Finite Group Databasebeta

← #22608919

Subgroups — #22608919

Order 9344.

280 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 53 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#17989149C211yesmaximal, characteristic
2#17988901C212yesmaximal, complemented
3#17988512C211yesmaximal, characteristic, complemented
4#17988322C212yesmaximal, complemented
5#323×C73C211yesmaximal, characteristic, complemented
6C22×C22⋊D73—21no—
7#14556575—22no—
8#14556565—21no—
9#14556565C2212yes—
10#14556561—22no—
11C2×C4⋊Dic73C2211yescharacteristic, complemented
12C2×C22⋊Dic73—21no—
13#14556525—22no—
14#14556513—22no—
15#14556498—21no—
16#14556498C2211yescharacteristic, complemented
17C2×C22⋊C4×C73C2211yescharacteristic
18C22⋊C8×C73C2212yescomplemented
19C23×D73—21no—
20C2×D292—21no—
21C2×D292D412yes—
22C2×C22⋊D73—22no—
23C2×C22⋊D73—22no—
24C2×C22⋊D73—42no—
25C2×C22⋊D73—42no—
26C22×Dic73—21no—
27C22×Dic73—21no—
28C22×Dic73—21no—
29C4⋊Dic73—21no—
30C4⋊Dic73—22no—
31C4⋊Dic73D412yes—
32C22⋊Dic73—42no—
33#11924005—22no—
34#11924005—22no—
35C24×C73D411yescharacteristic
36C22×C4×C73D411yescharacteristic
37C22×C4×C73C2311yescharacteristic
38C2×C8×C73—22no—
39C22⋊C4×C73—22no—
40C23×C73—21no—
41C23×C73—21no—
42C23×C73—41no—
43C23×C73—41no—
44C23×C73D812yes—
45C23×C73C2×D411yescharacteristic
46C22×D73—22no—
47C22×D73—42no—
48C22×D73—81no—
49C22×D73—81no—
50C2×C4×C73—21no—
51C2×C4×C73—41no—
52C2×C4×C73—41no—
53C2×C4×C73C2×D412yes—
54C22⋊D73—44no—
55C22⋊D73—42no—
56C22⋊D73—42no—
57C2×Dic73—22no—
58C2×Dic73—42no—
59C2×Dic73—41no—
60C2×Dic73—41no—
61C2×Dic73—41no—
62C2×Dic73—41no—
63C2×Dic73—41no—
64C2×Dic73—41no—
65D292—42no—
66D292—81no—
67C8×C73—42no—
68C22×C73—21no—
69C22×C73—21no—
70C22×C73—22no—
71C22×C73—42no—
72C22×C73—41no—
73C22×C73—41no—
74C22×C73—81no—
75C22×C73#12011yescharacteristic
76C22×C73C2×D811yescharacteristic
77C22×C73AGL(1,ℤ/8)11yescharacteristic
78C2×D73—42no—
79C2×D73—42no—
80C2×D73—42no—
81C2×D73—84no—
82C4×C73—22no—
83C4×C73—41no—
84Dic73—42no—
85Dic73—81no—
86Dic73—81no—
87C2×C73—21no—
88C2×C73—21no—
89C2×C73—42no—
90C2×C73#44711yescharacteristic
91C2×C73#45511yescharacteristic
92C2×C73#45811yescharacteristic
93D73—82no—
94#1607—731nomaximal, Sylow
95C73#160711yescharacteristic, complemented, Sylow
96#534—731no—
97#480—732no—
98#397—731no—
99#327—732no—
100#323D7311yescharacteristic, complemented
101C22×D4—1461no—
102#123—1462no—
103#121—732no—
104#121—1461no—
105#120—1462no—
106C2×C4⋊C4—731no—
107C2×C22⋊C4—1461no—
108C2×C22⋊C4C2×D7311yescharacteristic
109#107—1462no—
110#102—1462no—
111C22⋊C8C2×D7312yescomplemented
112#95—731no—
113#95—1461no—
114C24—1461no—
115C24D29211yescharacteristic
116C2×D4—2922no—
117C2×D4—2922no—
118C2×D4—732no—
119C2×D4—1461no—
120C2×D4—1462no—
121C2×D4—1462no—
122C22×C4—1461no—
123C22×C4—1461no—
124C22×C4—1461no—
125C22×C4D29211yescharacteristic
126C22×C4C22×D7311yescharacteristic
127C2×C8—22no—
128C4⋊C4—732no—
129C4⋊C4—1461no—
130C4⋊C4—1462no—
131C22⋊C4—22no—
132C22⋊C4—2922no—
133C22⋊C4—1462no—
134C22⋊C4—1462no—
135C23—21no—
136C23—21no—
137C23—41no—
138C23—41no—
139C23—2922no—
140C23—5841no—
141C23—5841no—
142C23—1462no—
143C23D58412yes—
144C23C2×D29211yescharacteristic
145D4—2922no—
146D4—2924no—
147D4—2922no—
148D4—2922no—
149D4—5841no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—2922no—
154C2×C4—2921no—
155C2×C4—2921no—
156C2×C4—2921no—
157C2×C4—2921no—
158C2×C4—2921no—
159C2×C4—2921no—
160C2×C4—1462no—
161C2×C4D4×D7312yes—
162C8—42no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—42no—
167C22—41no—
168C22—41no—
169C22—81no—
170C22—2922no—
171C22—2922no—
172C22—2922no—
173C22—5844no—
174C22#1455656111yescharacteristic
175C22C2×D58411yescharacteristic
176C22#1455661911yescharacteristic
177C4—22no—
178C4—41no—
179C4—2922no—
180C4—5841no—
181C4—5841no—
182C2—21no—
183C2—21no—
184C2—42no—
185C2—5842no—
186C2#1798872311yescharacteristic
187C2#1798876711yescharacteristic
188C2#1798877811yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#323×C73C2
socleC22×C73#120
hypercenter#323D73
hypocenterC73#1607
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #17988901C2semidirect
3. #17988512C2semidirect
4. #17988322C2semidirect
5. #323×C73C2semidirect
11. C2×C4⋊Dic73C22semidirect
16. #14556498C22semidirect
18. C22⋊C8×C73C22semidirect
95. C73#1607semidirect
100. #323D73semidirect
111. C22⋊C8C2×D73semidirect