Finite Group Databasebeta

← #22625397

Subgroups — #22625397

Order 9344.

216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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#17989607C211yesmaximal, characteristic, complemented
2C4×#11924037C211yesmaximal, characteristic, complemented
3#17989444C212yesmaximal, complemented
4#17989442C212yesmaximal, complemented
5#17989118C211yesmaximal, characteristic
6C2×#11924037—21no—
7#14556658—21no—
8C22⋊#10596833—21no—
9#14556646C2212yes—
10#14556646C2212yes—
11C4×#10596833—21no—
12#14556584—21no—
13#14556582C2211yescharacteristic
14#14556578C2211yescharacteristic
15#14556572—21no—
16#14556570C411yescharacteristic
17#14556556C411yescharacteristic
18D4×Dic73—21no—
19D4×Dic73C411yescharacteristic
20#14556547—21no—
21C2×C4×Dic73C2211yescharacteristic
22#121×C73C411yescharacteristic
23#11924037—24no—
24C2×#10596833—22no—
25C2×#10596833—22no—
26C2×Dic146C2×C411yescharacteristic
27C22×Dic73—21no—
28C22×Dic73D411yescharacteristic
29C22×Dic73D411yescharacteristic
30C4⋊Dic73—21no—
31C4⋊Dic73C2×C411yescharacteristic
32#11924007—21no—
33#11924007—21no—
34#11924007—21no—
35C22⋊Dic73—21no—
36C22⋊Dic73—21no—
37C22⋊Dic73—21no—
38C22⋊Dic73—21no—
39C4×Dic73—21no—
40C4×Dic73C2×C411yescharacteristic
41C4×Dic73D411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4×Dic73C2311yescharacteristic
44C2×D4×C73—21no—
45C2×D4×C73C2×C411yescharacteristic
46C22×C4×C73C2×C411yescharacteristic
47C4⋊C4×C73C2×C411yescharacteristic
48C22⋊C4×C73—21no—
49C23×C73—21no—
50C23×C73C22⋊C411yescharacteristic
51D4×C73—41no—
52D4×C73—42no—
53C2×C4×C73—21no—
54C2×C4×C73—41no—
55C2×C4×C73C22⋊C411yescharacteristic
56C2×C4×C73C22×C411yescharacteristic
57C2×Dic73—22no—
58C2×Dic73—21no—
59C2×Dic73—21no—
60C2×Dic73—41no—
61C2×Dic73—42no—
62C2×Dic73C22⋊C411yescharacteristic
63C2×Dic73C22⋊C411yescharacteristic
64C2×Dic73C2×D411yescharacteristic
65C2×Dic73C2×D411yescharacteristic
66Dic146—41no—
67#10596833—24no—
68#10596833—42no—
69C22×C73—21no—
70C22×C73—21no—
71C22×C73—21no—
72C22×C73—41no—
73C22×C73—41no—
74C22×C73—41no—
75C22×C73C2×C22⋊C411yescharacteristic
76C4×C73—21no—
77C4×C73—21no—
78C4×C73—41no—
79Dic73—21no—
80Dic73—21no—
81Dic73—21no—
82Dic73—41no—
83Dic73—41no—
84Dic73#10412yes—
85C2×C73—41no—
86C2×C73—81no—
87C2×C73#41311yescharacteristic
88C2×C73C2×#10411yescharacteristic
89C2×C73#42111yescharacteristic
90#1529—731nomaximal, Sylow
91C73#152911yescharacteristic, complemented, Sylow
92#529—731no—
93#432—731no—
94C4×M16—731no—
95#330—732no—
96#329—732no—
97C2×M16—1461no—
98#126—1461no—
99#125—731no—
100#124—731no—
101#123—1461no—
102C22⋊Q8—731no—
103#121#6440811yescharacteristic
104C4×Q8—731no—
105C4×D4—731no—
106C4×D4—1461no—
107#117—1461no—
108C2×C42—731no—
109C4⋊C8—1461no—
110C22⋊C8—1461no—
111#97—732no—
112#97—732no—
113C4×C8—1461no—
114C2×Q8—731no—
115C2×D4—21no—
116C2×D4C2×#6440811yescharacteristic
117C22×C4—731no—
118C22×C4—731no—
119C22×C4—1461no—
120C22×C4C2×#6440811yescharacteristic
121M16—1464no—
122C2×C8—1462no—
123C2×C8—1462no—
124C4⋊C4—731no—
125C4⋊C4—1461no—
126C4⋊C4—1461no—
127C4⋊C4—1461no—
128C4⋊C4—1461no—
129C4⋊C4C2×#6440811yescharacteristic
130C22⋊C4—21no—
131C22⋊C4—1461no—
132C22⋊C4—1461no—
133C22⋊C4—1461no—
134C22⋊C4—1461no—
135C42—731no—
136C42—731no—
137C42—731no—
138C42—731no—
139C42—1461no—
140C23—21no—
141C23C22⋊#6440811yescharacteristic
142Q8—2921no—
143D4—41no—
144D4—42no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—2922no—
148C2×C4—2921no—
149C2×C4—731no—
150C2×C4—731no—
151C2×C4—731no—
152C2×C4—731no—
153C2×C4—1461no—
154C2×C4—1461no—
155C2×C4—1462no—
156C2×C4C22⋊#6440811yescharacteristic
157C2×C4C22×#6440811yescharacteristic
158C8—2922no—
159C8—1464no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—41no—
164C22—41no—
165C22—41no—
166C22C2×C22⋊#6440811yescharacteristic
167C4—21no—
168C4—21no—
169C4—41no—
170C4—2921no—
171C4—2921no—
172C4—732no—
173C4—1461no—
174C4—1461no—
175C4—1461no—
176C2—41no—
177C2—81no—
178C2#1798957411yescharacteristic
179C2D73⋊#10411yescharacteristic
180C2#1798958511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#121×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#121#64408
hypocenterC73#1529
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #17989607C2semidirect
2. C4×#11924037C2semidirect
3. #17989444C2semidirect
4. #17989442C2semidirect
91. C73#1529semidirect