Finite Group Databasebeta

← #34080184

Subgroups — #34080184

Order 19328.

396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752824C211yesmaximal, characteristic, complemented
2#23752781C211yesmaximal, characteristic
3#23752606C211yesmaximal, characteristic, complemented
4#23752585C211yesmaximal, characteristic, complemented
5#23752577C211yesmaximal, characteristic, complemented
6#23752567C211yesmaximal, characteristic, complemented
7#23752435C212yesmaximal, complemented
8#23752413C212yesmaximal, complemented
9#23752376C212yesmaximal, complemented
10#23752365C212yesmaximal, complemented
11#433×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13C22×D604C2211yescharacteristic
14C2×Dic604C2212yescomplemented
15C2×#14558993C2212yes—
16C2×#14558993C2212yes—
17C2×#14558993C2212yescomplemented
18#18012739C2211yescharacteristic, complemented
19#18012736C2211yescharacteristic
20#18012736C2211yescharacteristic
21#18012732—22no—
22#18012731C2211yescharacteristic, complemented
23#18012729—22no—
24#18012727C2211yescharacteristic
25#18012727C2211yescharacteristic
26#18012718C2212yes—
27#18012714—22no—
28#18012709—22no—
29C4×Dic302C2212yescomplemented
30#18012664C2212yescomplemented
31#18012661C2212yes—
32#18012661C2212yes—
33#18012661C2212yescomplemented
34#117×C151C2211yescharacteristic
35C4⋊C8×C151C2212yescomplemented
36C22⋊C8×C151C2212yes—
37#97×C151C2211yescharacteristic, complemented
38C4×C8×C151C2211yescharacteristic, complemented
39C23×D151—21no—
40#14559004—42no—
41C2×Dic302C2312yes—
42C2×Dic302C2311yescharacteristic
43C2×D604—21no—
44C2×D604—22no—
45C2×D604—22no—
46C2×D604—42no—
47C2×D604C2311yescharacteristic
48C2×D604C2311yescharacteristic
49C2×D604C2311yescharacteristic
50C2×C22⋊D151—21no—
51C2×C4×D151—21no—
52Dic604—42no—
53#14558993—42no—
54#14558993—42no—
55#14558993—42no—
56C4⋊Dic151—22no—
57C4⋊Dic151C2312yes—
58Dic151⋊C4—22no—
59Dic151⋊C4—22no—
60Dic151⋊C4—22no—
61C22⋊Dic151—22no—
62(C2×D151)⋊C4—22no—
63(C2×D151)⋊C4—22no—
64C4×Dic151—22no—
65C22×C4×C151C2311yescharacteristic
66C2×C8×C151C2312yes—
67C2×C8×C151C2312yes—
68C4⋊C4×C151D412yes—
69C22⋊C4×C151D412yes—
70C42×C151C2311yescharacteristic
71C42×C151C2311yescharacteristic
72C22×D151—21no—
73C22×D151—21no—
74C22×D151—21no—
75C22×D151—42no—
76C22×D151—82no—
77Dic302—22no—
78Dic302—22no—
79Dic302—22no—
80D604—22no—
81D604—22no—
82D604—22no—
83D604—42no—
84D604—82no—
85D604—82no—
86C22⋊D151—42no—
87C2×Dic151—22no—
88C2×Dic151—22no—
89C2×Dic151—21no—
90C4×D151—42no—
91C23×C151C2×D411yescharacteristic
92C2×C4×C151—22no—
93C2×C4×C151C2×D412yes—
94C2×C4×C151C2×D412yes—
95C2×C4×C151C2×D411yescharacteristic
96C2×C4×C151C2411yescharacteristic
97C8×C151—22no—
98C8×C151—22no—
99C22×C151—21no—
100C22×C151—22no—
101C22×C151C22×D411yescharacteristic
102C2×D151—41no—
103C2×D151—41no—
104C2×D151—41no—
105C2×D151—42no—
106C2×D151—42no—
107C2×D151—42no—
108C2×D151—84no—
109C4×C151—21no—
110C4×C151—22no—
111C4×C151—22no—
112C4×C151H(5,𝔽2)12yes—
113Dic151—41no—
114Dic151—42no—
115Dic151—42no—
116C2×C151—41no—
117C2×C151#53511yescharacteristic
118C2×C151#57712yes—
119D151—81no—
120D151—81no—
121D151—81no—
122C151#322211yescharacteristic, complemented, Sylow
123#3222—1511nomaximal, Sylow
124#541—1511no—
125#535—1511no—
126#497—1511no—
127#492—1511no—
128#490—1511no—
129#488—1511no—
130#464—1512no—
131#460—1512no—
132#452—1512no—
133#450—1512no—
134#433D15111yescharacteristic, complemented
135C2×#41—1511no—
136C22×D4—1511no—
137C2×Q16—1512no—
138C2×SD16—1512no—
139C2×SD16—1512no—
140C2×SD16—1512no—
141C4⋊Q8—1511no—
142#127—1511no—
143#127—1511no—
144#126—3022no—
145#125—3022no—
146#125—1511no—
147#124—1511no—
148#124—1511no—
149C22⋊Q8—1512no—
150#121—3022no—
151#120—3022no—
152C4×Q8—1512no—
153#117C2×D15111yescharacteristic
154C4⋊C8C2×D15112yescomplemented
155#103—1512no—
156#102—1512no—
157#102—1512no—
158#102—1512no—
159C22⋊C8C2×D15112yes—
160#97C2×D15111yescharacteristic, complemented
161C4×C8C2×D15111yescharacteristic, complemented
162C24—3021no—
163#41—6042no—
164C2×Q8—1511no—
165C2×Q8—1512no—
166C2×D4—3021no—
167C2×D4—3021no—
168C2×D4—3022no—
169C2×D4—3022no—
170C2×D4—6042no—
171C2×D4—1511no—
172C2×D4—1511no—
173C2×D4—1511no—
174C22×C4—3021no—
175C22×C4C22×D15111yescharacteristic
176Q16—6042no—
177SD16—6042no—
178SD16—6042no—
179SD16—6042no—
180C2×C8C22×D15112yes—
181C2×C8C22×D15112yes—
182C4⋊C4—3022no—
183C4⋊C4—3022no—
184C4⋊C4—3022no—
185C4⋊C4—3022no—
186C4⋊C4—1512no—
187C4⋊C4D60412yes—
188C22⋊C4—3022no—
189C22⋊C4—3022no—
190C22⋊C4—3022no—
191C22⋊C4D60412yes—
192C42—3022no—
193C42C22×D15111yescharacteristic
194C42C22×D15111yescharacteristic
195C23—3021no—
196C23—3021no—
197C23—3021no—
198C23—6042no—
199C23—12082no—
200C23C2×D60411yescharacteristic
201Q8—3022no—
202Q8—3022no—
203Q8—3022no—
204D4—3022no—
205D4—3022no—
206D4—3022no—
207D4—6042no—
208D4—6042no—
209D4—12082no—
210D4—12082no—
211C2×C4—22no—
212C2×C4—3022no—
213C2×C4—3022no—
214C2×C4—3021no—
215C2×C4—6042no—
216C2×C4C2×D60412yes—
217C2×C4C2×D60412yes—
218C2×C4C2×D60411yescharacteristic
219C2×C4C23×D15111yescharacteristic
220C8—22no—
221C8—22no—
222C22—22no—
223C22—21no—
224C22—6042no—
225C22—6042no—
226C22—6042no—
227C22—6041no—
228C22—6041no—
229C22—6041no—
230C22—12084no—
231C22C22×D60411yescharacteristic
232C4—22no—
233C4—22no—
234C4—21no—
235C4—6042no—
236C4—6041no—
237C4—6042no—
238C4#1801278512yes—
239C2—41no—
240C2—12081no—
241C2—12081no—
242C2—12081no—
243C2#2375278111yescharacteristic
244C2#2375302412yes—
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#433×C151C2
socleC22×C151C22×D4
prime radical#23752781C2
hypercenter#433D151
hypocenterC151#3222
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23752824C2semidirect
3. #23752606C2semidirect
4. #23752585C2semidirect
5. #23752577C2semidirect
6. #23752567C2semidirect
7. #23752435C2semidirect
8. #23752413C2semidirect
9. #23752376C2semidirect
10. #23752365C2semidirect
11. #433×C151C2semidirect
14. C2×Dic604C22semidirect
17. C2×#14558993C22semidirect
18. #18012739C22semidirect
22. #18012731C22semidirect
29. C4×Dic302C22semidirect
30. #18012664C22semidirect
33. #18012661C22semidirect
35. C4⋊C8×C151C22semidirect
37. #97×C151C22semidirect
38. C4×C8×C151C22semidirect
122. C151#3222semidirect
134. #433D151semidirect
154. C4⋊C8C2×D151semidirect
160. #97C2×D151semidirect
161. C4×C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528242
#237527812
#237526062
#237525852
#237525772
#237525672
#237524352
#237524132
#237523762
#237523652
#433×C1512
#3222151