Finite Group Databasebeta

← #36352572

Subgroups — #36352572

Order 22144.

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

normal subgroups only

This group has 210 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#26011822C211yesmaximal, characteristic
3#26011819C211yesmaximal, characteristic
4#26011423C211yesmaximal, 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⋊Dic173—21no—
16C2×C4⋊Dic173C2211yescharacteristic
17C2×#14583805C2211yescharacteristic
18#19149611—21no—
19#19149610—21no—
20#19149604—21no—
21#19149603—21no—
22C22⋊#13063436C2211yescharacteristic
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⋊Dic173—42no—
37C4⋊Dic173D411yescharacteristic
38#14583805—21no—
39#14583805—21no—
40#14583805—21no—
41#14583805—21no—
42#14583805—21no—
43#14583805—21no—
44#14583805—21no—
45C22⋊Dic173—21no—
46C4×Dic173—21no—
47C4×Dic173—21no—
48C2×Q8×C173D411yescharacteristic
49C22×C4×C173—21no—
50C22×C4×C173C2311yescharacteristic
51C2×C8×C173—21no—
52C4⋊C4×C173—21no—
53C4⋊C4×C173D411yescharacteristic
54C22⋊C4×C173—21no—
55Dic346—41no—
56Dic346—81no—
57C2×Dic173—21no—
58C2×Dic173—21no—
59C2×Dic173—21no—
60C2×Dic173—21no—
61C2×Dic173—21no—
62C2×Dic173—41no—
63C2×Dic173—41no—
64C2×Dic173—41no—
65C2×Dic173—41no—
66C2×Dic173SD1612yes—
67#13063436—41no—
68C23×C173C2×D411yescharacteristic
69Q8×C173—41no—
70C2×C4×C173—22no—
71C2×C4×C173—21no—
72C2×C4×C173—21no—
73C2×C4×C173—41no—
74C2×C4×C173—41no—
75C2×C4×C173—41no—
76C2×C4×C173C2×D411yescharacteristic
77C2×C4×C173C2×D411yescharacteristic
78C8×C173—41no—
79C22×C173—21no—
80C22×C173—21no—
81C22×C173#12011yescharacteristic
82C22×C173C2×SD1611yescharacteristic
83C22×C173#13711yescharacteristic
84C4×C173—21no—
85C4×C173—21no—
86C4×C173—42no—
87C4×C173—41no—
88C4×C173—41no—
89Dic173—22no—
90Dic173—41no—
91Dic173—41no—
92Dic173—41no—
93Dic173—81no—
94C2×C173—21no—
95C2×C173—21no—
96C2×C173#44811yescharacteristic
97C2×C173#45611yescharacteristic
98C2×C173#45811yescharacteristic
99C173#161111yescharacteristic, complemented, Sylow
100#1611—1731nomaximal, Sylow
101#544—1731no—
102#483—1731no—
103#483—1731no—
104#398—1731no—
105#328—1731no—
106#328D17311yescharacteristic
107#324—1731no—
108C4⋊Q8—3461no—
109C4⋊Q8—3461no—
110#125—3461no—
111#125—3461no—
112C22⋊Q8—3461no—
113C22⋊Q8—1731no—
114C22⋊Q8C2×D17311yescharacteristic
115#117—3461no—
116C2×C4⋊C4—3461no—
117C2×C4⋊C4—1731no—
118C2×C4⋊C4—1731no—
119#106—3461no—
120#106—3461no—
121#103—3461no—
122#103—3461no—
123C22⋊C8—1731no—
124C22⋊C8C2×D17311yescharacteristic
125#95—3461no—
126#95C2×D17311yescharacteristic
127C2×Q8—3461no—
128C2×Q8—1731no—
129C2×Q8D69211yescharacteristic
130C22×C4—21no—
131C22×C4—3461no—
132C22×C4—1731no—
133C22×C4—1731no—
134C22×C4C22×D17311yescharacteristic
135C2×C8—21no—
136C2×C8—3461no—
137C4⋊C4—21no—
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—3461no—
147C4⋊C4—3461no—
148C4⋊C4—1731no—
149C4⋊C4—6922no—
150C4⋊C4D69211yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3461no—
153C42—3461no—
154C42—3461no—
155C23D4×D17311yescharacteristic
156Q8—41no—
157Q8—13841no—
158Q8—6921no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—3461no—
166C2×C4—3461no—
167C2×C4—3461no—
168C2×C4—3461no—
169C2×C4—3461no—
170C2×C4—1732no—
171C2×C4—6921no—
172C2×C4—6921no—
173C2×C4—6921no—
174C2×C4—6921no—
175C2×C4D4×D17311yescharacteristic
176C2×C4C2×D69211yescharacteristic
177C8—41no—
178C8—6921no—
179C22—21no—
180C22—21no—
181C22#1914964911yescharacteristic
182C22SD16×D17311yescharacteristic
183C22#1914971111yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—3462no—
190C4—13841no—
191C4—6921no—
192C4—6921no—
193C4—6921no—
194C2—21no—
195C2—21no—
196C2#2601163111yescharacteristic
197C2#2601167511yescharacteristic
198C2#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#1611
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
99. C173#1611semidirect

Maximal subgroups

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

subgroupindex
#260121202
#260118222
#260118192
#260114232
#260112272
#260112162
#328×C1732
#1611173