Finite Group Databasebeta

← #22610312

Subgroups — #22610312

Order 9344.

332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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#17989354C211yesmaximal, characteristic, complemented
2#17989133C211yesmaximal, characteristic
3#17988605C212yesmaximal, complemented
4#17988346C212yesmaximal, complemented
5#410×C73C211yesmaximal, characteristic, complemented
6C2×#11924028C2211yescharacteristic
7#14556598—24no—
8C2×#11924012—22no—
9C2×#11924012C2212yes—
10#14556589C411yescharacteristic, complemented
11#14556587C411yescharacteristic, complemented
12#14556580C411yescharacteristic, complemented
13#14556578C411yescharacteristic, complemented
14#14556563—22no—
15C4×C22⋊D73—22no—
16C2×C4×Dic73C2211yescharacteristic
17#14556519—24no—
18C2×#41×C73C2211yescharacteristic
19#117×C73C2212yes—
20#99×C73—22no—
21#11924028—22no—
22#11924028—22no—
23C2×Dic146C2×C411yescharacteristic
24C2×D292C2×C411yescharacteristic
25C2×C22⋊D73—22no—
26C2×C22⋊D73—21no—
27C22×Dic73—21no—
28C2×C4×D73—21no—
29#11924012—24no—
30#11924012—22no—
31#11924012D414yescomplemented
32C2×#10596831—24no—
33C2×#10596831—22no—
34#11924007—22no—
35C22⋊Dic73—22no—
36#11924005—22no—
37C4×Dic73—21no—
38C4×Dic73C2×C411yescharacteristic
39C4×Dic73C2×C411yescharacteristic
40#41×C73—22no—
41#41×C73—22no—
42C2×Q8×C73C2×C411yescharacteristic
43C2×D4×C73C2×C411yescharacteristic
44C2×D4×C73D412yes—
45C22×C4×C73D412yes—
46C22×C4×C73C2311yescharacteristic
47C4⋊C4×C73—22no—
48C22⋊C4×C73—22no—
49C42×C73—22no—
50C23×C73C22⋊C412yes—
51C23×C73C2×D411yescharacteristic
52C22×D73—21no—
53Q8×C73—22no—
54D4×C73—24no—
55D4×C73—22no—
56C2×C4×C73—22no—
57C2×C4×C73—22no—
58C2×C4×C73—42no—
59C2×C4×C73C22⋊C412yes—
60C2×C4×C73C22×C411yescharacteristic
61C2×C4×C73C2×D412yes—
62C2×C4×C73C2×D411yescharacteristic
63C2×C4×C73#4112yes—
64C22⋊D73—44no—
65C22⋊D73—42no—
66C2×Dic73—21no—
67C2×Dic73—21no—
68C2×Dic73—21no—
69C2×Dic73—42no—
70D292—22no—
71C4×D73—41no—
72C4×D73—41no—
73Dic146—22no—
74#10596831—24no—
75C22×C73—22no—
76C22×C73—41no—
77C22×C73—42no—
78C22×C73C2×C22⋊C411yescharacteristic
79C22×C73#12112yes—
80C2×D73—42no—
81C2×D73—41no—
82C4×C73—22no—
83C4×C73—82no—
84C4×C73C4×D412yes—
85C4×C73#12011yescharacteristic
86C4×C73#12311yescharacteristic
87Dic73—22no—
88Dic73—41no—
89Dic73—41no—
90C2×C73—21no—
91C2×C73—22no—
92C2×C73—42no—
93C2×C73#38611yescharacteristic
94D73—81no—
95#1884—731nomaximal, Sylow
96C73#188411yescharacteristic, complemented, Sylow
97#568—731no—
98#532—731no—
99#421—732no—
100#410D7311yescharacteristic, complemented
101#339—732no—
102C2×#41—731no—
103C2×#41C2×D7311yescharacteristic
104#131—1464no—
105C2×M16—732no—
106C2×M16—1462no—
107C4⋊Q8—731no—
108#127—731no—
109#124—731no—
110#124—731no—
111#121—1462no—
112C4×D4—1462no—
113#117C2×D7312yes—
114C2×C42—731no—
115#104—1464no—
116#99—22no—
117#41—22no—
118#41—22no—
119#41—1462no—
120#41—1462no—
121C2×Q8—731no—
122C2×Q8C4×D7311yescharacteristic
123C2×D4—731no—
124C2×D4—1462no—
125C2×D4—1461no—
126C2×D4C4×D7311yescharacteristic
127C2×D4C22⋊D7312yes—
128C22×C4—1461no—
129C22×C4—1461no—
130C22×C4D29212yes—
131C22×C4C22×D7311yescharacteristic
132M16—734no—
133M16—1464no—
134M16—1462no—
135C2×C8—1464no—
136C2×C8—1462no—
137C4⋊C4—22no—
138C4⋊C4—1462no—
139C22⋊C4—22no—
140C22⋊C4—1462no—
141C22⋊C4—1462no—
142C42—22no—
143C42—731no—
144C42—731no—
145C42—1461no—
146C23—1461no—
147C23#1192400512yes—
148C23C2×C22⋊D7311yescharacteristic
149Q8—22no—
150Q8—1462no—
151D4—24no—
152D4—22no—
153D4—2922no—
154D4—2924no—
155D4—1462no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—2922no—
160C2×C4—2921no—
161C2×C4—2921no—
162C2×C4—1461no—
163C2×C4—1461no—
164C2×C4—1461no—
165C2×C4#1192400512yes—
166C2×C4C2×C4×D7311yescharacteristic
167C2×C4D4×D7312yes—
168C2×C4C2×D29211yescharacteristic
169C2×C4#1192402712yes—
170C8—1464no—
171C22—22no—
172C22—41no—
173C22—42no—
174C22—2922no—
175C22—2921no—
176C22C2×#1192400511yescharacteristic
177C22#1455656312yes—
178C4—22no—
179C4—82no—
180C4—2921no—
181C4—2921no—
182C4—1462no—
183C4#1455655112yes—
184C4#1455656111yescharacteristic
185C4#1455657511yescharacteristic
186C2—22no—
187C2—21no—
188C2—42no—
189C2—5841no—
190C2#1798846411yescharacteristic
subgroupG/H
centerC4#14556561
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#410×C73C2
socleC2×C73#386
hypercenter#410D73
hypocenterC73#1884
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #17989354C2semidirect
3. #17988605C2semidirect
4. #17988346C2semidirect
5. #410×C73C2semidirect
10. #14556589C4semidirect
11. #14556587C4semidirect
12. #14556580C4semidirect
13. #14556578C4semidirect
31. #11924012D4semidirect
96. C73#1884semidirect
100. #410D73semidirect