Finite Group Databasebeta

← #22625936

Subgroups — #22625936

Order 9344.

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

normal subgroups only

This group has 360 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#17989654C211yesmaximal, characteristic
2#17989580C212yesmaximal, complemented
3D73⋊#100C211yesmaximal, characteristic
4#17989458C212yesmaximal, complemented
5#124×D73C211yesmaximal, characteristic
6D73⋊M16C2212yes—
7D4×#64408—24no—
8#14556670C2212yes—
9C2×C22⋊#64408—22no—
10#14556654—24no—
11#14556651—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
21C22×#64408—24no—
22#11924038—22no—
23#11924037—22no—
24#11924036—22no—
25C4⋊#64408D414yes—
26C22⋊#64408—24no—
27C22⋊#64408—22no—
28C4×#64408—22no—
29C23×D73D412yes—
30C2×Dic146—21no—
31C2×Dic146C2×C411yescharacteristic, complemented
32Q8×D73—22no—
33Q8×D73—22no—
34C2×D292C2×C411yescharacteristic
35C2×C22⋊D73D412yes—
36D4×D73—22no—
37D4×D73—22no—
38C2×C4×D73—21no—
39C2×C4×D73—21no—
40C2×C4×D73C2311yescharacteristic
41C22⋊Dic73—22no—
42#11924005—22no—
43#11924005—22no—
44C4×Dic73—21no—
45C4×Dic73C2×C411yescharacteristic, complemented
46C2×Q8×C73C2×C411yescharacteristic, complemented
47C2×D4×C73C2×C411yescharacteristic
48C22⋊C4×C73—22no—
49C42×C73C2×C411yescharacteristic, complemented
50C23×C73C22⋊C412yes—
51C22×D73—22no—
52C22×D73—22no—
53C22×D73—44no—
54C22×D73C22⋊C412yes—
55C22×D73C2×D411yescharacteristic
56C2×#64408—24no—
57C2×#64408—84no—
58Q8×C73—22no—
59D4×C73—22no—
60C2×C4×C73—21no—
61C2×C4×C73—21no—
62C2×C4×C73C22×C411yescharacteristic
63C22⋊D73—24no—
64C2×Dic73—21no—
65C2×Dic73—21no—
66C2×Dic73C2×D411yescharacteristic
67D292—22no—
68C4×D73—42no—
69C4×D73—41no—
70C4×D73—41no—
71C4×D73C2×D412yes—
72C4×D73#4112yes—
73Dic146—22no—
74Dic146—42no—
75#10596833—42no—
76C22×C73—22no—
77C22×C73—42no—
78C22×C73C2×C22⋊C411yescharacteristic
79C2×D73—22no—
80C2×D73—22no—
81C2×D73—44no—
82C2×D73—42no—
83C2×D73—82no—
84C2×D73#12011yescharacteristic
85C2×D73#12311yescharacteristic
86#64408—44no—
87C4×C73—41no—
88C4×C73—41no—
89C4×C73C4×D412yes—
90Dic73—41no—
91Dic73—41no—
92Dic73#12112yes—
93C2×C73—21no—
94C2×C73—42no—
95C2×C73#38611yescharacteristic
96D73—21no—
97D73—42no—
98D73#45512yes—
99#1885—731nomaximal, Sylow
100C73#188511yescharacteristic, complemented, Sylow
101C2×#124—731no—
102#518—731no—
103#419—732no—
104C2×#100—731no—
105#339—732no—
106C22×Q8—731no—
107C22×D4—731no—
108C2×M16—732no—
109#124—731no—
110#124—731no—
111#124—731no—
112#124—1462no—
113#124#6440811yescharacteristic, complemented
114C4×D4—1464no—
115#117—732no—
116C2×C22⋊C4—1462no—
117C2×C22⋊C4—1462no—
118C2×C42—731no—
119#103—1464no—
120#100—1462no—
121C24—732no—
122C2×Q8—731no—
123C2×Q8—1461no—
124C2×Q8—1462no—
125C2×Q8—1462no—
126C2×Q8C2×#6440811yescharacteristic, complemented
127C2×D4—732no—
128C2×D4—731no—
129C2×D4—1462no—
130C2×D4—1462no—
131C2×D4C2×#6440811yescharacteristic
132C22×C4—731no—
133C22×C4—1461no—
134C22×C4—1461no—
135C22×C4—1464no—
136M16—1462no—
137M16—1462no—
138C2×C8—1462no—
139C4⋊C4—734no—
140C22⋊C4—22no—
141C22⋊C4—1462no—
142C22⋊C4—1462no—
143C22⋊C4—1462no—
144C22⋊C4—1464no—
145C22⋊C4—1462no—
146C42—731no—
147C42—1461no—
148C42—1462no—
149C42C2×#6440811yescharacteristic, complemented
150C23—2924no—
151C23—732no—
152C23—731no—
153C23—1462no—
154C23—1462no—
155C23C22⋊#6440812yes—
156Q8—22no—
157Q8—2922no—
158Q8—1462no—
159D4—22no—
160D4—1464no—
161D4—1462no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—2921no—
165C2×C4—2921no—
166C2×C4—2922no—
167C2×C4—5844no—
168C2×C4—731no—
169C2×C4—732no—
170C2×C4—732no—
171C2×C4—1464no—
172C2×C4—1461no—
173C2×C4—1461no—
174C2×C4C22×#6440811yescharacteristic
175C8—2922no—
176C22—22no—
177C22—42no—
178C22—2922no—
179C22—2924no—
180C22—5842no—
181C22—731no—
182C22—731no—
183C22—1462no—
184C22—1462no—
185C22C2×C22⋊#6440811yescharacteristic
186C4—41no—
187C4—41no—
188C4—2921no—
189C4—2924no—
190C4—2921no—
191C4—732no—
192C4D4×#6440812yes—
193C2—21no—
194C2—42no—
195C2—2922no—
196C2—732no—
197C2—1461no—
198C2#1798953511yescharacteristic
subgroupG/H
centerC2#17989535
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#124×C73C4
socleC2×C73#386
hypercenter#124#64408
hypocenterC73#1885
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
2. #17989580C2semidirect
4. #17989458C2semidirect
14. #14556580C4semidirect
15. #14556579C4semidirect
16. #14556578C4semidirect
20. #124×C73C4semidirect
31. C2×Dic146C2×C4semidirect
45. C4×Dic73C2×C4semidirect
46. C2×Q8×C73C2×C4semidirect
49. C42×C73C2×C4semidirect
100. C73#1885semidirect
113. #124#64408semidirect
126. C2×Q8C2×#64408semidirect
149. C42C2×#64408semidirect