Finite Group Databasebeta

← #353×D73 #22611587

Subgroups — #353×D73 #22611587

Order 9344.

368 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 57 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#127×D73C211yesmaximal, characteristic
2#99×D73C212yesmaximal, complemented
3#17988380C211yesmaximal, characteristic, complemented
4#17988379C212yesmaximal, complemented
5#353×C73C211yesmaximal, characteristic, complemented
6C2×D4×D73—22no—
7C2×D4×D73C411yescharacteristic, complemented
8C2×D4×D73C2211yescharacteristic
9#14556588C411yescharacteristic, complemented
10#14556587—22no—
11#14556587C411yescharacteristic, complemented
12#14556587C2211yescharacteristic
13C22⋊C4×D73—22no—
14C42×D73C411yescharacteristic, complemented
15#14556506C2212yescomplemented
16#14556505—22no—
17#127×C73C2211yescharacteristic
18#99×C73C2212yescomplemented
19C23×D73—21no—
20C23×D73D412yes—
21C2×D292—22no—
22C2×D292C2×C411yescharacteristic
23C2×D292C2×C411yescharacteristic, complemented
24C2×C22⋊D73—22no—
25C2×C22⋊D73—22no—
26C2×C22⋊D73—21no—
27C2×C22⋊D73D412yes—
28D4×D73—41no—
29D4×D73—41no—
30D4×D73—41no—
31D4×D73—41no—
32D4×D73—48no—
33C2×C4×D73—21no—
34C2×C4×D73—42no—
35C2×C4×D73C2×C411yescharacteristic
36C22⋊Dic73—22no—
37#11924005—42no—
38C4×Dic73—21no—
39C4×Dic73C2×C411yescharacteristic, complemented
40C2×D4×C73—22no—
41C2×D4×C73C2×C411yescharacteristic, complemented
42C2×D4×C73C2311yescharacteristic
43C22⋊C4×C73—22no—
44C42×C73C2×C411yescharacteristic, complemented
45C23×C73—21no—
46C23×C73C2×D412yes—
47C22×D73—22no—
48C22×D73—22no—
49C22×D73—21no—
50C22×D73—44no—
51C22×D73—44no—
52C22×D73—41no—
53C22×D73—41no—
54C22×D73C22⋊C411yescharacteristic
55C22×D73C22⋊C412yes—
56D4×C73—41no—
57D4×C73—41no—
58D4×C73—44no—
59C2×C4×C73—21no—
60C2×C4×C73—42no—
61C2×C4×C73C22×C411yescharacteristic
62C22⋊D73—42no—
63C22⋊D73—44no—
64C22⋊D73—44no—
65C22⋊D73—42no—
66C2×Dic73—21no—
67C2×Dic73—42no—
68C2×Dic73C22⋊C411yescharacteristic
69D292—41no—
70D292—41no—
71D292—44no—
72C4×D73—24no—
73C4×D73—21no—
74C4×D73—21no—
75C4×D73—84no—
76C22×C73—22no—
77C22×C73—42no—
78C22×C73—42no—
79C22×C73—41no—
80C22×C73C2×C22⋊C411yescharacteristic
81C2×D73—22no—
82C2×D73—22no—
83C2×D73—44no—
84C2×D73—42no—
85C2×D73—42no—
86C2×D73—41no—
87C2×D73—82no—
88C2×D73—82no—
89C2×D73—82no—
90C2×D73#9911yescharacteristic
91C2×D73#9911yescharacteristic
92C4×C73—22no—
93C4×C73—21no—
94C4×C73—82no—
95Dic73—22no—
96Dic73—21no—
97Dic73—82no—
98C2×C73—21no—
99C2×C73—42no—
100C2×C73—81no—
101C2×C73C2×#9911yescharacteristic
102D73—21no—
103D73—42no—
104D73—81no—
105D73#35312yesdirect product factor
106C2×#353—731nomaximal, Sylow
107C73C2×#35311yescharacteristic, complemented, Sylow
108C2×#127—731no—
109C2×#99—732no—
110#353—731no—
111#353—732no—
112#353D7311yescharacteristic, direct product factor
113C22×D4—731no—
114C22×D4—731no—
115C22×D4—1462no—
116#127—731no—
117#127—731no—
118#127—731no—
119#127—1462no—
120#127C2×D7311yescharacteristic
121C2×C22⋊C4—1462no—
122C2×C42—731no—
123#99—732no—
124#99—1462no—
125#99C2×D7312yescomplemented
126C24—732no—
127C24—1461no—
128C2×D4—22no—
129C2×D4—2921no—
130C2×D4—2921no—
131C2×D4—2928no—
132C2×D4—2921no—
133C2×D4—2921no—
134C2×D4—732no—
135C2×D4—731no—
136C2×D4—731no—
137C2×D4—1462no—
138C2×D4—1461no—
139C2×D4—1462no—
140C2×D4—1462no—
141C2×D4C4×D7311yescharacteristic, complemented
142C2×D4C22×D7311yescharacteristic
143C22×C4—2922no—
144C22×C4—731no—
145C22×C4—1461no—
146C22⋊C4—22no—
147C22⋊C4—2922no—
148C22⋊C4—1462no—
149C42—731no—
150C42—1461no—
151C42C4×D7311yescharacteristic, complemented
152C23—21no—
153C23—2924no—
154C23—2921no—
155C23—2921no—
156C23—2924no—
157C23—732no—
158C23—731no—
159C23—1462no—
160C23—1462no—
161C23—1461no—
162C23D4×D7312yes—
163D4—41no—
164D4—41no—
165D4—44no—
166D4—2921no—
167D4—2924no—
168D4—2921no—
169D4—2922no—
170D4—2924no—
171D4—2924no—
172D4—2922no—
173C2×C4—21no—
174C2×C4—42no—
175C2×C4—2922no—
176C2×C4—5844no—
177C2×C4—731no—
178C2×C4—1461no—
179C2×C4—1461no—
180C2×C4—1464no—
181C2×C4—1461no—
182C2×C4C2×C4×D7311yescharacteristic
183C22—22no—
184C22—42no—
185C22—42no—
186C22—41no—
187C22—2922no—
188C22—2922no—
189C22—2924no—
190C22—2921no—
191C22—5842no—
192C22—5842no—
193C22—5842no—
194C22—731no—
195C22—731no—
196C22—1462no—
197C22—1462no—
198C22C22⋊C4×D7311yescharacteristic
199C4—22no—
200C4—21no—
201C4—82no—
202C4—5842no—
203C4—1462no—
204C4—1461no—
205C2—21no—
206C2—42no—
207C2—81no—
208C2—2922no—
209C2—5841no—
210C2—732no—
211C2—1461no—
212C2#99×D7311yescharacteristic
subgroupG/H
centerC2#99×D73
commutatorC2×C4×C73C22×C4
FrattiniC2×D4C22×D73
Fitting#353×C73C2
socleC2×C73C2×#99
hypercenter#353D73
hypocenterC73C2×#353
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #99×D73C2semidirect
3. #17988380C2semidirect
4. #17988379C2semidirect
5. #353×C73C2semidirect
7. C2×D4×D73C4semidirect
9. #14556588C4semidirect
11. #14556587C4semidirect
14. C42×D73C4semidirect
15. #14556506C22semidirect
18. #99×C73C22semidirect
23. C2×D292C2×C4semidirect
39. C4×Dic73C2×C4semidirect
41. C2×D4×C73C2×C4semidirect
44. C42×C73C2×C4semidirect
105. D73#353direct (N × H)
107. C73C2×#353semidirect
112. #353D73direct (N × H)
125. #99C2×D73semidirect
141. C2×D4C4×D73semidirect
151. C42C4×D73semidirect