Finite Group Databasebeta

← #34069664

Subgroups — #34069664

Order 19328.

240 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 105 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×C8×Dic151C211yesmaximal, characteristic
2C4×Dic151⋊C4C211yesmaximal, characteristic
3#23751967C211yesmaximal, characteristic
4#23751966C211yesmaximal, characteristic
5#23751966C211yesmaximal, characteristic
6#23751966C211yesmaximal, characteristic
7C2×C4⋊C8×C151C211yesmaximal, characteristic
8C22×C151⋊C8C2211yescharacteristic
9C22×C151⋊C8C2211yescharacteristic
10C2×Dic151⋊C4C411yescharacteristic
11C2×Dic151⋊C4C411yescharacteristic
12C2×C4×Dic151C2211yescharacteristic
13C2×C4×Dic151C2211yescharacteristic
14C8×Dic151—22no—
15C151⋊#95C411yescharacteristic
16C151⋊#95C411yescharacteristic
17C22×C8×C151C2211yescharacteristic
18C22×C8×C151C2211yescharacteristic
19C2×C42×C151C2211yescharacteristic
20C4⋊C8×C151—22no—
21C22×Dic151C2×C411yescharacteristic
22C22×Dic151C2×C411yescharacteristic
23C22×Dic151C2×C411yescharacteristic
24C22×Dic151C2×C411yescharacteristic
25C2×C151⋊C8—21no—
26C2×C151⋊C8—21no—
27C2×C151⋊C8—21no—
28C2×C151⋊C8—21no—
29C2×C151⋊C8—21no—
30C2×C151⋊C8Q812yes—
31Dic151⋊C4—22no—
32Dic151⋊C4C814yescomplemented
33C4×Dic151—21no—
34C4×Dic151—21no—
35C4×Dic151—21no—
36C4×Dic151—21no—
37C22×C4×C151C2×C411yescharacteristic
38C22×C4×C151C2×C411yescharacteristic
39C22×C4×C151C2311yescharacteristic
40C2×C8×C151—21no—
41C2×C8×C151—21no—
42C2×C8×C151—21no—
43C2×C8×C151—21no—
44C2×C8×C151—21no—
45C2×C8×C151D412yes—
46C42×C151—21no—
47C42×C151—21no—
48C2×Dic151—21no—
49C2×Dic151—21no—
50C2×Dic151—21no—
51C2×Dic151—21no—
52C2×Dic151—21no—
53C2×Dic151—21no—
54C2×Dic151—21no—
55C2×Dic151—21no—
56C2×Dic151—21no—
57C2×Dic151C2×C812yes—
58C2×Dic151C2×C812yes—
59C2×Dic151M1612yes—
60C151⋊C8—22no—
61C151⋊C8—41no—
62C23×C151C22×C411yescharacteristic
63C2×C4×C151—21no—
64C2×C4×C151—21no—
65C2×C4×C151—21no—
66C2×C4×C151—21no—
67C2×C4×C151—21no—
68C2×C4×C151C2×C812yes—
69C2×C4×C151C2×D411yescharacteristic
70C2×C4×C151C2×Q811yescharacteristic
71C2×C4×C151#4111yescharacteristic
72C2×C4×C151#4111yescharacteristic
73C2×C4×C151#4111yescharacteristic
74C2×C4×C151#4111yescharacteristic
75C8×C151—22no—
76C8×C151—41no—
77C22×C151#11711yescharacteristic
78C22×C151C4×D411yescharacteristic
79C22×C151C4×Q811yescharacteristic
80C22×C151C22×C811yescharacteristic
81C22×C151C2×M1611yescharacteristic
82C22×C151#13111yescharacteristic
83C22×C151#13111yescharacteristic
84C4×C151—22no—
85C4×C151—41no—
86C4×C151C22⋊Q811yescharacteristic
87C4×C151#12311yescharacteristic
88C4×C151#12511yescharacteristic
89C4×C151#12611yescharacteristic
90Dic151—22no—
91Dic151—22no—
92Dic151—22no—
93Dic151—41no—
94C2×C151#38711yescharacteristic
95C2×C151#43111yescharacteristic
96C2×C151#43311yescharacteristic
97C2×C151C8×D411yescharacteristic
98C2×C151#43511yescharacteristic
99C2×C151C8×Q811yescharacteristic
100C2×C151#44611yescharacteristic
101C151#191611yescharacteristic, complemented, Sylow
102#1916—1511nomaximal, Sylow
103C2×C4⋊C8D15111yescharacteristic
104C2×C4×C8—1511no—
105C4×C4⋊C4—1511no—
106#336—1511no—
107#336—1511no—
108#336—1511no—
109#336—1511no—
110C22×C8—1511no—
111C22×C8—1511no—
112C22×C8C2×D15111yescharacteristic
113C22×C8C2×D15111yescharacteristic
114C2×C4⋊C4—1511no—
115C2×C4⋊C4—1511no—
116C2×C42—1511no—
117C2×C42—1511no—
118C2×C42C2×D15111yescharacteristic
119C4⋊C8—22no—
120C4×C8—3022no—
121#95—1511no—
122#95—1511no—
123C22×C4—1511no—
124C22×C4—1511no—
125C22×C4—1511no—
126C22×C4—1511no—
127C22×C4C4×D15111yescharacteristic
128C22×C4C4×D15111yescharacteristic
129C22×C4C22×D15111yescharacteristic
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—3021no—
136C2×C8—3021no—
137C2×C8—3021no—
138C2×C8—3021no—
139C2×C8—3021no—
140C2×C8—1512no—
141C2×C8C22⋊D15112yes—
142C4⋊C4—3022no—
143C4⋊C4—1514no—
144C42—21no—
145C42—21no—
146C42—3021no—
147C42—3021no—
148C42—3021no—
149C42—3021no—
150C23C2×C4×D15111yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—3021no—
157C2×C4—3021no—
158C2×C4—3021no—
159C2×C4—3021no—
160C2×C4—3021no—
161C2×C4—3021no—
162C2×C4—3021no—
163C2×C4—3021no—
164C2×C4—3021no—
165C2×C4—1512no—
166C2×C4—1512no—
167C2×C4—1512no—
168C2×C4C8×D15112yes—
169C2×C4C2×C22⋊D15111yescharacteristic
170C2×C4Q8×D15111yescharacteristic
171C2×C4#1455900311yescharacteristic
172C2×C4#1455900311yescharacteristic
173C2×C4#1455900411yescharacteristic
174C2×C4#1455900511yescharacteristic
175C8—22no—
176C8—41no—
177C8—3022no—
178C8—6041no—
179C22#1801269711yescharacteristic
180C22C4×C22⋊D15111yescharacteristic
181C22#1801270411yescharacteristic
182C22C2×C8×D15111yescharacteristic
183C22M16×D15111yescharacteristic
184C22#1801274511yescharacteristic
185C22#1801274711yescharacteristic
186C4—22no—
187C4—41no—
188C4—3022no—
189C4—3022no—
190C4—3022no—
191C4—6041no—
192C4#1801271511yescharacteristic
193C4#1801272011yescharacteristic
194C4#1801272911yescharacteristic
195C4#1801273411yescharacteristic
196C2#2375209311yescharacteristic
197C2#2375226411yescharacteristic
198C2#2375227211yescharacteristic
199C2C8×C22⋊D15111yescharacteristic
200C2#2375228111yescharacteristic
201C2#2375233611yescharacteristic
202C2#2375234111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D151
commutatorC22×C151C22×C8
FittingC2×C4⋊C8×C151C2
socle, prime radicalC23×C151C22×C4
cosocleC22×C4×C151C23
hypercenterC2×C4⋊C8D151
hypocenterC151#1916
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
32. Dic151⋊C4C8semidirect
101. C151#1916semidirect

Maximal subgroups

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

subgroupindex
C2×C8×Dic1512
C4×Dic151⋊C42
#237519672
#237519662
C2×C4⋊C8×C1512
#1916151