Finite Group Databasebeta

← #36369565

Subgroups — #36369565

Order 22144.

332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 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#26012571C211yesmaximal, characteristic, complemented
2#26012490C212yesmaximal, complemented
3#26012472C211yesmaximal, characteristic, complemented
4#26012362C212yesmaximal, complemented
5#26012042C211yesmaximal, characteristic
6#19149767—24no—
7D173⋊M16—22no—
8D173⋊M16C2212yes—
9#19149758C2212yes—
10#19149744—24no—
11#19149738—22no—
12C2×#14583827C2211yescharacteristic
13C2×#14583827C2211yescharacteristic
14#19149676C411yescharacteristic, complemented
15#19149668C411yescharacteristic, complemented
16#19149668C411yescharacteristic, complemented
17#19149654—22no—
18#19149641—22no—
19C42×D173C2211yescharacteristic
20C4⋊Q8×C173C411yescharacteristic, complemented
21#14583836—24no—
22#14583836D414yescomplemented
23#14583835—22no—
24D173⋊C8—24no—
25D173⋊C8—22no—
26C4⋊#10621924—22no—
27C22⋊#10621924—22no—
28C4×#10621924—22no—
29#14583827—22no—
30#14583827—22no—
31#14583827—22no—
32#14583827—22no—
33C2×D692—22no—
34C2×D692—21no—
35C2×D692C2×C411yescharacteristic
36C2×D692C2×C411yescharacteristic
37C2×D692D412yes—
38C2×C4×D173—21no—
39C2×C4×D173—21no—
40C2×C4×D173D412yes—
41C2×C4×D173C2311yescharacteristic
42#14583803—22no—
43#14583803—22no—
44C4×Dic173—21no—
45C4×Dic173C2×C411yescharacteristic
46C2×Q8×C173C2×C411yescharacteristic
47C2×Q8×C173C2×C411yescharacteristic
48C4⋊C4×C173—22no—
49C42×C173C2×C411yescharacteristic
50C2×#10621924—42no—
51#13063443—24no—
52C22×D173—21no—
53C22×D173C22⋊C412yes—
54C22×D173C2×D411yescharacteristic
55D692—24no—
56D692—22no—
57D692—22no—
58D692—44no—
59D692—42no—
60C2×Dic173—21no—
61C2×Dic173C2×D411yescharacteristic
62C4×D173—22no—
63C4×D173—22no—
64C4×D173—42no—
65C4×D173—41no—
66C4×D173—41no—
67C4×D173C2×D412yes—
68C4×D173#4112yes—
69Q8×C173—22no—
70Q8×C173—22no—
71C2×C4×C173—21no—
72C2×C4×C173—21no—
73C2×C4×C173C22⋊C412yes—
74C2×C4×C173C22×C411yescharacteristic
75C22×C173C2×C22⋊C411yescharacteristic
76C2×D173—22no—
77C2×D173—41no—
78C2×D173—42no—
79C2×D173—42no—
80C2×D173—41no—
81C2×D173#12112yes—
82#10621924—82no—
83C4×C173—22no—
84C4×C173—22no—
85C4×C173—41no—
86C4×C173C4×D412yes—
87Dic173—41no—
88Dic173#12011yescharacteristic
89Dic173#12311yescharacteristic
90C2×C173—21no—
91C2×C173#38611yescharacteristic
92D173—22no—
93D173—42no—
94D173—81no—
95C173#188411yescharacteristic, complemented, Sylow
96#1884—1731nomaximal, Sylow
97#568—1731no—
98#532—1731no—
99#421—1732no—
100#410—1731no—
101#339—1732no—
102C2×#41—1731no—
103C2×#41—1731no—
104#131—3464no—
105C2×M16—3462no—
106C2×M16—1732no—
107C4⋊Q8#1062192411yescharacteristic, complemented
108#127—1731no—
109#124—1731no—
110#124—1731no—
111#121—3462no—
112C4×D4—3462no—
113#117—1732no—
114C2×C42—1731no—
115#104—3464no—
116#99—3462no—
117#41—3462no—
118#41—3462no—
119#41—3462no—
120#41—3462no—
121C2×Q8C2×#1062192411yescharacteristic
122C2×Q8C2×#1062192411yescharacteristic
123C2×D4—3462no—
124C2×D4—3461no—
125C2×D4—1732no—
126C2×D4—1731no—
127C2×D4—1731no—
128C22×C4—3461no—
129C22×C4—3461no—
130C22×C4—1732no—
131C22×C4—1731no—
132M16—3464no—
133M16—3462no—
134M16—1734no—
135C2×C8—3464no—
136C2×C8—3462no—
137C4⋊C4—22no—
138C4⋊C4—3462no—
139C22⋊C4—3462no—
140C22⋊C4—3462no—
141C22⋊C4—3462no—
142C42—3461no—
143C42—3462no—
144C42—1731no—
145C42C2×#1062192411yescharacteristic
146C23—3461no—
147C23—1732no—
148C23—1731no—
149Q8—22no—
150Q8—22no—
151D4—3464no—
152D4—3462no—
153D4—3462no—
154D4—6924no—
155D4—6922no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—3462no—
159C2×C4—3462no—
160C2×C4—3461no—
161C2×C4—1731no—
162C2×C4—1732no—
163C2×C4—1732no—
164C2×C4—6922no—
165C2×C4—6921no—
166C2×C4—6921no—
167C2×C4—6922no—
168C2×C4C22⋊#1062192412yes—
169C2×C4C22×#1062192411yescharacteristic
170C8—3464no—
171C22—3462no—
172C22—1732no—
173C22—6921no—
174C22—6922no—
175C22—6922no—
176C22—6921no—
177C22C2×C22⋊#1062192411yescharacteristic
178C4—22no—
179C4—22no—
180C4—41no—
181C4—13842no—
182C4—1731no—
183C4—1731no—
184C4—6921no—
185C4D4×#1062192412yes—
186C2—21no—
187C2—3462no—
188C2—13841no—
189C2—6922no—
190C2#2601243911yescharacteristic
subgroupG/H
centerC2#26012439
commutatorC2×C4×C173C22×C4
FrattiniC2×C4C22×#10621924
FittingC4⋊Q8×C173C4
socleC2×C173#386
prime radical#26012042C2
cosocleC2×C4×D173C23
hypercenterC4⋊Q8#10621924
hypocenterC173#1884
LCSG ▷ C2×C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #26012571C2semidirect
2. #26012490C2semidirect
3. #26012472C2semidirect
4. #26012362C2semidirect
14. #19149676C4semidirect
15. #19149668C4semidirect
16. #19149668C4semidirect
20. C4⋊Q8×C173C4semidirect
22. #14583836D4semidirect
95. C173#1884semidirect
107. C4⋊Q8#10621924semidirect

Maximal subgroups

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

subgroupindex
#260125712
#260124902
#260124722
#260123622
#260120422
#1884173