Finite Group Databasebeta

← #34080462

Subgroups — #34080462

Order 19328.

360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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#23752746C212yesmaximal, complemented
2#23752520C212yesmaximal, complemented
3#23752513C212yesmaximal, complemented
4#23752453C211yesmaximal, characteristic, complemented
5#23752448C211yesmaximal, characteristic
6#23752441C212yesmaximal, complemented
7#23752435C212yesmaximal, complemented
8#23752428C212yesmaximal, complemented
9C2×C4⋊C8×C151C211yesmaximal, characteristic, complemented
10C2×Dic604C2211yescharacteristic
11C2×#14558993C2212yes—
12C2×D1208C2211yescharacteristic
13#18012733—22no—
14#18012731C2212yes—
15#18012727C2212yes—
16#18012722—22no—
17#18012718C2212yes—
18#18012713C2212yes—
19C4×Dic302C2212yes—
20C4×D604C2212yes—
21C4×C22⋊D151—22no—
22#18012696—22no—
23#18012673C2211yescharacteristic
24#18012673C2211yescharacteristic
25#18012671C2212yes—
26#18012664C2212yes—
27#18012664C2212yes—
28#18012661C2212yes—
29#18012661C2212yes—
30C22×C8×C151C2211yescharacteristic
31C22×C8×C151C2211yescharacteristic
32C2×C42×C151C2211yescharacteristic
33C4⋊C8×C151C2212yes—
34C4⋊C8×C151C2212yes—
35C2×Dic302C2312yes—
36C2×D604C2312yes—
37C2×C22⋊D151—22no—
38C2×C4×D151—22no—
39Dic604—41no—
40#14558993—42no—
41D1208—41no—
42C4⋊Dic151C2312yes—
43C4⋊Dic151C2312yes—
44Dic151⋊C4—22no—
45Dic151⋊C4—22no—
46Dic151⋊C4—22no—
47Dic151⋊C4—22no—
48C22⋊Dic151—22no—
49(C2×D151)⋊C4—22no—
50(C2×D151)⋊C4—22no—
51(C2×D151)⋊C4—22no—
52(C2×D151)⋊C4—22no—
53C4×Dic151—22no—
54C22×C4×C151D411yescharacteristic
55C22×C4×C151D411yescharacteristic
56C22×C4×C151C2311yescharacteristic
57C2×C8×C151—41no—
58C2×C8×C151—41no—
59C2×C8×C151C2311yescharacteristic
60C2×C8×C151C2311yescharacteristic
61C2×C8×C151C2312yes—
62C42×C151D412yes—
63C42×C151C2312yes—
64C22×D151—22no—
65Dic302—22no—
66Dic302—22no—
67D604—22no—
68D604—22no—
69C22⋊D151—44no—
70C2×Dic151—22no—
71C2×Dic151—22no—
72C2×Dic151—22no—
73C4×D151—44no—
74C23×C151C2×D411yescharacteristic
75C2×C4×C151—22no—
76C2×C4×C151—21no—
77C2×C4×C151—21no—
78C2×C4×C151—41no—
79C2×C4×C151C2×D412yes—
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×D412yes—
82C2×C4×C151C2411yescharacteristic
83C8×C151—21no—
84C8×C151—22no—
85C8×C151—21no—
86C22×C151—21no—
87C22×C151—21no—
88C22×C151#13512yes—
89C22×C151C22×D411yescharacteristic
90C2×D151—42no—
91C2×D151—42no—
92C2×D151—42no—
93C4×C151—21no—
94C4×C151—22no—
95C4×C151—22no—
96C4×C151H(5,𝔽2)11yescharacteristic
97C4×C1512−1+411yescharacteristic
98Dic151—42no—
99Dic151—42no—
100Dic151—42no—
101C2×C151—22no—
102C2×C151#53711yescharacteristic
103C2×C151C2×#13511yescharacteristic
104C2×C151#57511yescharacteristic
105D151—82no—
106C151#325011yescharacteristic, complemented, Sylow
107#3250—1511nomaximal, Sylow
108#529—1512no—
109#479—1512no—
110#478—1512no—
111#467—1511no—
112#466—1511no—
113#465—1512no—
114#464—1512no—
115#463—1512no—
116C2×C4⋊C8D15111yescharacteristic, complemented
117C2×Q16—1511no—
118C2×SD16—1512no—
119C2×D8—1511no—
120C22×C8C2×D15111yescharacteristic
121C22×C8C2×D15111yescharacteristic
122#126—3022no—
123#125—1512no—
124#124—1512no—
125#123—3022no—
126C22⋊Q8—1512no—
127#121—1512no—
128C4×Q8—1512no—
129C4×D4—3022no—
130C4×D4—1512no—
131#117—3022no—
132C2×C42C2×D15111yescharacteristic
133#107—1511no—
134#107—1511no—
135#106—1512no—
136C4⋊C8C2×D15112yes—
137C4⋊C8C2×D15112yes—
138#103—1512no—
139#103—1512no—
140#102—1512no—
141#102—1512no—
142C2×Q8—1512no—
143C2×D4—3022no—
144C2×D4—1512no—
145C22×C4—3022no—
146C22×C4D60411yescharacteristic
147C22×C4D60411yescharacteristic
148C22×C4C22×D15111yescharacteristic
149Q16—6041no—
150SD16—6042no—
151D8—6041no—
152C2×C8—41no—
153C2×C8—41no—
154C2×C8C22×D15111yescharacteristic
155C2×C8C22×D15112yes—
156C2×C8C22×D15111yescharacteristic
157C4⋊C4—3022no—
158C4⋊C4—3022no—
159C4⋊C4—3022no—
160C4⋊C4—3022no—
161C4⋊C4—1512no—
162C4⋊C4—1512no—
163C22⋊C4—3022no—
164C22⋊C4—3022no—
165C22⋊C4—3022no—
166C22⋊C4—3022no—
167C22⋊C4—3022no—
168C42—3022no—
169C42D60412yes—
170C42C22×D15112yes—
171C23—3022no—
172C23C2×D60411yescharacteristic
173Q8—3022no—
174Q8—3022no—
175D4—3022no—
176D4—3022no—
177D4—6044no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—3022no—
183C2×C4—3022no—
184C2×C4—3022no—
185C2×C4—6044no—
186C2×C4C2×D60412yes—
187C2×C4C2×D60411yescharacteristic
188C2×C4C2×D60412yes—
189C2×C4C23×D15111yescharacteristic
190C8—21no—
191C8—22no—
192C8—21no—
193C22—21no—
194C22—21no—
195C22—6042no—
196C22—6042no—
197C22—6042no—
198C22#1801276112yes—
199C22C22×D60411yescharacteristic
200C4—22no—
201C4—22no—
202C4—21no—
203C4—6042no—
204C4—6042no—
205C4—6042no—
206C4#1801278411yescharacteristic
207C4#1801278711yescharacteristic
208C2—22no—
209C2—12082no—
210C2#2375279311yescharacteristic
211C2C2×#1801276111yescharacteristic
212C2#2375301211yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×C4⋊C8×C151C2
socleC22×C151C22×D4
prime radical#23752448C2
hypercenterC2×C4⋊C8D151
hypocenterC151#3250
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #23752746C2semidirect
2. #23752520C2semidirect
3. #23752513C2semidirect
4. #23752453C2semidirect
6. #23752441C2semidirect
7. #23752435C2semidirect
8. #23752428C2semidirect
9. C2×C4⋊C8×C151C2semidirect
106. C151#3250semidirect
116. C2×C4⋊C8D151semidirect

Maximal subgroups

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

subgroupindex
#237527462
#237525202
#237525132
#237524532
#237524482
#237524412
#237524352
#237524282
C2×C4⋊C8×C1512
#3250151