Finite Group Databasebeta

← #34079851

Subgroups — #34079851

Order 19328.

358 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 129 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#23752769C211yesmaximal, characteristic
2#23752608C211yesmaximal, characteristic, complemented
3#23752591C211yesmaximal, characteristic, complemented
4#23752564C211yesmaximal, characteristic, complemented
5#23752562C211yesmaximal, characteristic, complemented
6#23752468C214yesmaximal
7#23752317C214yesmaximal, complemented
8C4×#14558988C211yesmaximal, characteristic
9#533×C151C211yesmaximal, characteristic
10C2×#14558994C2214yes—
11C2×#14558988C2212yes—
12#18012739C2211yescharacteristic
13#18012739C2211yescharacteristic
14#18012731—21no—
15#18012718—21no—
16#18012718C2212yes—
17C4×Dic302—21no—
18C4×Dic302C2212yes—
19#18012698—21no—
20#18012670C2214yes—
21#18012663C2214yes—
22#18012662C2214yes—
23#18012650C2212yes—
24C4×C151⋊C8C2211yescharacteristic
25C4×C151⋊C8C2211yescharacteristic
26C4⋊Q8×C151C2211yescharacteristic
27C4⋊Q8×C151C2211yescharacteristic
28#125×C151—21no—
29C22⋊Q8×C151—21no—
30C22⋊Q8×C151C2212yes—
31C4×Q8×C151—21no—
32C4×Q8×C151C2212yes—
33#117×C151—21no—
34C2×C42×C151C2211yescharacteristic
35C2×Dic302—21no—
36C2×Dic302C2312yes—
37#14558994—28no—
38#14558988—24no—
39C2×C151⋊C8C2312yes—
40C2×C151⋊C8C2312yes—
41C4⋊Dic151—21no—
42C4⋊Dic151—21no—
43C4⋊Dic151—21no—
44C4⋊Dic151C2312yes—
45Dic151⋊C4—22no—
46Dic151⋊C4—22no—
47C22⋊Dic151—22no—
48C4×Dic151—22no—
49C2×Q8×C151—21no—
50C2×Q8×C151C2312yes—
51C22×C4×C151D411yescharacteristic
52C22×C4×C151D411yescharacteristic
53C22×C4×C151C2311yescharacteristic
54C4⋊C4×C151—21no—
55C4⋊C4×C151—21no—
56C4⋊C4×C151—21no—
57C4⋊C4×C151—22no—
58C4⋊C4×C151—22no—
59C4⋊C4×C151C2312yes—
60C22⋊C4×C151—22no—
61C42×C151—22no—
62C42×C151D411yescharacteristic
63C42×C151D411yescharacteristic
64C42×C151C2311yescharacteristic
65C42×C151C2311yescharacteristic
66Dic302—24no—
67Dic302—42no—
68C2×Dic151—22no—
69C2×Dic151—22no—
70C151⋊C8—22no—
71C151⋊C8#4114yes—
72C23×C151C2×D411yescharacteristic
73Q8×C151—24no—
74Q8×C151—42no—
75C2×C4×C151—22no—
76C2×C4×C151—22no—
77C2×C4×C151—22no—
78C2×C4×C151—22no—
79C2×C4×C151—22no—
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151C2×D411yescharacteristic
83C2×C4×C151C2×D411yescharacteristic
84C2×C4×C151C2×D411yescharacteristic
85C2×C4×C151C2411yescharacteristic
86C22×C151—21no—
87C22×C151—21no—
88C22×C151—21no—
89C22×C151C22×D411yescharacteristic
90C4×C151—21no—
91C4×C151—21no—
92C4×C151—21no—
93C4×C151—42no—
94C4×C151—42no—
95C4×C151#13712yes—
96C4×C151#13712yes—
97C4×C151C2×#4112yes—
98Dic151—42no—
99Dic151—42no—
100C2×C151—41no—
101C2×C151#53211yescharacteristic
102C2×C151C2×#13711yescharacteristic
103C2×C151C2×#13711yescharacteristic
104C151#318511yescharacteristic, complemented, Sylow
105#3185—1511nomaximal, Sylow
106#533—1511no—
107#533D15111yescharacteristic
108#498—1511no—
109#494—1511no—
110#487—1511no—
111#487—1511no—
112#470—1514no—
113#441—1514no—
114C4×M16—1511no—
115C2×Q16—1514no—
116C2×M16—1512no—
117C4⋊Q8—1511no—
118C4⋊Q8—1511no—
119C4⋊Q8C2×D15111yescharacteristic
120C4⋊Q8C2×D15111yescharacteristic
121#125—21no—
122#125—3021no—
123C22⋊Q8—21no—
124C22⋊Q8—3021no—
125C22⋊Q8—1512no—
126C22⋊Q8C2×D15112yes—
127C4×Q8—21no—
128C4×Q8—3021no—
129C4×Q8—1512no—
130C4×Q8C2×D15112yes—
131#117—21no—
132#117—3021no—
133C2×C42C2×D15111yescharacteristic
134#106—1514no—
135#103—1514no—
136#103—1514no—
137#97—1512no—
138C4×C8—1511no—
139C4×C8—1511no—
140C2×Q8—21no—
141C2×Q8—3021no—
142C2×Q8—1512no—
143C2×Q8C22×D15112yes—
144C22×C4C22⋊D15111yescharacteristic
145C22×C4C22⋊D15111yescharacteristic
146C22×C4C22×D15111yescharacteristic
147Q16—3028no—
148M16—3024no—
149C2×C8—1512no—
150C2×C8—1512no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—3022no—
157C4⋊C4—3022no—
158C4⋊C4—3021no—
159C4⋊C4—3021no—
160C4⋊C4—3021no—
161C4⋊C4—1512no—
162C4⋊C4C22×D15112yes—
163C22⋊C4—22no—
164C22⋊C4—3022no—
165C42—22no—
166C42—3022no—
167C42C22⋊D15111yescharacteristic
168C42C22⋊D15111yescharacteristic
169C42C22×D15111yescharacteristic
170C42C22×D15111yescharacteristic
171C23C2×C22⋊D15111yescharacteristic
172Q8—24no—
173Q8—42no—
174Q8—3024no—
175Q8—6042no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—3022no—
182C2×C4—3022no—
183C2×C4C2×C22⋊D15111yescharacteristic
184C2×C4C2×C22⋊D15111yescharacteristic
185C2×C4C2×C22⋊D15111yescharacteristic
186C2×C4C2×C22⋊D15111yescharacteristic
187C2×C4C2×C22⋊D15111yescharacteristic
188C2×C4C23×D15111yescharacteristic
189C8—3022no—
190C8—1514no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22C22×C22⋊D15111yescharacteristic
195C4—21no—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—42no—
200C4—6042no—
201C4—6042no—
202C4#1801276912yes—
203C4#1801277012yes—
204C4#41×D15112yes—
205C2—41no—
206C2#2375275811yescharacteristic
207C2C2×#1801276911yescharacteristic
208C2C2×#1801277011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#533×C151C2
socleC22×C151C22×D4
prime radicalC23×C151C2×D4
hypercenter#533D151
hypocenterC151#3185
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #23752608C2semidirect
3. #23752591C2semidirect
4. #23752564C2semidirect
5. #23752562C2semidirect
7. #23752317C2semidirect
104. C151#3185semidirect

Maximal subgroups

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

subgroupindex
#237527692
#237526082
#237525912
#237525642
#237525622
#237524682
#237523172
C4×#145589882
#533×C1512
#3185151