Finite Group Databasebeta

← #34071132

Subgroups — #34071132

Order 19328.

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

normal subgroups only

This group has 216 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#23752961C211yesmaximal, characteristic, complemented
2#23752397C211yesmaximal, characteristic, complemented
3#23752394C211yesmaximal, characteristic, complemented
4#23752387C211yesmaximal, characteristic
5#23752010C211yesmaximal, characteristic, complemented
6#23752008C211yesmaximal, characteristic, complemented
7#356×C151C211yesmaximal, characteristic, complemented
8#18012787C2211yescharacteristic
9#18012772—21no—
10#18012770—21no—
11#18012767—21no—
12#18012737C2211yescharacteristic
13#18012734—21no—
14#18012733—21no—
15#18012729—21no—
16#18012728C2211yescharacteristic
17#18012724—21no—
18#18012717—21no—
19#18012715—21no—
20#18012667—21no—
21#18012665—21no—
22#18012665—21no—
23#18012658C2211yescharacteristic
24C4⋊Q8×C151C2211yescharacteristic
25#101×C151C2211yescharacteristic
26#101×C151C2211yescharacteristic
27#14559005—41no—
28#14559004—21no—
29#14559004—21no—
30#14559004—21no—
31C2×Dic302D411yescharacteristic
32Q8×D151—41no—
33C2×D604D411yescharacteristic
34C2×C4×D151—21no—
35Dic604—41no—
36#14558994—41no—
37#14558993—41no—
38#14558993—41no—
39#14558991—41no—
40D1208—41no—
41#14558988—21no—
42C4⋊Dic151—21no—
43Dic151⋊C4—21no—
44Dic151⋊C4—21no—
45Dic151⋊C4—21no—
46Dic151⋊C4—21no—
47Dic151⋊C4—21no—
48(C2×D151)⋊C4—21no—
49(C2×D151)⋊C4—21no—
50(C2×D151)⋊C4—21no—
51(C2×D151)⋊C4—21no—
52(C2×D151)⋊C4—21no—
53C4×Dic151D411yescharacteristic
54C4×Dic151D411yescharacteristic
55C2×Q8×C151D411yescharacteristic
56C2×Q8×C151C2311yescharacteristic
57M16×C151—21no—
58M16×C151—21no—
59C4⋊C4×C151—21no—
60C4⋊C4×C151—21no—
61C42×C151D411yescharacteristic
62C22×D151—21no—
63Dic302—21no—
64Dic302—21no—
65Dic302—21no—
66Dic302—41no—
67D604—21no—
68D604—21no—
69D604—21no—
70D604—41no—
71C22⋊D151—41no—
72C2×Dic151—21no—
73C2×Dic151—21no—
74C2×Dic151—21no—
75C4×D151—41no—
76C4×D151—41no—
77C4×D151—41no—
78C4×D151—81no—
79C151⋊C8—41no—
80Q8×C151—41no—
81Q8×C151—41no—
82C2×C4×C151—21no—
83C2×C4×C151—21no—
84C2×C4×C151C2×D411yescharacteristic
85C2×C4×C151C2×D411yescharacteristic
86C2×C4×C151C2×D411yescharacteristic
87C8×C151—41no—
88C8×C151—41no—
89C22×C151#12011yescharacteristic
90C2×D151—42no—
91C2×D151—41no—
92C2×D151—41no—
93C4×C151—21no—
94C4×C151—21no—
95C4×C151—21no—
96C4×C151—41no—
97C4×C151—41no—
98Dic151—41no—
99Dic151—41no—
100Dic151—41no—
101Dic151—41no—
102C2×C151—21no—
103C2×C151B(4,𝔽2)11yescharacteristic
104D151—81no—
105D151—81no—
106C151#220311yescharacteristic, complemented, Sylow
107#2203—1511nomaximal, Sylow
108#563—1511no—
109#456—1511no—
110#456—1511no—
111#454—1511no—
112#356—1511no—
113#356D15111yescharacteristic, complemented
114#355—1511no—
1152−1+4—1511no—
116#137—3021no—
117#137—3021no—
118AGL(1,ℤ/8)—3021no—
119C4⋊Q8—1511no—
120C4⋊Q8C2×D15111yescharacteristic
121#126—3021no—
122#126—3021no—
123#125—3021no—
124#124—1511no—
125#123—3021no—
126C22⋊Q8—3021no—
127C22⋊Q8—3021no—
128#104—3021no—
129#104—3021no—
130#104—3021no—
131#101—1511no—
132#101C2×D15111yescharacteristic
133#101C2×D15111yescharacteristic
134#41—3021no—
135#41—3021no—
136#41—3021no—
137#41—6041no—
138C2×Q8—6041no—
139C2×Q8—1511no—
140C2×Q8D60411yescharacteristic
141C2×Q8C22×D15111yescharacteristic
142C2×D4—1511no—
143C22×C4—3021no—
144Q16—6041no—
145Q16—6041no—
146SD16—6041no—
147SD16—6041no—
148SD16—6041no—
149D8—6041no—
150M16—21no—
151M16—21no—
152M16—3021no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—3021no—
156C4⋊C4—3021no—
157C4⋊C4—3021no—
158C4⋊C4—3021no—
159C4⋊C4—3021no—
160C4⋊C4—3021no—
161C22⋊C4—3021no—
162C22⋊C4—3021no—
163C22⋊C4—3021no—
164C22⋊C4—3021no—
165C22⋊C4—3021no—
166C42—1511no—
167C42—1511no—
168C42D60411yescharacteristic
169C23—3021no—
170Q8—41no—
171Q8—41no—
172Q8—3021no—
173Q8—3021no—
174Q8—3021no—
175Q8—6041no—
176D4—3021no—
177D4—3021no—
178D4—3021no—
179D4—6041no—
180D4—6041no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—3021no—
184C2×C4—3021no—
185C2×C4—3021no—
186C2×C4—6041no—
187C2×C4—6041no—
188C2×C4—6041no—
189C2×C4—12081no—
190C2×C4D4×D15111yescharacteristic
191C2×C4D4×D15111yescharacteristic
192C2×C4C2×D60411yescharacteristic
193C8—41no—
194C8—41no—
195C8—6041no—
196C22—6042no—
197C22—6041no—
198C22—6041no—
199C22#1801270911yescharacteristic
200C4—21no—
201C4—21no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4—6041no—
206C4—6041no—
207C4—6041no—
208C4—6041no—
209C2—21no—
210C2—12081no—
211C2—12081no—
212C2#2375240011yescharacteristic
subgroupG/H
centerC2#23752400
commutator, cosocleC2×Q8×C151C23
FrattiniC2×Q8C22×D151
Fitting#356×C151C2
socleC2×C151B(4,𝔽2)
prime radical#23752387C2
hypercenter#356D151
hypocenterC151#2203
LCSG ▷ C2×Q8×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
1. #23752961C2semidirect
2. #23752397C2semidirect
3. #23752394C2semidirect
5. #23752010C2semidirect
6. #23752008C2semidirect
7. #356×C151C2semidirect
106. C151#2203semidirect
113. #356D151semidirect

Maximal subgroups

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

subgroupindex
#237529612
#237523972
#237523942
#237523872
#237520102
#237520082
#356×C1512
#2203151