Finite Group Databasebeta

← #22614928

Subgroups — #22614928

Order 9344.

604 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14556589C211yesmaximal, characteristic, complemented
2C2×#14556580C211yesmaximal, characteristic
3C2×#14556579C211yesmaximal, characteristic
4C2×#14556553C211yesmaximal, characteristic
5#17988516C214yesmaximal, complemented
6#17988492C211yesmaximal, characteristic, complemented
7#17988446C214yesmaximal, complemented
8C4×#11924007C211yesmaximal, characteristic, complemented
9#391×C73C211yesmaximal, characteristic, complemented
10C22×Dic146C2211yescharacteristic
11C22×D292C2211yescharacteristic
12C22×C4×D73C2212yes—
13#14556589—24no—
14#14556580—24no—
15#14556579—24no—
16#14556553—24no—
17C2×#11924007C2212yes—
18C2×#11924007C2212yes—
19C2×#11924007C2212yes—
20C2×#11924005C2214yes—
21C2×#11924005C2214yes—
22C2×#11924005C2212yes—
23C2×C4×Dic73C2211yescharacteristic
24C2×C4×Dic73C2211yescharacteristic
25#14556498C2212yes—
26#14556498C2214yes—
27C22×Q8×C73C2211yescharacteristic
28C2×C4⋊C4×C73C2211yescharacteristic
29C2×C42×C73C2211yescharacteristic
30#95×C73C2214yes—
31C23×D73C2312yes—
32C2×Dic146—22no—
33C2×Dic146—22no—
34C2×Dic146—22no—
35C2×D292—22no—
36C2×D292—22no—
37C2×D292D414yes—
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C22×Dic73C2311yescharacteristic
41C22×Dic73C2311yescharacteristic
42C2×C4×D73—24no—
43C2×C4×D73—28no—
44#11924007—24no—
45#11924007—24no—
46#11924007—24no—
47#11924005—28no—
48#11924005—28no—
49#11924005—24no—
50C4×Dic73—22no—
51C4×Dic73D414yes—
52C2×Q8×C73—22no—
53C2×Q8×C73—22no—
54C2×Q8×C73—22no—
55C22×C4×C73C2312yes—
56C22×C4×C73C2312yes—
57C22×C4×C73C2312yes—
58C22×C4×C73C2311yescharacteristic
59C4⋊C4×C73—22no—
60C42×C73—22no—
61C23×C73C2411yescharacteristic
62C22×D73—22no—
63C22×D73—24no—
64C22×D73—22no—
65C22×D73—24no—
66C22×D73C2×D414yes—
67Q8×C73—44no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—24no—
75C2×C4×C73—22no—
76C2×C4×C73C2×D412yes—
77C2×C4×C73C2×D412yes—
78C2×C4×C73#4112yes—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73C2×D412yes—
87C2×Dic73C2×D412yes—
88C2×Dic73#4114yes—
89D292—28no—
90C4×D73—48no—
91Dic146—44no—
92C22×C73C22×D411yescharacteristic
93C22×C73C22×D411yescharacteristic
94C22×C73C2×#4112yes—
95C22×C73C2×#4111yescharacteristic
96C22×C732−1+412yes—
97C2×D73—24no—
98C2×D73—28no—
99C2×D73—42no—
100C2×D73—42no—
101C2×D73—44no—
102C4×C73—42no—
103C4×C73—42no—
104C4×C73—42no—
105C4×C73#12114yes—
106Dic73—22no—
107Dic73—42no—
108Dic73—42no—
109Dic73#12414yescomplemented
110C2×C73C2×#12111yescharacteristic
111C2×C73C2×#12411yescharacteristic
112C2×C73#53611yescharacteristic
113C2×C73#54712yes—
114C2×C73#55612yes—
115D73—44no—
116#2547—731nomaximal, Sylow
117C73#254711yescharacteristic, complemented, Sylow
118C2×C4⋊Q8—731no—
119C2×#124—731no—
120C2×#124—731no—
121C2×C4×D4—731no—
122#397—734no—
123#391—731no—
124#391D7311yescharacteristic, complemented
125#380—734no—
126C4×C4⋊C4—731no—
127C22×Q8—731no—
128C22×Q8C2×D7311yescharacteristic
129C22×D4—731no—
130C23×C4—732no—
131C4⋊Q8—1464no—
132#124—1464no—
133#124—1464no—
134C4×D4—1464no—
135C2×C4⋊C4—732no—
136C2×C4⋊C4—732no—
137C2×C4⋊C4—732no—
138C2×C4⋊C4C2×D7311yescharacteristic
139C2×C22⋊C4—732no—
140C2×C22⋊C4—734no—
141C2×C22⋊C4—734no—
142C2×C42—731no—
143C2×C42—731no—
144C2×C42C2×D7311yescharacteristic
145#95—732no—
146#95—734no—
147#95C2×D7314yes—
148C24—732no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—22no—
152C2×Q8—1462no—
153C2×Q8—1462no—
154C2×Q8—1462no—
155C2×D4—734no—
156C2×D4—1462no—
157C2×D4—1462no—
158C22×C4—731no—
159C22×C4—731no—
160C22×C4—732no—
161C22×C4—732no—
162C22×C4—1464no—
163C22×C4—1468no—
164C22×C4C22×D7312yes—
165C22×C4C22×D7312yes—
166C22×C4C22×D7312yes—
167C22×C4C22×D7311yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—1464no—
170C4⋊C4—1464no—
171C4⋊C4—1464no—
172C22⋊C4—1464no—
173C22⋊C4—1468no—
174C22⋊C4—1468no—
175C42—22no—
176C42—734no—
177C42—1462no—
178C23—734no—
179C23—1462no—
180C23—1464no—
181C23—1462no—
182C23—1464no—
183C23C23×D7311yescharacteristic
184Q8—44no—
185Q8—2924no—
186D4—1468no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—2928no—
196C2×C4—732no—
197C2×C4—734no—
198C2×C4—732no—
199C2×C4—1462no—
200C2×C4—1462no—
201C2×C4—1462no—
202C2×C4—1462no—
203C2×C4—1462no—
204C2×C4—1462no—
205C2×C4—1462no—
206C2×C4D4×D7312yes—
207C2×C4D4×D7312yes—
208C2×C4#1192402812yes—
209C22—2922no—
210C22—2924no—
211C22—2922no—
212C22—1468no—
213C22—1464no—
214C22C2×D4×D7311yescharacteristic
215C22C2×D4×D7311yescharacteristic
216C22#41×D7312yes—
217C22C2×#1192402811yescharacteristic
218C22#1455663912yes—
219C4—42no—
220C4—42no—
221C4—42no—
222C4—2922no—
223C4—2922no—
224C4—734no—
225C4—1462no—
226C4#1455656414yes—
227C2—2924no—
228C2C2×#1455656411yescharacteristic
229C2#124×D7311yescharacteristic
230C2#1798916211yescharacteristic
231C2#1798923912yes—
232C2#1798930912yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#391×C73C2
hypercenter#391D73
hypocenterC73#2547
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#14556589C2semidirect
5. #17988516C2semidirect
6. #17988492C2semidirect
7. #17988446C2semidirect
8. C4×#11924007C2semidirect
9. #391×C73C2semidirect
109. Dic73#124semidirect
117. C73#2547semidirect
124. #391D73semidirect