Finite Group Databasebeta

← #22610331

Subgroups — #22610331

Order 9344.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#14556578C211yesmaximal, characteristic
2#17989064C211yesmaximal, characteristic, complemented
3#17988592C211yesmaximal, characteristic
4C2×#14556509C211yesmaximal, characteristic, complemented
5#17988348C211yesmaximal, characteristic, complemented
6#17988346C211yesmaximal, characteristic, complemented
7#418×C73C211yesmaximal, characteristic
8C22×Dic146C2211yescharacteristic
9C2×#11924012C2211yescharacteristic
10#14556578—22no—
11#14556578C414yescomplemented
12C4×Dic146—22no—
13#14556556—22no—
14#14556550C2211yescharacteristic
15#14556547—22no—
16C2×C22⋊Dic73—22no—
17C2×C4×Dic73C2211yescharacteristic
18#14556512—22no—
19#14556509—22no—
20C22×D4×C73C2211yescharacteristic
21C2×M16×C73C2211yescharacteristic
22#117×C73C2211yescharacteristic
23#102×C73—22no—
24C2×Dic146—21no—
25C2×Dic146—21no—
26C2×Dic146—21no—
27C2×Dic146—21no—
28C2×Dic146C2×C412yes—
29C2×Dic146D412yes—
30C22×Dic73—21no—
31C22×Dic73D412yes—
32#11924012—21no—
33#11924012—21no—
34C2×#10596831—21no—
35C4⋊Dic73D412yes—
36#11924007—24no—
37C22⋊Dic73—21no—
38C22⋊Dic73—28no—
39C4×Dic73—24no—
40C4×Dic73—21no—
41C4×Dic73—21no—
42C4×Dic73C2×C412yes—
43C24×C73—21no—
44C2×D4×C73—21no—
45C2×D4×C73—21no—
46C2×D4×C73—21no—
47C2×D4×C73—21no—
48C2×D4×C73—21no—
49C2×D4×C73C2×C412yes—
50C22×C4×C73C2311yescharacteristic
51M16×C73—21no—
52M16×C73—21no—
53C2×C8×C73—21no—
54C4⋊C4×C73D412yes—
55C22⋊C4×C73—21no—
56C42×C73—21no—
57C23×C73—22no—
58C23×C73—44no—
59C23×C73—41no—
60C23×C73—41no—
61C23×C73C2×D411yescharacteristic
62D4×C73—22no—
63D4×C73—22no—
64D4×C73—41no—
65D4×C73—41no—
66C2×C4×C73—22no—
67C2×C4×C73C22×C411yescharacteristic
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73#4111yescharacteristic
72C2×C4×C73#4111yescharacteristic
73C2×Dic73—22no—
74C2×Dic73—22no—
75C2×Dic73—22no—
76C2×Dic73—22no—
77C2×Dic73—42no—
78C2×Dic73C22⋊C414yes—
79Dic146—22no—
80Dic146—22no—
81Dic146—22no—
82Dic146—22no—
83C8×C73—41no—
84#10596831—41no—
85C22×C73—22no—
86C22×C73—44no—
87C22×C73—42no—
88C22×C73—82no—
89C22×C73—82no—
90C22×C73C2×C22⋊C411yescharacteristic
91C22×C73#12011yescharacteristic
92C22×C73#12311yescharacteristic
93C4×C73—42no—
94C4×C73C4×D411yescharacteristic
95C4×C73C4×D411yescharacteristic
96C4×C73#12111yescharacteristic
97C4×C73#12111yescharacteristic
98Dic73—24no—
99Dic73—42no—
100Dic73—42no—
101C2×C73—21no—
102C2×C73—21no—
103C2×C73—82no—
104C2×C73#38611yescharacteristic
105C2×C73#45412yes—
106#1888—731nomaximal, Sylow
107C73#188811yescharacteristic, complemented, Sylow
108C2×#124—731no—
109#519—731no—
110#418—731no—
111#418D7311yescharacteristic
112C2×#101—731no—
113#339—731no—
114#339—731no—
115C22×Q8—731no—
116C22×D4C2×D7311yescharacteristic
117C2×M16—731no—
118C2×M16C2×D7311yescharacteristic
119#124—734no—
120#124—1462no—
121C4×Q8—1462no—
122C4×Q8—1462no—
123#117—731no—
124#117—1462no—
125#117C2×D7311yescharacteristic
126C2×C22⋊C4—1462no—
127C2×C42—731no—
128#102—22no—
129#102—1462no—
130#101—1462no—
131C24—21no—
132C2×Q8—732no—
133C2×Q8—732no—
134C2×Q8—1461no—
135C2×Q8—1461no—
136C2×Q8—1461no—
137C2×Q8—1461no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4C4×D7312yes—
144C22×C4—732no—
145C22×C4—1461no—
146C22×C4C22×D7311yescharacteristic
147M16—21no—
148M16—21no—
149M16—1461no—
150M16—1461no—
151C2×C8—21no—
152C2×C8—1461no—
153C4⋊C4—732no—
154C4⋊C4—1464no—
155C4⋊C4C22⋊D7312yes—
156C22⋊C4—21no—
157C22⋊C4—1468no—
158C22⋊C4—1461no—
159C42—21no—
160C42—732no—
161C42—1464no—
162C42—1461no—
163C42—1461no—
164C23—22no—
165C23—44no—
166C23—41no—
167C23—41no—
168C23D4×D7311yescharacteristic
169Q8—1462no—
170Q8—1462no—
171Q8—1462no—
172Q8—1462no—
173D4—22no—
174D4—22no—
175D4—41no—
176D4—41no—
177C2×C4—22no—
178C2×C4—2922no—
179C2×C4—734no—
180C2×C4—1462no—
181C2×C4—1462no—
182C2×C4—1462no—
183C2×C4—1462no—
184C2×C4C2×C4×D7311yescharacteristic
185C2×C4D4×D7311yescharacteristic
186C2×C4D4×D7311yescharacteristic
187C2×C4C2×C22⋊D7311yescharacteristic
188C2×C4#1192402711yescharacteristic
189C2×C4#1192402811yescharacteristic
190C8—41no—
191C8—2921no—
192C22—22no—
193C22—44no—
194C22—42no—
195C22—82no—
196C22—82no—
197C22C22⋊C4×D7311yescharacteristic
198C22#1455655911yescharacteristic
199C22#1455657311yescharacteristic
200C4—42no—
201C4—2922no—
202C4—2922no—
203C4—1464no—
204C4#1455655111yescharacteristic
205C4C4×C22⋊D7311yescharacteristic
206C4#1455656211yescharacteristic
207C4#1455656411yescharacteristic
208C2—21no—
209C2—21no—
210C2—82no—
211C2#1798846311yescharacteristic
212C2#1798875812yes—
subgroupG/H
centerC22#14556559
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#418×C73C2
socleC22×C73#120
hypercenter#418D73
hypocenterC73#1888
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #17989064C2semidirect
4. C2×#14556509C2semidirect
5. #17988348C2semidirect
6. #17988346C2semidirect
11. #14556578C4semidirect
107. C73#1888semidirect