Finite Group Databasebeta

← #22608368

Subgroups — #22608368

Order 9344.

266 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C4×#11924028C211yesmaximal, characteristic
2C4×#11924012C211yesmaximal, characteristic, complemented
3#17988317C212yesmaximal, complemented
4#17988314C212yesmaximal, complemented
5#423×C73C211yesmaximal, characteristic, complemented
6C2×#11924028C411yescharacteristic
7C2×#11924012—21no—
8C4×Dic146C411yescharacteristic
9C4×Dic146C2211yescharacteristic
10C4×D292C411yescharacteristic
11C4×D292C2211yescharacteristic
12C4×C22⋊D73—21no—
13C4×C22⋊D73—21no—
14#14556550C411yescharacteristic
15#14556548—21no—
16C42×D73—21no—
17#14556502—21no—
18C4×#10596831C2212yes—
19C2×M16×C73—21no—
20C2×C42×C73C2211yescharacteristic
21C4⋊C8×C73—21no—
22C4⋊C8×C73C2212yes—
23#11924028—22no—
24#11924028—22no—
25C2×Dic146C2×C411yescharacteristic
26C2×D292C2×C411yescharacteristic
27C2×C22⋊D73—21no—
28C2×C4×D73—21no—
29C2×C4×D73—21no—
30C2×C4×D73—21no—
31#11924012—24no—
32C2×#10596831—22no—
33C4⋊Dic73C2×C411yescharacteristic
34C4⋊Dic73C2×C411yescharacteristic
35#11924007—21no—
36#11924007—21no—
37C22⋊Dic73—21no—
38#11924005—21no—
39#11924005—21no—
40C4×Dic73—21no—
41C4×Dic73—21no—
42C4×Dic73—21no—
43C22×C4×C73C2×C411yescharacteristic
44C22×C4×C73D411yescharacteristic
45C22×C4×C73D411yescharacteristic
46M16×C73—42no—
47C2×C8×C73—22no—
48C42×C73C2×C411yescharacteristic
49C42×C73D411yescharacteristic
50C42×C73D411yescharacteristic
51C42×C73C2311yescharacteristic
52C23×C73C22⋊C411yescharacteristic
53C22×D73—21no—
54C2×C4×C73—22no—
55C2×C4×C73—21no—
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73—21no—
59C2×C4×C73C22⋊C411yescharacteristic
60C2×C4×C73C22⋊C411yescharacteristic
61C2×C4×C73C22⋊C411yescharacteristic
62C2×C4×C73C22×C411yescharacteristic
63C2×C4×C73C2×D411yescharacteristic
64C2×C4×C73C2×D411yescharacteristic
65C22⋊D73—24no—
66C2×Dic73—21no—
67C2×Dic73—21no—
68C2×Dic73—21no—
69D292—21no—
70D292M1612yescomplemented
71C4×D73—24no—
72C4×D73—42no—
73C4×D73—41no—
74C4×D73—41no—
75Dic146—21no—
76Dic146M1612yescomplemented
77C8×C73—42no—
78#10596831—24no—
79C22×C73—21no—
80C22×C73—21no—
81C22×C73—21no—
82C22×C73C2×C22⋊C411yescharacteristic
83C2×D73—22no—
84C2×D73—41no—
85C2×D73—41no—
86C4×C73—21no—
87C4×C73—21no—
88C4×C73—21no—
89C4×C73#10412yes—
90C4×C73C2×M1611yescharacteristic
91C4×C73C2×M1611yescharacteristic
92C4×C73AGL(1,ℤ/8)11yescharacteristic
93C4×C73#13711yescharacteristic
94Dic73—22no—
95Dic73—41no—
96Dic73—41no—
97C2×C73—41no—
98C2×C73#40711yescharacteristic
99C2×C73#41711yescharacteristic
100C2×C73C2×#10411yescharacteristic
101D73—42no—
102#1489—731nomaximal, Sylow
103C73#148911yescharacteristic, complemented, Sylow
104C4×#41—731no—
105#423D7311yescharacteristic, complemented
106C4×M16—731no—
107Q8⋊C8—732no—
108D4⋊C8—732no—
109C2×#41—731no—
110C2×M16—21no—
111C2×M16—1461no—
112C4×Q8—731no—
113C4×Q8—731no—
114C4×D4—731no—
115C4×D4—731no—
116C4×D4—1461no—
117C4×D4—1461no—
118#117—731no—
119#117—1461no—
120C2×C42—1461no—
121C2×C42C2×D7311yescharacteristic
122C4⋊C8—21no—
123C4⋊C8C2×D7312yes—
124#97—1461no—
125C4×C8—732no—
126#41—1462no—
127#41—1462no—
128C2×Q8—731no—
129C2×D4—731no—
130C2×D4—1461no—
131C22×C4—1461no—
132C22×C4—1461no—
133C22×C4—1461no—
134C22×C4C4×D7311yescharacteristic
135C22×C4D29211yescharacteristic
136C22×C4C22⋊D7311yescharacteristic
137M16—42no—
138M16—1464no—
139C2×C8—22no—
140C2×C8—1462no—
141C4⋊C4—731no—
142C4⋊C4—731no—
143C4⋊C4—1461no—
144C4⋊C4—1461no—
145C22⋊C4—1461no—
146C22⋊C4—1461no—
147C22⋊C4—1461no—
148C42—1461no—
149C42—1461no—
150C42—1461no—
151C42C4×D7311yescharacteristic
152C42D29211yescharacteristic
153C42C22⋊D7311yescharacteristic
154C42C22×D7311yescharacteristic
155C23—1461no—
156C23#1192400511yescharacteristic
157Q8—732no—
158Q8—1461no—
159D4—732no—
160D4—1464no—
161D4—1461no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—2922no—
168C2×C4—2921no—
169C2×C4—2921no—
170C2×C4—1464no—
171C2×C4—1461no—
172C2×C4—1461no—
173C2×C4—1461no—
174C2×C4#1192400511yescharacteristic
175C2×C4#1192400511yescharacteristic
176C2×C4#1192400511yescharacteristic
177C2×C4C2×C4×D7311yescharacteristic
178C2×C4C2×C22⋊D7311yescharacteristic
179C2×C4C2×D29211yescharacteristic
180C8—42no—
181C8—1464no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—2921no—
186C22—2921no—
187C22—1462no—
188C22C2×#1192400511yescharacteristic
189C4—21no—
190C4—21no—
191C4—21no—
192C4—2921no—
193C4—2921no—
194C4—1462no—
195C4#1455651712yes—
196C4M16×D7311yescharacteristic
197C4M16×D7311yescharacteristic
198C4#1455661711yescharacteristic
199C4#1455662211yescharacteristic
200C2—41no—
201C2—2922no—
202C2#1798855011yescharacteristic
203C2#1798858611yescharacteristic
204C2C2×#1455651711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D73
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#423×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#423D73
hypocenterC73#1489
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. C4×#11924012C2semidirect
3. #17988317C2semidirect
4. #17988314C2semidirect
5. #423×C73C2semidirect
70. D292M16semidirect
76. Dic146M16semidirect
103. C73#1489semidirect
105. #423D73semidirect