Finite Group Databasebeta

← #34079402

Subgroups — #34079402

Order 19328.

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

normal subgroups only

This group has 382 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#23752817C211yesmaximal, characteristic
2#23752689C211yesmaximal, characteristic, complemented
3#23752537C212yesmaximal, complemented
4#23752520C212yesmaximal, complemented
5#23752413C212yesmaximal, complemented
6#23752353C212yesmaximal, complemented
7#23752314C212yesmaximal, complemented
8C4×#14558993C212yesmaximal, complemented
9#433×C151C211yesmaximal, characteristic, complemented
10C22×Dic302C2211yescharacteristic
11C2×#14558993C2212yes—
12C2×#14558993C2212yes—
13#18012736C2211yescharacteristic
14#18012731C2211yescharacteristic
15#18012724—22no—
16#18012713C2212yes—
17#18012712—22no—
18C4×Dic302C2212yes—
19C4×Dic302C2212yes—
20#18012704—22no—
21C4×D604C2212yes—
22#18012698C2211yescharacteristic
23#18012695—22no—
24#18012673C2212yes—
25#18012671C2212yes—
26#18012664C2212yes—
27#18012664C2212yes—
28#18012661C2212yes—
29#18012661C2212yes—
30#117×C151C2211yescharacteristic
31C4⋊C8×C151C2212yes—
32C22⋊C8×C151C2212yes—
33#97×C151C2211yescharacteristic
34C4×C8×C151C2211yescharacteristic
35C2×Dic302—24no—
36C2×Dic302—21no—
37C2×Dic302C2312yes—
38C2×D604—22no—
39C2×D604C2312yes—
40C2×C22⋊D151—22no—
41C22×Dic151—21no—
42C2×C4×D151—22no—
43#14558993—24no—
44#14558993—24no—
45C4⋊Dic151C2312yes—
46C4⋊Dic151C2312yes—
47Dic151⋊C4—22no—
48Dic151⋊C4—22no—
49Dic151⋊C4—22no—
50C22⋊Dic151—21no—
51(C2×D151)⋊C4—22no—
52(C2×D151)⋊C4—22no—
53C4×Dic151—22no—
54C4×Dic151—22no—
55C4×Dic151—21no—
56C22×C4×C151C2311yescharacteristic
57C2×C8×C151C2312yes—
58C2×C8×C151C2312yes—
59C4⋊C4×C151D412yes—
60C22⋊C4×C151D412yes—
61C42×C151C2311yescharacteristic
62C42×C151C2311yescharacteristic
63C22×D151—22no—
64Dic302—24no—
65Dic302—22no—
66Dic302#4114yes—
67D604—22no—
68D604—22no—
69D604—82no—
70C22⋊D151—82no—
71C2×Dic151—24no—
72C2×Dic151—22no—
73C2×Dic151—22no—
74C2×Dic151—22no—
75C4×D151—82no—
76C23×C151C2×D411yescharacteristic
77C2×C4×C151—22no—
78C2×C4×C151C2×D411yescharacteristic
79C2×C4×C151C2×D412yes—
80C2×C4×C151C2×D412yes—
81C2×C4×C151C2411yescharacteristic
82C8×C151—22no—
83C8×C151—22no—
84C22×C151—21no—
85C22×C151—22no—
86C22×C151C22×D411yescharacteristic
87C2×D151—42no—
88C2×D151—42no—
89C2×D151—42no—
90C4×C151—21no—
91C4×C151—22no—
92C4×C151—22no—
93C4×C151C2×#4112yes—
94Dic151—24no—
95Dic151—42no—
96Dic151—42no—
97C2×C151—41no—
98C2×C151#52511yescharacteristic
99C2×C151#57712yes—
100D151—82no—
101C151#312611yescharacteristic, complemented, Sylow
102#3126—1511nomaximal, Sylow
103#540—1511no—
104#519—1511no—
105#482—1512no—
106#479—1512no—
107#460—1512no—
108#448—1512no—
109#440—1512no—
110C4×SD16—1512no—
111#433D15111yescharacteristic, complemented
112C22×Q8—1511no—
113C2×SD16—1512no—
114C2×SD16—1512no—
115#127—1511no—
116#125—1511no—
117#123—3022no—
118#121—3022no—
119#121—1512no—
120C4×Q8—3022no—
121C4×Q8—1512no—
122C4×Q8—1512no—
123C4×D4—1512no—
124#117—3022no—
125#117—1511no—
126#117C2×D15111yescharacteristic
127#107—1512no—
128#106—1512no—
129C4⋊C8C2×D15112yes—
130#103—1512no—
131#103—1512no—
132#102—1512no—
133#102—1512no—
134C22⋊C8C2×D15112yes—
135#97C2×D15111yescharacteristic
136C4×C8C2×D15111yescharacteristic
137C2×Q8—3024no—
138C2×Q8—3021no—
139C2×Q8—1512no—
140C2×D4—3022no—
141C2×D4—3022no—
142C2×D4—1512no—
143C22×C4—3021no—
144C22×C4—3022no—
145C22×C4C22×D15111yescharacteristic
146SD16—3024no—
147SD16—3024no—
148C2×C8C22×D15112yes—
149C2×C8C22×D15112yes—
150C4⋊C4—3022no—
151C4⋊C4—3022no—
152C4⋊C4—3022no—
153C4⋊C4—1512no—
154C4⋊C4—1512no—
155C4⋊C4D60412yes—
156C22⋊C4—3021no—
157C22⋊C4—3022no—
158C22⋊C4—3022no—
159C22⋊C4D60412yes—
160C42—3022no—
161C42—3022no—
162C42—3021no—
163C42C22×D15111yescharacteristic
164C42C22×D15111yescharacteristic
165C23—3022no—
166C23C2×D60411yescharacteristic
167Q8—3024no—
168Q8—3022no—
169Q8—1514no—
170D4—3022no—
171D4—3022no—
172D4—12082no—
173D4—12082no—
174C2×C4—22no—
175C2×C4—3024no—
176C2×C4—3022no—
177C2×C4—3022no—
178C2×C4—3022no—
179C2×C4—12082no—
180C2×C4C2×D60412yes—
181C2×C4C2×D60412yes—
182C2×C4C2×D60411yescharacteristic
183C2×C4C23×D15111yescharacteristic
184C8—22no—
185C8—22no—
186C22—21no—
187C22—22no—
188C22—6042no—
189C22—6042no—
190C22—6042no—
191C22C22×D60411yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—3024no—
196C4—6042no—
197C4—6042no—
198C4#41×D15112yes—
199C2—41no—
200C2—12082no—
201C2#2375272411yescharacteristic
202C2#2375302412yes—
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#433×C151C2
socleC22×C151C22×D4
prime radical#23752817C2
hypercenter#433D151
hypocenterC151#3126
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #23752689C2semidirect
3. #23752537C2semidirect
4. #23752520C2semidirect
5. #23752413C2semidirect
6. #23752353C2semidirect
7. #23752314C2semidirect
8. C4×#14558993C2semidirect
9. #433×C151C2semidirect
101. C151#3126semidirect
111. #433D151semidirect

Maximal subgroups

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

subgroupindex
#237528172
#237526892
#237525372
#237525202
#237524132
#237523532
#237523142
C4×#145589932
#433×C1512
#3126151