Finite Group Databasebeta

← #34080571

Subgroups — #34080571

Order 19328.

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

normal subgroups only

This group has 346 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#23752833C212yesmaximal, complemented
2#23752508C212yesmaximal, complemented
3#23752493C212yesmaximal, complemented
4#23752458C212yesmaximal, complemented
5#23752453C211yesmaximal, characteristic, complemented
6#23752448C211yesmaximal, characteristic
7#23752435C212yesmaximal, complemented
8#23752428C212yesmaximal, complemented
9#424×C151C211yesmaximal, characteristic, complemented
10C2×Dic604C2211yescharacteristic
11C2×#14558993C2212yes—
12C2×D1208C2211yescharacteristic
13#18012739C2212yes—
14#18012734—22no—
15#18012727C2212yes—
16#18012725—22no—
17#18012721—22no—
18#18012718C2212yes—
19#18012717—22no—
20#18012713C2212yes—
21C4×Dic302C2212yes—
22C4×D604C2212yes—
23#18012673C2211yescharacteristic
24#18012673C2211yescharacteristic
25#18012673C2212yes—
26#18012664C2212yes—
27#18012664C2212yes—
28#18012661C2212yes—
29#18012661C2212yes—
30C2×M16×C151C2211yescharacteristic
31C22×C8×C151C2211yescharacteristic
32#117×C151C2211yescharacteristic
33C4⋊C8×C151C2212yes—
34C4⋊C8×C151C2212yes—
35C2×Dic302—22no—
36C2×Dic302C2312yes—
37C2×D604C2312yes—
38C2×C22⋊D151—22no—
39C2×C4×D151—22no—
40Dic604—41no—
41#14558993—42no—
42D1208—41no—
43C4⋊Dic151—22no—
44C4⋊Dic151C2312yes—
45C4⋊Dic151C2312yes—
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×C151C2311yescharacteristic
55M16×C151—41no—
56C2×C8×C151—41no—
57C2×C8×C151C2311yescharacteristic
58C2×C8×C151C2312yes—
59C2×C8×C151C2311yescharacteristic
60C4⋊C4×C151D411yescharacteristic
61C4⋊C4×C151D411yescharacteristic
62C22⋊C4×C151D412yes—
63C42×C151C2312yes—
64C22×D151—22no—
65Dic302—22no—
66Dic302—22no—
67Dic302—82no—
68D604—22no—
69D604—22no—
70C22⋊D151—82no—
71C2×Dic151—22no—
72C2×Dic151—22no—
73C2×Dic151—22no—
74C4×D151—82no—
75C23×C151C2×D411yescharacteristic
76C2×C4×C151—21no—
77C2×C4×C151—21no—
78C2×C4×C151C2×D412yes—
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D412yes—
81C2×C4×C151C2411yescharacteristic
82C8×C151—21no—
83C8×C151—22no—
84C8×C151—21no—
85C22×C151—21no—
86C22×C151—21no—
87C22×C151—21no—
88C22×C151C22×D411yescharacteristic
89C2×D151—42no—
90C2×D151—42no—
91C2×D151—42no—
92C4×C151—21no—
93C4×C151—22no—
94C4×C151—22no—
95C4×C151H(5,𝔽2)11yescharacteristic
96C4×C1512−1+411yescharacteristic
97Dic151—42no—
98Dic151—42no—
99Dic151—42no—
100C2×C151—41no—
101C2×C151#53711yescharacteristic
102C2×C151#57611yescharacteristic
103C2×C151#57811yescharacteristic
104D151—82no—
105C151#326211yescharacteristic, complemented, Sylow
106#3262—1511nomaximal, Sylow
107#542—1512no—
108#477—1512no—
109#474—1512no—
110#468—1512no—
111#467—1511no—
112#466—1511no—
113#464—1512no—
114#463—1512no—
115#424D15111yescharacteristic, complemented
116C2×Q16—1511no—
117C2×SD16—1512no—
118C2×D8—1511no—
119C2×M16C2×D15111yescharacteristic
120C22×C8C2×D15111yescharacteristic
121C4⋊Q8—1512no—
122#126—3022no—
123#124—3022no—
124#124—1512no—
125#123—3022no—
126C22⋊Q8—3022no—
127C22⋊Q8—1512no—
128#121—1512no—
129C4×Q8—1512no—
130C4×D4—1512no—
131#117C2×D15111yescharacteristic
132#107—1511no—
133#107—1511no—
134#107—1512no—
135C4⋊C8C2×D15112yes—
136C4⋊C8C2×D15112yes—
137#103—1512no—
138#103—1512no—
139#102—1512no—
140#102—1512no—
141C2×Q8—3022no—
142C2×Q8—1512no—
143C2×D4—3022no—
144C2×D4—1512no—
145C22×C4—3022no—
146C22×C4C22×D15111yescharacteristic
147Q16—6041no—
148SD16—6042no—
149D8—6041no—
150M16—41no—
151C2×C8—41no—
152C2×C8C22×D15111yescharacteristic
153C2×C8C22×D15112yes—
154C2×C8C22×D15111yescharacteristic
155C4⋊C4—3022no—
156C4⋊C4—3022no—
157C4⋊C4—3022no—
158C4⋊C4—1512no—
159C4⋊C4—1512no—
160C4⋊C4D60411yescharacteristic
161C4⋊C4D60411yescharacteristic
162C22⋊C4—3022no—
163C22⋊C4—3022no—
164C22⋊C4—3022no—
165C22⋊C4—3022no—
166C22⋊C4—3022no—
167C22⋊C4D60412yes—
168C42—3022no—
169C42C22×D15112yes—
170C23—3022no—
171C23C2×D60411yescharacteristic
172Q8—3022no—
173Q8—3022no—
174Q8—12082no—
175D4—3022no—
176D4—3022no—
177D4—12082no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—3022no—
181C2×C4—3022no—
182C2×C4—3022no—
183C2×C4—12082no—
184C2×C4C2×D60412yes—
185C2×C4C2×D60412yes—
186C2×C4C2×D60411yescharacteristic
187C2×C4C23×D15111yescharacteristic
188C8—21no—
189C8—21no—
190C8—22no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—6042no—
195C22—6042no—
196C22—6042no—
197C22C22×D60411yescharacteristic
198C4—22no—
199C4—22no—
200C4—21no—
201C4—6042no—
202C4—6042no—
203C4—6042no—
204C4#1801278411yescharacteristic
205C4#1801278711yescharacteristic
206C2—41no—
207C2—12082no—
208C2#2375279311yescharacteristic
209C2#2375301711yescharacteristic
210C2#2375302911yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#424×C151C2
socleC22×C151C22×D4
prime radical#23752448C2
hypercenter#424D151
hypocenterC151#3262
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #23752833C2semidirect
2. #23752508C2semidirect
3. #23752493C2semidirect
4. #23752458C2semidirect
5. #23752453C2semidirect
7. #23752435C2semidirect
8. #23752428C2semidirect
9. #424×C151C2semidirect
105. C151#3262semidirect
115. #424D151semidirect

Maximal subgroups

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

subgroupindex
#237528332
#237525082
#237524932
#237524582
#237524532
#237524482
#237524352
#237524282
#424×C1512
#3262151