Finite Group Databasebeta

← #34071103

Subgroups — #34071103

Order 19328.

258 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 41 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#23752892C211yesmaximal, characteristic, complemented
2#23752403C211yesmaximal, characteristic, complemented
3#23752400C211yesmaximal, characteristic
4#23752389C211yesmaximal, characteristic, complemented
5#23752001C211yesmaximal, characteristic, complemented
6#23751998C211yesmaximal, characteristic, complemented
7#354×C151C211yesmaximal, characteristic, complemented
8#18012784C2211yescharacteristic
9#18012770—21no—
10#18012732—21no—
11#18012723—21no—
12#18012721—21no—
13#18012720C2211yescharacteristic
14#18012715—21no—
15#18012709—21no—
16#18012707C2211yescharacteristic
17(C22⋊D151)⋊C4—21no—
18#18012696—21no—
19C22⋊C4×D151—21no—
20#18012667—21no—
21#18012656C2211yescharacteristic
22#18012653—21no—
23#18012653—21no—
24#124×C151C2211yescharacteristic
25#99×C151C2211yescharacteristic
26#99×C151C2211yescharacteristic
27C23×D151D411yescharacteristic
28#14559004—21no—
29#14559003—41no—
30C2×D604—41no—
31C2×C22⋊D151—21no—
32C2×C22⋊D151—21no—
33C2×C22⋊D151—21no—
34D4×D151—41no—
35C22×Dic151D411yescharacteristic, complemented
36C2×C4×D151—21no—
37C2×C4×D151—21no—
38#14558994—41no—
39#14558991—41no—
40#14558988—21no—
41C4⋊Dic151—21no—
42C4⋊Dic151—41no—
43Dic151⋊C4—21no—
44Dic151⋊C4—21no—
45Dic151⋊C4—21no—
46C22⋊Dic151—21no—
47C22⋊Dic151D411yescharacteristic
48C22⋊Dic151D411yescharacteristic, complemented
49(C2×D151)⋊C4—21no—
50(C2×D151)⋊C4—21no—
51(C2×D151)⋊C4—21no—
52(C2×D151)⋊C4—41no—
53(C2×D151)⋊C4—41no—
54C4×Dic151—21no—
55C2×Q8×C151D411yescharacteristic, complemented
56C2×D4×C151C2311yescharacteristic
57C22⋊C4×C151—21no—
58C22⋊C4×C151—21no—
59C22⋊C4×C151—21no—
60C22⋊C4×C151—21no—
61C42×C151D411yescharacteristic, complemented
62C22×D151—21no—
63C22×D151—21no—
64C22×D151—21no—
65C22×D151—42no—
66C22×D151—41no—
67Dic302—21no—
68D604—21no—
69D604—82no—
70C22⋊D151—42no—
71C22⋊D151—41no—
72C22⋊D151—41no—
73C22⋊D151—41no—
74C2×Dic151—21no—
75C2×Dic151—21no—
76C2×Dic151—21no—
77C2×Dic151—21no—
78C2×Dic151—21no—
79C2×Dic151—41no—
80C4×D151—41no—
81C4×D151—42no—
82C4×D151—81no—
83C151⋊C8—41no—
84C23×C151C2×D411yescharacteristic
85C23×C151C2×D411yescharacteristic
86Q8×C151—41no—
87D4×C151—41no—
88C2×C4×C151—21no—
89C2×C4×C151—21no—
90C2×C4×C151—41no—
91C2×C4×C151—41no—
92C2×C4×C151C2×D411yescharacteristic
93C22×C151—21no—
94C22×C151—21no—
95C22×C151—41no—
96C22×C151—41no—
97C22×C151#12011yescharacteristic
98C2×D151—22no—
99C2×D151—41no—
100C2×D151—41no—
101C2×D151—42no—
102C2×D151—41no—
103C2×D151—81no—
104C2×D151—81no—
105C2×D151—81no—
106C4×C151—21no—
107C4×C151—41no—
108C4×C151—41no—
109C4×C151—81no—
110C4×C151—81no—
111Dic151—41no—
112Dic151—41no—
113Dic151—41no—
114Dic151—41no—
115C2×C151—21no—
116C2×C151—41no—
117C2×C151—41no—
118C2×C151B(4,𝔽2)11yescharacteristic
119D151—42no—
120D151—81no—
121C151#219711yescharacteristic, complemented, Sylow
122#2197—1511nomaximal, Sylow
123#551—1511no—
124#458—1511no—
125B(4,𝔽2)—1511no—
126#455—1511no—
127#354D15111yescharacteristic, complemented
128#352—1511no—
129AΣL(1,𝔽16)—1511no—
130H(5,𝔽2)—1511no—
131#137—3021no—
132#126—3021no—
133#124C2×D15111yescharacteristic
134#123—3021no—
135#123—3021no—
136#123—1511no—
137C22⋊Q8—3021no—
138#120—3021no—
139#120—1511no—
140C4×D4—3021no—
141#117—3021no—
142C2×C22⋊C4—3021no—
143#104—3021no—
144#100—1511no—
145#99—3021no—
146#99—3021no—
147#99C2×D15111yescharacteristic
148#99C2×D15111yescharacteristic
149C24—1511no—
150#41—3021no—
151#41—6041no—
152C2×Q8D60411yescharacteristic, complemented
153C2×D4—3021no—
154C2×D4—3021no—
155C2×D4—3021no—
156C2×D4—6041no—
157C2×D4—6041no—
158C2×D4C22×D15111yescharacteristic
159C22×C4—3021no—
160C22×C4—3021no—
161C22×C4—1511no—
162Q16—6041no—
163SD16—6041no—
164M16—3021no—
165C4⋊C4—3021no—
166C4⋊C4—3021no—
167C4⋊C4—3021no—
168C4⋊C4—3021no—
169C4⋊C4—6041no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—21no—
173C22⋊C4—21no—
174C22⋊C4—3021no—
175C22⋊C4—3021no—
176C22⋊C4—3021no—
177C22⋊C4—3021no—
178C22⋊C4—6041no—
179C22⋊C4—6041no—
180C22⋊C4—1511no—
181C22⋊C4—1511no—
182C42—3021no—
183C42D60411yescharacteristic, complemented
184C23—3021no—
185C23—3021no—
186C23—3021no—
187C23—6041no—
188C23—6042no—
189C23D4×D15111yescharacteristic
190C23D4×D15111yescharacteristic
191Q8—41no—
192Q8—3021no—
193D4—41no—
194D4—3021no—
195D4—6041no—
196D4—6041no—
197D4—6042no—
198D4—6041no—
199D4—12082no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—3021no—
205C2×C4—3021no—
206C2×C4—3021no—
207C2×C4—3021no—
208C2×C4—3021no—
209C2×C4—6041no—
210C2×C4—6042no—
211C2×C4—6041no—
212C2×C4—12081no—
213C2×C4C2×D60411yescharacteristic
214C8—6041no—
215C22—21no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—3022no—
220C22—6041no—
221C22—6042no—
222C22—6041no—
223C22—6041no—
224C22—12081no—
225C22—12081no—
226C22—12081no—
227C22#1801270911yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—81no—
232C4—81no—
233C4—6041no—
234C4—6041no—
235C4—6041no—
236C4—6041no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—6042no—
241C2—12081no—
242C2#2375240011yescharacteristic
subgroupG/H
centerC2#23752400
commutator, cosocleC2×D4×C151C23
FrattiniC2×D4C22×D151
Fitting#354×C151C2
socleC2×C151B(4,𝔽2)
prime radical#23752400C2
hypercenter#354D151
hypocenterC151#2197
LCSG ▷ C2×D4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
1. #23752892C2semidirect
2. #23752403C2semidirect
4. #23752389C2semidirect
5. #23752001C2semidirect
6. #23751998C2semidirect
7. #354×C151C2semidirect
35. C22×Dic151D4semidirect
48. C22⋊Dic151D4semidirect
55. C2×Q8×C151D4semidirect
61. C42×C151D4semidirect
121. C151#2197semidirect
127. #354D151semidirect
152. C2×Q8D604semidirect
183. C42D604semidirect

Maximal subgroups

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

subgroupindex
#237528922
#237524032
#237524002
#237523892
#237520012
#237519982
#354×C1512
#2197151