Finite Group Databasebeta

← #22614882

Subgroups — #22614882

Order 9344.

676 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 185 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×#14556590C211yesmaximal, characteristic, complemented
2C2×#14556568C214yesmaximal, complemented
3C2×D4×Dic73C211yesmaximal, characteristic
4#17988523C214yesmaximal, complemented
5#17988490C211yesmaximal, characteristic
6#17988457C211yesmaximal, characteristic, complemented
7#17988456C211yesmaximal, characteristic, complemented
8C4×#11924007C211yesmaximal, characteristic, complemented
9#390×C73C211yesmaximal, characteristic
10C22×Dic146C2212yes—
11C23×Dic73C2212yes—
12#14556590—24no—
13#14556568—216no—
14D4×Dic73—24no—
15C2×C4⋊Dic73C2211yescharacteristic
16C2×C4⋊Dic73C2211yescharacteristic
17C2×C4⋊Dic73C2214yes—
18C2×#11924007C2212yes—
19C2×#11924007C2214yes—
20C2×#11924007C2212yes—
21C2×C22⋊Dic73C2214yes—
22C2×C22⋊Dic73C2212yes—
23C2×C4×Dic73C2211yescharacteristic
24C2×C4×Dic73C2211yescharacteristic
25#14556498C2212yes—
26C22×D4×C73C2211yescharacteristic
27C2×C4⋊C4×C73C2211yescharacteristic
28C2×C22⋊C4×C73C2214yes—
29C2×C42×C73C2211yescharacteristic
30C2×Dic146—28no—
31C2×Dic146—24no—
32C22×Dic73—24no—
33C22×Dic73—28no—
34C22×Dic73C2312yes—
35C22×Dic73C2312yes—
36C22×Dic73C2311yescharacteristic
37C22×Dic73C2312yes—
38C22×Dic73C2311yescharacteristic
39C4⋊Dic73—22no—
40C4⋊Dic73—28no—
41C4⋊Dic73—22no—
42#11924007—28no—
43#11924007—24no—
44#11924007D418yescomplemented
45C22⋊Dic73—24no—
46C22⋊Dic73—28no—
47C4×Dic73—22no—
48C4×Dic73D414yes—
49C24×C73C2312yes—
50C2×D4×C73—22no—
51C2×D4×C73—22no—
52C2×D4×C73Q814yescomplemented
53C22×C4×C73C2312yes—
54C22×C4×C73C2312yes—
55C22×C4×C73C2311yescharacteristic
56C4⋊C4×C73—22no—
57C22⋊C4×C73—28no—
58C42×C73—22no—
59C23×C73—24no—
60C23×C73—22no—
61C23×C73—22no—
62C23×C73—24no—
63C23×C73C2×Q814yes—
64C23×C73C2411yescharacteristic
65D4×C73—28no—
66C2×C4×C73—22no—
67C2×C4×C73—22no—
68C2×C4×C73—24no—
69C2×C4×C73—22no—
70C2×C4×C73C2×D414yes—
71C2×C4×C73C2×D412yes—
72C2×C4×C73C2×Q812yes—
73C2×C4×C73#4112yes—
74C2×Dic73—22no—
75C2×Dic73—22no—
76C2×Dic73—22no—
77C2×Dic73—22no—
78C2×Dic73—24no—
79C2×Dic73—24no—
80C2×Dic73—22no—
81C2×Dic73—48no—
82C2×Dic73C2×D412yes—
83C2×Dic73C2×D414yes—
84C2×Dic73C2×D412yes—
85C2×Dic73C2×D414yes—
86Dic146—48no—
87C22×C73—24no—
88C22×C73—28no—
89C22×C73—42no—
90C22×C73—42no—
91C22×C73—44no—
92C22×C73C22×D411yescharacteristic
93C22×C73C22×D412yes—
94C22×C73C22×Q811yescharacteristic
95C22×C73C2×#4111yescharacteristic
96C22×C732−1+412yes—
97C4×C73—24no—
98C4×C73—42no—
99C4×C73C22⋊Q814yescomplemented
100Dic73—22no—
101Dic73—24no—
102Dic73—42no—
103Dic73—42no—
104Dic73#12714yes—
105C2×C73—44no—
106C2×C73C2×C22⋊Q811yescharacteristic
107C2×C73C2×#12711yescharacteristic
108C2×C73#53611yescharacteristic
109C2×C73#54712yes—
110C2×C73D4×Q812yes—
111#2542—731nomaximal, Sylow
112C73#254211yescharacteristic, complemented, Sylow
113C2×C4⋊Q8—731no—
114C2×C22⋊Q8—734no—
115C2×C4×D4—731no—
116#399—734no—
117#390—731no—
118#390D7311yescharacteristic
119#384—731no—
120#384—731no—
121C4×C4⋊C4—731no—
122C22×Q8—732no—
123C22×D4C2×D7311yescharacteristic
124C23×C4—732no—
125C4⋊Q8—1464no—
126C22⋊Q8—14616no—
127C4×D4—1464no—
128C2×C4⋊C4—732no—
129C2×C4⋊C4—731no—
130C2×C4⋊C4—734no—
131C2×C4⋊C4—734no—
132C2×C4⋊C4—731no—
133C2×C4⋊C4—732no—
134C2×C4⋊C4C2×D7311yescharacteristic
135C2×C22⋊C4—732no—
136C2×C22⋊C4—734no—
137C2×C22⋊C4C2×D7314yes—
138C2×C42—731no—
139C2×C42—731no—
140C2×C42C2×D7311yescharacteristic
141#95—732no—
142C24C22×D7312yes—
143C2×Q8—1468no—
144C2×Q8—1464no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4Dic14614yescomplemented
148C22×C4—731no—
149C22×C4—731no—
150C22×C4—732no—
151C22×C4—732no—
152C22×C4—732no—
153C22×C4—1464no—
154C22×C4—1468no—
155C22×C4C22×D7312yes—
156C22×C4C22×D7312yes—
157C22×C4C22×D7311yescharacteristic
158C4⋊C4—22no—
159C4⋊C4—738no—
160C4⋊C4—1468no—
161C4⋊C4—1464no—
162C4⋊C4—1462no—
163C4⋊C4—1468no—
164C4⋊C4—1462no—
165C22⋊C4—28no—
166C22⋊C4—1464no—
167C22⋊C4—1468no—
168C42—22no—
169C42—734no—
170C42—1462no—
171C23—24no—
172C23—22no—
173C23—22no—
174C23—24no—
175C23C2×Dic14614yes—
176C23C23×D7311yescharacteristic
177Q8—2928no—
178D4—28no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—22no—
183C2×C4—2928no—
184C2×C4—732no—
185C2×C4—734no—
186C2×C4—732no—
187C2×C4—734no—
188C2×C4—1462no—
189C2×C4—1464no—
190C2×C4—1464no—
191C2×C4—1462no—
192C2×C4—1462no—
193C2×C4—1462no—
194C2×C4—1462no—
195C2×C4D4×D7314yes—
196C2×C4D4×D7312yes—
197C2×C4C2×Dic14612yes—
198C2×C4#1192402712yes—
199C22—28no—
200C22—24no—
201C22—42no—
202C22—42no—
203C22—44no—
204C22C2×D4×D7311yescharacteristic
205C22C2×D4×D7312yes—
206C22C22×Dic14611yescharacteristic
207C22C2×#1192402711yescharacteristic
208C22#1455663812yes—
209C4—24no—
210C4—42no—
211C4—2922no—
212C4—2922no—
213C4—734no—
214C4—1462no—
215C4—1464no—
216C4#1455656814yescomplemented
217C2—44no—
218C2C2×#1455656811yescharacteristic
219C2#127×D7311yescharacteristic
220C2#1798915711yescharacteristic
221C2#1798923712yes—
222C2D4×Dic14612yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#390×C73C2
hypercenter#390D73
hypocenterC73#2542
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14556590C2semidirect
2. C2×#14556568C2semidirect
4. #17988523C2semidirect
6. #17988457C2semidirect
7. #17988456C2semidirect
8. C4×#11924007C2semidirect
44. #11924007D4semidirect
52. C2×D4×C73Q8semidirect
99. C4×C73C22⋊Q8semidirect
112. C73#2542semidirect
147. C2×D4Dic146semidirect
216. C4#14556568semidirect