Finite Group Databasebeta

← #36352606

Subgroups — #36352606

Order 22144.

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#26012120C211yesmaximal, characteristic
2#26011827C211yesmaximal, characteristic
3#26011824C211yesmaximal, characteristic
4#26011431C211yesmaximal, characteristic
5#26011227C211yesmaximal, characteristic
6#26011216C211yesmaximal, characteristic
7#328×C173C211yesmaximal, characteristic
8#19149678—21no—
9#19149677—21no—
10#19149669—21no—
11#19149669—21no—
12#19149658C2211yescharacteristic
13#19149656—21no—
14#19149635—21no—
15C2×C4⋊Dic173C2211yescharacteristic
16C2×#14583805C2211yescharacteristic
17#19149613—21no—
18#19149612—21no—
19#19149604—21no—
20#19149603—21no—
21C22⋊#13063436C2211yescharacteristic
22#19149586—21no—
23#19149586—21no—
24C22⋊Q8×C173C2211yescharacteristic
25C22⋊C8×C173C2211yescharacteristic
26#95×C173C2211yescharacteristic
27C2×Dic346—21no—
28C2×Dic346D411yescharacteristic
29C22×Dic173—21no—
30C22×Dic173D411yescharacteristic
31C22×Dic173D411yescharacteristic
32C2×#13063436—21no—
33C4⋊Dic173—21no—
34C4⋊Dic173—21no—
35C4⋊Dic173—21no—
36C4⋊Dic173D411yescharacteristic
37#14583805—21no—
38#14583805—21no—
39#14583805—21no—
40#14583805—21no—
41#14583805—21no—
42#14583805—21no—
43#14583805—21no—
44C22⋊Dic173—21no—
45C4×Dic173—21no—
46C4×Dic173—21no—
47C2×Q8×C173D411yescharacteristic
48C22×C4×C173—21no—
49C22×C4×C173C2311yescharacteristic
50C2×C8×C173—21no—
51C4⋊C4×C173—21no—
52C4⋊C4×C173D411yescharacteristic
53C22⋊C4×C173—21no—
54Dic346—41no—
55Dic346—81no—
56C2×Dic173—21no—
57C2×Dic173—21no—
58C2×Dic173—21no—
59C2×Dic173—21no—
60C2×Dic173—21no—
61C2×Dic173—41no—
62C2×Dic173—42no—
63C2×Dic173—41no—
64C2×Dic173Q1612yes—
65#13063436—41no—
66C23×C173C2×D411yescharacteristic
67Q8×C173—41no—
68C2×C4×C173—21no—
69C2×C4×C173—21no—
70C2×C4×C173—41no—
71C2×C4×C173—41no—
72C2×C4×C173—41no—
73C2×C4×C173—41no—
74C2×C4×C173C2×D411yescharacteristic
75C2×C4×C173C2×D411yescharacteristic
76C8×C173—41no—
77C22×C173—21no—
78C22×C173—21no—
79C22×C173#12011yescharacteristic
80C22×C173C2×Q1611yescharacteristic
81C22×C173#13711yescharacteristic
82C4×C173—21no—
83C4×C173—21no—
84C4×C173—41no—
85C4×C173—41no—
86C4×C173—81no—
87Dic173—22no—
88Dic173—41no—
89Dic173—41no—
90Dic173—41no—
91Dic173—81no—
92C2×C173—21no—
93C2×C173—21no—
94C2×C173#45111yescharacteristic
95C2×C173#45411yescharacteristic
96C2×C173#45811yescharacteristic
97C173#161711yescharacteristic, complemented, Sylow
98#1617—1731nomaximal, Sylow
99#544—1731no—
100#484—1731no—
101#484—1731no—
102#400—1731no—
103#328—1731no—
104#328D17311yescharacteristic
105#324—1731no—
106C4⋊Q8—3461no—
107C4⋊Q8—3461no—
108#125—3461no—
109#125—3461no—
110C22⋊Q8—3461no—
111C22⋊Q8—1731no—
112C22⋊Q8C2×D17311yescharacteristic
113#117—3461no—
114C2×C4⋊C4—1731no—
115C2×C4⋊C4—1731no—
116#107—3461no—
117#107—3461no—
118#103—3461no—
119#103—3461no—
120C22⋊C8—1731no—
121C22⋊C8C2×D17311yescharacteristic
122#95—3461no—
123#95—3461no—
124#95C2×D17311yescharacteristic
125C2×Q8—3461no—
126C2×Q8—1731no—
127C2×Q8D69211yescharacteristic
128C22×C4—21no—
129C22×C4—3461no—
130C22×C4—1731no—
131C22×C4—1731no—
132C22×C4C22×D17311yescharacteristic
133C2×C8—21no—
134C2×C8—3461no—
135C4⋊C4—21no—
136C4⋊C4—3461no—
137C4⋊C4—3461no—
138C4⋊C4—3461no—
139C4⋊C4—3461no—
140C4⋊C4—3461no—
141C4⋊C4—3461no—
142C4⋊C4—3461no—
143C4⋊C4—3461no—
144C4⋊C4—3461no—
145C4⋊C4—3461no—
146C4⋊C4—1731no—
147C4⋊C4D69211yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—3461no—
150C42—3461no—
151C42—3461no—
152C23D4×D17311yescharacteristic
153Q8—41no—
154Q8—13841no—
155Q8—6921no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—3461no—
163C2×C4—3461no—
164C2×C4—3461no—
165C2×C4—3461no—
166C2×C4—3461no—
167C2×C4—1732no—
168C2×C4—6922no—
169C2×C4—6921no—
170C2×C4—6921no—
171C2×C4D4×D17311yescharacteristic
172C2×C4C2×D69211yescharacteristic
173C8—41no—
174C8—6921no—
175C22—21no—
176C22—21no—
177C22#1914964911yescharacteristic
178C22Q16×D17311yescharacteristic
179C22#1914970811yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—3462no—
186C4—13841no—
187C4—6921no—
188C4—6921no—
189C4—6921no—
190C2—21no—
191C2—21no—
192C2#2601164811yescharacteristic
193C2#2601166511yescharacteristic
194C2#2601168211yescharacteristic
subgroupG/H
centerC22#19149649
commutator, cosocleC22×C4×C173C23
FrattiniC22×C4C22×D173
Fitting#328×C173C2
socleC22×C173#120
prime radicalC23×C173C2×D4
hypercenter#328D173
hypocenterC173#1617
LCSG ▷ C22×C4×C173 ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
97. C173#1617semidirect

Maximal subgroups

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

subgroupindex
#260121202
#260118272
#260118242
#260114312
#260112272
#260112162
#328×C1732
#1617173