Finite Group Databasebeta

← #22611285

Subgroups — #22611285

Order 9344.

314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 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#17989213C211yesmaximal, characteristic
2#17988462C212yesmaximal
3#17988459C211yesmaximal, characteristic
4#17988353C212yesmaximal
5#342×C73C211yesmaximal, characteristic
6C23×Dic73C2211yescharacteristic
7#14556570—21no—
8#14556570—21no—
9#14556568—22no—
10#14556568—22no—
11C2×C4⋊Dic73—22no—
12C2×#11924007—21no—
13C2×C22⋊Dic73C2212yes—
14C2×C22⋊Dic73C2211yescharacteristic
15#14556498—22no—
16#14556498—21no—
17C2×C22⋊C4×C73C2211yescharacteristic
18C2×C22⋊C4×C73C2212yes—
19C2×Dic146—21no—
20C2×Dic146—21no—
21C22×Dic73—21no—
22C22×Dic73—21no—
23C22×Dic73—22no—
24C22×Dic73—42no—
25C22×Dic73D412yes—
26C22×Dic73D412yes—
27C4⋊Dic73—21no—
28C4⋊Dic73—21no—
29C4⋊Dic73—44no—
30#11924007—22no—
31#11924007—22no—
32#11924007—42no—
33C22⋊Dic73—22no—
34C22⋊Dic73—22no—
35C22⋊Dic73—21no—
36C22⋊Dic73Q812yescomplemented
37C24×C73C2311yescharacteristic
38C22×C4×C73—22no—
39C22×C4×C73D411yescharacteristic
40C22×C4×C73D411yescharacteristic
41C22⋊C4×C73—22no—
42C22⋊C4×C73—22no—
43C22⋊C4×C73Q814yescomplemented
44C23×C73—41no—
45C23×C73—41no—
46C23×C73C2×D412yes—
47C23×C73C2×D411yescharacteristic
48C23×C73C2×Q811yescharacteristic
49C23×C73C2×Q812yes—
50C23×C73#4111yescharacteristic
51C2×C4×C73—21no—
52C2×C4×C73—21no—
53C2×C4×C73—24no—
54C2×C4×C73—42no—
55C2×C4×C73—42no—
56C2×C4×C73—41no—
57C2×C4×C73—41no—
58C2×Dic73—22no—
59C2×Dic73—24no—
60C2×Dic73—22no—
61C2×Dic73—22no—
62C2×Dic73—22no—
63C2×Dic73—41no—
64C2×Dic73—41no—
65C2×Dic73—41no—
66C2×Dic73—42no—
67C2×Dic73—41no—
68C2×Dic73—42no—
69C2×Dic73—42no—
70Dic146—81no—
71Dic146—81no—
72C22×C73—22no—
73C22×C73—21no—
74C22×C73—22no—
75C22×C73—21no—
76C22×C73—41no—
77C22×C73—42no—
78C22×C73—41no—
79C22×C73#12011yescharacteristic
80C22×C73C22⋊Q812yes—
81C22×C73C22⋊Q811yescharacteristic
82C22×C73C4⋊Q812yes—
83C22×C73C4⋊Q811yescharacteristic
84C4×C73—44no—
85C4×C73—41no—
86C4×C73—41no—
87Dic73—42no—
88Dic73—42no—
89Dic73—42no—
90Dic73—42no—
91C2×C73—21no—
92C2×C73—22no—
93C2×C73—22no—
94C2×C73—21no—
95C2×C73#39511yescharacteristic
96C2×C73B(4,𝔽2)11yescharacteristic
97C2×C73#45811yescharacteristic
98#2062—731nomaximal, Sylow
99C73#206211yescharacteristic, complemented, Sylow
100#543—731no—
101#385—731no—
102#385—732no—
103#342—732no—
104#342D7311yescharacteristic
105C23×C4—731no—
106C22⋊Q8—1462no—
107C22⋊Q8—1462no—
108C22⋊Q8—1461no—
109C22⋊Q8—1461no—
110C2×C4⋊C4—1462no—
111C2×C4⋊C4—1461no—
112C2×C22⋊C4—731no—
113C2×C22⋊C4—732no—
114C2×C22⋊C4C2×D7311yescharacteristic
115C2×C22⋊C4C2×D7312yes—
116#95—1462no—
117#95—1461no—
118C24C22×D7311yescharacteristic
119C2×Q8—1461no—
120C2×Q8—1461no—
121C22×C4—22no—
122C22×C4—2922no—
123C22×C4—732no—
124C22×C4—732no—
125C22×C4—1462no—
126C22×C4—1461no—
127C22×C4—1461no—
128C22×C4D29211yescharacteristic
129C22×C4D29211yescharacteristic
130C4⋊C4—2922no—
131C4⋊C4—2924no—
132C4⋊C4—1462no—
133C4⋊C4—1462no—
134C4⋊C4—1461no—
135C4⋊C4—1461no—
136C22⋊C4—22no—
137C22⋊C4—22no—
138C22⋊C4—732no—
139C22⋊C4—1462no—
140C22⋊C4—1462no—
141C22⋊C4—1461no—
142C22⋊C4Dic14614yescomplemented
143C23—41no—
144C23—41no—
145C23D4×D7312yes—
146C23C2×D29211yescharacteristic
147C23Q8×D7311yescharacteristic
148C23C2×Dic14612yes—
149C23#1192402711yescharacteristic
150Q8—5841no—
151Q8—5841no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—24no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—2921no—
160C2×C4—2922no—
161C2×C4—2921no—
162C2×C4—2921no—
163C2×C4—2921no—
164C2×C4—2922no—
165C2×C4—2922no—
166C2×C4—1464no—
167C2×C4—1462no—
168C2×C4—1462no—
169C2×C4—1462no—
170C2×C4—1462no—
171C22—22no—
172C22—21no—
173C22—22no—
174C22—21no—
175C22—41no—
176C22—42no—
177C22—41no—
178C22#1455656111yescharacteristic
179C22#1455656812yes—
180C22#1455657111yescharacteristic
181C22#1455659012yes—
182C22#1455659111yescharacteristic
183C4—44no—
184C4—41no—
185C4—41no—
186C4—2922no—
187C4—2922no—
188C4—2922no—
189C4—2922no—
190C2—22no—
191C2—21no—
192C2—22no—
193C2—21no—
194C2#1798850811yescharacteristic
195C2#1798877511yescharacteristic
196C2#1798877811yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC24×C73C23
FrattiniC24C22×D73
Fitting#342×C73C2
socleC22×C73#120
hypercenter#342D73
hypocenterC73#2062
LCSG ▷ C24×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
36. C22⋊Dic73Q8semidirect
43. C22⋊C4×C73Q8semidirect
99. C73#2062semidirect
142. C22⋊C4Dic146semidirect