Finite Group Databasebeta

← #36369095

Subgroups — #36369095

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#26012511C211yesmaximal, characteristic, complemented
2#26012494C211yesmaximal, characteristic, complemented
3#26012350C212yesmaximal, complemented
4#26012349C212yesmaximal, complemented
5#26012036C211yesmaximal, characteristic
6C2×#14583835—21no—
7#19149746C2212yes—
8#19149746C2212yes—
9C4⋊#13063443—21no—
10C22⋊#13063443—21no—
11#19149734—21no—
12C2×#14583825—21no—
13#19149678C2211yescharacteristic
14#19149675C2211yescharacteristic
15#19149665—21no—
16#19149653C411yescharacteristic
17#19149651—21no—
18D4×Dic173C411yescharacteristic
19#19149641C411yescharacteristic
20#19149639—21no—
21C2×C4×Dic173C2211yescharacteristic
22#121×C173C411yescharacteristic
23#14583835—42no—
24C2×#13063443—22no—
25C2×#13063443—22no—
26#14583825—44no—
27C2×Dic346—21no—
28C2×D692C2×C411yescharacteristic
29C2×C22⋊D173—21no—
30C2×C22⋊D173—21no—
31C2×C22⋊D173—21no—
32C22×Dic173—21no—
33C22×Dic173D411yescharacteristic
34C22×Dic173D411yescharacteristic
35C2×C4×D173—21no—
36C4⋊Dic173C2×C411yescharacteristic
37#14583805—21no—
38C22⋊Dic173—21no—
39#14583803—21no—
40#14583803—21no—
41C4×Dic173C2×C411yescharacteristic
42C4×Dic173D411yescharacteristic
43C4×Dic173D411yescharacteristic
44C4×Dic173C2311yescharacteristic
45C2×D4×C173—21no—
46C2×D4×C173C2×C411yescharacteristic
47C22×C4×C173C2×C411yescharacteristic
48C4⋊C4×C173C2×C411yescharacteristic
49C22⋊C4×C173—21no—
50#13063443—42no—
51#13063443—42no—
52C22×D173—21no—
53Dic346—42no—
54D692—41no—
55C22⋊D173—42no—
56C22⋊D173—41no—
57C22⋊D173—42no—
58C22⋊D173—41no—
59C2×Dic173—22no—
60C2×Dic173—21no—
61C2×Dic173—21no—
62C2×Dic173—21no—
63C2×Dic173—42no—
64C2×Dic173C22⋊C411yescharacteristic
65C2×Dic173C22⋊C411yescharacteristic
66C2×Dic173C2×D411yescharacteristic
67C2×Dic173C2×D411yescharacteristic
68C4×D173—42no—
69C23×C173—21no—
70C23×C173C22⋊C411yescharacteristic
71D4×C173—41no—
72D4×C173—42no—
73C2×C4×C173—21no—
74C2×C4×C173—41no—
75C2×C4×C173C22⋊C411yescharacteristic
76C2×C4×C173C22×C411yescharacteristic
77C22×C173—21no—
78C22×C173—21no—
79C22×C173—21no—
80C22×C173—41no—
81C22×C173—41no—
82C22×C173—41no—
83C22×C173C2×C22⋊C411yescharacteristic
84C2×D173—41no—
85C2×D173—41no—
86C2×D173—41no—
87C4×C173—21no—
88C4×C173—21no—
89C4×C173—41no—
90Dic173—21no—
91Dic173—21no—
92Dic173—41no—
93Dic173AGL(1,ℤ/8)11yescharacteristic
94Dic173AGL(1,ℤ/8)12yes—
95Dic173#13711yescharacteristic
96C2×C173—41no—
97C2×C173—81no—
98C2×C173#41311yescharacteristic
99C2×C173#41711yescharacteristic
100C2×C173#41811yescharacteristic
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#1062192411yescharacteristic
117C4×D4—3461no—
118C4×D4—1731no—
119C4×D4—1731no—
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—21no—
129C2×D4—3461no—
130C2×D4—3461no—
131C2×D4—3461no—
132C2×D4—1731no—
133C2×D4C2×#1062192411yescharacteristic
134C22×C4—3461no—
135C22×C4—3461no—
136C22×C4—1731no—
137C22×C4—1731no—
138C22×C4C2×#1062192411yescharacteristic
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—
152C42—1731no—
153C23—21no—
154C23—3461no—
155C23C22⋊#1062192411yescharacteristic
156Q8—6922no—
157D4—41no—
158D4—42no—
159D4—6921no—
160D4—6921no—
161D4—6921no—
162D4—6922no—
163D4—6922no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—3461no—
167C2×C4—3461no—
168C2×C4—3462no—
169C2×C4—3461no—
170C2×C4—1731no—
171C2×C4—1731no—
172C2×C4—1731no—
173C2×C4—1731no—
174C2×C4—6922no—
175C2×C4—6922no—
176C2×C4C22⋊#1062192411yescharacteristic
177C2×C4C22×#1062192411yescharacteristic
178C8—6922no—
179C8—6922no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—41no—
184C22—41no—
185C22—41no—
186C22—6921no—
187C22—6921no—
188C22—6921no—
189C22C2×C22⋊#1062192411yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—3461no—
194C4—3461no—
195C4—1731no—
196C4—1731no—
197C4—1732no—
198C4—6921no—
199C2—41no—
200C2—81no—
201C2—13841no—
202C2#2601247811yescharacteristic
203C2#2601248211yescharacteristic
204C2#2601248311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10621924
commutatorC2×C4×C173C22×C4
FrattiniC2×C4C22×#10621924
Fitting#121×C173C4
socleC22×C173C2×C22⋊C4
prime radical#26012036C2
cosocleC4×Dic173C23
hypercenter#121#10621924
hypocenterC173#1557
LCSG ▷ C2×C4×C173 ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #26012511C2semidirect
2. #26012494C2semidirect
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
#260125112
#260124942
#260123502
#260123492
#260120362
#1557173