Finite Group Databasebeta

← #22615313

Subgroups — #22615313

Order 9344.

468 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 161 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×#14556581C211yesmaximal, characteristic
2C2×Q8×Dic73C211yesmaximal, characteristic
3#17988519C211yesmaximal, characteristic
4#17988517C211yesmaximal, characteristic
5#17988506C211yesmaximal, characteristic
6#17988486C212yesmaximal
7#17988484C212yesmaximal
8#17988484C212yesmaximal
9#17988482C212yesmaximal
10#17988438C211yesmaximal, characteristic
11#395×C73C211yesmaximal, characteristic
12#14556581—24no—
13Q8×Dic73—24no—
14C2×C4⋊Dic73C2212yes—
15C2×C4⋊Dic73C2211yescharacteristic
16C2×C4⋊Dic73C2211yescharacteristic
17C2×C4⋊Dic73C2212yes—
18C2×#11924007C2211yescharacteristic
19C2×#11924007C2212yes—
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2212yes—
24C2×#11924007C2212yes—
25C2×C4×Dic73C2212yes—
26C2×C4×Dic73C2212yes—
27C2×C4×Dic73C2211yescharacteristic
28#14556498C2211yescharacteristic
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C22×Q8×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2212yes—
34C2×C4⋊C4×C73C2211yescharacteristic
35#95×C73C2211yescharacteristic
36#95×C73C2212yes—
37C22×Dic73C2312yes—
38C22×Dic73C2311yescharacteristic
39C22×Dic73C2311yescharacteristic
40C22×Dic73C2311yescharacteristic
41C22×Dic73C2312yes—
42C22×Dic73C2311yescharacteristic
43C4⋊Dic73—22no—
44C4⋊Dic73—24no—
45C4⋊Dic73—22no—
46C4⋊Dic73—42no—
47#11924007—22no—
48#11924007—24no—
49#11924007—22no—
50#11924007—22no—
51#11924007—22no—
52#11924007—42no—
53#11924007Q818yescomplemented
54C4×Dic73—24no—
55C4×Dic73—42no—
56C4×Dic73D414yes—
57C2×Q8×C73—22no—
58C2×Q8×C73—24no—
59C22×C4×C73C2311yescharacteristic
60C22×C4×C73C2311yescharacteristic
61C22×C4×C73C2311yescharacteristic
62C22×C4×C73C2312yes—
63C22×C4×C73C2312yes—
64C4⋊C4×C73—22no—
65C4⋊C4×C73—24no—
66C23×C73C2411yescharacteristic
67Q8×C73—28no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—21no—
74C2×C4×C73—21no—
75C2×C4×C73—22no—
76C2×C4×C73—21no—
77C2×C4×C73—21no—
78C2×C4×C73C2×D412yes—
79C2×C4×C73C2×Q814yes—
80C2×C4×C73#4114yes—
81C2×Dic73—22no—
82C2×Dic73—21no—
83C2×Dic73—22no—
84C2×Dic73—21no—
85C2×Dic73—22no—
86C2×Dic73—21no—
87C2×Dic73—21no—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—21no—
91C2×Dic73—22no—
92C2×Dic73—21no—
93C2×Dic73C2×D412yes—
94C2×Dic73C2×D412yes—
95C2×Dic73C2×Q814yes—
96C2×Dic73C2×Q814yes—
97C22×C73C22×D411yescharacteristic
98C22×C73C22×Q812yes—
99C22×C73C2×#4112yes—
100C22×C73H(5,𝔽2)11yescharacteristic
101C22×C732−1+411yescharacteristic
102C4×C73—22no—
103C4×C73—24no—
104C4×C73—24no—
105C4×C73—41no—
106C4×C73—41no—
107Dic73—22no—
108Dic73—24no—
109Dic73—41no—
110Dic73—42no—
111Dic73—41no—
112Dic73C4⋊Q814yes—
113C2×C73#52511yescharacteristic
114C2×C73C2×C4⋊Q811yescharacteristic
115C2×C73#53711yescharacteristic
116C2×C73#55412yes—
117C2×C73#55712yes—
118#2584—731nomaximal, Sylow
119C73#258411yescharacteristic, complemented, Sylow
120C2×#125—731no—
121C2×C4×Q8—731no—
122#398—731no—
123#398—731no—
124#395—731no—
125#395D7311yescharacteristic
126#389—732no—
127#389—732no—
128#389—732no—
129#389—732no—
130C4×C4⋊C4—731no—
131C22×Q8C2×D7311yescharacteristic
132#125—1464no—
133C4×Q8—1464no—
134C2×C4⋊C4—732no—
135C2×C4⋊C4—732no—
136C2×C4⋊C4—732no—
137C2×C4⋊C4—732no—
138C2×C4⋊C4—731no—
139C2×C4⋊C4—731no—
140C2×C4⋊C4—731no—
141C2×C4⋊C4—731no—
142C2×C4⋊C4—731no—
143C2×C4⋊C4—731no—
144C2×C4⋊C4—732no—
145C2×C4⋊C4C2×D7311yescharacteristic
146C2×C4⋊C4C2×D7312yes—
147C2×C42—732no—
148C2×C42—731no—
149C2×C42—732no—
150#95—731no—
151#95—732no—
152#95—732no—
153#95—732no—
154#95C2×D7311yescharacteristic
155#95C2×D7312yes—
156C2×Q8—22no—
157C2×Q8—24no—
158C22×C4—731no—
159C22×C4—732no—
160C22×C4—731no—
161C22×C4—732no—
162C22×C4—731no—
163C22×C4—731no—
164C22×C4C22×D7311yescharacteristic
165C22×C4C22×D7311yescharacteristic
166C22×C4C22×D7311yescharacteristic
167C22×C4C22×D7312yes—
168C22×C4C22×D7312yes—
169C4⋊C4—22no—
170C4⋊C4—24no—
171C4⋊C4—2922no—
172C4⋊C4—2922no—
173C4⋊C4—738no—
174C4⋊C4—1462no—
175C4⋊C4—1462no—
176C4⋊C4—1462no—
177C4⋊C4—1464no—
178C4⋊C4—1462no—
179C4⋊C4—1462no—
180C4⋊C4—1462no—
181C4⋊C4—1464no—
182C42—2922no—
183C42—734no—
184C42—1464no—
185C23C23×D7311yescharacteristic
186Q8—28no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—732no—
198C2×C4—734no—
199C2×C4—732no—
200C2×C4—734no—
201C2×C4—1462no—
202C2×C4—1461no—
203C2×C4—1461no—
204C2×C4—1462no—
205C2×C4—1462no—
206C2×C4—1461no—
207C2×C4—1462no—
208C2×C4—1461no—
209C2×C4—1462no—
210C2×C4—1461no—
211C2×C4—1462no—
212C2×C4—1461no—
213C2×C4D4×D7312yes—
214C2×C4Q8×D7314yes—
215C2×C4#1192402714yes—
216C22C2×D4×D7311yescharacteristic
217C22C2×Q8×D7312yes—
218C22C2×#1192402712yes—
219C22#1455663711yescharacteristic
220C22#1455663911yescharacteristic
221C4—24no—
222C4—22no—
223C4—24no—
224C4—41no—
225C4—41no—
226C4—2922no—
227C4—2921no—
228C4—2921no—
229C4—734no—
230C4—1462no—
231C4—1464no—
232C2#1798909311yescharacteristic
233C2C4⋊Q8×D7311yescharacteristic
234C2#1798916711yescharacteristic
235C2#1798929512yes—
236C2#1798931212yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#395×C73C2
hypercenter#395D73
hypocenterC73#2584
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
53. #11924007Q8semidirect
119. C73#2584semidirect