Finite Group Databasebeta

← #36352095

Subgroups — #36352095

Order 22144.

274 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#19149658C211yesmaximal, characteristic
2#26011455C211yesmaximal, characteristic
3#26011227C214yesmaximal, complemented
4#381×C173C211yesmaximal, characteristic
5C22×Dic346C411yescharacteristic, complemented
6C2×#14583810—21no—
7#19149658—21no—
8#19149658—21no—
9#19149658C412yescomplemented
10#19149658C2212yes—
11C2×C4⋊Dic173C411yescharacteristic, complemented
12C2×#14583805—21no—
13C2×C22⋊Dic173—21no—
14C22⋊#13063436—21no—
15C22⋊#13063436C2212yes—
16C23×C4×C173C2211yescharacteristic
17C2×C22⋊C4×C173—21no—
18#95×C173—21no—
19#95×C173C2212yes—
20C2×Dic346—21no—
21C2×Dic346—42no—
22C2×Dic346C2×C412yes—
23C22×Dic173—21no—
24C22×Dic173—21no—
25#14583810—42no—
26C2×#13063436—22no—
27C4⋊Dic173—21no—
28C4⋊Dic173C2×C412yes—
29#14583805—22no—
30#14583805—22no—
31C22⋊Dic173—22no—
32C22⋊Dic173—22no—
33C24×C173D411yescharacteristic
34C22×C4×C173—22no—
35C22×C4×C173—42no—
36C22×C4×C173C2×C411yescharacteristic
37C22×C4×C173C2×C411yescharacteristic
38C22×C4×C173D411yescharacteristic
39C22×C4×C173D411yescharacteristic
40C22×C4×C173D411yescharacteristic
41C22×C4×C173C2311yescharacteristic
42C22⋊C4×C173—42no—
43Dic346—42no—
44Dic346—42no—
45C2×Dic173—22no—
46C2×Dic173—22no—
47C2×Dic173—42no—
48C2×Dic173—42no—
49#13063436—42no—
50C23×C173—22no—
51C23×C173—22no—
52C23×C173—41no—
53C23×C173C22⋊C411yescharacteristic
54C23×C173C22⋊C411yescharacteristic
55C23×C173C2×D411yescharacteristic
56C2×C4×C173—22no—
57C2×C4×C173—22no—
58C2×C4×C173—41no—
59C2×C4×C173—41no—
60C2×C4×C173—41no—
61C2×C4×C173—41no—
62C2×C4×C173—42no—
63C2×C4×C173—42no—
64C2×C4×C173—42no—
65C2×C4×C173C22⋊C411yescharacteristic
66C2×C4×C173C22⋊C411yescharacteristic
67C2×C4×C173C22×C411yescharacteristic
68C2×C4×C173C2×D411yescharacteristic
69C22×C173—21no—
70C22×C173—21no—
71C22×C173—21no—
72C22×C173—21no—
73C22×C173—21no—
74C22×C173—21no—
75C22×C173—21no—
76C22×C173—44no—
77C22×C173#9912yes—
78C22×C173C2×C22⋊C411yescharacteristic
79C22×C173#13712yes—
80C4×C173—21no—
81C4×C173—21no—
82C4×C173—21no—
83C4×C173—21no—
84C4×C173—82no—
85Dic173—42no—
86Dic173—42no—
87C2×C173—22no—
88C2×C173—22no—
89C2×C173—41no—
90C2×C173C2×#9911yescharacteristic
91C2×C173#41911yescharacteristic
92C2×C173#42111yescharacteristic
93C173#151111yescharacteristic, complemented, Sylow
94#1511—1731nomaximal, Sylow
95C2×C22⋊Q8—1731no—
96#407—1731no—
97#381D17311yescharacteristic
98#328—1734no—
99C22×Q8—1731no—
100C23×C4C2×D17311yescharacteristic
101C2×M16—3461no—
102C22⋊Q8—3461no—
103C22⋊Q8—3461no—
104C22⋊Q8—1732no—
105C22⋊Q8—1732no—
106C2×C4⋊C4—3461no—
107C2×C4⋊C4—1731no—
108C2×C22⋊C4—21no—
109C2×C22⋊C4—3461no—
110C22⋊C8—3461no—
111C22⋊C8—1732no—
112#95—21no—
113#95C2×D17312yes—
114C24C22⋊D17311yescharacteristic
115C2×Q8—3461no—
116C2×Q8—1732no—
117C2×Q8—6922no—
118C22×C4—22no—
119C22×C4—42no—
120C22×C4—3461no—
121C22×C4—3461no—
122C22×C4C4×D17311yescharacteristic
123C22×C4C4×D17311yescharacteristic
124C22×C4C22⋊D17311yescharacteristic
125C22×C4D69211yescharacteristic
126C22×C4D69211yescharacteristic
127C22×C4C22×D17311yescharacteristic
128M16—6922no—
129C2×C8—3462no—
130C4⋊C4—3462no—
131C4⋊C4—3462no—
132C4⋊C4—3461no—
133C4⋊C4—1732no—
134C22⋊C4—42no—
135C22⋊C4—3462no—
136C22⋊C4—3462no—
137C23—22no—
138C23—22no—
139C23—41no—
140C23#1458380311yescharacteristic
141C23#1458380311yescharacteristic
142C23C2×C22⋊D17311yescharacteristic
143Q8—6922no—
144Q8—6922no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—3462no—
155C2×C4—3462no—
156C2×C4—6922no—
157C2×C4—6922no—
158C2×C4#1458380311yescharacteristic
159C2×C4#1458380311yescharacteristic
160C2×C4C2×C4×D17311yescharacteristic
161C2×C4C2×D69211yescharacteristic
162C8—6922no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—44no—
171C22#1914959312yes—
172C22C2×#1458380311yescharacteristic
173C22#1914970912yes—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—82no—
179C4—6922no—
180C4—6922no—
181C2—22no—
182C2—22no—
183C2—41no—
184C2C2×#1914959311yescharacteristic
185C2#2601149911yescharacteristic
186C2#2601150911yescharacteristic
subgroupG/H
centerC22C2×#14583803
commutatorC2×C4×C173C22×C4
FrattiniC22×C4C22×D173
Fitting#381×C173C2
socleC22×C173C2×C22⋊C4
prime radicalC24×C173D4
cosocleC22×C4×C173C23
hypercenter#381D173
hypocenterC173#1511
LCSG ▷ C2×C4×C173 ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
3. #26011227C2semidirect
5. C22×Dic346C4semidirect
9. #19149658C4semidirect
11. C2×C4⋊Dic173C4semidirect
93. C173#1511semidirect

Maximal subgroups

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

subgroupindex
C2×#191496582
#260114552
#260112272
#381×C1732
#1511173