Finite Group Databasebeta

← #22608518

Subgroups — #22608518

Order 9344.

234 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 61 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#17989122C211yesmaximal, characteristic
2#17988539C211yesmaximal, characteristic, complemented
3#97×D73C211yesmaximal, characteristic, complemented
4#17988329C211yesmaximal, characteristic, complemented
5#17988326C211yesmaximal, characteristic, complemented
6#17988326C211yesmaximal, characteristic, complemented
7#330×C73C211yesmaximal, characteristic, complemented
8C2×#11924011—21no—
9C2×C8×D73—21no—
10#14556586—21no—
11#14556579C2211yescharacteristic
12#14556576—21no—
13#14556571C411yescharacteristic
14#14556566C411yescharacteristic
15#14556556C411yescharacteristic
16#14556553—21no—
17#14556553C411yescharacteristic
18#14556549—21no—
19C42×D73C2211yescharacteristic
20#14556502C2211yescharacteristic
21#14556502C2211yescharacteristic
22#14556501—21no—
23C8×Dic73—21no—
24#125×C73C2211yescharacteristic
25#97×C73C2211yescharacteristic
26#97×C73C2211yescharacteristic
27C2×Dic146C2×C411yescharacteristic
28C2×D292—21no—
29C2×D292C2×C411yescharacteristic
30C2×C4×D73—21no—
31C2×C4×D73C2×C411yescharacteristic
32C2×C4×D73D411yescharacteristic
33C2×C4×D73D411yescharacteristic
34#11924011—24no—
35C2×#10596831—21no—
36C2×#10596831—21no—
37C8×D73—24no—
38C4⋊Dic73—21no—
39#11924007—21no—
40#11924005—21no—
41#11924005—21no—
42#11924005—21no—
43#11924005—21no—
44#11924005—21no—
45C4×Dic73—21no—
46C4×Dic73C2×C411yescharacteristic
47C4×Dic73D411yescharacteristic
48C4×Dic73D411yescharacteristic
49C2×C8×C73—21no—
50C2×C8×C73—21no—
51C4⋊C4×C73—21no—
52C4⋊C4×C73—21no—
53C4⋊C4×C73C2×C411yescharacteristic
54C4⋊C4×C73C2×C411yescharacteristic
55C42×C73C2311yescharacteristic
56C22×D73—21no—
57C22×D73C22⋊C411yescharacteristic
58C2×C4×C73—21no—
59C2×C4×C73—21no—
60C2×C4×C73C22×C411yescharacteristic
61C2×C4×C73C2×D411yescharacteristic
62C2×C4×C73C2×D411yescharacteristic
63C2×Dic73—21no—
64C2×Dic73C22⋊C411yescharacteristic
65C2×Dic73C22⋊C411yescharacteristic
66C2×Dic73C22⋊C411yescharacteristic
67D292—41no—
68D292—42no—
69C4×D73—22no—
70C4×D73—22no—
71C4×D73—41no—
72C4×D73—42no—
73Dic146—41no—
74C8×C73—22no—
75C8×C73—22no—
76#10596831—22no—
77#10596831—22no—
78C22×C73C2×C22⋊C411yescharacteristic
79C2×D73—21no—
80C2×D73—21no—
81C2×D73—41no—
82C2×D73—41no—
83C2×D73—41no—
84C2×D73#10412yes—
85C4×C73—21no—
86C4×C73—21no—
87C4×C73—21no—
88C4×C73—41no—
89C4×C73—41no—
90Dic73—21no—
91Dic73—21no—
92Dic73—41no—
93Dic73#10412yes—
94C2×C73#41311yescharacteristic
95C2×C73C2×#10411yescharacteristic
96C2×C73C2×#10411yescharacteristic
97D73—22no—
98D73—81no—
99#1524—731nomaximal, Sylow
100C73#152411yescharacteristic, complemented, Sylow
101#529—731no—
102C4×M16—731no—
103C2×#97—731no—
104#330—731no—
105#330D7311yescharacteristic, complemented
106#329—731no—
107#329—731no—
108C2×M16—1461no—
109C22×C8—1461no—
110#126—1461no—
111#125C2×D7311yescharacteristic
112#124—731no—
113#123—1461no—
114C22⋊Q8—731no—
115#121—731no—
116C4×Q8—731no—
117C4×D4—731no—
118C4×D4—1461no—
119#117—1461no—
120C2×C42—731no—
121#97—731no—
122#97—731no—
123#97—1461no—
124#97C2×D7311yescharacteristic
125#97C2×D7311yescharacteristic
126C4×C8—1461no—
127C2×Q8—731no—
128C2×D4—731no—
129C2×D4—1461no—
130C22×C4—731no—
131C22×C4—731no—
132C22×C4—731no—
133C22×C4—1461no—
134M16—1464no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—1464no—
138C2×C8—1461no—
139C2×C8—1461no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—1461no—
143C4⋊C4—1461no—
144C4⋊C4C4×D7311yescharacteristic
145C4⋊C4C4×D7311yescharacteristic
146C22⋊C4—1461no—
147C22⋊C4—1461no—
148C22⋊C4—1461no—
149C22⋊C4—1461no—
150C22⋊C4—1461no—
151C42—731no—
152C42—731no—
153C42—731no—
154C42—1461no—
155C42C22×D7311yescharacteristic
156C23—731no—
157C23—1461no—
158Q8—2921no—
159D4—2921no—
160D4—2922no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—2921no—
164C2×C4—2922no—
165C2×C4—731no—
166C2×C4—731no—
167C2×C4—731no—
168C2×C4—1462no—
169C2×C4—1462no—
170C2×C4—1461no—
171C2×C4C2×C4×D7311yescharacteristic
172C2×C4D4×D7311yescharacteristic
173C2×C4D4×D7311yescharacteristic
174C8—22no—
175C8—22no—
176C8—1462no—
177C8—1462no—
178C22—2921no—
179C22—2921no—
180C22—2921no—
181C22—732no—
182C22—1461no—
183C22—1461no—
184C22C22⋊C4×D7311yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—41no—
189C4—41no—
190C4—2921no—
191C4—732no—
192C4—1461no—
193C4—1461no—
194C2—5841no—
195C2—1462no—
196C2#1798857011yescharacteristic
197C2#104×D7311yescharacteristic
198C2#104×D7311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D73
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#330×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#330D73
hypocenterC73#1524
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #17988539C2semidirect
3. #97×D73C2semidirect
4. #17988329C2semidirect
5. #17988326C2semidirect
6. #17988326C2semidirect
7. #330×C73C2semidirect
100. C73#1524semidirect
105. #330D73semidirect