Finite Group Databasebeta

← #34069510

Subgroups — #34069510

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×#18012726C211yesmaximal, characteristic
2#23752689C211yesmaximal, characteristic, complemented
3#23752217C211yesmaximal, characteristic
4C2×#18012657C211yesmaximal, characteristic, complemented
5#23751973C211yesmaximal, characteristic, complemented
6#23751971C211yesmaximal, characteristic, complemented
7#418×C151C211yesmaximal, characteristic
8C22×Dic302C2211yescharacteristic
9C2×#14558988C2211yescharacteristic
10#18012726—22no—
11#18012726C414yescomplemented
12C4×Dic302—22no—
13#18012704—22no—
14#18012698C2211yescharacteristic
15#18012695—22no—
16C2×C22⋊Dic151—22no—
17C2×C4×Dic151C2211yescharacteristic
18#18012660—22no—
19#18012657—22no—
20C22×D4×C151C2211yescharacteristic
21C2×M16×C151C2211yescharacteristic
22#117×C151C2211yescharacteristic
23#102×C151—22no—
24C2×Dic302—21no—
25C2×Dic302—21no—
26C2×Dic302—21no—
27C2×Dic302—21no—
28C2×Dic302C2×C412yes—
29C2×Dic302D412yes—
30C22×Dic151—21no—
31C22×Dic151D412yes—
32#14558988—21no—
33#14558988—21no—
34C2×C151⋊C8—21no—
35C4⋊Dic151D412yes—
36Dic151⋊C4—24no—
37C22⋊Dic151—28no—
38C22⋊Dic151—21no—
39C4×Dic151—24no—
40C4×Dic151—21no—
41C4×Dic151—21no—
42C4×Dic151C2×C412yes—
43C24×C151—21no—
44C2×D4×C151—21no—
45C2×D4×C151—21no—
46C2×D4×C151—21no—
47C2×D4×C151—21no—
48C2×D4×C151—21no—
49C2×D4×C151C2×C412yes—
50C22×C4×C151C2311yescharacteristic
51M16×C151—21no—
52M16×C151—21no—
53C2×C8×C151—21no—
54C4⋊C4×C151D412yes—
55C22⋊C4×C151—21no—
56C42×C151—21no—
57Dic302—22no—
58Dic302—22no—
59Dic302—22no—
60Dic302—22no—
61C2×Dic151—22no—
62C2×Dic151—22no—
63C2×Dic151—22no—
64C2×Dic151—22no—
65C2×Dic151—42no—
66C2×Dic151C22⋊C414yes—
67C151⋊C8—41no—
68C23×C151—22no—
69C23×C151—44no—
70C23×C151—41no—
71C23×C151—41no—
72C23×C151C2×D411yescharacteristic
73D4×C151—22no—
74D4×C151—22no—
75D4×C151—41no—
76D4×C151—41no—
77C2×C4×C151—22no—
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×C151—44no—
87C22×C151—42no—
88C22×C151—82no—
89C22×C151—82no—
90C22×C151C2×C22⋊C411yescharacteristic
91C22×C151#12011yescharacteristic
92C22×C151#12311yescharacteristic
93C4×C151—42no—
94C4×C151C4×D411yescharacteristic
95C4×C151C4×D411yescharacteristic
96C4×C151#12111yescharacteristic
97C4×C151#12111yescharacteristic
98Dic151—24no—
99Dic151—42no—
100Dic151—42no—
101C2×C151—21no—
102C2×C151—21no—
103C2×C151—82no—
104C2×C151#38611yescharacteristic
105C2×C151#45412yes—
106C151#188811yescharacteristic, complemented, Sylow
107#1888—1511nomaximal, Sylow
108C2×#124—1511no—
109#519—1511no—
110#418—1511no—
111#418D15111yescharacteristic
112C2×#101—1511no—
113#339—1511no—
114#339—1511no—
115C22×Q8—1511no—
116C22×D4C2×D15111yescharacteristic
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×C42—1511no—
128#102—22no—
129#102—3022no—
130#101—3022no—
131C24—21no—
132C2×Q8—3021no—
133C2×Q8—3021no—
134C2×Q8—3021no—
135C2×Q8—3021no—
136C2×Q8—1512no—
137C2×Q8—1512no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4C4×D15112yes—
144C22×C4—3021no—
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⋊C4C22⋊D15112yes—
156C22⋊C4—21no—
157C22⋊C4—3021no—
158C22⋊C4—3028no—
159C42—21no—
160C42—3024no—
161C42—3021no—
162C42—3021no—
163C42—1512no—
164C23—22no—
165C23—44no—
166C23—41no—
167C23—41no—
168C23D4×D15111yescharacteristic
169Q8—3022no—
170Q8—3022no—
171Q8—3022no—
172Q8—3022no—
173D4—22no—
174D4—22no—
175D4—41no—
176D4—41no—
177C2×C4—22no—
178C2×C4—3022no—
179C2×C4—3022no—
180C2×C4—3022no—
181C2×C4—3022no—
182C2×C4—6042no—
183C2×C4—1514no—
184C2×C4C2×C4×D15111yescharacteristic
185C2×C4D4×D15111yescharacteristic
186C2×C4D4×D15111yescharacteristic
187C2×C4C2×C22⋊D15111yescharacteristic
188C2×C4#1455900311yescharacteristic
189C2×C4#1455900411yescharacteristic
190C8—41no—
191C8—6041no—
192C22—22no—
193C22—44no—
194C22—42no—
195C22—82no—
196C22—82no—
197C22C22⋊C4×D15111yescharacteristic
198C22#1801270711yescharacteristic
199C22#1801272111yescharacteristic
200C4—42no—
201C4—3024no—
202C4—6042no—
203C4—6042no—
204C4(C22⋊D151)⋊C411yescharacteristic
205C4C4×C22⋊D15111yescharacteristic
206C4#1801271011yescharacteristic
207C4#1801271211yescharacteristic
208C2—21no—
209C2—21no—
210C2—82no—
211C2#2375208811yescharacteristic
212C2#2375238312yes—
subgroupG/H
centerC22#18012707
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#418×C151C2
socleC22×C151#120
prime radicalC22×D4×C151C22
cosocleC22×C4×C151C23
hypercenter#418D151
hypocenterC151#1888
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #23752689C2semidirect
4. C2×#18012657C2semidirect
5. #23751973C2semidirect
6. #23751971C2semidirect
11. #18012726C4semidirect
106. C151#1888semidirect

Maximal subgroups

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

subgroupindex
C2×#180127262
#237526892
#237522172
C2×#180126572
#237519732
#237519712
#418×C1512
#1888151