Finite Group Databasebeta

← #22619862

Subgroups — #22619862

Order 9344.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#17989098C211yesmaximal, characteristic
2#17988928C214yesmaximal, complemented
3#17988911C214yesmaximal, complemented
4#17988627C212yesmaximal, complemented
5#17988586C212yesmaximal, complemented
6#17988551C211yesmaximal, characteristic, complemented
7C2×#117×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9C2×#11924012C2212yes—
10#14556574—21no—
11#14556570C2212yes—
12#14556565C2212yes—
13#14556560—21no—
14C4×C22⋊D73—22no—
15#14556550C2211yescharacteristic
16#14556524C2214yescomplemented
17#14556522C2214yescomplemented
18#14556514C2214yescomplemented
19#14556511C2214yescomplemented
20C22⋊#10596831C2214yes—
21C23×C4×C73C2211yescharacteristic
22#117×C73—22no—
23#117×C73C2214yes—
24C2×C4⋊C4×C73C2212yes—
25C2×C22⋊C4×C73—21no—
26C2×C42×C73—21no—
27#11924028—24no—
28C2×Dic146C2311yescharacteristic
29C2×D292C2311yescharacteristic
30C2×C22⋊D73—22no—
31C2×C22⋊D73—21no—
32C2×C4×D73—21no—
33#11924012—24no—
34C2×#10596831C2314yes—
35C4⋊Dic73C2312yes—
36#11924007—22no—
37C22⋊Dic73—21no—
38C22⋊Dic73—22no—
39#11924005—22no—
40C4×Dic73—21no—
41C24×C73D411yescharacteristic
42C22×C4×C73—24no—
43C22×C4×C73—22no—
44C22×C4×C73D411yescharacteristic
45C22×C4×C73D412yes—
46C22×C4×C73C2312yes—
47C22×C4×C73C2311yescharacteristic
48C4⋊C4×C73—22no—
49C4⋊C4×C73C2314yes—
50C22⋊C4×C73—24no—
51C42×C73—24no—
52C23×C73—22no—
53C23×C73—42no—
54C23×C73C2×D412yes—
55C23×C73C2×D411yescharacteristic
56C22×D73—21no—
57C2×C4×C73—22no—
58C2×C4×C73—24no—
59C2×C4×C73—24no—
60C2×C4×C73—24no—
61C2×C4×C73—44no—
62C2×C4×C73C2×D412yes—
63C2×C4×C73C2×D411yescharacteristic
64C2×C4×C73#4114yes—
65C2×C4×C73C2411yescharacteristic
66C22⋊D73—44no—
67C22⋊D73—42no—
68C2×Dic73—22no—
69C2×Dic73—21no—
70D292—22no—
71C4×D73—42no—
72Dic146—22no—
73#10596831—24no—
74C22×C73—22no—
75C22×C73—22no—
76C22×C73—22no—
77C22×C73—22no—
78C22×C73—44no—
79C22×C73#12312yes—
80C22×C73C22×D411yescharacteristic
81C2×D73—41no—
82C2×D73—42no—
83C4×C73—22no—
84C4×C73—44no—
85C4×C73#12312yes—
86C4×C73C2×#4112yes—
87Dic73—41no—
88Dic73—42no—
89C2×C73—22no—
90C2×C73—42no—
91C2×C73C2×#12311yescharacteristic
92C2×C73#57512yes—
93D73—81no—
94#3093—731nomaximal, Sylow
95C73#309311yescharacteristic, complemented, Sylow
96#525—731no—
97C2×#117D7311yescharacteristic, complemented
98#485—734no—
99#482—734no—
100#428—732no—
101#417—732no—
102#407—731no—
103C2×#41—731no—
104C23×C4C2×D7311yescharacteristic
105C2×M16—732no—
106#123—1461no—
107C22⋊Q8—732no—
108#121—732no—
109#120—1461no—
110C4×D4—1462no—
111#117—22no—
112#117—731no—
113#117C2×D7314yes—
114C2×C4⋊C4C2×D7312yes—
115C2×C22⋊C4—21no—
116C2×C42—21no—
117#107—734no—
118#106—734no—
119#103—734no—
120#102—734no—
121C22⋊C8—734no—
122C24C22⋊D7311yescharacteristic
123#41—1464no—
124C2×Q8—731no—
125C2×D4—731no—
126C2×D4—1462no—
127C2×D4—1461no—
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—1461no—
131C22×C4C22⋊D7311yescharacteristic
132C22×C4C22⋊D7312yes—
133C22×C4C22×D7312yes—
134C22×C4C22×D7311yescharacteristic
135M16—1464no—
136C2×C8—734no—
137C4⋊C4—22no—
138C4⋊C4—732no—
139C4⋊C4—1462no—
140C4⋊C4C22×D7314yes—
141C22⋊C4—24no—
142C22⋊C4—1461no—
143C22⋊C4—1462no—
144C22⋊C4—1462no—
145C42—24no—
146C42—1461no—
147C23—22no—
148C23—42no—
149C23—1461no—
150C23C2×C22⋊D7312yes—
151C23C2×C22⋊D7311yescharacteristic
152Q8—1462no—
153D4—2924no—
154D4—2922no—
155D4—1462no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—2922no—
162C2×C4—1462no—
163C2×C4—1461no—
164C2×C4C2×C22⋊D7312yes—
165C2×C4C2×C22⋊D7311yescharacteristic
166C2×C4#1192402814yes—
167C2×C4C23×D7311yescharacteristic
168C8—1464no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—2922no—
175C22—2921no—
176C22#1455657412yes—
177C22C22×C22⋊D7311yescharacteristic
178C4—22no—
179C4—44no—
180C4—2922no—
181C4—2921no—
182C4#1455657412yes—
183C4C2×#1192402812yes—
184C2—22no—
185C2—42no—
186C2—5841no—
187C2C2×#1455657411yescharacteristic
188C2#1798938512yes—
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#117×C73C2
socleC22×C73C22×D4
hypercenterC2×#117D73
hypocenterC73#3093
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #17988928C2semidirect
3. #17988911C2semidirect
4. #17988627C2semidirect
5. #17988586C2semidirect
6. #17988551C2semidirect
7. C2×#117×C73C2semidirect
16. #14556524C22semidirect
17. #14556522C22semidirect
18. #14556514C22semidirect
19. #14556511C22semidirect
95. C73#3093semidirect
97. C2×#117D73semidirect