Finite Group Databasebeta

← #36369327

Subgroups — #36369327

Order 22144.

320 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 92 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×#19149744C212yesmaximal
2C4×#14583836C211yesmaximal, characteristic, complemented
3#26012427C211yesmaximal, characteristic, complemented
4#26012361C212yesmaximal, complemented
5C4×#14583827C211yesmaximal, characteristic
6C2×#14583836C2212yes—
7C2×C4×#10621924C2212yes—
8#19149744C418yescomplemented
9#19149734—21no—
10C4×#13063443—21no—
11(C2×#10621924)⋊C4—21no—
12(C2×#10621924)⋊C4—21no—
13C2×#14583827C2211yescharacteristic
14Q8×Dic173C411yescharacteristic, complemented
15C4×D692—21no—
16C4×D692C411yescharacteristic, complemented
17#19149641—21no—
18#19149641C411yescharacteristic, complemented
19#19149637—21no—
20#19149637C2211yescharacteristic
21C42×D173—21no—
22C42×D173C2211yescharacteristic
23C4×Q8×C173C411yescharacteristic, complemented
24C22×#10621924—22no—
25#14583836—22no—
26#14583836C2×C414yescomplemented
27C2×#13063443—22no—
28C4×#10621924—22no—
29C4×#10621924C2×C414yescomplemented
30#14583827—22no—
31#14583827C2×C414yes—
32C2×D692—21no—
33C2×D692C2×C411yescharacteristic
34C2×C4×D173—21no—
35C2×C4×D173—21no—
36C2×C4×D173—21no—
37C2×C4×D173D411yescharacteristic
38C2×C4×D173D411yescharacteristic
39C2×C4×D173C2311yescharacteristic
40C4⋊Dic173—21no—
41C4⋊Dic173C2×C411yescharacteristic
42#14583803—21no—
43#14583803—21no—
44#14583803—21no—
45C4×Dic173—21no—
46C4×Dic173—21no—
47C4×Dic173C2×C411yescharacteristic
48C4×Dic173D411yescharacteristic
49C4×Dic173D411yescharacteristic
50C2×Q8×C173C2×C411yescharacteristic
51C4⋊C4×C173—21no—
52C4⋊C4×C173C2×C411yescharacteristic
53C42×C173—21no—
54C42×C173C2×C411yescharacteristic
55C2×#10621924—24no—
56C2×#10621924—42no—
57C2×#10621924—42no—
58#13063443—24no—
59C22×D173—21no—
60C22×D173C2×D411yescharacteristic
61D692—24no—
62D692—21no—
63D692C4212yes—
64C2×Dic173—21no—
65C2×Dic173C22⋊C411yescharacteristic
66C2×Dic173C22⋊C411yescharacteristic
67C2×Dic173C2×D411yescharacteristic
68C4×D173—24no—
69C4×D173—41no—
70C4×D173—41no—
71C4×D173—42no—
72C4×D173—42no—
73C4×D173C22×C412yes—
74C4×D173#4112yes—
75Q8×C173—21no—
76Q8×C173C4212yes—
77C2×C4×C173—21no—
78C2×C4×C173—21no—
79C2×C4×C173C22⋊C411yescharacteristic
80C2×C4×C173C22⋊C411yescharacteristic
81C2×C4×C173C22×C411yescharacteristic
82C22×C173C2×C22⋊C411yescharacteristic
83C2×D173—21no—
84C2×D173—21no—
85C2×D173—22no—
86C2×D173—41no—
87C2×D173—41no—
88C2×D173C4×D412yes—
89#10621924—44no—
90C4×C173—22no—
91C4×C173—21no—
92C4×C173—21no—
93C4×C173—41no—
94C4×C173C2×C4211yescharacteristic
95C4×C173#11711yescharacteristic
96Dic173—21no—
97Dic173—21no—
98Dic173—41no—
99Dic173C4×D412yes—
100C2×C173C4×C22⋊C411yescharacteristic
101C2×C173#42111yescharacteristic
102C2×C173#42111yescharacteristic
103D173—22no—
104D173—42no—
105C173#175911yescharacteristic, complemented, Sylow
106#1759—1731nomaximal, Sylow
107C4×#41—1731no—
108C2×#104—1732no—
109C4×M16—1731no—
110#376—1731no—
111#339—1732no—
112C2×#41—1731no—
113C2×M16—1732no—
114C4×Q8—1731no—
115C4×Q8#1062192411yescharacteristic, complemented
116C4×D4—3461no—
117C4×D4—3461no—
118C4×D4—1731no—
119C4×D4—1731no—
120#117—3461no—
121#117—1731no—
122C2×C42—3461no—
123C2×C42—1732no—
124C2×C42—1731no—
125#104—1738no—
126#97—3461no—
127C4×C8—3461no—
128#95—3461no—
129#95—3461no—
130#41—3462no—
131#41—1734no—
132C2×Q8C2×#1062192411yescharacteristic
133C2×D4—3461no—
134C2×D4—1731no—
135C22×C4—3461no—
136C22×C4—3461no—
137C22×C4—3462no—
138C22×C4—3461no—
139C22×C4—1731no—
140C22×C4—1731no—
141C22×C4—1731no—
142M16—3462no—
143M16—1734no—
144C2×C8—3462no—
145C4⋊C4—21no—
146C4⋊C4—3461no—
147C4⋊C4—1731no—
148C4⋊C4C2×#1062192411yescharacteristic
149C22⋊C4—3461no—
150C22⋊C4—3461no—
151C22⋊C4—3461no—
152C42—21no—
153C42—3461no—
154C42—3461no—
155C42—3462no—
156C42—1734no—
157C42—1731no—
158C42—1731no—
159C42—1731no—
160C42C2×#1062192411yescharacteristic
161C23—3461no—
162C23—1731no—
163Q8—21no—
164Q8C4×#1062192412yes—
165D4—3464no—
166D4—3461no—
167D4—1732no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—3464no—
171C2×C4—3464no—
172C2×C4—3461no—
173C2×C4—1731no—
174C2×C4—1731no—
175C2×C4—1731no—
176C2×C4—1732no—
177C2×C4—1732no—
178C2×C4—6921no—
179C2×C4—6921no—
180C2×C4—6922no—
181C2×C4—6922no—
182C2×C4—6922no—
183C2×C4—6922no—
184C2×C4C22⋊#1062192411yescharacteristic
185C2×C4C22⋊#1062192411yescharacteristic
186C2×C4C22×#1062192411yescharacteristic
187C8—3464no—
188C22—3461no—
189C22—3461no—
190C22—3462no—
191C22—1732no—
192C22—6921no—
193C22—6921no—
194C22C2×C22⋊#1062192411yescharacteristic
195C4—22no—
196C4—21no—
197C4—21no—
198C4—41no—
199C4—3461no—
200C4—3461no—
201C4—1732no—
202C4—6924no—
203C4—6921no—
204C4C2×C4×#1062192411yescharacteristic
205C4#1914975811yescharacteristic
206C2—3462no—
207C2—6922no—
208C2C4×C22⋊#1062192411yescharacteristic
209C2#2601248811yescharacteristic
210C2#2601249011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10621924
commutatorC4×C173C2×C42
FrattiniC2×C4C22×#10621924
FittingC4×Q8×C173C4
socleC22×C173C2×C22⋊C4
prime radicalC2×#14583827C22
cosocleC2×C4×D173C23
hypercenterC4×Q8#10621924
hypocenterC173#1759
LCSG ▷ C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C4×#14583836C2semidirect
3. #26012427C2semidirect
4. #26012361C2semidirect
8. #19149744C4semidirect
14. Q8×Dic173C4semidirect
16. C4×D692C4semidirect
18. #19149641C4semidirect
23. C4×Q8×C173C4semidirect
26. #14583836C2×C4semidirect
29. C4×#10621924C2×C4semidirect
105. C173#1759semidirect
115. C4×Q8#10621924semidirect

Maximal subgroups

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

subgroupindex
C2×#191497442
C4×#145838362
#260124272
#260123612
C4×#145838272
#1759173