—22no—
57C2×Dic151—22no—
58C2×Dic151—22no—
59C2×Dic151—22no—
60C2×Dic151—22no—
61C2×Dic151—22no—
62C2×Dic151—22no—
63C2×Dic151—22no—
64C2×Dic151—22no—
65C2×Dic151—22no—
66C23×C151—22no—
67C23×C151—21no—
68C23×C151—22no—
69C23×C151—21no—
70C23×C151#4112yes—
71C23×C151C2411yescharacteristic
72C2×C4×C151—22no—
73C2×C4×C151—22no—
74C2×C4×C151—22no—
75C2×C4×C151—22no—
76C2×C4×C151—21no—
77C2×C4×C151—21no—
78C2×C4×C151—22no—
79C2×C4×C151—22no—
80C2×C4×C151—22no—
81C2×C4×C151—22no—
82C2×C4×C151—44no—
83C22×C151—24no—
84C22×C151—22no—
85C22×C151—41no—
86C22×C151—42no—
87C22×C151—41no—
88C22×C151C2×#4111yescharacteristic
89C22×C151H(5,𝔽2)12yes—
90C22×C151H(5,𝔽2)11yescharacteristic
91C22×C1512−1+412yes—
92C22×C1512−1+411yescharacteristic
93C4×C151—42no—
94C4×C151—42no—
95C4×C151—41no—
96C4×C151—41no—
97Dic151—42no—
98Dic151—42no—
99Dic151—42no—
100Dic151—42no—
101C2×C151—42no—
102C2×C151#53912yes—
103C2×C151#53911yescharacteristic
104C2×C151H(3,𝔽4)11yescharacteristic
105C2×C151#56312yes—
106C2×C151#56311yescharacteristic
107C151#283511yescharacteristic, complemented, Sylow
108#2835—1511nomaximal, Sylow
109#400—1512no—
110#400—1512no—
111#400—1512no—
112#397—1511no—
113#397—1512no—
114#395—1512no—
115#393—1511no—
116#385—1512no—
117#385D15111yescharacteristic
118C22×Q8—1511no—
119C23×C4C2×D15111yescharacteristic
120C2×C4⋊C4—1512no—
121C2×C4⋊C4—1512no—
122C2×C4⋊C4—1512no—
123C2×C4⋊C4—1511no—
124C2×C4⋊C4C2×D15112yes—
125C2×C22⋊C4—1512no—
126C2×C22⋊C4—1512no—
127C2×C22⋊C4C2×D15111yescharacteristic
128C2×C22⋊C4C2×D15111yescharacteristic
129#95—1512no—
130#95—1512no—
131#95—1511no—
132#95—1512no—
133#95—1512no—
134#95—1512no—
135#95—1512no—
136#95—1512no—
137#95—1511no—
138#95C2×D15112yes—
139C24C22×D15111yescharacteristic
140C2×Q8—6041no—
141C2×Q8—6042no—
142C22×C4—42no—
143C22×C4—41no—
144C22×C4—1512no—
145C22×C4—1512no—
146C22×C4—1512no—
147C22×C4—1512no—
148C22×C4C22×D15111yescharacteristic
149C22×C4C22×D15112yes—
150C22×C4C22×D15111yescharacteristic
151C22×C4C22×D15112yes—
152C4⋊C4—42no—
153C4⋊C4—6042no—
154C4⋊C4—6042no—
155C4⋊C4—6042no—
156C4⋊C4—6041no—
157C22⋊C4—22no—
158C22⋊C4—41no—
159C22⋊C4—3024no—
160C22⋊C4—6042no—
161C23—21no—
162C23—22no—
163C23—22no—
164C23—21no—
165C23#1455900412yes—
166C23C23×D15111yescharacteristic
167Q8—6044no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—3022no—
180C2×C4—3022no—
181C2×C4—3022no—
182C2×C4—3022no—
183C2×C4—3022no—
184C2×C4—3022no—
185C2×C4—3022no—
186C2×C4—3022no—
187C2×C4—3022no—
188C2×C4—3022no—
189C2×C4—3022no—
190C2×C4—3022no—
191C22—24no—
192C22—22no—
193C22—42no—
194C22—41no—
195C22—41no—
196C22C2×#1455900411yescharacteristic
197C22#1801278412yes—
198C22#1801278411yescharacteristic
199C22#1801278612yes—
200C22#1801278711yescharacteristic
201C4—41no—
202C4—42no—
203C4—42no—
204C4—41no—
205C4—6042no—
206C4—6042no—
207C4—6042no—
208C4—6042no—
209C2—42no—
210C2#2375280412yes—
211C2#2375280911yescharacteristic
212C2#2375295511yescharacteristic
213C2#2375296312yes—
214C2#2375296511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#385×C151C2
prime radicalC24×C151C23
hypercenter#385D151
hypocenterC151#2835
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #23752154C2semidirect
2. #23752153C2semidirect
3. #23752150C2semidirect
6. #23752132C2semidirect
107. C151#2835semidirect

Maximal subgroups

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

subgroupindex
#237521542
#237521532
#237521502
#237521402
#237521372
#237521322
#237521242
#237520852
#385×C1512
#2835151