Finite Group Databasebeta

← #22616049

Subgroups — #22616049

Order 9344.

448 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 153 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
2C2×#14556581C211yesmaximal, characteristic
3#17988521C212yesmaximal
4#17988520C212yesmaximal
5#17988508C211yesmaximal, characteristic
6#17988507C211yesmaximal, characteristic
7#17988506C211yesmaximal, characteristic
8#17988456C212yesmaximal
9#17988451C212yesmaximal
10#17988432C211yesmaximal, characteristic
11#395×C73C211yesmaximal, characteristic
12C22×Dic146C2211yescharacteristic
13#14556589—24no—
14#14556581—24no—
15C2×C4⋊Dic73C2211yescharacteristic
16C2×C4⋊Dic73C2212yes—
17C2×#11924007C2212yes—
18C2×#11924007C2212yes—
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2212yes—
24C2×#11924007C2212yes—
25C2×C4×Dic73C2211yescharacteristic
26C2×C4×Dic73C2212yes—
27#14556498C2211yescharacteristic
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C22×Q8×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C4⋊C4×C73C2212yes—
35#95×C73C2211yescharacteristic
36#95×C73C2212yes—
37C2×Dic146—22no—
38C2×Dic146—42no—
39C22×Dic73C2311yescharacteristic
40C22×Dic73C2312yes—
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2311yescharacteristic
43C22×Dic73C2312yes—
44C22×Dic73C2311yescharacteristic
45C4⋊Dic73—22no—
46C4⋊Dic73—42no—
47#11924007—22no—
48#11924007—22no—
49#11924007—22no—
50#11924007—22no—
51#11924007—24no—
52#11924007—24no—
53#11924007—42no—
54#11924007—42no—
55C4×Dic73D414yes—
56C4×Dic73Q818yescomplemented
57C2×Q8×C73—22no—
58C2×Q8×C73—42no—
59C22×C4×C73C2311yescharacteristic
60C22×C4×C73C2312yes—
61C22×C4×C73C2311yescharacteristic
62C22×C4×C73C2311yescharacteristic
63C22×C4×C73C2312yes—
64C4⋊C4×C73—22no—
65C4⋊C4×C73—42no—
66C23×C73C2411yescharacteristic
67Q8×C73—44no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73C2×D412yes—
80C2×C4×C73C2×Q814yes—
81C2×Dic73—22no—
82C2×Dic73—21no—
83C2×Dic73—21no—
84C2×Dic73—22no—
85C2×Dic73—21no—
86C2×Dic73—21no—
87C2×Dic73—22no—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—21no—
92C2×Dic73—21no—
93C2×Dic73C2×D412yes—
94C2×Dic73C2×D412yes—
95C2×Dic73C2×Q814yes—
96C2×Dic73C2×Q814yes—
97Dic146—44no—
98C22×C73C22×D411yescharacteristic
99C22×C73C22×Q812yes—
100C22×C73H(5,𝔽2)12yes—
101C22×C732−1+411yescharacteristic
102C22×C732−1+411yescharacteristic
103C4×C73—22no—
104C4×C73—24no—
105C4×C73—41no—
106C4×C73—42no—
107C4×C73—41no—
108Dic73—22no—
109Dic73—24no—
110Dic73—42no—
111Dic73—41no—
112Dic73—41no—
113Dic73C4⋊Q814yes—
114C2×C73C2×C4⋊Q811yescharacteristic
115C2×C73#53511yescharacteristic
116C2×C73#53611yescharacteristic
117C2×C73#54412yes—
118C2×C73#54412yes—
119#2660—731nomaximal, Sylow
120C73#266011yescharacteristic, complemented, Sylow
121C2×C4⋊Q8—731no—
122C2×#125—731no—
123#398—732no—
124#398—732no—
125#395—731no—
126#395—731no—
127#395—731no—
128#395D7311yescharacteristic
129#384—732no—
130#382—732no—
131#376—731no—
132C22×Q8—731no—
133C22×Q8C2×D7311yescharacteristic
134C4⋊Q8—1464no—
135#125—1464no—
136C2×C4⋊C4—732no—
137C2×C4⋊C4—732no—
138C2×C4⋊C4—732no—
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⋊C4—732no—
146C2×C4⋊C4C2×D7311yescharacteristic
147C2×C4⋊C4C2×D7312yes—
148C2×C42—731no—
149C2×C42—732no—
150#95—731no—
151#95—732no—
152#95—732no—
153#95—732no—
154#95—732no—
155#95C2×D7311yescharacteristic
156#95C2×D7312yes—
157C2×Q8—22no—
158C2×Q8—42no—
159C2×Q8—2922no—
160C2×Q8—1462no—
161C22×C4—731no—
162C22×C4—732no—
163C22×C4—731no—
164C22×C4—731no—
165C22×C4—732no—
166C22×C4—731no—
167C22×C4C22×D7311yescharacteristic
168C22×C4C22×D7312yes—
169C22×C4C22×D7311yescharacteristic
170C22×C4C22×D7311yescharacteristic
171C22×C4C22×D7312yes—
172C4⋊C4—22no—
173C4⋊C4—42no—
174C4⋊C4—2922no—
175C4⋊C4—2922no—
176C4⋊C4—2922no—
177C4⋊C4—1462no—
178C4⋊C4—1462no—
179C4⋊C4—1462no—
180C4⋊C4—1464no—
181C4⋊C4—1464no—
182C4⋊C4—1462no—
183C4⋊C4—1462no—
184C42—734no—
185C42—738no—
186C23C23×D7311yescharacteristic
187Q8—44no—
188Q8—2924no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—732no—
201C2×C4—734no—
202C2×C4—732no—
203C2×C4—734no—
204C2×C4—1461no—
205C2×C4—1461no—
206C2×C4—1462no—
207C2×C4—1462no—
208C2×C4—1462no—
209C2×C4—1462no—
210C2×C4—1461no—
211C2×C4—1461no—
212C2×C4—1462no—
213C2×C4—1461no—
214C2×C4—1461no—
215C2×C4—1462no—
216C2×C4D4×D7312yes—
217C2×C4Q8×D7314yes—
218C22C2×D4×D7311yescharacteristic
219C22C2×Q8×D7312yes—
220C22#1455663612yes—
221C22#1455663811yescharacteristic
222C22#1455663911yescharacteristic
223C4—22no—
224C4—24no—
225C4—42no—
226C4—41no—
227C4—41no—
228C4—2922no—
229C4—2921no—
230C4—2921no—
231C4—734no—
232C4—1462no—
233C4—1464no—
234C2C4⋊Q8×D7311yescharacteristic
235C2#1798915211yescharacteristic
236C2#1798916011yescharacteristic
237C2#1798921412yes—
238C2#1798921612yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#395×C73C2
hypercenter#395D73
hypocenterC73#2660
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
56. C4×Dic73Q8semidirect
120. C73#2660semidirect