Finite Group Databasebeta

← #22625939

Subgroups — #22625939

Order 9344.

344 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 68 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#17989655C211yesmaximal, characteristic, complemented
2#17989579C212yesmaximal
3D73⋊#101C211yesmaximal, characteristic, complemented
4#17989458C212yesmaximal, complemented
5#124×D73C211yesmaximal, characteristic
6D73⋊M16C2212yes—
7Q8×#64408—24no—
8#14556670—22no—
9#14556670C2212yes—
10#14556653—24no—
11#14556652—22no—
12C2×Q8×D73C2211yescharacteristic
13C2×D4×D73C2211yescharacteristic
14#14556580C411yescharacteristic, complemented
15#14556579C411yescharacteristic, complemented
16#14556578C411yescharacteristic, complemented
17#14556577—22no—
18C22⋊C4×D73—22no—
19C42×D73C2211yescharacteristic
20#124×C73C411yescharacteristic, complemented
21#11924038—22no—
22#11924037—22no—
23#11924036—22no—
24C4⋊#64408—24no—
25C4⋊#64408D414yes—
26C22⋊#64408—22no—
27C4×#64408—24no—
28C4×#64408—22no—
29C23×D73—21no—
30C2×Dic146C2×C411yescharacteristic
31C2×Dic146D412yes—
32Q8×D73—22no—
33Q8×D73—22no—
34C2×D292C2×C411yescharacteristic
35C2×C22⋊D73—21no—
36D4×D73—22no—
37D4×D73—22no—
38C2×C4×D73—21no—
39C2×C4×D73D412yes—
40C2×C4×D73C2311yescharacteristic
41C22⋊Dic73—22no—
42#11924005—22no—
43#11924005—22no—
44C4×Dic73—21no—
45C4×Dic73C2×C411yescharacteristic
46C2×Q8×C73C2×C411yescharacteristic
47C2×D4×C73C2×C411yescharacteristic
48C22⋊C4×C73—22no—
49C42×C73C2×C411yescharacteristic
50C23×C73—21no—
51C22×D73—21no—
52C22×D73—44no—
53C22×D73—41no—
54C22×D73—41no—
55C22×D73C2×D411yescharacteristic
56C2×#64408—24no—
57Q8×C73—22no—
58D4×C73—22no—
59C2×C4×C73—21no—
60C2×C4×C73C22⋊C412yes—
61C2×C4×C73C22×C411yescharacteristic
62C22⋊D73—42no—
63C2×Dic73—21no—
64C2×Dic73C22⋊C412yes—
65C2×Dic73C2×D411yescharacteristic
66D292—22no—
67C4×D73—22no—
68C4×D73—22no—
69C4×D73—42no—
70C4×D73C2×D412yes—
71C4×D73#4112yes—
72Dic146—22no—
73Dic146—24no—
74#10596833—42no—
75C22×C73—42no—
76C22×C73—41no—
77C22×C73C2×C22⋊C411yescharacteristic
78C2×D73—22no—
79C2×D73—42no—
80C2×D73—41no—
81C2×D73—82no—
82C2×D73—82no—
83C2×D73#12011yescharacteristic
84C2×D73#12311yescharacteristic
85#64408—44no—
86C4×C73—22no—
87C4×C73—41no—
88C4×C73C4×D412yes—
89Dic73—22no—
90Dic73—41no—
91Dic73#12112yes—
92C2×C73—21no—
93C2×C73—81no—
94C2×C73#38611yescharacteristic
95D73—21no—
96D73—81no—
97D73#45412yes—
98#1888—731nomaximal, Sylow
99C73#188811yescharacteristic, complemented, Sylow
100C2×#124—731no—
101#519—731no—
102#418—732no—
103C2×#101—731no—
104#339—732no—
105C22×Q8—731no—
106C22×D4—731no—
107C2×M16—732no—
108#124—731no—
109#124—731no—
110#124—731no—
111#124—1462no—
112#124#6440811yescharacteristic, complemented
113C4×Q8—1464no—
114#117—732no—
115#117—1462no—
116C2×C22⋊C4—1462no—
117C2×C42—731no—
118#102—1464no—
119#101—1462no—
120C24—1461no—
121C2×Q8—732no—
122C2×Q8—731no—
123C2×Q8—1462no—
124C2×Q8—1462no—
125C2×Q8C2×#6440811yescharacteristic
126C2×D4—731no—
127C2×D4—1462no—
128C2×D4—1462no—
129C2×D4—1461no—
130C2×D4C2×#6440811yescharacteristic
131C22×C4—731no—
132C22×C4—732no—
133C22×C4—1461no—
134M16—1462no—
135M16—1462no—
136C2×C8—1462no—
137C4⋊C4—734no—
138C4⋊C4—1464no—
139C22⋊C4—22no—
140C22⋊C4—1462no—
141C22⋊C4—1462no—
142C22⋊C4—1462no—
143C22⋊C4—1462no—
144C42—731no—
145C42—1461no—
146C42—1462no—
147C42—1464no—
148C42C2×#6440811yescharacteristic
149C23—21no—
150C23—2921no—
151C23—2921no—
152C23—2924no—
153C23—731no—
154C23—1461no—
155Q8—22no—
156Q8—1464no—
157Q8—1462no—
158D4—22no—
159D4—2922no—
160D4—1462no—
161C2×C4—21no—
162C2×C4—2922no—
163C2×C4—731no—
164C2×C4—732no—
165C2×C4—732no—
166C2×C4—732no—
167C2×C4—1462no—
168C2×C4—1462no—
169C2×C4—1464no—
170C2×C4—1461no—
171C2×C4C22⋊#6440812yes—
172C2×C4C22×#6440811yescharacteristic
173C8—2922no—
174C22—42no—
175C22—41no—
176C22—2922no—
177C22—2921no—
178C22—5842no—
179C22—5842no—
180C22—731no—
181C22—731no—
182C22—1462no—
183C22C2×C22⋊#6440811yescharacteristic
184C4—22no—
185C4—41no—
186C4—2921no—
187C4—2924no—
188C4—732no—
189C4—1462no—
190C4D4×#6440812yes—
191C2—21no—
192C2—81no—
193C2—5841no—
194C2—732no—
195C2—1461no—
196C2#1798953511yescharacteristic
subgroupG/H
centerC2#17989535
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#124×C73C4
socleC2×C73#386
hypercenter#124#64408
hypocenterC73#1888
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #17989655C2semidirect
3. D73⋊#101C2semidirect
4. #17989458C2semidirect
14. #14556580C4semidirect
15. #14556579C4semidirect
16. #14556578C4semidirect
20. #124×C73C4semidirect
99. C73#1888semidirect
112. #124#64408semidirect