Finite Group Databasebeta

← #22609118

Subgroups — #22609118

Order 9344.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#17989323C211yesmaximal, characteristic
2#17988933C211yesmaximal, characteristic
3#17988873C211yesmaximal, characteristic, complemented
4#17988798C211yesmaximal, characteristic, complemented
5#17988317C211yesmaximal, characteristic, complemented
6#17988317C211yesmaximal, characteristic, complemented
7#331×C73C211yesmaximal, characteristic
8C2×Dic292—21no—
9#14556591C2211yescharacteristic
10#14556578—21no—
11#14556578—21no—
12#14556572—22no—
13C4×Dic146C2211yescharacteristic
14C4×Dic146C2211yescharacteristic
15D4×Dic73—21no—
16D4×Dic73—21no—
17#14556523—21no—
18#14556516—21no—
19#14556516—21no—
20#14556512—22no—
21C4×#10596831C2211yescharacteristic
22#127×C73C2211yescharacteristic
23C4⋊C8×C73C2211yescharacteristic
24C4⋊C8×C73C2211yescharacteristic
25C2×Dic146—21no—
26C2×Dic146D411yescharacteristic
27C2×Dic146D411yescharacteristic
28C22×Dic73—22no—
29Dic292—42no—
30C2×#10596831—21no—
31C4⋊Dic73—21no—
32C4⋊Dic73—21no—
33C4⋊Dic73D411yescharacteristic
34C4⋊Dic73D411yescharacteristic
35#11924007—21no—
36#11924007—21no—
37C22⋊Dic73—22no—
38C22⋊Dic73—22no—
39C22⋊Dic73—22no—
40C4×Dic73—21no—
41C4×Dic73—21no—
42C2×D4×C73—21no—
43C2×D4×C73—21no—
44C2×D4×C73D412yes—
45C2×C8×C73—21no—
46C2×C8×C73—21no—
47C42×C73C2311yescharacteristic
48C23×C73—22no—
49D4×C73—42no—
50D4×C73—41no—
51D4×C73—41no—
52D4×C73—41no—
53D4×C73—41no—
54C2×C4×C73C2×D411yescharacteristic
55C2×C4×C73C2×D411yescharacteristic
56C2×C4×C73C2×D411yescharacteristic
57C2×Dic73—21no—
58C2×Dic73—21no—
59C2×Dic73—21no—
60C2×Dic73—21no—
61C2×Dic73—41no—
62C2×Dic73—82no—
63Dic146—21no—
64Dic146—21no—
65Dic146—21no—
66Dic146—21no—
67Dic146—41no—
68Dic146—41no—
69C8×C73—41no—
70C8×C73—41no—
71#10596831—41no—
72C22×C73—42no—
73C22×C73—42no—
74C22×C73—42no—
75C22×C73#12011yescharacteristic
76C4×C73—21no—
77C4×C73#13511yescharacteristic
78C4×C73#13511yescharacteristic
79C4×C73AGL(1,ℤ/8)11yescharacteristic
80C4×C73#13711yescharacteristic
81Dic73—41no—
82Dic73—41no—
83Dic73—41no—
84Dic73—41no—
85Dic73—81no—
86C2×C73—82no—
87C2×C73#44911yescharacteristic
88C2×C73#45211yescharacteristic
89C2×C73#45511yescharacteristic
90#1640—731nomaximal, Sylow
91C73#164011yescharacteristic, complemented, Sylow
92#559—731no—
93#486—731no—
94#475—731no—
95#462—731no—
96#331D7311yescharacteristic
97Q8⋊C8—731no—
98Q8⋊C8—731no—
99C2×Q16—1461no—
100C4⋊Q8—731no—
101#127C2×D7311yescharacteristic
102#124—1461no—
103#124—1461no—
104#123—1462no—
105C4×Q8—731no—
106C4×Q8—731no—
107C4×D4—1461no—
108C4×D4—1461no—
109#106—1461no—
110C4⋊C8C2×D7311yescharacteristic
111C4⋊C8C2×D7311yescharacteristic
112#103—1461no—
113#103—1461no—
114#102—1462no—
115C4×C8—731no—
116C2×Q8—731no—
117C2×Q8—731no—
118C2×Q8—1461no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4D29212yes—
122C22×C4—1462no—
123Q16—2922no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—1461no—
127C4⋊C4—731no—
128C4⋊C4—731no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C4⋊C4—1461no—
132C4⋊C4—1461no—
133C22⋊C4—1462no—
134C22⋊C4—1462no—
135C22⋊C4—1462no—
136C42—1461no—
137C42—1461no—
138C42C22×D7311yescharacteristic
139C23—22no—
140Q8—2921no—
141Q8—2921no—
142Q8—1461no—
143Q8—1461no—
144Q8—1461no—
145Q8—1461no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—2921no—
152C2×C4—5842no—
153C2×C4—1461no—
154C2×C4—1461no—
155C2×C4—1461no—
156C2×C4—1461no—
157C2×C4D4×D7311yescharacteristic
158C2×C4D4×D7311yescharacteristic
159C2×C4C2×D29211yescharacteristic
160C8—41no—
161C8—41no—
162C8—2921no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#1455656111yescharacteristic
167C4—21no—
168C4—2921no—
169C4—2921no—
170C4—2921no—
171C4—2921no—
172C4—5841no—
173C4#1455661011yescharacteristic
174C4#1455661211yescharacteristic
175C4#1455661511yescharacteristic
176C4#1455662011yescharacteristic
177C2—82no—
178C2#1798873311yescharacteristic
179C2#1798875011yescharacteristic
180C2#1798876711yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#331×C73C2
socleC22×C73#120
hypercenter#331D73
hypocenterC73#1640
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
3. #17988873C2semidirect
4. #17988798C2semidirect
5. #17988317C2semidirect
6. #17988317C2semidirect
91. C73#1640semidirect