Finite Group Databasebeta

← #22608397

Subgroups — #22608397

Order 9344.

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

normal subgroups only

This group has 216 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#17988611C211yesmaximal, characteristic, complemented
3#17988319C212yesmaximal, complemented
4#17988316C212yesmaximal, complemented
5#431×C73C211yesmaximal, characteristic, complemented
6C2×#11924012—21no—
7#14556585—21no—
8#14556583C411yescharacteristic
9#14556579C411yescharacteristic
10#14556574—21no—
11#14556570C411yescharacteristic
12#14556565C411yescharacteristic
13C4×Dic146C2211yescharacteristic
14C4×D292C2211yescharacteristic
15C4×C22⋊D73—21no—
16#14556548—21no—
17C4⋊#10596831—21no—
18C4⋊#10596831C2212yes—
19C2×C42×C73C2211yescharacteristic
20C4⋊C8×C73—21no—
21C22⋊C8×C73—21no—
22C4×C8×C73C2212yes—
23C2×Dic146C2×C411yescharacteristic
24C2×D292C2×C411yescharacteristic
25C2×C22⋊D73—21no—
26C2×C4×D73—21no—
27#11924012—42no—
28C2×#10596831—22no—
29C4⋊Dic73C2×C411yescharacteristic
30C4⋊Dic73C2×C411yescharacteristic
31#11924007—21no—
32#11924007—21no—
33#11924007—21no—
34#11924007—21no—
35C22⋊Dic73—21no—
36#11924005—21no—
37#11924005—21no—
38#11924005—21no—
39#11924005—21no—
40C4×Dic73—21no—
41C22×C4×C73C2×C411yescharacteristic
42C22×C4×C73D411yescharacteristic
43C22×C4×C73D411yescharacteristic
44C2×C8×C73—22no—
45C42×C73C2×C411yescharacteristic
46C42×C73D411yescharacteristic
47C42×C73D411yescharacteristic
48C42×C73C2311yescharacteristic
49C23×C73C22⋊C411yescharacteristic
50C22×D73—21no—
51C2×C4×C73—22no—
52C2×C4×C73—21no—
53C2×C4×C73—21no—
54C2×C4×C73—41no—
55C2×C4×C73C22⋊C411yescharacteristic
56C2×C4×C73C22⋊C411yescharacteristic
57C2×C4×C73C22⋊C411yescharacteristic
58C2×C4×C73C22×C411yescharacteristic
59C2×C4×C73C2×D411yescharacteristic
60C2×C4×C73C2×D411yescharacteristic
61C22⋊D73—42no—
62C2×Dic73—21no—
63C2×Dic73—21no—
64C2×Dic73—21no—
65D292—22no—
66C4×D73—41no—
67C4×D73—41no—
68Dic146—22no—
69C8×C73—42no—
70#10596831—42no—
71C22×C73—21no—
72C22×C73—21no—
73C22×C73—21no—
74C22×C73C2×C22⋊C411yescharacteristic
75C2×D73—41no—
76C2×D73—41no—
77C2×D73—41no—
78C4×C73—21no—
79C4×C73—21no—
80C4×C73—21no—
81C4×C73—21no—
82C4×C73#13112yes—
83C4×C73AGL(1,ℤ/8)11yescharacteristic
84C4×C73#13711yescharacteristic
85Dic73—41no—
86Dic73—41no—
87Dic73—41no—
88C2×C73—41no—
89C2×C73#40811yescharacteristic
90C2×C73#41711yescharacteristic
91C2×C73#42111yescharacteristic
92D73—81no—
93#1495—731nomaximal, Sylow
94C73#149511yescharacteristic, complemented, Sylow
95#529—731no—
96#431D7311yescharacteristic, complemented
97#423—731no—
98Q8⋊C8—732no—
99D4⋊C8—732no—
100C2×M16—1461no—
101#126—1461no—
102#125—731no—
103#124—731no—
104#123—1461no—
105C22⋊Q8—731no—
106#121—731no—
107C4×Q8—731no—
108C4×D4—731no—
109C4×D4—1461no—
110#117—1461no—
111C2×C42C2×D7311yescharacteristic
112C4⋊C8—21no—
113C4⋊C8—732no—
114C4⋊C8—1461no—
115C22⋊C8—21no—
116C4×C8C2×D7312yes—
117C2×Q8—731no—
118C2×D4—731no—
119C2×D4—1461no—
120C22×C4—1461no—
121C22×C4C4×D7311yescharacteristic
122C22×C4D29211yescharacteristic
123C22×C4C22⋊D7311yescharacteristic
124M16—2922no—
125C2×C8—22no—
126C2×C8—1462no—
127C4⋊C4—731no—
128C4⋊C4—731no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C4⋊C4—1461no—
132C4⋊C4—1461no—
133C22⋊C4—1461no—
134C22⋊C4—1461no—
135C22⋊C4—1461no—
136C22⋊C4—1461no—
137C22⋊C4—1461no—
138C42—1461no—
139C42C4×D7311yescharacteristic
140C42D29211yescharacteristic
141C42C22⋊D7311yescharacteristic
142C42C22×D7311yescharacteristic
143C23—1461no—
144C23#1192400511yescharacteristic
145Q8—1462no—
146D4—2922no—
147D4—1462no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—2921no—
153C2×C4—2921no—
154C2×C4—1461no—
155C2×C4—1461no—
156C2×C4—1461no—
157C2×C4#1192400511yescharacteristic
158C2×C4#1192400511yescharacteristic
159C2×C4#1192400511yescharacteristic
160C2×C4C2×C4×D7311yescharacteristic
161C2×C4C2×C22⋊D7311yescharacteristic
162C2×C4C2×D29211yescharacteristic
163C8—42no—
164C8—2922no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—2921no—
169C22—2921no—
170C22—2921no—
171C22C2×#1192400511yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—2921no—
177C4—2921no—
178C4—2921no—
179C4#1455659712yes—
180C4#1455661911yescharacteristic
181C4#1455662411yescharacteristic
182C2—41no—
183C2—5841no—
184C2#1798855311yescharacteristic
185C2#1798858911yescharacteristic
186C2#1798860511yescharacteristic
subgroupG/H
centerC2×C4C2×D292
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#431×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#431D73
hypocenterC73#1495
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. #17988611C2semidirect
3. #17988319C2semidirect
4. #17988316C2semidirect
5. #431×C73C2semidirect
94. C73#1495semidirect
96. #431D73semidirect