Finite Group Databasebeta

← #34069097

Subgroups — #34069097

Order 19328.

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

normal subgroups only

This group has 380 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×(C22⋊D151)⋊C4C211yesmaximal, characteristic
2C2×#18012653C212yesmaximal
3#23752070C212yesmaximal, complemented
4#23751979C211yesmaximal, characteristic, complemented
5#342×C151C211yesmaximal, characteristic, complemented
6C22×C22⋊D151C2211yescharacteristic
7C23×Dic151C2211yescharacteristic
8C22×C4×D151C411yescharacteristic, complemented
9(C22⋊D151)⋊C4—22no—
10(C22⋊D151)⋊C4—22no—
11C2×Dic151⋊C4—22no—
12C2×Dic151⋊C4C411yescharacteristic, complemented
13C2×C22⋊Dic151C2212yes—
14C2×(C2×D151)⋊C4C411yescharacteristic, complemented
15C2×C4×Dic151C411yescharacteristic, complemented
16#18012653—24no—
17C151⋊#95—22no—
18C2×C22⋊C4×C151C2212yes—
19C2×C22⋊C4×C151C2211yescharacteristic
20C23×D151C2×C411yescharacteristic
21C2×C22⋊D151—22no—
22C2×C22⋊D151—22no—
23C2×C22⋊D151D412yes—
24C2×C22⋊D151Q812yes—
25C22×Dic151—22no—
26C22×Dic151—42no—
27C22×Dic151C2×C411yescharacteristic
28C22×Dic151C2×C411yescharacteristic
29C22×Dic151C2×C411yescharacteristic
30C22×Dic151D412yes—
31C22×Dic151D412yes—
32C2×C4×D151—21no—
33C2×C4×D151—21no—
34C2×C4×D151—42no—
35Dic151⋊C4—22no—
36Dic151⋊C4—44no—
37C22⋊Dic151—22no—
38C22⋊Dic151—22no—
39(C2×D151)⋊C4—22no—
40C4×Dic151—21no—
41C4×Dic151—21no—
42C24×C151C2311yescharacteristic
43C22×C4×C151—22no—
44C22×C4×C151C2×C411yescharacteristic
45C22×C4×C151C2×C411yescharacteristic
46C22⋊C4×C151—22no—
47C22⋊C4×C151—22no—
48C22⋊C4×C151—22no—
49C22×D151—21no—
50C22×D151—21no—
51C22×D151—41no—
52C22×D151—41no—
53C22×D151C4⋊C412yescomplemented
54C22⋊D151—24no—
55C22⋊D151—24no—
56C2×Dic151—21no—
57C2×Dic151—21no—
58C2×Dic151—24no—
59C2×Dic151—22no—
60C2×Dic151—41no—
61C2×Dic151—42no—
62C2×Dic151—42no—
63C2×Dic151—42no—
64C2×Dic151—42no—
65C2×Dic151C22⋊C411yescharacteristic
66C2×Dic151C22⋊C412yes—
67C2×Dic151C22⋊C411yescharacteristic
68C2×Dic151C4⋊C412yescomplemented
69C4×D151—42no—
70C4×D151—42no—
71C23×C151—41no—
72C23×C151—41no—
73C23×C151C22×C411yescharacteristic
74C23×C151C2×D412yes—
75C23×C151C2×D411yescharacteristic
76C23×C151C2×Q811yescharacteristic
77C23×C151#4112yes—
78C2×C4×C151—21no—
79C2×C4×C151—21no—
80C2×C4×C151—41no—
81C2×C4×C151—41no—
82C2×C4×C151—42no—
83C2×C4×C151—42no—
84C2×C4×C151—42no—
85C22×C151—21no—
86C22×C151—22no—
87C22×C151—21no—
88C22×C151—22no—
89C22×C151—41no—
90C22×C151—41no—
91C22×C151—42no—
92C22×C151C2×C22⋊C411yescharacteristic
93C22×C151C2×C4⋊C411yescharacteristic
94C22×C151#11711yescharacteristic
95C22×C151#12112yes—
96C22×C151C22⋊Q812yes—
97C2×D151—22no—
98C2×D151—42no—
99C2×D151—41no—
100C2×D151—41no—
101C2×D151—42no—
102C4×C151—41no—
103C4×C151—41no—
104C4×C151—82no—
105Dic151—22no—
106Dic151—21no—
107Dic151—22no—
108Dic151—82no—
109Dic151#9912yescomplemented
110C2×C151—22no—
111C2×C151—21no—
112C2×C151—21no—
113C2×C151—22no—
114C2×C151#38011yescharacteristic
115C2×C151C2×#9911yescharacteristic
116C2×C151#41011yescharacteristic
117D151—42no—
118C151#179911yescharacteristic, complemented, Sylow
119#1799—1511nomaximal, Sylow
120C2×C4×D4—1511no—
121C2×#99—1512no—
122#380—1512no—
123#342—1511no—
124#342D15111yescharacteristic, complemented
125C22×D4—1511no—
126C23×C4—1511no—
127C23×C4—1511no—
128C4×D4—3022no—
129C4×D4—3022no—
130C2×C4⋊C4—3022no—
131C2×C4⋊C4—1511no—
132C2×C22⋊C4—1512no—
133C2×C22⋊C4—1511no—
134C2×C22⋊C4C2×D15112yes—
135C2×C22⋊C4C2×D15111yescharacteristic
136C2×C42—1511no—
137#99—3024no—
138#95—3022no—
139C24—1511no—
140C24C22×D15111yescharacteristic
141C2×D4—3022no—
142C2×D4—3022no—
143C2×D4—1512no—
144C2×D4—1512no—
145C22×C4—22no—
146C22×C4—3021no—
147C22×C4—3021no—
148C22×C4—3022no—
149C22×C4—6042no—
150C22×C4—6042no—
151C22×C4—1511no—
152C22×C4—1511no—
153C22×C4—1512no—
154C22×C4—1511no—
155C22×C4—1512no—
156C22×C4C4×D15111yescharacteristic
157C22×C4C4×D15111yescharacteristic
158C4⋊C4—3022no—
159C4⋊C4—6044no—
160C22⋊C4—22no—
161C22⋊C4—22no—
162C22⋊C4—22no—
163C22⋊C4—3022no—
164C22⋊C4—3022no—
165C22⋊C4—3022no—
166C42—3021no—
167C42—3021no—
168C23—41no—
169C23—41no—
170C23—3021no—
171C23—3021no—
172C23—6041no—
173C23—6041no—
174C23—1512no—
175C23C2×C4×D15111yescharacteristic
176C23D4×D15112yes—
177C23D4×D15111yescharacteristic
178C23Q8×D15111yescharacteristic
179C23#1455900412yes—
180D4—3024no—
181D4—3024no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—3021no—
190C2×C4—3021no—
191C2×C4—3024no—
192C2×C4—3022no—
193C2×C4—6042no—
194C2×C4—6042no—
195C2×C4—6042no—
196C2×C4—6041no—
197C2×C4—6042no—
198C2×C4—6042no—
199C2×C4—6042no—
200C2×C4—1511no—
201C2×C4—1512no—
202C2×C4—1512no—
203C2×C4—1511no—
204C22—22no—
205C22—21no—
206C22—22no—
207C22—21no—
208C22—41no—
209C22—41no—
210C22—42no—
211C22—3022no—
212C22—6042no—
213C22—6042no—
214C22—6041no—
215C22—6041no—
216C22C22⋊C4×D15111yescharacteristic
217C22C4⋊C4×D15111yescharacteristic
218C22#1801269611yescharacteristic
219C22#1801271212yes—
220C22#1801271712yes—
221C4—41no—
222C4—41no—
223C4—82no—
224C4—3022no—
225C4—3021no—
226C4—3022no—
227C4—1512no—
228C4—12082no—
229C2—22no—
230C2—21no—
231C2—21no—
232C2—22no—
233C2—6042no—
234C2#2375207111yescharacteristic
235C2#99×D15111yescharacteristic
236C2#2375218411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D151
commutatorC23×C151C22×C4
FrattiniC24C22×D151
Fitting#342×C151C2
socleC22×C151C2×C22⋊C4
prime radicalC22×C22⋊D151C22
cosocleC24×C151C23
hypercenter#342D151
hypocenterC151#1799
LCSG ▷ C23×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. #23752070C2semidirect
4. #23751979C2semidirect
5. #342×C151C2semidirect
8. C22×C4×D151C4semidirect
12. C2×Dic151⋊C4C4semidirect
14. C2×(C2×D151)⋊C4C4semidirect
15. C2×C4×Dic151C4semidirect
53. C22×D151C4⋊C4semidirect
68. C2×Dic151C4⋊C4semidirect
109. Dic151#99semidirect
118. C151#1799semidirect
124. #342D151semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D151)⋊C42
C2×#180126532
#237520702
#237519792
#342×C1512
#1799151