Finite Group Databasebeta

← #34077398

Subgroups — #34077398

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×#18012719C212yesmaximal, complemented
3C2×#18012718C211yesmaximal, characteristic, complemented
4#23752087C212yesmaximal, complemented
5#23752086C214yesmaximal, complemented
6#23752069C212yesmaximal, complemented
7#23752067C212yesmaximal
8#380×C151C211yesmaximal, characteristic, complemented
9C24×D151C2211yescharacteristic
10C22×Dic302C2211yescharacteristic, complemented
11C23×Dic151C2211yescharacteristic
12C22×C4×D151—24no—
13C22×C4×D151—28no—
14C22×C4×D151C2212yes—
15C22×C4×D151C2212yes—
16#18012719—28no—
17#18012718—24no—
18C2×C4⋊Dic151C2211yescharacteristic, complemented
19C2×C4⋊Dic151C2214yescomplemented
20C2×Dic151⋊C4C2212yescomplemented
21C2×C22⋊Dic151C2212yes—
22C2×(C2×D151)⋊C4C2214yes—
23C2×(C2×D151)⋊C4C2214yes—
24C151⋊#95C2214yescomplemented
25C23×C4×C151C2211yescharacteristic
26C2×C4⋊C4×C151C2212yescomplemented
27C2×C22⋊C4×C151C2212yes—
28#95×C151C2212yescomplemented
29C23×D151—24no—
30C23×D151—24no—
31C23×D151—22no—
32C23×D151—22no—
33C23×D151Q814yescomplemented
34C23×D151C2312yes—
35C2×Dic302—22no—
36C2×Dic302—24no—
37C22×Dic151—24no—
38C22×Dic151—22no—
39C22×Dic151C2312yes—
40C22×Dic151C2312yes—
41C22×Dic151C2312yes—
42C2×C4×D151—232no—
43C2×C4×D151—24no—
44C2×C4×D151—24no—
45C2×C4×D151—24no—
46C2×C4×D151—24no—
47C2×C4×D151—24no—
48C2×C4×D151D418yes—
49C4⋊Dic151—28no—
50C4⋊Dic151—22no—
51Dic151⋊C4—24no—
52C22⋊Dic151—24no—
53(C2×D151)⋊C4—28no—
54(C2×D151)⋊C4—28no—
55C24×C151C2311yescharacteristic
56C22×C4×C151—24no—
57C22×C4×C151D414yes—
58C22×C4×C151C2314yes—
59C22×C4×C151C2311yescharacteristic
60C22×C4×C151C2311yescharacteristic
61C4⋊C4×C151—24no—
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—
75Dic302—44no—
76C2×Dic151—28no—
77C2×Dic151—22no—
78C2×Dic151—22no—
79C2×Dic151—24no—
80C2×Dic151—22no—
81C2×Dic151—22no—
82C2×Dic151—24no—
83C2×Dic151C2×D414yes—
84C4×D151—216no—
85C4×D151—216no—
86C23×C151—22no—
87C23×C151—22no—
88C23×C151C2×D412yes—
89C23×C151C2×Q812yes—
90C23×C151#4112yes—
91C23×C151C2411yescharacteristic
92C2×C4×C151—22no—
93C2×C4×C151—28no—
94C2×C4×C151—24no—
95C2×C4×C151—24no—
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—44no—
120C4×C151#12014yes—
121Dic151—24no—
122Dic151—42no—
123Dic151—42no—
124C2×C151—24no—
125C2×C151C2×#12011yescharacteristic
126C2×C151C2×C22⋊Q812yes—
127C2×C151C2×C22⋊Q811yescharacteristic
128C2×C151#52512yes—
129C2×C151#52511yescharacteristic
130D151—28no—
131C151#284811yescharacteristic, complemented, Sylow
132#2848—1511nomaximal, Sylow
133C24×C4—1511no—
134C2×C22⋊Q8—1511no—
135C2×C22⋊Q8—1512no—
136#385—1512no—
137#385—1514no—
138#380—1512no—
139#380D15111yescharacteristic, complemented
140#379—1512no—
141C25—1511no—
142C22×Q8—1511no—
143C23×C4—3028no—
144C23×C4—3024no—
145C23×C4—1511no—
146C23×C4—1512no—
147C23×C4—1512no—
148C23×C4C2×D15111yescharacteristic
149C22⋊Q8—3028no—
150C22⋊Q8—3024no—
151C2×C4⋊C4—1512no—
152C2×C4⋊C4—1511no—
153C2×C4⋊C4—1514no—
154C2×C4⋊C4C2×D15112yescomplemented
155C2×C22⋊C4—1512no—
156C2×C22⋊C4—1514no—
157C2×C22⋊C4—1514no—
158C2×C22⋊C4C2×D15112yes—
159#95—1514no—
160#95C2×D15112yescomplemented
161C24—3024no—
162C24—3024no—
163C24—3022no—
164C24—3022no—
165C24—1514no—
166C24—1512no—
167C24C22×D15111yescharacteristic
168C2×Q8—3024no—
169C2×Q8—3022no—
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—1512no—
180C22×C4—1512no—
181C22×C4—1512no—
182C22×C4—1518no—
183C22×C4D60414yes—
184C22×C4C22×D15114yes—
185C22×C4C22×D15111yescharacteristic
186C22×C4C22×D15111yescharacteristic
187C4⋊C4—24no—
188C4⋊C4—3028no—
189C4⋊C4—3024no—
190C4⋊C4—3022no—
191C22⋊C4—24no—
192C22⋊C4—3028no—
193C22⋊C4—3028no—
194C22⋊C4—3024no—
195C23—22no—
196C23—22no—
197C23—3028no—
198C23—30216no—
199C23—3028no—
200C23—30216no—
201C23—3028no—
202C23—3022no—
203C23—3022no—
204C23—3022no—
205C23—3022no—
206C23—1514no—
207C23—1514no—
208C23—1514no—
209C23C2×D60412yes—
210C23Q8×D15112yes—
211C23#1455900312yes—
212C23C23×D15111yescharacteristic
213Q8—6044no—
214C2×C4—22no—
215C2×C4—28no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—24no—
219C2×C4—30216no—
220C2×C4—3028no—
221C2×C4—3022no—
222C2×C4—3022no—
223C2×C4—30216no—
224C2×C4—3024no—
225C2×C4—3022no—
226C2×C4—3022no—
227C2×C4—3024no—
228C2×C4—1514no—
229C2×C4D4×D15114yes—
230C2×C4C2×D60412yes—
231C2×C4C2×D60412yes—
232C22—24no—
233C22—24no—
234C22—22no—
235C22—22no—
236C22—30232no—
237C22—3024no—
238C22—3024no—
239C22—3024no—
240C22—3024no—
241C22—3024no—
242C22—3024no—
243C22—1518no—
244C22#1801271914yescomplemented
245C22C2×D4×D15112yes—
246C22C22×D60411yescharacteristic
247C22C2×Q8×D15111yescharacteristic
248C22#41×D15112yes—
249C22C2×#1455900311yescharacteristic
250C4—22no—
251C4—44no—
252C4—3024no—
253C4—6042no—
254C4—6042no—
255C4#1801270914yes—
256C2—24no—
257C2—3028no—
258C2C2×#1801270911yescharacteristic
259C2C22⋊Q8×D15112yes—
260C2C2×#1801271911yescharacteristic
261C2#2375272212yes—
262C2#2375272411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#380×C151C2
prime radicalC24×D151C22
hypercenter#380D151
hypocenterC151#2848
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#18012719C2semidirect
3. C2×#18012718C2semidirect
4. #23752087C2semidirect
5. #23752086C2semidirect
6. #23752069C2semidirect
8. #380×C151C2semidirect
10. C22×Dic302C22semidirect
18. C2×C4⋊Dic151C22semidirect
19. C2×C4⋊Dic151C22semidirect
20. C2×Dic151⋊C4C22semidirect
24. C151⋊#95C22semidirect
26. C2×C4⋊C4×C151C22semidirect
28. #95×C151C22semidirect
33. C23×D151Q8semidirect
104. C22×C151C22⋊Q8semidirect
117. C2×D151C22⋊Q8semidirect
131. C151#2848semidirect
139. #380D151semidirect
154. C2×C4⋊C4C2×D151semidirect
160. #95C2×D151semidirect
244. C22#18012719semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D1512
C2×#180127192
C2×#180127182
#237520872
#237520862
#237520692
#237520672
#380×C1512
#2848151