Finite Group Databasebeta

← #34070250

Subgroups — #34070250

Order 19328.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#18012738C211yesmaximal, characteristic
2C2×#18012664C211yesmaximal, characteristic
3C2×#18012662C211yesmaximal, characteristic
4#23752117C211yesmaximal, characteristic
5#23751974C211yesmaximal, characteristic
6#23751966C211yesmaximal, characteristic
7#340×C151C211yesmaximal, characteristic
8C22×Dic302—21no—
9C22×Dic302C2211yescharacteristic
10C22×C151⋊C8C2211yescharacteristic
11#18012738—22no—
12#18012738—22no—
13C2×C4⋊Dic151C2211yescharacteristic
14C2×Dic151⋊C4—21no—
15C2×C4×Dic151C2211yescharacteristic
16#18012664—22no—
17#18012662—22no—
18C151⋊#95—21no—
19C151⋊#95—21no—
20C22×C8×C151C2211yescharacteristic
21C2×C4⋊C4×C151C2211yescharacteristic
22C2×C4⋊C4×C151C2211yescharacteristic
23C2×Dic302—24no—
24C2×Dic302—21no—
25C2×Dic302—21no—
26C2×Dic302—21no—
27C2×Dic302—21no—
28C2×Dic302—21no—
29C2×Dic302—42no—
30C2×Dic302—42no—
31C2×Dic302Q812yescomplemented
32C22×Dic151—21no—
33C22×Dic151—21no—
34C22×Dic151D411yescharacteristic
35C22×Dic151D411yescharacteristic
36C2×C151⋊C8—21no—
37C2×C151⋊C8—21no—
38C2×C151⋊C8—21no—
39C4⋊Dic151—21no—
40C4⋊Dic151D412yes—
41Dic151⋊C4—24no—
42C4×Dic151—21no—
43C4×Dic151—21no—
44C22×C4×C151—21no—
45C22×C4×C151—21no—
46C22×C4×C151C2311yescharacteristic
47C2×C8×C151—21no—
48C2×C8×C151—21no—
49C2×C8×C151—21no—
50C4⋊C4×C151—21no—
51C4⋊C4×C151—21no—
52C4⋊C4×C151—21no—
53C4⋊C4×C151D412yes—
54Dic302—22no—
55Dic302—22no—
56Dic302—48no—
57Dic302—41no—
58Dic302—41no—
59C2×Dic151—21no—
60C2×Dic151—21no—
61C2×Dic151—21no—
62C2×Dic151—21no—
63C2×Dic151—22no—
64C2×Dic151—22no—
65C2×Dic151—41no—
66C2×Dic151—41no—
67C2×Dic151—41no—
68C2×Dic151—41no—
69C2×Dic151SD1612yes—
70C2×Dic151Q1612yes—
71C151⋊C8—41no—
72C23×C151C2×D411yescharacteristic
73C2×C4×C151—22no—
74C2×C4×C151—41no—
75C2×C4×C151—41no—
76C2×C4×C151—41no—
77C2×C4×C151—41no—
78C2×C4×C151—41no—
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×Q811yescharacteristic
82C2×C4×C151#4111yescharacteristic
83C2×C4×C151#4111yescharacteristic
84C2×C4×C151#4111yescharacteristic
85C8×C151—41no—
86C22×C151#12011yescharacteristic
87C22×C151C22⋊Q811yescharacteristic
88C22×C151#12411yescharacteristic
89C22×C151C2×SD1611yescharacteristic
90C22×C151C2×Q1611yescharacteristic
91C22×C151AGL(1,ℤ/8)11yescharacteristic
92C22×C151#13711yescharacteristic
93C4×C151—42no—
94C4×C151—81no—
95C4×C151C22⋊Q811yescharacteristic
96C4×C151C22⋊Q811yescharacteristic
97C4×C151#12411yescharacteristic
98C4×C151#12411yescharacteristic
99Dic151—22no—
100Dic151—22no—
101Dic151—42no—
102Dic151—42no—
103C2×C151#39311yescharacteristic
104C2×C151#45011yescharacteristic
105C2×C151#45111yescharacteristic
106C2×C151#47511yescharacteristic
107C2×C151#47711yescharacteristic
108C2×C151#48711yescharacteristic
109C2×C151#48911yescharacteristic
110C151#202411yescharacteristic, complemented, Sylow
111#2024—1511nomaximal, Sylow
112C2×C4⋊Q8—1511no—
113C2×#103—1511no—
114C2×#103—1511no—
115#391—1511no—
116#340—1511no—
117#340D15111yescharacteristic
118#336—1511no—
119C22×Q8—3021no—
120C22×Q8—1511no—
121C22×C8—1511no—
122C22×C8C2×D15111yescharacteristic
123C4⋊Q8—3022no—
124C4⋊Q8—3022no—
125C2×C4⋊C4—3021no—
126C2×C4⋊C4—1511no—
127C2×C4⋊C4C2×D15111yescharacteristic
128C2×C4⋊C4C2×D15111yescharacteristic
129C2×C42—1511no—
130#103—3022no—
131#103—3022no—
132#95—3021no—
133#95—3021no—
134C2×Q8—3024no—
135C2×Q8—3021no—
136C2×Q8—3021no—
137C2×Q8—3021no—
138C2×Q8—3021no—
139C2×Q8—3021no—
140C2×Q8—6042no—
141C2×Q8—6042no—
142C2×Q8—1512no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—3021no—
146C22×C4—3021no—
147C22×C4—1511no—
148C22×C4—1511no—
149C22×C4C22×D15111yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—3021no—
154C2×C8—3021no—
155C2×C8—3021no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—3024no—
160C4⋊C4—3021no—
161C4⋊C4—1512no—
162C4⋊C4D60412yes—
163C42—3021no—
164C42—3021no—
165C23D4×D15111yescharacteristic
166Q8—3022no—
167Q8—3022no—
168Q8—6048no—
169Q8—6041no—
170Q8—6041no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—3021no—
178C2×C4—3021no—
179C2×C4—3021no—
180C2×C4—3021no—
181C2×C4—3022no—
182C2×C4—3022no—
183C2×C4—6041no—
184C2×C4—6041no—
185C2×C4—6041no—
186C2×C4—6041no—
187C2×C4—1512no—
188C2×C4—1512no—
189C2×C4D4×D15111yescharacteristic
190C2×C4C2×D60411yescharacteristic
191C2×C4Q8×D15111yescharacteristic
192C2×C4#1455900311yescharacteristic
193C2×C4#1455900411yescharacteristic
194C2×C4#1455900411yescharacteristic
195C8—41no—
196C8—6041no—
197C22#1801270911yescharacteristic
198C22#1801271711yescharacteristic
199C22#1801272511yescharacteristic
200C22SD16×D15111yescharacteristic
201C22Q16×D15111yescharacteristic
202C22#1801276311yescharacteristic
203C22#1801276811yescharacteristic
204C4—42no—
205C4—81no—
206C4—3022no—
207C4—3022no—
208C4—6042no—
209C4—6042no—
210C4#1801271711yescharacteristic
211C4#1801271911yescharacteristic
212C4#1801272511yescharacteristic
213C4#1801272711yescharacteristic
214C2#2375212511yescharacteristic
215C2#2375236411yescharacteristic
216C2#2375236911yescharacteristic
217C2#2375249611yescharacteristic
218C2#2375250611yescharacteristic
219C2#2375256111yescharacteristic
220C2#2375257011yescharacteristic
subgroupG/H
centerC23D4×D151
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#340×C151C2
socle, prime radicalC23×C151C2×D4
hypercenter#340D151
hypocenterC151#2024
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
31. C2×Dic302Q8semidirect
110. C151#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#180127382
C2×#180126642
C2×#180126622
#237521172
#237519742
#237519662
#340×C1512
#2024151