Finite Group Databasebeta

← #22608652

Subgroups — #22608652

Order 9344.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#17989138C211yesmaximal, characteristic
2#17988643C211yesmaximal, characteristic, complemented
3#17988609C211yesmaximal, characteristic, complemented
4#17988333C211yesmaximal, characteristic, complemented
5#17988330C211yesmaximal, characteristic, complemented
6#17988330C211yesmaximal, characteristic, complemented
7#332×C73C211yesmaximal, characteristic, complemented
8C2×#11924029—21no—
9C2×#11924011—21no—
10#14556588C2211yescharacteristic
11#14556580—21no—
12#14556566—21no—
13#14556566C412yes—
14#14556553—21no—
15#14556553C412yes—
16C42×D73C2211yescharacteristic
17C4⋊#10596831C2211yescharacteristic
18C4⋊#10596831C2211yescharacteristic
19#14556520—21no—
20#14556503—21no—
21#14556501—21no—
22C4⋊Q8×C73C2211yescharacteristic
23C4⋊C8×C73C2211yescharacteristic
24C4⋊C8×C73C2211yescharacteristic
25#11924029—42no—
26#11924029—42no—
27C2×D292—22no—
28C2×D292—21no—
29C2×D292—21no—
30C2×D292C2×C412yes—
31C2×C4×D73—22no—
32C2×C4×D73C2×C411yescharacteristic
33C2×C4×D73D411yescharacteristic
34C2×C4×D73D411yescharacteristic
35#11924011—42no—
36C2×#10596831—21no—
37C2×#10596831—21no—
38#11924005—22no—
39#11924005—22no—
40C4×Dic73C2×C411yescharacteristic
41C4×Dic73D411yescharacteristic
42C4×Dic73D411yescharacteristic
43C2×Q8×C73—21no—
44C2×C8×C73—21no—
45C2×C8×C73—21no—
46C4⋊C4×C73—21no—
47C4⋊C4×C73C2×C412yes—
48C42×C73C2311yescharacteristic
49C22×D73—22no—
50C22×D73C22⋊C411yescharacteristic
51Q8×C73—41no—
52Q8×C73—41no—
53C2×C4×C73—22no—
54C2×C4×C73C22×C411yescharacteristic
55C2×C4×C73C2×D411yescharacteristic
56C2×C4×C73C2×D411yescharacteristic
57C2×Dic73C22⋊C411yescharacteristic
58C2×Dic73C22⋊C411yescharacteristic
59C2×Dic73C22⋊C411yescharacteristic
60D292—42no—
61D292—44no—
62D292—41no—
63D292—41no—
64D292—41no—
65D292—41no—
66C4×D73—21no—
67C4×D73—21no—
68C4×D73—21no—
69C4×D73—21no—
70C4×D73—41no—
71C4×D73—44no—
72C8×C73—41no—
73C8×C73—41no—
74#10596831—41no—
75#10596831—41no—
76C22×C73C2×C22⋊C411yescharacteristic
77C2×D73—21no—
78C2×D73—21no—
79C2×D73—21no—
80C2×D73—42no—
81C2×D73—42no—
82C2×D73—42no—
83C4×C73—21no—
84C4×C73—42no—
85C4×C73AGL(1,ℤ/8)11yescharacteristic
86C4×C73AGL(1,ℤ/8)11yescharacteristic
87C4×C73AGL(1,ℤ/8)11yescharacteristic
88C4×C73#13711yescharacteristic
89Dic73—21no—
90Dic73—21no—
91Dic73—21no—
92C2×C73#41311yescharacteristic
93C2×C73#41711yescharacteristic
94C2×C73#41811yescharacteristic
95D73—41no—
96D73—82no—
97#1557—731nomaximal, Sylow
98C73#155711yescharacteristic, complemented, Sylow
99#532—731no—
100#432—731no—
101#423—731no—
102#332—731no—
103#332D7311yescharacteristic, complemented
104#331—731no—
105#331—731no—
106C2×#41—1461no—
107C2×M16—1461no—
108C4⋊Q8C2×D7311yescharacteristic
109#127—731no—
110#124—1461no—
111#121—732no—
112#121—1461no—
113C4×D4—732no—
114C4×D4—1461no—
115C2×C42—731no—
116C4⋊C8—731no—
117C4⋊C8—731no—
118C4⋊C8—1461no—
119C4⋊C8C2×D7311yescharacteristic
120C4⋊C8C2×D7311yescharacteristic
121C22⋊C8—1461no—
122#97—1461no—
123#41—2922no—
124#41—2922no—
125C2×Q8—21no—
126C2×D4—732no—
127C2×D4—1462no—
128C2×D4—1461no—
129C2×D4—1461no—
130C22×C4—731no—
131C22×C4—731no—
132C22×C4—731no—
133C22×C4—1462no—
134M16—2922no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—1461no—
138C2×C8—1461no—
139C4⋊C4—21no—
140C4⋊C4C4×D7312yes—
141C22⋊C4—1462no—
142C22⋊C4—1462no—
143C42—731no—
144C42—731no—
145C42—731no—
146C42C22×D7311yescharacteristic
147C23—731no—
148C23—1462no—
149Q8—41no—
150Q8—41no—
151D4—2922no—
152D4—2924no—
153D4—2921no—
154D4—2921no—
155D4—2921no—
156D4—2921no—
157C2×C4—22no—
158C2×C4—2921no—
159C2×C4—2924no—
160C2×C4—731no—
161C2×C4—731no—
162C2×C4—731no—
163C2×C4—1461no—
164C2×C4—1461no—
165C2×C4—1461no—
166C2×C4—1461no—
167C2×C4C2×C4×D7311yescharacteristic
168C2×C4D4×D7311yescharacteristic
169C2×C4D4×D7311yescharacteristic
170C8—41no—
171C8—41no—
172C8—2921no—
173C8—2921no—
174C22—2922no—
175C22—2922no—
176C22—2922no—
177C22—1461no—
178C22—1461no—
179C22—1461no—
180C22C22⋊C4×D7311yescharacteristic
181C4—21no—
182C4—42no—
183C4—1461no—
184C4—1461no—
185C4—1461no—
186C4#1455661511yescharacteristic
187C4#1455661811yescharacteristic
188C4#1455661811yescharacteristic
189C4#1455662311yescharacteristic
190C2—2921no—
191C2—5842no—
192C2#1798857011yescharacteristic
193C2#1798858711yescharacteristic
194C2#1798859011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D73
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#332×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#332D73
hypocenterC73#1557
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #17988643C2semidirect
3. #17988609C2semidirect
4. #17988333C2semidirect
5. #17988330C2semidirect
6. #17988330C2semidirect
7. #332×C73C2semidirect
98. C73#1557semidirect
103. #332D73semidirect