Finite Group Databasebeta

← #22609083

Subgroups — #22609083

Order 9344.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#17989240C211yesmaximal, characteristic
2#17988939C211yesmaximal, characteristic, complemented
3#17988878C211yesmaximal, characteristic, complemented
4#17988878C211yesmaximal, characteristic, complemented
5#17988314C211yesmaximal, characteristic, complemented
6#17988314C211yesmaximal, characteristic, complemented
7#332×C73C211yesmaximal, characteristic, complemented
8C2×#11924029—21no—
9#14556591C2211yescharacteristic
10#14556576—22no—
11#14556567—21no—
12#14556566—21no—
13C4×D292C2211yescharacteristic
14C4×D292C2211yescharacteristic
15C4⋊C4×D73—21no—
16#14556523—21no—
17#14556523—21no—
18#14556514—22no—
19#14556513—21no—
20#14556513—21no—
21C4×#10596831C2211yescharacteristic
22C4⋊Q8×C73C2211yescharacteristic
23C4⋊C8×C73C2211yescharacteristic
24C4⋊C8×C73C2211yescharacteristic
25#11924029—42no—
26#11924029—42no—
27C2×Dic146—21no—
28C2×D292—22no—
29C2×D292D411yescharacteristic
30C2×D292D411yescharacteristic
31C2×C4×D73—22no—
32C2×C4×D73—21no—
33C2×C4×D73—21no—
34C2×#10596831—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73—21no—
37C4⋊Dic73D411yescharacteristic
38C4⋊Dic73D411yescharacteristic
39#11924007—22no—
40#11924005—22no—
41#11924005—21no—
42#11924005—21no—
43C2×Q8×C73—21no—
44C2×C8×C73—21no—
45C2×C8×C73—21no—
46C4⋊C4×C73—21no—
47C4⋊C4×C73D412yes—
48C42×C73C2311yescharacteristic
49C22×D73—21no—
50C22×D73—21no—
51Q8×C73—41no—
52Q8×C73—41no—
53C2×C4×C73—22no—
54C2×C4×C73C2×D411yescharacteristic
55C2×C4×C73C2×D411yescharacteristic
56C2×C4×C73C2×D411yescharacteristic
57C2×Dic73—21no—
58C2×Dic73—21no—
59C2×Dic73—41no—
60D292—21no—
61D292—21no—
62D292—21no—
63D292—44no—
64D292SD1612yes—
65C4×D73—44no—
66C4×D73—41no—
67C4×D73—41no—
68C4×D73—41no—
69C4×D73—41no—
70Dic146—42no—
71C8×C73—41no—
72C8×C73—41no—
73#10596831—41no—
74C22×C73#12011yescharacteristic
75C2×D73—22no—
76C2×D73—41no—
77C2×D73—41no—
78C2×D73—41no—
79C2×D73—41no—
80C2×D73—41no—
81C4×C73—21no—
82C4×C73—42no—
83C4×C73C2×SD1611yescharacteristic
84C4×C73#13511yescharacteristic
85C4×C73AGL(1,ℤ/8)11yescharacteristic
86C4×C73#13711yescharacteristic
87Dic73—41no—
88Dic73—41no—
89Dic73—81no—
90C2×C73#45011yescharacteristic
91C2×C73#45211yescharacteristic
92C2×C73#45411yescharacteristic
93D73—42no—
94D73—81no—
95#1635—731nomaximal, Sylow
96C73#163511yescharacteristic, complemented, Sylow
97#547—731no—
98#487—731no—
99#476—731no—
100#476—731no—
101#332D7311yescharacteristic, complemented
102D4⋊C8—731no—
103D4⋊C8—731no—
104C2×#41—1461no—
105C4⋊Q8—731no—
106C4⋊Q8C2×D7311yescharacteristic
107#123—1462no—
108C22⋊Q8—1461no—
109#121—1461no—
110C4×D4—731no—
111C4×D4—731no—
112C2×C4⋊C4—1461no—
113#106—1461no—
114#106—1461no—
115C4⋊C8C2×D7311yescharacteristic
116C4⋊C8C2×D7311yescharacteristic
117#103—1462no—
118#102—1461no—
119#102—1461no—
120C4×C8—731no—
121#41—2922no—
122#41—2922no—
123C2×Q8—21no—
124C2×Q8—1461no—
125C2×D4—731no—
126C2×D4—731no—
127C2×D4—1462no—
128C22×C4—1462no—
129C22×C4—1461no—
130C22×C4—1461no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—1461no—
134C4⋊C4—21no—
135C4⋊C4—731no—
136C4⋊C4—731no—
137C4⋊C4—1462no—
138C4⋊C4—1461no—
139C4⋊C4—1461no—
140C4⋊C4D29212yes—
141C22⋊C4—1462no—
142C22⋊C4—1461no—
143C22⋊C4—1461no—
144C42C22×D7311yescharacteristic
145C23—1461no—
146C23—1461no—
147Q8—41no—
148Q8—41no—
149Q8—2922no—
150D4—2924no—
151D4—732no—
152D4—1461no—
153D4—1461no—
154D4—1461no—
155C2×C4—22no—
156C2×C4—2924no—
157C2×C4—2921no—
158C2×C4—2921no—
159C2×C4—2921no—
160C2×C4—2921no—
161C2×C4—2921no—
162C2×C4—1461no—
163C2×C4—1461no—
164C2×C4D4×D7311yescharacteristic
165C2×C4D4×D7311yescharacteristic
166C2×C4C2×D29211yescharacteristic
167C8—41no—
168C8—41no—
169C8—2921no—
170C22—2921no—
171C22—2921no—
172C22—2921no—
173C22—2921no—
174C22—2921no—
175C22—1462no—
176C22#1455656111yescharacteristic
177C4—21no—
178C4—42no—
179C4—2921no—
180C4—2921no—
181C4—5841no—
182C4SD16×D7311yescharacteristic
183C4#1455661211yescharacteristic
184C4#1455661511yescharacteristic
185C4#1455662311yescharacteristic
186C2—2922no—
187C2—5841no—
188C2#1798873911yescharacteristic
189C2#1798875211yescharacteristic
190C2#1798876211yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#332×C73C2
socleC22×C73#120
hypercenter#332D73
hypocenterC73#1635
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #17988939C2semidirect
3. #17988878C2semidirect
4. #17988878C2semidirect
5. #17988314C2semidirect
6. #17988314C2semidirect
7. #332×C73C2semidirect
96. C73#1635semidirect
101. #332D73semidirect