Finite Group Databasebeta

← #22611595

Subgroups — #22611595

Order 9344.

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

normal subgroups only

This group has 258 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#17989136C211yesmaximal, characteristic
2#17988559C212yesmaximal, complemented
3#17988382C211yesmaximal, characteristic, complemented
4#17988379C212yesmaximal, complemented
5#354×C73C211yesmaximal, characteristic, complemented
6C2×#11924029C411yescharacteristic, complemented
7C2×#11924027C2211yescharacteristic
8#14556589C411yescharacteristic, complemented
9#14556587C2211yescharacteristic
10#14556579C411yescharacteristic, complemented
11#14556564—22no—
12#14556551—22no—
13#14556547—22no—
14C42×D73C411yescharacteristic, complemented
15#14556506C2212yes—
16#14556505—22no—
17#124×C73C2211yescharacteristic
18#99×C73C2212yes—
19#11924029—41no—
20#11924029—41no—
21#11924027—41no—
22#11924027—41no—
23C2×Dic146C2×C411yescharacteristic
24C2×D292—21no—
25C2×D292C2×C411yescharacteristic
26C2×C22⋊D73—22no—
27C2×C22⋊D73D412yes—
28C22×Dic73D412yes—
29C2×C4×D73—21no—
30C2×C4×D73—21no—
31C2×C4×D73C2×C411yescharacteristic
32#11924007—22no—
33#11924007—42no—
34C22⋊Dic73—22no—
35#11924005—22no—
36C4×Dic73—21no—
37C4×Dic73—42no—
38C4×Dic73C2×C411yescharacteristic
39C2×Q8×C73C2×C411yescharacteristic
40C2×D4×C73C2311yescharacteristic
41C22⋊C4×C73—22no—
42C22⋊C4×C73—22no—
43C42×C73C2×C411yescharacteristic
44C23×C73C2×D412yes—
45C22×D73—21no—
46C22×D73C22⋊C411yescharacteristic
47Q8×C73—41no—
48D4×C73—41no—
49C2×C4×C73—21no—
50C2×C4×C73—21no—
51C2×C4×C73—42no—
52C2×C4×C73C22×C411yescharacteristic
53C22⋊D73—42no—
54C22⋊D73—44no—
55C2×Dic73—21no—
56C2×Dic73—22no—
57C2×Dic73—22no—
58C2×Dic73—42no—
59C2×Dic73C22⋊C412yes—
60C2×Dic73C22⋊C411yescharacteristic
61D292—41no—
62D292—42no—
63C4×D73—21no—
64C4×D73—21no—
65C4×D73—42no—
66C4×D73—41no—
67C4×D73—41no—
68Dic146—41no—
69C22×C73—22no—
70C22×C73—42no—
71C22×C73C2×C22⋊C411yescharacteristic
72C2×D73—21no—
73C2×D73—41no—
74C2×D73—42no—
75C2×D73—41no—
76C4×C73—21no—
77C4×C73—41no—
78C4×C73—41no—
79C4×C73—82no—
80Dic73—22no—
81Dic73—22no—
82Dic73—82no—
83Dic73#9911yescharacteristic
84Dic73#9911yescharacteristic
85C2×C73—21no—
86C2×C73—42no—
87C2×C73C2×#9911yescharacteristic
88D73—41no—
89D73—81no—
90#2126—731nomaximal, Sylow
91C73#212611yescharacteristic, complemented, Sylow
92#532—731no—
93#410—732no—
94#354—731no—
95#354D7311yescharacteristic, complemented
96#353—732no—
97C2×#41—731no—
98C2×#41—731no—
99C4⋊Q8—731no—
100#127—731no—
101#124—731no—
102#124C2×D7311yescharacteristic
103#121—1462no—
104C4×D4—1462no—
105#117—1462no—
106C2×C42—731no—
107#99—732no—
108#99—1462no—
109#99C2×D7312yes—
110#41—2921no—
111#41—2921no—
112#41—2921no—
113#41—2921no—
114C2×Q8—731no—
115C2×Q8C4×D7311yescharacteristic
116C2×D4—732no—
117C2×D4—731no—
118C2×D4—1461no—
119C2×D4—1462no—
120C2×D4C22×D7311yescharacteristic
121C22×C4—732no—
122C22×C4—731no—
123C22×C4—1461no—
124C22×C4—1461no—
125C4⋊C4—2922no—
126C4⋊C4—1462no—
127C22⋊C4—22no—
128C22⋊C4—22no—
129C22⋊C4—1462no—
130C22⋊C4—1462no—
131C42—2922no—
132C42—731no—
133C42—1461no—
134C42C4×D7311yescharacteristic
135C23—731no—
136C23—1461no—
137C23D4×D7312yes—
138Q8—41no—
139Q8—2921no—
140D4—41no—
141D4—2921no—
142D4—2922no—
143D4—2922no—
144D4—2924no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—2921no—
149C2×C4—2921no—
150C2×C4—2922no—
151C2×C4—2922no—
152C2×C4—731no—
153C2×C4—732no—
154C2×C4—1461no—
155C2×C4—1461no—
156C2×C4—1462no—
157C2×C4—1462no—
158C2×C4—1461no—
159C2×C4C2×C4×D7311yescharacteristic
160C22—22no—
161C22—42no—
162C22—2921no—
163C22—2922no—
164C22—2921no—
165C22—1461no—
166C22C22⋊C4×D7311yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—82no—
171C4—5842no—
172C4—731no—
173C4—731no—
174C4—1462no—
175C4—1462no—
176C2—21no—
177C2—42no—
178C2—2921no—
179C2—5841no—
180C2#99×D7311yescharacteristic
subgroupG/H
centerC2#99×D73
commutatorC2×C4×C73C22×C4
FrattiniC2×D4C22×D73
Fitting#354×C73C2
socleC2×C73C2×#99
hypercenter#354D73
hypocenterC73#2126
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #17988559C2semidirect
3. #17988382C2semidirect
4. #17988379C2semidirect
5. #354×C73C2semidirect
6. C2×#11924029C4semidirect
8. #14556589C4semidirect
10. #14556579C4semidirect
14. C42×D73C4semidirect
91. C73#2126semidirect
95. #354D73semidirect