Finite Group Databasebeta

← #36369854

Subgroups — #36369854

Order 22144.

250 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 54 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#26012477C212yesmaximal, complemented
2#26012401C212yesmaximal, complemented
3#26012399C212yesmaximal, complemented
4#26012037C211yesmaximal, characteristic
5D173⋊M16—22no—
6#19149740C2214yes—
7#19149739—22no—
8C2×#14583826C2211yescharacteristic
9#19149677C2211yescharacteristic
10#19149675C411yescharacteristic
11#19149668C411yescharacteristic
12#19149666C2211yescharacteristic
13#19149651—22no—
14C4×C22⋊D173—22no—
15C2×C4×Dic173C411yescharacteristic
16C2×#41×C173C411yescharacteristic
17#14583836—42no—
18#14583835—24no—
19D173⋊C8—42no—
20#14583826—41no—
21#14583826—41no—
22C2×Dic346C2311yescharacteristic
23C2×D692C2×C411yescharacteristic
24C2×C22⋊D173—22no—
25C2×C22⋊D173D412yes—
26C22×Dic173—21no—
27C2×C4×D173D412yes—
28#14583805—22no—
29C22⋊Dic173—22no—
30#14583803—22no—
31C4×Dic173—21no—
32C4×Dic173C2×C411yescharacteristic
33C4×Dic173C2×C411yescharacteristic
34#41×C173—41no—
35#41×C173—41no—
36C2×Q8×C173C2×C411yescharacteristic
37C2×D4×C173—21no—
38C2×D4×C173C2×C411yescharacteristic
39C22×C4×C173—21no—
40C22×C4×C173C2×C411yescharacteristic
41#13063443—44no—
42C22×D173C22⋊C412yes—
43Dic346—41no—
44D692—41no—
45C22⋊D173—42no—
46C22⋊D173—44no—
47C2×Dic173—21no—
48C2×Dic173—21no—
49C2×Dic173—42no—
50C2×Dic173C2×D412yes—
51C4×D173—22no—
52C4×D173—22no—
53C23×C173—21no—
54C23×C173C22⋊C411yescharacteristic
55Q8×C173—41no—
56D4×C173—41no—
57D4×C173—42no—
58C2×C4×C173—21no—
59C2×C4×C173—21no—
60C2×C4×C173—21no—
61C2×C4×C173—41no—
62C2×C4×C173—41no—
63C2×C4×C173C22⋊C411yescharacteristic
64C2×C4×C173C22×C411yescharacteristic
65C22×C173—21no—
66C22×C173—41no—
67C22×C173—42no—
68C22×C173—41no—
69C22×C173C2×C22⋊C411yescharacteristic
70C2×D173—22no—
71C2×D173—42no—
72C4×C173—21no—
73C4×C173—41no—
74C4×C173#9911yescharacteristic
75C4×C173#9911yescharacteristic
76Dic173—22no—
77Dic173—22no—
78Dic173—41no—
79C2×C173—21no—
80C2×C173—41no—
81C2×C173—81no—
82C2×C173C2×#9911yescharacteristic
83D173—42no—
84C173#213211yescharacteristic, complemented, Sylow
85#2132—1731nomaximal, Sylow
86#532—1731no—
87#413—1732no—
88#356—1732no—
89#355—1732no—
90C2×#41—1731no—
91C2×#41#1062192411yescharacteristic
92C2×M16—3462no—
93C4⋊Q8—1731no—
94#127—1731no—
95#124—1731no—
96#124—1731no—
97#121—3462no—
98C4×D4—3462no—
99C2×C42—1731no—
100#101—1734no—
101#100—3462no—
102#41—41no—
103#41—41no—
104#41—6921no—
105#41—6921no—
106C2×Q8—1731no—
107C2×Q8C2×#1062192411yescharacteristic
108C2×D4—21no—
109C2×D4—3462no—
110C2×D4—1732no—
111C2×D4—1731no—
112C2×D4C2×#1062192411yescharacteristic
113C22×C4—21no—
114C22×C4—3461no—
115C22×C4—1732no—
116C22×C4C2×#1062192411yescharacteristic
117M16—3464no—
118M16—6922no—
119C2×C8—6922no—
120C4⋊C4—3462no—
121C22⋊C4—3462no—
122C22⋊C4—3462no—
123C42—3461no—
124C42—1731no—
125C42—1731no—
126C23—21no—
127C23—1732no—
128C23C22⋊#1062192411yescharacteristic
129Q8—41no—
130Q8—6921no—
131D4—41no—
132D4—42no—
133D4—6921no—
134D4—6922no—
135D4—6924no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—3461no—
142C2×C4—3462no—
143C2×C4—3462no—
144C2×C4—3461no—
145C2×C4—1732no—
146C2×C4—6922no—
147C2×C4C22⋊#1062192411yescharacteristic
148C2×C4C22×#1062192411yescharacteristic
149C8—6924no—
150C22—21no—
151C22—41no—
152C22—42no—
153C22—41no—
154C22—3462no—
155C22—6922no—
156C22C2×C22⋊#1062192411yescharacteristic
157C4—21no—
158C4—41no—
159C4—3462no—
160C4—3462no—
161C4—6921no—
162C4#1914973711yescharacteristic
163C4#1914973711yescharacteristic
164C2—21no—
165C2—41no—
166C2—81no—
167C2—6922no—
168C2C2×#1914973711yescharacteristic
subgroupG/H
centerC4#19149737
commutatorC2×C4×C173C22×C4
FrattiniC2×C4C22×#10621924
FittingC2×#41×C173C4
socleC2×C173C2×#99
prime radical#26012037C2
cosocleC2×Dic346C23
hypercenterC2×#41#10621924
hypocenterC173#2132
LCSG ▷ C2×C4×C173 ▷ C22×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #26012477C2semidirect
2. #26012401C2semidirect
3. #26012399C2semidirect
84. C173#2132semidirect

Maximal subgroups

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

subgroupindex
#260124772
#260124012
#260123992
#260120372
#2132173