Finite Group Databasebeta

← #36323181

Subgroups — #36323181

Order 21376.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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#24923898C211yesmaximal, characteristic
2#24923605C211yesmaximal, characteristic
3#24923602C211yesmaximal, characteristic
4#24923209C211yesmaximal, characteristic
5#24923005C211yesmaximal, characteristic
6#24922994C211yesmaximal, characteristic
7#328×C167C211yesmaximal, characteristic
8#19128831—21no—
9#19128830—21no—
10#19128822—21no—
11#19128822—21no—
12#19128811C2211yescharacteristic
13#19128809—21no—
14#19128788—21no—
15C2×C4⋊Dic167C2211yescharacteristic
16C2×Dic167⋊C4C2211yescharacteristic
17#19128766—21no—
18#19128765—21no—
19#19128757—21no—
20#19128756—21no—
21C22⋊(C167⋊C8)C2211yescharacteristic
22C167⋊#95—21no—
23C167⋊#95—21no—
24C22⋊Q8×C167C2211yescharacteristic
25C22⋊C8×C167C2211yescharacteristic
26#95×C167C2211yescharacteristic
27C2×Dic334—21no—
28C2×Dic334D411yescharacteristic
29C22×Dic167—21no—
30C22×Dic167D411yescharacteristic
31C22×Dic167D411yescharacteristic
32C2×C167⋊C8—21no—
33C4⋊Dic167—21no—
34C4⋊Dic167—21no—
35C4⋊Dic167—21no—
36C4⋊Dic167D411yescharacteristic
37Dic167⋊C4—21no—
38Dic167⋊C4—21no—
39Dic167⋊C4—21no—
40Dic167⋊C4—21no—
41Dic167⋊C4—21no—
42Dic167⋊C4—21no—
43Dic167⋊C4—21no—
44C22⋊Dic167—21no—
45C4×Dic167—21no—
46C4×Dic167—21no—
47C2×Q8×C167D411yescharacteristic
48C22×C4×C167—21no—
49C22×C4×C167C2311yescharacteristic
50C2×C8×C167—21no—
51C4⋊C4×C167—21no—
52C4⋊C4×C167D411yescharacteristic
53C22⋊C4×C167—21no—
54Dic334—41no—
55Dic334—81no—
56C2×Dic167—21no—
57C2×Dic167—21no—
58C2×Dic167—21no—
59C2×Dic167—21no—
60C2×Dic167—21no—
61C2×Dic167—41no—
62C2×Dic167—42no—
63C2×Dic167—41no—
64C2×Dic167Q1612yes—
65C167⋊C8—41no—
66C23×C167C2×D411yescharacteristic
67Q8×C167—41no—
68C2×C4×C167—21no—
69C2×C4×C167—21no—
70C2×C4×C167—41no—
71C2×C4×C167—41no—
72C2×C4×C167—41no—
73C2×C4×C167—41no—
74C2×C4×C167C2×D411yescharacteristic
75C2×C4×C167C2×D411yescharacteristic
76C8×C167—41no—
77C22×C167—21no—
78C22×C167—21no—
79C22×C167#12011yescharacteristic
80C22×C167C2×Q1611yescharacteristic
81C22×C167#13711yescharacteristic
82C4×C167—21no—
83C4×C167—21no—
84C4×C167—41no—
85C4×C167—41no—
86C4×C167—81no—
87Dic167—22no—
88Dic167—41no—
89Dic167—41no—
90Dic167—41no—
91Dic167—81no—
92C2×C167—21no—
93C2×C167—21no—
94C2×C167#45111yescharacteristic
95C2×C167#45411yescharacteristic
96C2×C167#45811yescharacteristic
97C167#161711yescharacteristic, complemented, Sylow
98#1617—1671nomaximal, Sylow
99#544—1671no—
100#484—1671no—
101#484—1671no—
102#400—1671no—
103#328—1671no—
104#328D16711yescharacteristic
105#324—1671no—
106C4⋊Q8—3341no—
107C4⋊Q8—3341no—
108#125—3341no—
109#125—3341no—
110C22⋊Q8—3341no—
111C22⋊Q8—1671no—
112C22⋊Q8C2×D16711yescharacteristic
113#117—3341no—
114C2×C4⋊C4—1671no—
115C2×C4⋊C4—1671no—
116#107—3341no—
117#107—3341no—
118#103—3341no—
119#103—3341no—
120C22⋊C8—1671no—
121C22⋊C8C2×D16711yescharacteristic
122#95—3341no—
123#95—3341no—
124#95C2×D16711yescharacteristic
125C2×Q8—3341no—
126C2×Q8—1671no—
127C2×Q8D66811yescharacteristic
128C22×C4—21no—
129C22×C4—3341no—
130C22×C4—1671no—
131C22×C4—1671no—
132C22×C4C22×D16711yescharacteristic
133C2×C8—21no—
134C2×C8—3341no—
135C4⋊C4—21no—
136C4⋊C4—3341no—
137C4⋊C4—3341no—
138C4⋊C4—3341no—
139C4⋊C4—3341no—
140C4⋊C4—3341no—
141C4⋊C4—3341no—
142C4⋊C4—3341no—
143C4⋊C4—3341no—
144C4⋊C4—3341no—
145C4⋊C4—3341no—
146C4⋊C4—1671no—
147C4⋊C4D66811yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—3341no—
150C42—3341no—
151C42—3341no—
152C23D4×D16711yescharacteristic
153Q8—41no—
154Q8—13361no—
155Q8—6681no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—3341no—
163C2×C4—3341no—
164C2×C4—3341no—
165C2×C4—3341no—
166C2×C4—3341no—
167C2×C4—6682no—
168C2×C4—6681no—
169C2×C4—6681no—
170C2×C4—1672no—
171C2×C4D4×D16711yescharacteristic
172C2×C4C2×D66811yescharacteristic
173C8—41no—
174C8—6681no—
175C22—21no—
176C22—21no—
177C22#1912880211yescharacteristic
178C22Q16×D16711yescharacteristic
179C22#1912886111yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—13361no—
186C4—3342no—
187C4—6681no—
188C4—6681no—
189C4—6681no—
190C2—21no—
191C2—21no—
192C2#2492342611yescharacteristic
193C2#2492344311yescharacteristic
194C2#2492346011yescharacteristic
subgroupG/H
centerC22#19128802
commutator, cosocleC22×C4×C167C23
FrattiniC22×C4C22×D167
Fitting#328×C167C2
socleC22×C167#120
prime radicalC23×C167C2×D4
hypercenter#328D167
hypocenterC167#1617
LCSG ▷ C22×C4×C167 ▷ C22×C167 ▷ C167
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
97. C167#1617semidirect

Maximal subgroups

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

subgroupindex
#249238982
#249236052
#249236022
#249232092
#249230052
#249229942
#328×C1672
#1617167