Finite Group Databasebeta

← #22610397

Subgroups — #22610397

Order 9344.

338 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×#11924012C211yesmaximal, characteristic
2C2×#14556570C211yesmaximal, characteristic
3C2×#14556509C212yesmaximal, complemented
4#17988355C212yesmaximal, complemented
5#407×C73C211yesmaximal, characteristic
6C22×Dic146C2211yescharacteristic
7C2×#11924012—24no—
8C2×#11924012—21no—
9C2×#11924012C2212yes—
10C22×#10596831—21no—
11#14556570—21no—
12#14556570—21no—
13#14556570—21no—
14#14556570—21no—
15C2×C4⋊Dic73C2211yescharacteristic
16C2×#11924007C412yes—
17C2×C22⋊Dic73C412yes—
18#14556509—24no—
19C23×C4×C73C2211yescharacteristic
20C2×M16×C73C2212yes—
21C22⋊C8×C73—21no—
22C22⋊C8×C73—21no—
23C2×Dic146—22no—
24C2×Dic146—21no—
25C2×Dic146—21no—
26C2×Dic146—22no—
27C22×Dic73C2×C412yes—
28C22×Dic73C2×C412yes—
29#11924012—24no—
30#11924012—22no—
31#11924012D414yes—
32C2×#10596831—24no—
33C2×#10596831—22no—
34C4⋊Dic73—21no—
35C4⋊Dic73—21no—
36#11924007—22no—
37#11924007—22no—
38C22⋊Dic73—22no—
39C22⋊Dic73—22no—
40C24×C73C2×C411yescharacteristic
41C22×C4×C73—22no—
42C22×C4×C73—22no—
43C22×C4×C73C2×C411yescharacteristic
44C22×C4×C73D411yescharacteristic
45C22×C4×C73D411yescharacteristic
46C22×C4×C73D411yescharacteristic
47C22×C4×C73D411yescharacteristic
48C22×C4×C73C2311yescharacteristic
49M16×C73—22no—
50M16×C73—22no—
51C2×C8×C73—22no—
52C23×C73—22no—
53C23×C73—22no—
54C23×C73—41no—
55C23×C73C22⋊C411yescharacteristic
56C23×C73C22⋊C411yescharacteristic
57C23×C73C22×C411yescharacteristic
58C2×C4×C73—22no—
59C2×C4×C73—21no—
60C2×C4×C73—21no—
61C2×C4×C73—22no—
62C2×C4×C73—22no—
63C2×C4×C73—21no—
64C2×C4×C73—21no—
65C2×C4×C73C22⋊C411yescharacteristic
66C2×C4×C73C22⋊C411yescharacteristic
67C2×C4×C73C2×D412yes—
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73#4112yes—
71C2×Dic73—22no—
72C2×Dic73—22no—
73C2×Dic73—24no—
74C2×Dic73—42no—
75Dic146—41no—
76Dic146—42no—
77Dic146—41no—
78C8×C73—42no—
79#10596831—24no—
80C22×C73—21no—
81C22×C73—21no—
82C22×C73—21no—
83C22×C73—21no—
84C22×C73—21no—
85C22×C73—21no—
86C22×C73—21no—
87C22×C73—44no—
88C22×C73#10112yescomplemented
89C22×C73C2×C22⋊C411yescharacteristic
90C22×C73C4×D412yes—
91C4×C73—21no—
92C4×C73—21no—
93C4×C73#12011yescharacteristic
94C4×C73#12112yes—
95C4×C73#12311yescharacteristic
96Dic73—42no—
97Dic73—42no—
98C2×C73—22no—
99C2×C73—22no—
100C2×C73—41no—
101C2×C73#38611yescharacteristic
102C2×C73C2×#10111yescharacteristic
103C2×C73#41311yescharacteristic
104#1901—731nomaximal, Sylow
105C73#190111yescharacteristic, complemented, Sylow
106C22×M16—731no—
107C2×C22⋊Q8—731no—
108C2×#101—732no—
109#407D7311yescharacteristic
110#343—732no—
111C22×Q8—731no—
112C23×C4C2×D7311yescharacteristic
113C2×M16—732no—
114C2×M16—1464no—
115C2×M16—1461no—
116C2×M16C2×D7312yes—
117C22×C8—1461no—
118C22⋊Q8—1461no—
119C22⋊Q8—1461no—
120C22⋊Q8—1461no—
121C22⋊Q8—1461no—
122C2×C4⋊C4—732no—
123C2×C4⋊C4—731no—
124C2×C22⋊C4—732no—
125#101—1464no—
126C22⋊C8—21no—
127C22⋊C8—21no—
128C24C4×D7311yescharacteristic
129C2×Q8—1462no—
130C2×Q8—1461no—
131C2×Q8—1461no—
132C2×Q8—1462no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—732no—
136C22×C4—732no—
137C22×C4C4×D7311yescharacteristic
138C22×C4D29211yescharacteristic
139C22×C4D29211yescharacteristic
140C22×C4C22⋊D7311yescharacteristic
141C22×C4C22⋊D7311yescharacteristic
142C22×C4C22×D7311yescharacteristic
143M16—22no—
144M16—22no—
145M16—734no—
146M16—1464no—
147M16—1462no—
148C2×C8—22no—
149C2×C8—1464no—
150C2×C8—1462no—
151C4⋊C4—1462no—
152C4⋊C4—1462no—
153C4⋊C4—1461no—
154C4⋊C4—1461no—
155C22⋊C4—1462no—
156C22⋊C4—1462no—
157C23—22no—
158C23—22no—
159C23—41no—
160C23#1192400511yescharacteristic
161C23#1192400511yescharacteristic
162C23C2×C4×D7311yescharacteristic
163Q8—2921no—
164Q8—2922no—
165Q8—2921no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—2922no—
174C2×C4—1462no—
175C2×C4—1462no—
176C2×C4—1464no—
177C2×C4#1192400511yescharacteristic
178C2×C4#1192400511yescharacteristic
179C2×C4D4×D7312yes—
180C2×C4C2×C22⋊D7311yescharacteristic
181C2×C4C2×D29211yescharacteristic
182C2×C4#1192402712yes—
183C8—42no—
184C8—1464no—
185C22—21no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—44no—
193C22#1455650912yescomplemented
194C22C2×#1192400511yescharacteristic
195C22#1455655112yes—
196C4—21no—
197C4—21no—
198C4—2922no—
199C4—2922no—
200C4#1455656111yescharacteristic
201C4#1455656312yes—
202C4#1455657511yescharacteristic
203C2—22no—
204C2—22no—
205C2—41no—
206C2#1798846411yescharacteristic
207C2C2×#1455650911yescharacteristic
208C2#1798856911yescharacteristic
subgroupG/H
centerC22C2×#11924005
commutatorC23×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#407×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#407D73
hypocenterC73#1901
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. C2×#14556509C2semidirect
4. #17988355C2semidirect
88. C22×C73#101semidirect
105. C73#1901semidirect
193. C22#14556509semidirect