Finite Group Databasebeta

← #22609191

Subgroups — #22609191

Order 9344.

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

normal subgroups only

This group has 234 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#17988869C211yesmaximal, characteristic, complemented
3#17988789C211yesmaximal, characteristic
4#17988333C211yesmaximal, characteristic, complemented
5#17988319C211yesmaximal, characteristic, complemented
6#17988316C211yesmaximal, characteristic
7#498×C73C211yesmaximal, characteristic, complemented
8C2×Q8×D73—21no—
9C2×#11924015—21no—
10#14556590—21no—
11#14556569—22no—
12#14556567—21no—
13C4×Dic146C2211yescharacteristic
14C4×D292C2211yescharacteristic
15#14556553—21no—
16#14556522—21no—
17C4⋊#10596831C2211yescharacteristic
18C4⋊#10596831C2211yescharacteristic
19#14556515—21no—
20#14556514—21no—
21C4⋊Q8×C73C2211yescharacteristic
22C4⋊Q8×C73C2211yescharacteristic
23#106×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—
32#11924015—42no—
33C2×#10596831—21no—
34C2×#10596831—21no—
35C4⋊Dic73D411yescharacteristic
36C4⋊Dic73D411yescharacteristic
37#11924007—22no—
38#11924007—21no—
39#11924005—22no—
40#11924005—21no—
41C4×Dic73—21no—
42C2×Q8×C73—21no—
43C2×Q8×C73—21no—
44C2×C8×C73—21no—
45C4⋊C4×C73—21no—
46C4⋊C4×C73—21no—
47C4⋊C4×C73—21no—
48C4⋊C4×C73D412yes—
49C42×C73C2311yescharacteristic
50C22×D73—21no—
51Q8×C73—41no—
52Q8×C73—41no—
53Q8×C73—41no—
54Q8×C73—41no—
55C2×C4×C73—22no—
56C2×C4×C73—41no—
57C2×C4×C73C2×D411yescharacteristic
58C2×C4×C73C2×D411yescharacteristic
59C2×C4×C73C2×D411yescharacteristic
60C2×Dic73—21no—
61C2×Dic73—21no—
62C2×Dic73—21no—
63D292—21no—
64D292SD1612yes—
65C4×D73—44no—
66C4×D73—41no—
67C4×D73—41no—
68Dic146—21no—
69Dic146—44no—
70Dic146SD1612yescomplemented
71C8×C73—22no—
72#10596831—41no—
73#10596831—41no—
74C22×C73#12011yescharacteristic
75C2×D73—22no—
76C2×D73—41no—
77C2×D73—41no—
78C4×C73—21no—
79C4×C73—42no—
80C4×C73—81no—
81C4×C73C2×SD1611yescharacteristic
82C4×C73C2×SD1611yescharacteristic
83C4×C73AGL(1,ℤ/8)11yescharacteristic
84C4×C73#13711yescharacteristic
85Dic73—22no—
86Dic73—41no—
87Dic73—41no—
88C2×C73#44811yescharacteristic
89C2×C73#45011yescharacteristic
90C2×C73#45611yescharacteristic
91D73—42no—
92#1651—731nomaximal, Sylow
93C73#165111yescharacteristic, complemented, Sylow
94D4×Q8—731no—
95#498D7311yescharacteristic, complemented
96#475—731no—
97#461—731no—
98#332—731no—
99Q8⋊C8—731no—
100D4⋊C8—731no—
101C22×Q8—1461no—
102C2×SD16—1461no—
103C4⋊Q8—1461no—
104C4⋊Q8C2×D7311yescharacteristic
105C4⋊Q8C2×D7311yescharacteristic
106C22⋊Q8—1461no—
107C22⋊Q8—1462no—
108C4×Q8—731no—
109C4×D4—731no—
110C4×D4—1461no—
111#106—22no—
112#106—1461no—
113C4⋊C8—731no—
114C4⋊C8—731no—
115#103—1461no—
116#103—1461no—
117C4×C8C2×D7311yescharacteristic
118C2×Q8—21no—
119C2×Q8—21no—
120C2×Q8—2922no—
121C2×Q8—2922no—
122C2×Q8—731no—
123C2×Q8—1462no—
124C2×D4—731no—
125C22×C4—1462no—
126C22×C4—1461no—
127SD16—2922no—
128C2×C8—21no—
129C2×C8—1461no—
130C2×C8—1461no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—731no—
135C4⋊C4—731no—
136C4⋊C4—1462no—
137C4⋊C4—1461no—
138C4⋊C4C22⋊D7312yes—
139C22⋊C4—1462no—
140C22⋊C4—1461no—
141C42—1461no—
142C42C22×D7311yescharacteristic
143C23—1461no—
144Q8—41no—
145Q8—41no—
146Q8—41no—
147Q8—41no—
148Q8—2924no—
149Q8—732no—
150Q8—1461no—
151D4—732no—
152D4—1461no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—2924no—
156C2×C4—2921no—
157C2×C4—2921no—
158C2×C4—1461no—
159C2×C4—1461no—
160C2×C4—1461no—
161C2×C4D4×D7311yescharacteristic
162C2×C4D4×D7311yescharacteristic
163C2×C4C2×C22⋊D7311yescharacteristic
164C8—22no—
165C8—2921no—
166C8—2921no—
167C22—2921no—
168C22—2921no—
169C22—1462no—
170C22#1455655911yescharacteristic
171C4—21no—
172C4—42no—
173C4—81no—
174C4—2921no—
175C4—2921no—
176C4—1462no—
177C4SD16×D7311yescharacteristic
178C4SD16×D7311yescharacteristic
179C4#1455661811yescharacteristic
180C4#1455662011yescharacteristic
181C2—2922no—
182C2#1798872411yescharacteristic
183C2#1798873611yescharacteristic
184C2#1798876911yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#498×C73C2
socleC22×C73#120
hypercenter#498D73
hypocenterC73#1651
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
2. #17988869C2semidirect
4. #17988333C2semidirect
5. #17988319C2semidirect
7. #498×C73C2semidirect
70. Dic146SD16semidirect
93. C73#1651semidirect
95. #498D73semidirect