Finite Group Databasebeta

← #22608337

Subgroups — #22608337

Order 9344.

212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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#17989121C211yesmaximal, characteristic
2#17988640C211yesmaximal, characteristic, complemented
3#17988317C212yesmaximal, complemented
4#17988314C212yesmaximal, complemented
5#431×C73C211yesmaximal, characteristic, complemented
6#14556585—21no—
7#14556583C411yescharacteristic
8#14556579C411yescharacteristic
9#14556574—21no—
10#14556570C411yescharacteristic
11#14556565C411yescharacteristic
12C4×Dic146C2211yescharacteristic
13C4×D292C2211yescharacteristic
14C4×C22⋊D73—21no—
15#14556548—21no—
16C4⋊#10596831—21no—
17C22⋊#10596831—21no—
18C4×#10596831C2212yes—
19C2×C42×C73C2211yescharacteristic
20C4⋊C8×C73C2212yes—
21C22⋊C8×C73—21no—
22C4×C8×C73—21no—
23C2×Dic146C2×C411yescharacteristic
24C2×D292C2×C411yescharacteristic
25C2×C22⋊D73—21no—
26C2×C4×D73—21no—
27C2×#10596831—22no—
28C4⋊Dic73C2×C411yescharacteristic
29C4⋊Dic73C2×C411yescharacteristic
30#11924007—21no—
31#11924007—21no—
32#11924007—21no—
33#11924007—21no—
34C22⋊Dic73—21no—
35#11924005—21no—
36#11924005—21no—
37#11924005—21no—
38#11924005—21no—
39C4×Dic73—21no—
40C22×C4×C73C2×C411yescharacteristic
41C22×C4×C73D411yescharacteristic
42C22×C4×C73D411yescharacteristic
43C2×C8×C73—22no—
44C42×C73C2×C411yescharacteristic
45C42×C73D411yescharacteristic
46C42×C73D411yescharacteristic
47C42×C73C2311yescharacteristic
48C23×C73C22⋊C411yescharacteristic
49C22×D73—21no—
50C2×C4×C73—22no—
51C2×C4×C73—22no—
52C2×C4×C73—41no—
53C2×C4×C73C22⋊C411yescharacteristic
54C2×C4×C73C22⋊C411yescharacteristic
55C2×C4×C73C22⋊C411yescharacteristic
56C2×C4×C73C22×C411yescharacteristic
57C2×C4×C73C2×D411yescharacteristic
58C2×C4×C73C2×D411yescharacteristic
59C22⋊D73—42no—
60C2×Dic73—21no—
61C2×Dic73—21no—
62C2×Dic73—21no—
63D292—22no—
64C4×D73—42no—
65Dic146—22no—
66C8×C73—42no—
67#10596831—42no—
68C22×C73—21no—
69C22×C73—21no—
70C22×C73—21no—
71C22×C73C2×C22⋊C411yescharacteristic
72C2×D73—41no—
73C2×D73—41no—
74C2×D73—41no—
75C4×C73—21no—
76C4×C73—21no—
77C4×C73—21no—
78C4×C73—21no—
79C4×C73#13112yes—
80C4×C73#13512yes—
81Dic73—41no—
82Dic73—41no—
83Dic73—41no—
84C2×C73—41no—
85C2×C73#40811yescharacteristic
86C2×C73#41611yescharacteristic
87C2×C73#42111yescharacteristic
88D73—81no—
89#1482—731nomaximal, Sylow
90C73#148211yescharacteristic, complemented, Sylow
91#529—731no—
92#431—731no—
93#431D7311yescharacteristic, complemented
94Q8⋊C8—732no—
95D4⋊C8—732no—
96#126—1461no—
97#125—731no—
98#124—731no—
99#123—1461no—
100C22⋊Q8—731no—
101#121—731no—
102C4×Q8—731no—
103C4×D4—731no—
104C4×D4—1461no—
105#117—1461no—
106C2×C42C2×D7311yescharacteristic
107C4⋊C8—1461no—
108C4⋊C8C2×D7312yes—
109C22⋊C8—21no—
110C22⋊C8—1461no—
111C4×C8—21no—
112C4×C8—732no—
113C2×Q8—731no—
114C2×D4—731no—
115C2×D4—1461no—
116C22×C4—1461no—
117C22×C4C4×D7311yescharacteristic
118C22×C4D29211yescharacteristic
119C22×C4C22⋊D7311yescharacteristic
120C2×C8—22no—
121C2×C8—1462no—
122C4⋊C4—731no—
123C4⋊C4—731no—
124C4⋊C4—1461no—
125C4⋊C4—1461no—
126C4⋊C4—1461no—
127C4⋊C4—1461no—
128C22⋊C4—1461no—
129C22⋊C4—1461no—
130C22⋊C4—1461no—
131C22⋊C4—1461no—
132C22⋊C4—1461no—
133C42—1461no—
134C42C4×D7311yescharacteristic
135C42D29211yescharacteristic
136C42C22⋊D7311yescharacteristic
137C42C22×D7311yescharacteristic
138C23—1461no—
139C23#1192400511yescharacteristic
140Q8—1462no—
141D4—2922no—
142D4—1462no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—2922no—
147C2×C4—1461no—
148C2×C4—1461no—
149C2×C4—1461no—
150C2×C4#1192400511yescharacteristic
151C2×C4#1192400511yescharacteristic
152C2×C4#1192400511yescharacteristic
153C2×C4C2×C4×D7311yescharacteristic
154C2×C4C2×C22⋊D7311yescharacteristic
155C2×C4C2×D29211yescharacteristic
156C8—42no—
157C8—2922no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—2921no—
162C22—2921no—
163C22—2921no—
164C22C2×#1192400511yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—2921no—
170C4—2921no—
171C4—2921no—
172C4#1455659712yes—
173C4#1455661112yes—
174C2—41no—
175C2—5841no—
176C2#1798855311yescharacteristic
177C2#1798858111yescharacteristic
178C2#1798860311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D73
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#431×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#431D73
hypocenterC73#1482
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #17988640C2semidirect
3. #17988317C2semidirect
4. #17988314C2semidirect
5. #431×C73C2semidirect
90. C73#1482semidirect
93. #431D73semidirect