Finite Group Databasebeta

← #34069512

Subgroups — #34069512

Order 19328.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#18012727C211yesmaximal, characteristic
2#23752689C211yesmaximal, characteristic, complemented
3#23752218C211yesmaximal, characteristic
4#23752216C211yesmaximal, characteristic
5C2×#18012657C211yesmaximal, characteristic, complemented
6#23751972C211yesmaximal, characteristic, complemented
7#339×C151C211yesmaximal, characteristic, complemented
8C22×Dic302C2211yescharacteristic
9C22×D604C2211yescharacteristic
10C2×#14558988C2211yescharacteristic
11#18012727—22no—
12#18012727C414yescomplemented
13C4×Dic302—22no—
14#18012704—22no—
15#18012698C2211yescharacteristic
16#18012695—22no—
17C2×(C2×D151)⋊C4—22no—
18#18012661—22no—
19#18012659—22no—
20#18012657—22no—
21C2×M16×C151C2211yescharacteristic
22#117×C151C2211yescharacteristic
23C2×C42×C151C2211yescharacteristic
24C23×D151—21no—
25C2×Dic302—21no—
26C2×Dic302—21no—
27C2×Dic302—21no—
28C2×Dic302—21no—
29C2×Dic302C2×C412yes—
30C2×Dic302D412yes—
31C2×D604—21no—
32C2×D604—21no—
33C2×D604—21no—
34C2×D604—21no—
35C2×D604—21no—
36C2×D604C2×C412yes—
37C22×Dic151D412yes—
38#14558988—21no—
39#14558988—21no—
40C2×C151⋊C8—21no—
41C4⋊Dic151D412yes—
42Dic151⋊C4—24no—
43C22⋊Dic151—21no—
44(C2×D151)⋊C4—28no—
45C4×Dic151—24no—
46C4×Dic151—21no—
47C22×C4×C151—21no—
48C22×C4×C151C2311yescharacteristic
49M16×C151—21no—
50M16×C151—21no—
51C2×C8×C151—21no—
52C4⋊C4×C151D412yes—
53C22⋊C4×C151—21no—
54C42×C151—21no—
55C42×C151—21no—
56C42×C151C2×C412yes—
57C22×D151—22no—
58C22×D151—44no—
59C22×D151—41no—
60C22×D151—41no—
61Dic302—22no—
62Dic302—22no—
63Dic302—22no—
64Dic302—22no—
65D604—22no—
66D604—22no—
67D604—41no—
68D604—41no—
69C2×Dic151—22no—
70C2×Dic151—22no—
71C2×Dic151—22no—
72C2×Dic151C22⋊C414yes—
73C151⋊C8—41no—
74C23×C151C2×D411yescharacteristic
75C2×C4×C151—22no—
76C2×C4×C151—22no—
77C2×C4×C151—42no—
78C2×C4×C151C22×C411yescharacteristic
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151#4111yescharacteristic
83C2×C4×C151#4111yescharacteristic
84C8×C151—41no—
85C22×C151—22no—
86C22×C151C2×C22⋊C411yescharacteristic
87C22×C151#12011yescharacteristic
88C22×C151#12311yescharacteristic
89C2×D151—44no—
90C2×D151—42no—
91C2×D151—82no—
92C2×D151—82no—
93C4×C151—42no—
94C4×C151—42no—
95C4×C151C4×D411yescharacteristic
96C4×C151C4×D411yescharacteristic
97C4×C151#12111yescharacteristic
98C4×C151#12111yescharacteristic
99Dic151—24no—
100Dic151—42no—
101C2×C151—21no—
102C2×C151—21no—
103C2×C151#38611yescharacteristic
104C2×C151#45412yes—
105D151—82no—
106C151#188811yescharacteristic, complemented, Sylow
107#1888—1511nomaximal, Sylow
108C2×#124—1511no—
109#519—1511no—
110#418—1511no—
111#418—1511no—
112C2×#101—1511no—
113#339—1511no—
114#339D15111yescharacteristic, complemented
115C22×Q8—1511no—
116C22×D4—1511no—
117C2×M16—1511no—
118C2×M16C2×D15111yescharacteristic
119#124—3022no—
120#124—1514no—
121C4×Q8—3022no—
122C4×Q8—3022no—
123#117—3022no—
124#117—1511no—
125#117C2×D15111yescharacteristic
126C2×C22⋊C4—3022no—
127C2×C42C2×D15111yescharacteristic
128#102—3022no—
129#102—3022no—
130#101—3022no—
131C24—3021no—
132C2×Q8—3021no—
133C2×Q8—3021no—
134C2×Q8—3021no—
135C2×Q8—3021no—
136C2×Q8—1512no—
137C2×Q8—1512no—
138C2×D4—3021no—
139C2×D4—3021no—
140C2×D4—3021no—
141C2×D4—3021no—
142C2×D4—3021no—
143C2×D4—1512no—
144C22×C4—21no—
145C22×C4—1512no—
146C22×C4C22×D15111yescharacteristic
147M16—21no—
148M16—21no—
149M16—3021no—
150M16—3021no—
151C2×C8—21no—
152C2×C8—3021no—
153C4⋊C4—3024no—
154C4⋊C4—1512no—
155C4⋊C4D60412yes—
156C22⋊C4—21no—
157C22⋊C4—3028no—
158C22⋊C4—3021no—
159C42—21no—
160C42—21no—
161C42—3024no—
162C42—3021no—
163C42C4×D15112yes—
164C23—3022no—
165C23—6044no—
166C23—6041no—
167C23—6041no—
168C23D4×D15111yescharacteristic
169Q8—3022no—
170Q8—3022no—
171Q8—3022no—
172Q8—3022no—
173D4—3022no—
174D4—3022no—
175D4—6041no—
176D4—6041no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—3022no—
181C2×C4—3022no—
182C2×C4—3022no—
183C2×C4—1514no—
184C2×C4C2×C4×D15111yescharacteristic
185C2×C4D4×D15111yescharacteristic
186C2×C4D4×D15111yescharacteristic
187C2×C4C2×D60411yescharacteristic
188C2×C4#1455900411yescharacteristic
189C2×C4#1455900511yescharacteristic
190C8—41no—
191C8—6041no—
192C22—22no—
193C22—6044no—
194C22—6042no—
195C22—12082no—
196C22—12082no—
197C22C22⋊C4×D15111yescharacteristic
198C22#1801270911yescharacteristic
199C22#1801272411yescharacteristic
200C4—42no—
201C4—42no—
202C4—3024no—
203C4—6042no—
204C4#1801270111yescharacteristic
205C4C4×D60411yescharacteristic
206C4#1801271211yescharacteristic
207C4#1801271411yescharacteristic
208C2—21no—
209C2—21no—
210C2—12082no—
211C2#2375209011yescharacteristic
212C2#2375238612yes—
subgroupG/H
centerC22#18012709
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#339×C151C2
socleC22×C151#120
prime radicalC22×D604C22
cosocleC22×C4×C151C23
hypercenter#339D151
hypocenterC151#1888
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #23752689C2semidirect
5. C2×#18012657C2semidirect
6. #23751972C2semidirect
7. #339×C151C2semidirect
12. #18012727C4semidirect
106. C151#1888semidirect
114. #339D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127272
#237526892
#237522182
#237522162
C2×#180126572
#237519722
#339×C1512
#1888151