Finite Group Databasebeta

← #34077394

Subgroups — #34077394

Order 19328.

1068 conjugacy classes of subgroups; only the 201 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 201 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
1C23×C4×D151C211yesmaximal, characteristic
2C2×#18012715C212yesmaximal, complemented
3#23752084C212yesmaximal, complemented
4#23752083C214yesmaximal, complemented
5#23752072C211yesmaximal, characteristic, complemented
6#23752069C212yesmaximal, complemented
7#23752067C212yesmaximal
8C2×C22⋊Q8×C151C211yesmaximal, characteristic, complemented
9C24×D151C2211yescharacteristic
10C23×Dic151C2211yescharacteristic
11C22×C4×D151—24no—
12C22×C4×D151—28no—
13C22×C4×D151C2212yes—
14C22×C4×D151C2212yes—
15#18012715—28no—
16C2×C4⋊Dic151C2212yescomplemented
17C2×Dic151⋊C4C2214yescomplemented
18C2×C22⋊Dic151C2212yes—
19C2×(C2×D151)⋊C4C2214yes—
20C2×(C2×D151)⋊C4C2214yes—
21C151⋊#95C2214yescomplemented
22C151⋊#95C2212yescomplemented
23C22×Q8×C151C2211yescharacteristic, complemented
24C23×C4×C151C2211yescharacteristic
25C22⋊Q8×C151—24no—
26C2×C4⋊C4×C151C2211yescharacteristic, complemented
27C2×C4⋊C4×C151C2212yescomplemented
28C2×C22⋊C4×C151C2212yes—
29C23×D151—24no—
30C23×D151—24no—
31C23×D151—22no—
32C23×D151—22no—
33C23×D151Q814yescomplemented
34C23×D151C2312yes—
35C22×Dic151—24no—
36C22×Dic151—22no—
37C22×Dic151C2314yes—
38C22×Dic151C2312yes—
39C2×C4×D151—232no—
40C2×C4×D151—24no—
41C2×C4×D151—24no—
42C2×C4×D151—24no—
43C2×C4×D151—24no—
44C2×C4×D151—24no—
45C2×C4×D151D418yes—
46C4⋊Dic151—24no—
47Dic151⋊C4—28no—
48C22⋊Dic151—24no—
49(C2×D151)⋊C4—28no—
50(C2×D151)⋊C4—28no—
51C24×C151C2311yescharacteristic
52C2×Q8×C151—24no—
53C2×Q8×C151—22no—
54C22×C4×C151—24no—
55C22×C4×C151D414yes—
56C22×C4×C151C2312yes—
57C22×C4×C151C2312yes—
58C22×C4×C151C2311yescharacteristic
59C22×C4×C151C2311yescharacteristic
60C4⋊C4×C151—24no—
61C4⋊C4×C151—22no—
62C22⋊C4×C151—24no—
63C22×D151—28no—
64C22×D151—216no—
65C22×D151—28no—
66C22×D151—28no—
67C22×D151—22no—
68C22×D151—22no—
69C22×D151—22no—
70C22×D151—22no—
71C22×D151—216no—
72C22×D151C2×D414yes—
73C22×D151C2×Q814yes—
74C22×D151#4114yes—
75C2×Dic151—28no—
76C2×Dic151—22no—
77C2×Dic151—22no—
78C2×Dic151—24no—
79C2×Dic151—24no—
80C2×Dic151—24no—
81C2×Dic151C2×D414yes—
82C4×D151—216no—
83C4×D151—216no—
84C23×C151—22no—
85C23×C151—22no—
86C23×C151C2×D412yes—
87C23×C151C2×Q812yes—
88C23×C151#4112yes—
89C23×C151C2411yescharacteristic
90Q8×C151—44no—
91C2×C4×C151—22no—
92C2×C4×C151—28no—
93C2×C4×C151—24no—
94C2×C4×C151—22no—
95C2×C4×C151—22no—
96C2×C4×C151—24no—
97C2×C4×C151C2×D414yes—
98C2×C4×C151C2×D412yes—
99C2×C4×C151C2×D412yes—
100C22×C151—22no—
101C22×C151—24no—
102C22×C151—22no—
103C22×C151—24no—
104C22×C151C22⋊Q814yescomplemented
105C22×C151C22×D412yes—
106C22×C151C22×D411yescharacteristic
107C22×C151C22×Q811yescharacteristic
108C22×C151C2×#4112yes—
109C22×C151C2×#4111yescharacteristic
110C2×D151—232no—
111C2×D151—24no—
112C2×D151—24no—
113C2×D151—24no—
114C2×D151—24no—
115C2×D151—24no—
116C2×D151—24no—
117C2×D151C22⋊Q818yescomplemented
118C4×C151—22no—
119C4×C151—42no—
120C4×C151—42no—
121C4×C151#12014yes—
122Dic151—24no—
123Dic151—44no—
124C2×C151—24no—
125C2×C151C2×#12011yescharacteristic
126C2×C151C2×C22⋊Q812yes—
127C2×C151C2×C22⋊Q811yescharacteristic
128C2×C151#52511yescharacteristic
129C2×C151#52512yes—
130D151—28no—
131C151#284811yescharacteristic, complemented, Sylow
132#2848—1511nomaximal, Sylow
133C24×C4—1511no—
134C2×C22⋊Q8—1512no—
135C2×C22⋊Q8D15111yescharacteristic, complemented
136#385—1514no—
137#385—1512no—
138#380—1511no—
139#380—1512no—
140#379—1512no—
141C25—1511no—
142C22×Q8C2×D15111yescharacteristic, complemented
143C23×C4—3028no—
144C23×C4—3024no—
145C23×C4—1511no—
146C23×C4—1512no—
147C23×C4—1512no—
148C23×C4C2×D15111yescharacteristic
149C22⋊Q8—24no—
150C22⋊Q8—3028no—
151C2×C4⋊C4—1514no—
152C2×C4⋊C4—1512no—
153C2×C4⋊C4C2×D15111yescharacteristic, complemented
154C2×C4⋊C4C2×D15112yescomplemented
155C2×C22⋊C4—1512no—
156C2×C22⋊C4—1514no—
157C2×C22⋊C4—1514no—
158C2×C22⋊C4C2×D15112yes—
159#95—1512no—
160#95—1514no—
161C24—3024no—
162C24—3024no—
163C24—3022no—
164C24—3022no—
165C24—1514no—
166C24—1512no—
167C24C22×D15111yescharacteristic
168C2×Q8—24no—
169C2×Q8—22no—
170C22×C4—24no—
171C22×C4—30232no—
172C22×C4—3024no—
173C22×C4—3024no—
174C22×C4—3022no—
175C22×C4—3024no—
176C22×C4—3024no—
177C22×C4—3024no—
178C22×C4—3024no—
179C22×C4—1514no—
180C22×C4—1512no—
181C22×C4—1518no—
182C22×C4C22⋊D15114yes—
183C22×C4C22×D15112yes—
184C22×C4C22×D15112yes—
185C22×C4C22×D15111yescharacteristic
186C22×C4C22×D15111yescharacteristic
187C4⋊C4—22no—
188C4⋊C4—24no—
189C4⋊C4—3028no—
190C4⋊C4—3024no—
191C22⋊C4—24no—
192C22⋊C4—3028no—
193C22⋊C4—3028no—
194C22⋊C4—3024no—
195C23—22no—
196C23—22no—
197C23—3028no—
198C23—3028no—
199C23—30216no—
200C23—30216no—
201C23—3028no—
202C23—3022no—
203C23—3022no—
204C23—3022no—
205C23—3022no—
206C23—1514no—
207C23—1514no—
208C23—1514no—
209C23C2×C22⋊D15112yes—
210C23Q8×D15112yes—
211C23#1455900512yes—
212C23C23×D15111yescharacteristic
213Q8—44no—
214C2×C4—22no—
215C2×C4—28no—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—24no—
220C2×C4—30216no—
221C2×C4—3028no—
222C2×C4—3022no—
223C2×C4—3022no—
224C2×C4—30216no—
225C2×C4—3024no—
226C2×C4—3024no—
227C2×C4—3024no—
228C2×C4—1514no—
229C2×C4D4×D15114yes—
230C2×C4C2×C22⋊D15112yes—
231C2×C4C2×C22⋊D15112yes—
232C22—24no—
233C22—22no—
234C22—24no—
235C22—22no—
236C22—30232no—
237C22—3024no—
238C22—3024no—
239C22—3024no—
240C22—3024no—
241C22—3024no—
242C22—3024no—
243C22—1518no—
244C22#1801271514yescomplemented
245C22C2×D4×D15112yes—
246C22C22×C22⋊D15111yescharacteristic
247C22C2×Q8×D15111yescharacteristic
248C22#41×D15112yes—
249C22C2×#1455900511yescharacteristic
250C4—22no—
251C4—42no—
252C4—42no—
253C4—3024no—
254C4—6044no—
255C4#1801270714yes—
256C2—24no—
257C2—3028no—
258C2C2×#1801270711yescharacteristic
259C2C22⋊Q8×D15112yes—
260C2C2×#1801271511yescharacteristic
261C2#2375271911yescharacteristic
262C2#2375272512yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
FittingC2×C22⋊Q8×C151C2
prime radicalC24×D151C22
hypercenterC2×C22⋊Q8D151
hypocenterC151#2848
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#18012715C2semidirect
3. #23752084C2semidirect
4. #23752083C2semidirect
5. #23752072C2semidirect
6. #23752069C2semidirect
8. C2×C22⋊Q8×C151C2semidirect
16. C2×C4⋊Dic151C22semidirect
17. C2×Dic151⋊C4C22semidirect
21. C151⋊#95C22semidirect
22. C151⋊#95C22semidirect
23. C22×Q8×C151C22semidirect
26. C2×C4⋊C4×C151C22semidirect
27. C2×C4⋊C4×C151C22semidirect
33. C23×D151Q8semidirect
104. C22×C151C22⋊Q8semidirect
117. C2×D151C22⋊Q8semidirect
131. C151#2848semidirect
135. C2×C22⋊Q8D151semidirect
142. C22×Q8C2×D151semidirect
153. C2×C4⋊C4C2×D151semidirect
154. C2×C4⋊C4C2×D151semidirect
244. C22#18012715semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D1512
C2×#180127152
#237520842
#237520832
#237520722
#237520692
#237520672
C2×C22⋊Q8×C1512
#2848151