Finite Group Databasebeta

← #34070237

Subgroups — #34070237

Order 19328.

638 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 75 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#23752774C211yesmaximal, characteristic, complemented
2C2×#18012709C212yesmaximal, complemented
3C2×#18012653C212yesmaximal, complemented
4#23752067C211yesmaximal, characteristic, complemented
5#342×C151C211yesmaximal, characteristic, complemented
6C24×D151C2211yescharacteristic
7C22×D604—22no—
8C22×C22⋊D151C2212yes—
9#18012723—22no—
10#18012713—22no—
11#18012709—24no—
12#18012709—22no—
13#18012709—24no—
14C2×C22⋊Dic151C2211yescharacteristic
15C2×(C2×D151)⋊C4—22no—
16C2×(C2×D151)⋊C4—22no—
17#18012653—24no—
18C2×C22⋊C4×C151C2211yescharacteristic
19C2×C22⋊C4×C151C2212yes—
20C23×D151—21no—
21C23×D151—22no—
22C23×D151—22no—
23C23×D151—21no—
24C23×D151—44no—
25C23×D151D412yescomplemented
26C23×D151D412yescomplemented
27C2×D604—28no—
28C2×D604—22no—
29C2×D604—48no—
30C2×C22⋊D151—22no—
31C2×C22⋊D151—22no—
32C2×C22⋊D151—22no—
33C2×C22⋊D151—22no—
34C2×C22⋊D151—22no—
35C2×C22⋊D151—22no—
36C22×Dic151—21no—
37C22×Dic151D412yescomplemented
38C4⋊Dic151—22no—
39C22⋊Dic151—22no—
40(C2×D151)⋊C4—28no—
41(C2×D151)⋊C4—24no—
42(C2×D151)⋊C4—44no—
43C24×C151C2311yescharacteristic
44C22×C4×C151—22no—
45C22×C4×C151D412yescomplemented
46C22⋊C4×C151—22no—
47C22⋊C4×C151—22no—
48C22⋊C4×C151D414yescomplemented
49C22×D151—24no—
50C22×D151—28no—
51C22×D151—24no—
52C22×D151—22no—
53C22×D151—22no—
54C22×D151—22no—
55C22×D151—22no—
56C22×D151—44no—
57C22×D151—48no—
58C22×D151—44no—
59C22×D151—42no—
60C22×D151—44no—
61C22×D151—41no—
62C22×D151—42no—
63C22×D151—41no—
64C22×D151—44no—
65D604—416no—
66D604—82no—
67C22⋊D151—42no—
68C22⋊D151—42no—
69C22⋊D151—42no—
70C22⋊D151—42no—
71C2×Dic151—22no—
72C2×Dic151—22no—
73C2×Dic151—22no—
74C2×Dic151—42no—
75C2×Dic151—41no—
76C23×C151—42no—
77C23×C151C2×D412yes—
78C23×C151C2×D411yescharacteristic
79C23×C151C2×D411yescharacteristic
80C23×C151C2×D412yes—
81C23×C151#4111yescharacteristic
82C2×C4×C151—22no—
83C2×C4×C151—24no—
84C2×C4×C151—44no—
85C2×C4×C151—42no—
86C22×C151—22no—
87C22×C151—24no—
88C22×C151—41no—
89C22×C151—42no—
90C22×C151—41no—
91C22×C151#12012yes—
92C22×C151#12011yescharacteristic
93C22×C151#12112yes—
94C22×C151#12111yescharacteristic
95C22×C151#12711yescharacteristic
96C2×D151—28no—
97C2×D151—24no—
98C2×D151—44no—
99C2×D151—44no—
100C2×D151—42no—
101C2×D151—48no—
102C2×D151—42no—
103C2×D151—44no—
104C2×D151—44no—
105C2×D151—42no—
106C2×D151—44no—
107C2×D151—82no—
108C4×C151—44no—
109C4×C151—42no—
110Dic151—42no—
111Dic151—81no—
112C2×C151—21no—
113C2×C151—22no—
114C2×C151—21no—
115C2×C151—22no—
116C2×C151#39211yescharacteristic
117C2×C151B(4,𝔽2)12yes—
118D151—44no—
119D151—82no—
120C151#202111yescharacteristic, complemented, Sylow
121#2021—1511nomaximal, Sylow
122#534—1511no—
123C2×#120—1512no—
124C2×#99—1512no—
125#379—1511no—
126#342D15111yescharacteristic, complemented
127C25—1511no—
128C22×D4—3022no—
129C22×D4—1512no—
130#123—3022no—
131#121—3022no—
132#120—3024no—
133#120—3022no—
134#120—3024no—
135C2×C22⋊C4—3022no—
136C2×C22⋊C4—3022no—
137C2×C22⋊C4—1511no—
138C2×C22⋊C4C2×D15111yescharacteristic
139C2×C22⋊C4C2×D15112yes—
140#99—3024no—
141C24—3022no—
142C24—3021no—
143C24—3022no—
144C24—3021no—
145C24—6044no—
146C24—1512no—
147C24—1512no—
148C24C22×D15111yescharacteristic
149C2×D4—3028no—
150C2×D4—3022no—
151C2×D4—3022no—
152C2×D4—3022no—
153C2×D4—3022no—
154C2×D4—3022no—
155C2×D4—3022no—
156C2×D4—3022no—
157C2×D4—6048no—
158C22×C4—22no—
159C22×C4—3021no—
160C22×C4—1512no—
161C22×C4D60412yescomplemented
162C4⋊C4—3022no—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—3028no—
166C22⋊C4—3024no—
167C22⋊C4—3022no—
168C22⋊C4—6044no—
169C22⋊C4D60414yescomplemented
170C23—42no—
171C23—3024no—
172C23—3028no—
173C23—3024no—
174C23—3022no—
175C23—3022no—
176C23—3022no—
177C23—3022no—
178C23—6042no—
179C23—6044no—
180C23—6044no—
181C23—6044no—
182C23—6048no—
183C23—6044no—
184C23—6041no—
185C23—6042no—
186C23—6041no—
187C23D4×D15112yes—
188C23D4×D15111yescharacteristic
189C23C2×D60411yescharacteristic
190C23C2×D60412yes—
191C23#1455900511yescharacteristic
192D4—60416no—
193D4—6042no—
194D4—6042no—
195D4—6042no—
196D4—6042no—
197D4—12082no—
198C2×C4—24no—
199C2×C4—22no—
200C2×C4—44no—
201C2×C4—42no—
202C2×C4—3022no—
203C2×C4—3022no—
204C2×C4—3022no—
205C2×C4—6042no—
206C2×C4—6041no—
207C22—22no—
208C22—24no—
209C22—41no—
210C22—42no—
211C22—41no—
212C22—3028no—
213C22—3024no—
214C22—6044no—
215C22—6044no—
216C22—6042no—
217C22—6048no—
218C22—6044no—
219C22—6042no—
220C22—6044no—
221C22—6042no—
222C22—6044no—
223C22—12082no—
224C22#1801270912yes—
225C22#1801270911yescharacteristic
226C22#1801271412yes—
227C22#1801271411yescharacteristic
228C22#1801273611yescharacteristic
229C4—44no—
230C4—42no—
231C4—6042no—
232C4—12081no—
233C2—22no—
234C2—21no—
235C2—21no—
236C2—22no—
237C2—6044no—
238C2—12082no—
239C2#2375212211yescharacteristic
240C2#2375240012yes—
subgroupG/H
centerC22#18012709
commutator, cosocleC24×C151C23
FrattiniC24C22×D151
Fitting#342×C151C2
socleC22×C151#120
hypercenter#342D151
hypocenterC151#2021
LCSG ▷ C24×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #23752774C2semidirect
2. C2×#18012709C2semidirect
3. C2×#18012653C2semidirect
4. #23752067C2semidirect
5. #342×C151C2semidirect
25. C23×D151D4semidirect
26. C23×D151D4semidirect
37. C22×Dic151D4semidirect
45. C22×C4×C151D4semidirect
48. C22⋊C4×C151D4semidirect
120. C151#2021semidirect
126. #342D151semidirect
161. C22×C4D604semidirect
169. C22⋊C4D604semidirect

Maximal subgroups

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

subgroupindex
#237527742
C2×#180127092
C2×#180126532
#237520672
#342×C1512
#2021151