Finite Group Databasebeta

← #34071124

Subgroups — #34071124

Order 19328.

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

normal subgroups only

This group has 226 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#23752965C211yesmaximal, characteristic, complemented
2#23752403C211yesmaximal, characteristic
3#23752401C211yesmaximal, characteristic
4#23752392C211yesmaximal, characteristic
5#23752006C211yesmaximal, characteristic, complemented
6#23752003C211yesmaximal, characteristic, complemented
7#352×C151C211yesmaximal, characteristic, complemented
8#18012784C2211yescharacteristic
9#18012772—21no—
10#18012738—21no—
11#18012732—21no—
12#18012732—21no—
13#18012729—21no—
14#18012726C2211yescharacteristic
15#18012723—21no—
16#18012722—21no—
17#18012720C2211yescharacteristic
18#18012718—21no—
19#18012716—21no—
20#18012665—21no—
21#18012654C2211yescharacteristic
22#18012653—21no—
23#18012653—21no—
24#123×C151C2211yescharacteristic
25#100×C151C2211yescharacteristic
26#99×C151C2211yescharacteristic
27#14559004—21no—
28#14559003—41no—
29C2×Dic302—21no—
30C2×Dic302D411yescharacteristic
31C2×C22⋊D151—21no—
32C2×C22⋊D151—21no—
33D4×D151—41no—
34C22×Dic151D411yescharacteristic
35Dic604—41no—
36#14558993—41no—
37C4⋊Dic151—21no—
38C4⋊Dic151—21no—
39C4⋊Dic151—41no—
40Dic151⋊C4—21no—
41Dic151⋊C4—21no—
42Dic151⋊C4—21no—
43Dic151⋊C4—21no—
44Dic151⋊C4—21no—
45Dic151⋊C4—41no—
46C22⋊Dic151—21no—
47C22⋊Dic151—21no—
48C22⋊Dic151—21no—
49C22⋊Dic151—21no—
50C22⋊Dic151D411yescharacteristic
51(C2×D151)⋊C4—41no—
52(C2×D151)⋊C4—41no—
53C4×Dic151—21no—
54C4×Dic151D411yescharacteristic
55C2×D4×C151C2311yescharacteristic
56C22×C4×C151D411yescharacteristic
57M16×C151—21no—
58C4⋊C4×C151—21no—
59C22⋊C4×C151—21no—
60C22⋊C4×C151—21no—
61C22⋊C4×C151D411yescharacteristic
62C22×D151—21no—
63C22×D151—21no—
64Dic302—21no—
65Dic302—41no—
66Dic302—81no—
67D604—21no—
68C22⋊D151—41no—
69C22⋊D151—41no—
70C22⋊D151—41no—
71C2×Dic151—21no—
72C2×Dic151—21no—
73C2×Dic151—21no—
74C2×Dic151—21no—
75C2×Dic151—21no—
76C2×Dic151—21no—
77C2×Dic151—41no—
78C2×Dic151—41no—
79C4×D151—41no—
80C23×C151C2×D411yescharacteristic
81C23×C151C2×D411yescharacteristic
82D4×C151—41no—
83C2×C4×C151—21no—
84C2×C4×C151—21no—
85C2×C4×C151—41no—
86C2×C4×C151—41no—
87C2×C4×C151C2×D411yescharacteristic
88C8×C151—41no—
89C22×C151—21no—
90C22×C151—21no—
91C22×C151—41no—
92C22×C151—41no—
93C22×C151#12011yescharacteristic
94C2×D151—41no—
95C2×D151—81no—
96C2×D151—81no—
97C4×C151—21no—
98C4×C151—41no—
99C4×C151—41no—
100C4×C151—81no—
101Dic151—41no—
102Dic151—41no—
103Dic151—41no—
104Dic151—41no—
105Dic151—41no—
106Dic151—81no—
107C2×C151—21no—
108C2×C151—41no—
109C2×C151—41no—
110C2×C151B(4,𝔽2)11yescharacteristic
111D151—81no—
112C151#220111yescharacteristic, complemented, Sylow
113#2201—1511nomaximal, Sylow
114#563—1511no—
115#458—1511no—
116#458—1511no—
117#455—1511no—
118#354—1511no—
119#352—1511no—
120#352D15111yescharacteristic, complemented
121H(5,𝔽2)—1511no—
122#137—3021no—
123C4⋊Q8—3021no—
124#126—3021no—
125#126—3021no—
126#125—3021no—
127#124—1511no—
128#123—3021no—
129#123—3021no—
130#123—1511no—
131#123C2×D15111yescharacteristic
132C22⋊Q8—3021no—
133C22⋊Q8—3021no—
134#104—3021no—
135#100C2×D15111yescharacteristic
136#99—3021no—
137#99—3021no—
138#99—1511no—
139#99C2×D15111yescharacteristic
140#41—3021no—
141#41—6041no—
142C2×Q8—3021no—
143C2×Q8—1511no—
144C2×D4—3021no—
145C2×D4—3021no—
146C2×D4—6041no—
147C2×D4C22×D15111yescharacteristic
148C22×C4—1511no—
149C22×C4D60411yescharacteristic
150Q16—6041no—
151SD16—6041no—
152M16—21no—
153C4⋊C4—21no—
154C4⋊C4—3021no—
155C4⋊C4—3021no—
156C4⋊C4—3021no—
157C4⋊C4—3021no—
158C4⋊C4—3021no—
159C4⋊C4—3021no—
160C4⋊C4—3021no—
161C4⋊C4—6041no—
162C4⋊C4—6041no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—3021no—
166C22⋊C4—3021no—
167C22⋊C4—3021no—
168C22⋊C4—3021no—
169C22⋊C4—6041no—
170C22⋊C4—6041no—
171C22⋊C4—1511no—
172C22⋊C4D60411yescharacteristic
173C42—3021no—
174C42—1511no—
175C23—3021no—
176C23—3021no—
177C23D4×D15111yescharacteristic
178C23C2×D60411yescharacteristic
179Q8—3021no—
180Q8—6041no—
181Q8—12081no—
182D4—41no—
183D4—3021no—
184D4—6041no—
185D4—6041no—
186D4—6041no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—3021no—
192C2×C4—3021no—
193C2×C4—3021no—
194C2×C4—3021no—
195C2×C4—3021no—
196C2×C4—3021no—
197C2×C4—6041no—
198C2×C4—6041no—
199C2×C4—6041no—
200C2×C4D4×D15111yescharacteristic
201C8—41no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—6041no—
207C22—12081no—
208C22—12081no—
209C22#1801270911yescharacteristic
210C4—21no—
211C4—41no—
212C4—41no—
213C4—81no—
214C4—6041no—
215C4—6041no—
216C4—6041no—
217C4—6041no—
218C4—6041no—
219C4—12081no—
220C2—21no—
221C2—41no—
222C2—41no—
223C2—12081no—
224C2#2375240011yescharacteristic
subgroupG/H
centerC2#23752400
commutator, cosocleC2×D4×C151C23
FrattiniC2×D4C22×D151
Fitting#352×C151C2
socleC2×C151B(4,𝔽2)
prime radical#18012784C22
hypercenter#352D151
hypocenterC151#2201
LCSG ▷ C2×D4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
1. #23752965C2semidirect
5. #23752006C2semidirect
6. #23752003C2semidirect
7. #352×C151C2semidirect
112. C151#2201semidirect
120. #352D151semidirect

Maximal subgroups

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

subgroupindex
#237529652
#237524032
#237524012
#237523922
#237520062
#237520032
#352×C1512
#2201151