Finite Group Databasebeta

← #36369094

Subgroups — #36369094

Order 22144.

246 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 58 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#26012514C211yesmaximal, characteristic, complemented
2#26012496C211yesmaximal, characteristic, complemented
3#26012350C212yesmaximal, complemented
4#26012349C212yesmaximal, complemented
5#26012038C211yesmaximal, characteristic
6C2×#14583836—21no—
7#19149746—21no—
8#19149746C2212yes—
9#19149746C2212yes—
10#19149736—21no—
11#19149734—21no—
12C2×#14583826—21no—
13#19149678C2211yescharacteristic
14#19149675C2211yescharacteristic
15#19149665—21no—
16#19149654C411yescharacteristic
17#19149652—21no—
18#19149650C411yescharacteristic
19C4×D692C411yescharacteristic
20C4×C22⋊D173—21no—
21C42×D173C2211yescharacteristic
22C4×D4×C173C411yescharacteristic
23#14583836—42no—
24C2×#13063443—22no—
25C2×#13063443—22no—
26#14583826—44no—
27C2×Dic346—21no—
28C2×D692—21no—
29C2×D692C2×C411yescharacteristic
30C2×C22⋊D173—21no—
31C2×C22⋊D173—21no—
32C2×C22⋊D173—21no—
33C2×C4×D173—21no—
34C2×C4×D173C2×C411yescharacteristic
35C2×C4×D173D411yescharacteristic
36C2×C4×D173D411yescharacteristic
37C4⋊Dic173C2×C411yescharacteristic
38#14583805—21no—
39C22⋊Dic173—21no—
40#14583803—21no—
41#14583803—21no—
42C4×Dic173D411yescharacteristic
43C4×Dic173D411yescharacteristic
44C4×Dic173C2311yescharacteristic
45C2×D4×C173C2×C411yescharacteristic
46C22×C4×C173—21no—
47C4⋊C4×C173C2×C411yescharacteristic
48C22⋊C4×C173—21no—
49C42×C173C2×C411yescharacteristic
50#13063443—42no—
51#13063443—42no—
52C22×D173—21no—
53C22×D173C22⋊C411yescharacteristic
54Dic346—42no—
55D692—41no—
56D692—42no—
57C22⋊D173—42no—
58C22⋊D173—41no—
59C22⋊D173—42no—
60C22⋊D173—41no—
61C2×Dic173—21no—
62C2×Dic173C22⋊C411yescharacteristic
63C2×Dic173C2×D411yescharacteristic
64C2×Dic173C2×D411yescharacteristic
65C4×D173—22no—
66C4×D173—21no—
67C4×D173—21no—
68C4×D173—41no—
69C4×D173—42no—
70C23×C173—21no—
71D4×C173—41no—
72C2×C4×C173—21no—
73C2×C4×C173—42no—
74C2×C4×C173C22⋊C411yescharacteristic
75C2×C4×C173C22⋊C411yescharacteristic
76C2×C4×C173C22×C411yescharacteristic
77C22×C173—41no—
78C22×C173—41no—
79C22×C173—41no—
80C22×C173C2×C22⋊C411yescharacteristic
81C2×D173—21no—
82C2×D173—21no—
83C2×D173—21no—
84C2×D173—41no—
85C2×D173—41no—
86C2×D173—41no—
87C4×C173—21no—
88C4×C173—21no—
89C4×C173—21no—
90C4×C173—41no—
91Dic173—21no—
92Dic173—41no—
93Dic173AGL(1,ℤ/8)11yescharacteristic
94Dic173AGL(1,ℤ/8)12yes—
95Dic173#13711yescharacteristic
96C2×C173—81no—
97C2×C173#41311yescharacteristic
98C2×C173#41711yescharacteristic
99C2×C173#41811yescharacteristic
100D173—41no—
101D173—81no—
102C173#155711yescharacteristic, complemented, Sylow
103#1557—1731nomaximal, Sylow
104#532—1731no—
105#432—1731no—
106#423—1731no—
107#332—1732no—
108#331—1732no—
109C2×#41—3461no—
110C2×M16—3461no—
111C4⋊Q8—1731no—
112#127—1731no—
113#124—3461no—
114#121—3461no—
115#121—1731no—
116#121—1731no—
117C4×D4—3461no—
118C4×D4—1731no—
119C4×D4#1062192411yescharacteristic
120C2×C42—1731no—
121C4⋊C8—3461no—
122C4⋊C8—1732no—
123C4⋊C8—1732no—
124C22⋊C8—3461no—
125#97—3461no—
126#41—6924no—
127C2×Q8—3461no—
128C2×D4—3461no—
129C2×D4—3461no—
130C2×D4—3461no—
131C2×D4—3461no—
132C2×D4—1731no—
133C2×D4C2×#1062192411yescharacteristic
134C22×C4—21no—
135C22×C4—3461no—
136C22×C4—1731no—
137C22×C4—1731no—
138C22×C4—1731no—
139M16—6922no—
140C2×C8—3462no—
141C2×C8—3462no—
142C4⋊C4—3461no—
143C4⋊C4—1731no—
144C4⋊C4C2×#1062192411yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—3461no—
147C22⋊C4—3461no—
148C22⋊C4—3461no—
149C42—1731no—
150C42—1731no—
151C42—1731no—
152C42C2×#1062192411yescharacteristic
153C23—21no—
154C23—3461no—
155C23—1731no—
156Q8—6922no—
157D4—41no—
158D4—6921no—
159D4—6922no—
160D4—6921no—
161D4—6921no—
162D4—6922no—
163D4—6922no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—3461no—
167C2×C4—3461no—
168C2×C4—3462no—
169C2×C4—3461no—
170C2×C4—1731no—
171C2×C4—1731no—
172C2×C4—1731no—
173C2×C4—6921no—
174C2×C4—6922no—
175C2×C4C22⋊#1062192411yescharacteristic
176C2×C4C22⋊#1062192411yescharacteristic
177C2×C4C22×#1062192411yescharacteristic
178C8—6922no—
179C8—6922no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—3461no—
184C22—3461no—
185C22—3461no—
186C22—6921no—
187C22—6921no—
188C22—6921no—
189C22C2×C22⋊#1062192411yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—41no—
194C4—3461no—
195C4—1731no—
196C4—1731no—
197C4—1732no—
198C4—6921no—
199C2—81no—
200C2—13841no—
201C2—6921no—
202C2#2601247711yescharacteristic
203C2#2601248211yescharacteristic
204C2#2601248311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10621924
commutatorC2×C4×C173C22×C4
FrattiniC2×C4C22×#10621924
FittingC4×D4×C173C4
socleC22×C173C2×C22⋊C4
prime radical#26012038C2
cosocleC4×Dic173C23
hypercenterC4×D4#10621924
hypocenterC173#1557
LCSG ▷ C2×C4×C173 ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #26012514C2semidirect
2. #26012496C2semidirect
3. #26012350C2semidirect
4. #26012349C2semidirect
102. C173#1557semidirect

Maximal subgroups

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

subgroupindex
#260125142
#260124962
#260123502
#260123492
#260120382
#1557173