Finite Group Databasebeta

← #22609093

Subgroups — #22609093

Order 9344.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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#17989252C211yesmaximal, characteristic
2#17988879C211yesmaximal, characteristic, complemented
3#17988874C211yesmaximal, characteristic
4#17988333C211yesmaximal, characteristic, complemented
5#17988319C211yesmaximal, characteristic, complemented
6#17988316C211yesmaximal, characteristic
7#487×C73C211yesmaximal, characteristic, complemented
8C2×Q8×D73—21no—
9#14556590—21no—
10#14556569—22no—
11#14556567—21no—
12C4×Dic146C2211yescharacteristic
13C4×D292C2211yescharacteristic
14#14556553—21no—
15#14556524—21no—
16#14556522—21no—
17C4⋊#10596831C2211yescharacteristic
18C4⋊#10596831C2211yescharacteristic
19#14556514—21no—
20#14556511—21no—
21C4⋊Q8×C73C2211yescharacteristic
22C4⋊Q8×C73C2211yescharacteristic
23#103×C73—22no—
24C4×C8×C73C2211yescharacteristic
25C2×Dic146—22no—
26C2×Dic146D411yescharacteristic
27Q8×D73—42no—
28Q8×D73—42no—
29C2×D292D411yescharacteristic
30C2×C4×D73—22no—
31C2×C4×D73—21no—
32C2×#10596831—21no—
33C2×#10596831—21no—
34C4⋊Dic73D411yescharacteristic
35C4⋊Dic73D411yescharacteristic
36#11924007—22no—
37#11924007—21no—
38#11924005—22no—
39#11924005—21no—
40C4×Dic73—21no—
41C2×Q8×C73—21no—
42C2×Q8×C73—21no—
43C2×C8×C73—21no—
44C4⋊C4×C73—21no—
45C4⋊C4×C73—21no—
46C4⋊C4×C73—21no—
47C4⋊C4×C73D412yes—
48C42×C73C2311yescharacteristic
49C22×D73—21no—
50Q8×C73—42no—
51Q8×C73—41no—
52Q8×C73—41no—
53C2×C4×C73—22no—
54C2×C4×C73—41no—
55C2×C4×C73C2×D411yescharacteristic
56C2×C4×C73C2×D411yescharacteristic
57C2×C4×C73C2×D411yescharacteristic
58C2×Dic73—21no—
59C2×Dic73—21no—
60C2×Dic73—21no—
61D292—21no—
62D292Q1612yes—
63C4×D73—44no—
64C4×D73—41no—
65C4×D73—41no—
66Dic146—21no—
67Dic146—44no—
68Dic146SD1612yes—
69C8×C73—41no—
70#10596831—41no—
71#10596831—41no—
72C22×C73#12011yescharacteristic
73C2×D73—22no—
74C2×D73—41no—
75C2×D73—41no—
76C4×C73—21no—
77C4×C73—42no—
78C4×C73—81no—
79C4×C73C2×SD1611yescharacteristic
80C4×C73C2×Q1611yescharacteristic
81C4×C73AGL(1,ℤ/8)11yescharacteristic
82C4×C73#13711yescharacteristic
83Dic73—22no—
84Dic73—41no—
85Dic73—41no—
86C2×C73#45011yescharacteristic
87C2×C73#45111yescharacteristic
88C2×C73#45411yescharacteristic
89D73—42no—
90#1637—731nomaximal, Sylow
91C73#163711yescharacteristic, complemented, Sylow
92D4×Q8—731no—
93#487D7311yescharacteristic, complemented
94#477—731no—
95#476—731no—
96#332—731no—
97Q8⋊C8—731no—
98D4⋊C8—731no—
99C22×Q8—1461no—
100C4⋊Q8—1461no—
101C4⋊Q8C2×D7311yescharacteristic
102C4⋊Q8C2×D7311yescharacteristic
103C22⋊Q8—1461no—
104C22⋊Q8—1462no—
105C4×Q8—731no—
106C4×D4—731no—
107C4×D4—1461no—
108#107—1461no—
109#106—1461no—
110C4⋊C8—731no—
111C4⋊C8—731no—
112#103—22no—
113#103—1461no—
114#102—1461no—
115C4×C8C2×D7311yescharacteristic
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—2922no—
119C2×Q8—2922no—
120C2×Q8—731no—
121C2×Q8—1462no—
122C2×D4—731no—
123C22×C4—1462no—
124C22×C4—1461no—
125C2×C8—21no—
126C2×C8—1461no—
127C2×C8—1461no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—731no—
132C4⋊C4—731no—
133C4⋊C4—1462no—
134C4⋊C4—1461no—
135C4⋊C4C22⋊D7312yes—
136C22⋊C4—1462no—
137C22⋊C4—1461no—
138C42—1461no—
139C42C22×D7311yescharacteristic
140C23—1461no—
141Q8—42no—
142Q8—41no—
143Q8—41no—
144Q8—2924no—
145Q8—732no—
146Q8—1461no—
147D4—732no—
148D4—1461no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—2924no—
152C2×C4—2921no—
153C2×C4—2921no—
154C2×C4—1461no—
155C2×C4—1461no—
156C2×C4—1461no—
157C2×C4D4×D7311yescharacteristic
158C2×C4D4×D7311yescharacteristic
159C2×C4C2×C22⋊D7311yescharacteristic
160C8—41no—
161C8—2921no—
162C8—2921no—
163C22—2921no—
164C22—2921no—
165C22—1462no—
166C22#1455655911yescharacteristic
167C4—21no—
168C4—42no—
169C4—81no—
170C4—2921no—
171C4—2921no—
172C4—1462no—
173C4SD16×D7311yescharacteristic
174C4Q16×D7311yescharacteristic
175C4#1455661811yescharacteristic
176C4#1455662311yescharacteristic
177C2—2922no—
178C2#1798873611yescharacteristic
179C2#1798874111yescharacteristic
180C2#1798875911yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#487×C73C2
socleC22×C73#120
hypercenter#487D73
hypocenterC73#1637
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #17988879C2semidirect
4. #17988333C2semidirect
5. #17988319C2semidirect
7. #487×C73C2semidirect
91. C73#1637semidirect
93. #487D73semidirect