Finite Group Databasebeta

← #22609115

Subgroups — #22609115

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#17989322C211yesmaximal, characteristic
2#17988935C211yesmaximal, characteristic
3#17988869C211yesmaximal, characteristic, complemented
4#17988330C211yesmaximal, characteristic
5Q8⋊#10596831C211yesmaximal, characteristic, complemented
6#17988317C211yesmaximal, characteristic, complemented
7#462×C73C211yesmaximal, characteristic, complemented
8#14556588C2211yescharacteristic
9#14556580—21no—
10#14556579—21no—
11#14556576—22no—
12C4×Dic146C2211yescharacteristic
13C4×D292—21no—
14#14556553—21no—
15#14556522—21no—
16C4⋊#10596831C2211yescharacteristic
17#14556514—21no—
18#14556511—22no—
19C4×#10596831C2211yescharacteristic
20C2×Q16×C73—21no—
21C4⋊Q8×C73C2211yescharacteristic
22C4×Q8×C73C2211yescharacteristic
23C4⋊C8×C73C2211yescharacteristic
24#103×C73—21no—
25C2×Dic146D411yescharacteristic
26C2×D292—21no—
27C2×D292—21no—
28C2×D292D412yes—
29C2×C4×D73—22no—
30C2×#10596831—21no—
31C2×#10596831—21no—
32C4⋊Dic73D411yescharacteristic
33#11924007—21no—
34#11924005—22no—
35#11924005—22no—
36#11924005—22no—
37C4×Dic73—21no—
38C2×Q8×C73—21no—
39C2×Q8×C73D411yescharacteristic
40Q16×C73—42no—
41C2×C8×C73—21no—
42C4⋊C4×C73—21no—
43C4⋊C4×C73—21no—
44C4⋊C4×C73—21no—
45C4⋊C4×C73D411yescharacteristic
46C42×C73—21no—
47C42×C73C2311yescharacteristic
48C22×D73—22no—
49Q8×C73—21no—
50Q8×C73—21no—
51Q8×C73—41no—
52Q8×C73—41no—
53C2×C4×C73—21no—
54C2×C4×C73—21no—
55C2×C4×C73—41no—
56C2×C4×C73C2×D411yescharacteristic
57C2×C4×C73C2×D411yescharacteristic
58C2×C4×C73C2×D411yescharacteristic
59C2×Dic73—21no—
60C2×Dic73—21no—
61D292—42no—
62D292—41no—
63D292—41no—
64D292—41no—
65D292—41no—
66C4×D73—82no—
67Dic146—21no—
68Dic146—21no—
69C8×C73—41no—
70#10596831—41no—
71#10596831—41no—
72C22×C73#12011yescharacteristic
73C2×D73—42no—
74C2×D73—42no—
75C2×D73—42no—
76C4×C73—21no—
77C4×C73—41no—
78C4×C73—41no—
79C4×C73—81no—
80C4×C73#13511yescharacteristic
81C4×C73#13511yescharacteristic
82C4×C73AGL(1,ℤ/8)11yescharacteristic
83C4×C73#13711yescharacteristic
84Dic73—41no—
85Dic73—41no—
86C2×C73#44911yescharacteristic
87C2×C73#45211yescharacteristic
88C2×C73#45511yescharacteristic
89D73—82no—
90#1640—731nomaximal, Sylow
91C73#164011yescharacteristic, complemented, Sylow
92#559—731no—
93#486—731no—
94#475—731no—
95#462D7311yescharacteristic, complemented
96#331—731no—
97Q8⋊C8—731no—
98Q8⋊C8—731no—
99C2×Q16—21no—
100C4⋊Q8C2×D7311yescharacteristic
101#127—731no—
102#124—1461no—
103#124—1461no—
104#123—1462no—
105C4×Q8—731no—
106C4×Q8C2×D7311yescharacteristic
107C4×D4—1461no—
108C4×D4—1461no—
109#106—1461no—
110C4⋊C8—731no—
111C4⋊C8C2×D7311yescharacteristic
112#103—21no—
113#103—1461no—
114#102—1462no—
115C4×C8—731no—
116C2×Q8—21no—
117C2×Q8—731no—
118C2×Q8C22⋊D7311yescharacteristic
119C2×D4—732no—
120C2×D4—1461no—
121C2×D4—1461no—
122C22×C4—1462no—
123Q16—42no—
124C2×C8—21no—
125C2×C8—1461no—
126C2×C8—1461no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—731no—
131C4⋊C4—1461no—
132C4⋊C4C22⋊D7311yescharacteristic
133C22⋊C4—1462no—
134C22⋊C4—1462no—
135C22⋊C4—1462no—
136C42—21no—
137C42—1461no—
138C42C22×D7311yescharacteristic
139C23—1462no—
140Q8—21no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—1461no—
145Q8—1461no—
146D4—2922no—
147D4—2921no—
148D4—2921no—
149D4—2921no—
150D4—2921no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—5842no—
155C2×C4—1461no—
156C2×C4—1461no—
157C2×C4D4×D7311yescharacteristic
158C2×C4D4×D7311yescharacteristic
159C2×C4C2×C22⋊D7311yescharacteristic
160C8—41no—
161C8—2921no—
162C8—2921no—
163C22—2922no—
164C22—2922no—
165C22—2922no—
166C22#1455655911yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—81no—
171C4—2921no—
172C4—2921no—
173C4#1455661111yescharacteristic
174C4#1455661411yescharacteristic
175C4#1455661711yescharacteristic
176C4#1455662311yescharacteristic
177C2—5842no—
178C2#1798873011yescharacteristic
179C2#1798874811yescharacteristic
180C2#1798876311yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#462×C73C2
socleC22×C73#120
hypercenter#462D73
hypocenterC73#1640
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #17988869C2semidirect
5. Q8⋊#10596831C2semidirect
6. #17988317C2semidirect
7. #462×C73C2semidirect
91. C73#1640semidirect
95. #462D73semidirect