Finite Group Databasebeta

← #22614217

Subgroups — #22614217

Order 9344.

512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14556547C211yesmaximal, characteristic
2C22×C4⋊Dic73C211yesmaximal, characteristic
3#17988529C212yesmaximal, complemented
4#17988520C212yesmaximal, complemented
5#17988474C212yesmaximal, complemented
6#17988473C212yesmaximal, complemented
7#17988460C211yesmaximal, characteristic
8#17988448C211yesmaximal, characteristic
9#17988448C211yesmaximal, characteristic
10#17988448C211yesmaximal, characteristic
11#385×C73C211yesmaximal, characteristic
12C23×Dic73C2211yescharacteristic
13C23×Dic73C2211yescharacteristic
14#14556547—24no—
15C2×C4⋊Dic73—24no—
16C2×C4⋊Dic73C2212yes—
17C2×C4⋊Dic73C2212yes—
18C2×#11924007C2212yes—
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×C22⋊Dic73C2211yescharacteristic
22C2×C22⋊Dic73C2211yescharacteristic
23C2×C4×Dic73C2211yescharacteristic
24C2×C4×Dic73C2211yescharacteristic
25#14556498C2212yes—
26#14556498C2212yes—
27#14556498C2212yes—
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C23×C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2212yes—
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2211yescharacteristic
36#95×C73C2212yes—
37C22×Dic73—22no—
38C22×Dic73—22no—
39C22×Dic73—22no—
40C22×Dic73—22no—
41C22×Dic73—22no—
42C22×Dic73D414yes—
43C22×Dic73C2312yes—
44C22×Dic73C2311yescharacteristic
45C22×Dic73C2312yes—
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2311yescharacteristic
48C22×Dic73C2311yescharacteristic
49C4⋊Dic73—24no—
50C4⋊Dic73—24no—
51#11924007—24no—
52#11924007—22no—
53#11924007—22no—
54C22⋊Dic73—22no—
55C22⋊Dic73—22no—
56C4×Dic73—22no—
57C4×Dic73—22no—
58C24×C73C2311yescharacteristic
59C22×C4×C73—22no—
60C22×C4×C73—24no—
61C22×C4×C73C2311yescharacteristic
62C22×C4×C73C2312yes—
63C22×C4×C73C2311yescharacteristic
64C22×C4×C73C2312yes—
65C4⋊C4×C73—24no—
66C22⋊C4×C73—22no—
67C22⋊C4×C73—22no—
68C23×C73—22no—
69C23×C73—22no—
70C23×C73C2×D412yes—
71C23×C73#4112yes—
72C23×C73#4112yes—
73C23×C73C2411yescharacteristic
74C2×C4×C73—28no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—22no—
84C2×C4×C73#4114yes—
85C2×Dic73—28no—
86C2×Dic73—21no—
87C2×Dic73—21no—
88C2×Dic73—21no—
89C2×Dic73—21no—
90C2×Dic73—21no—
91C2×Dic73—21no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—22no—
100C2×Dic73—44no—
101C2×Dic73C2×D412yes—
102C2×Dic73C2×D412yes—
103C22×C73—22no—
104C22×C73—22no—
105C22×C73—24no—
106C22×C73—24no—
107C22×C73#12314yes—
108C22×C73C22×D411yescharacteristic
109C22×C73C2×#4112yes—
110C22×C73C2×#4111yescharacteristic
111C22×C73C2×#4111yescharacteristic
112C22×C732−1+412yes—
113C4×C73—24no—
114C4×C73—41no—
115C4×C73—41no—
116C4×C73—42no—
117Dic73—22no—
118Dic73—22no—
119Dic73—42no—
120Dic73—41no—
121Dic73—41no—
122Dic73—42no—
123C2×C73—24no—
124C2×C73C2×#12311yescharacteristic
125C2×C73#52511yescharacteristic
126C2×C73#53611yescharacteristic
127C2×C73#55212yes—
128C2×C73#55212yes—
129#2484—731nomaximal, Sylow
130C73#248411yescharacteristic, complemented, Sylow
131C2×#117—731no—
132C22×C4⋊C4—731no—
133#400—732no—
134#398—732no—
135#387—732no—
136#387—732no—
137#385—731no—
138#385D7311yescharacteristic
139#381—731no—
140#381—731no—
141#381—731no—
142C23×C4—731no—
143C23×C4—731no—
144C23×C4C2×D7311yescharacteristic
145#117—1464no—
146C2×C4⋊C4—732no—
147C2×C4⋊C4—732no—
148C2×C4⋊C4—731no—
149C2×C4⋊C4—731no—
150C2×C4⋊C4—732no—
151C2×C4⋊C4—1464no—
152C2×C4⋊C4C2×D7312yes—
153C2×C22⋊C4—731no—
154C2×C22⋊C4—731no—
155C2×C22⋊C4C2×D7311yescharacteristic
156C2×C22⋊C4C2×D7311yescharacteristic
157C2×C42—731no—
158C2×C42—731no—
159#95—732no—
160#95—732no—
161#95—732no—
162#95—732no—
163#95—732no—
164#95—732no—
165#95—732no—
166#95C2×D7312yes—
167C24C22×D7311yescharacteristic
168C22×C4—22no—
169C22×C4—24no—
170C22×C4—734no—
171C22×C4—731no—
172C22×C4—731no—
173C22×C4—732no—
174C22×C4—731no—
175C22×C4—732no—
176C22×C4—731no—
177C22×C4—1462no—
178C22×C4—1462no—
179C22×C4—1462no—
180C22×C4—1462no—
181C22×C4—1462no—
182C22×C4C22×D7312yes—
183C22×C4C22×D7311yescharacteristic
184C22×C4C22×D7311yescharacteristic
185C22×C4C22×D7312yes—
186C4⋊C4—24no—
187C4⋊C4—1462no—
188C4⋊C4—1462no—
189C4⋊C4—1464no—
190C4⋊C4—1464no—
191C4⋊C4—1464no—
192C22⋊C4—22no—
193C22⋊C4—22no—
194C22⋊C4—1462no—
195C22⋊C4—1462no—
196C42—1462no—
197C42—1462no—
198C23—22no—
199C23—22no—
200C23D4×D7312yes—
201C23#1192402812yes—
202C23#1192402912yes—
203C23C23×D7311yescharacteristic
204C2×C4—28no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—2924no—
215C2×C4—732no—
216C2×C4—732no—
217C2×C4—1461no—
218C2×C4—1461no—
219C2×C4—1462no—
220C2×C4—1462no—
221C2×C4—1462no—
222C2×C4—1462no—
223C2×C4—1462no—
224C2×C4—1462no—
225C2×C4—1462no—
226C2×C4—1462no—
227C2×C4—1468no—
228C2×C4—1461no—
229C2×C4—1461no—
230C2×C4—1461no—
231C2×C4—1461no—
232C2×C4#1192402714yes—
233C22—22no—
234C22—24no—
235C22—24no—
236C22—22no—
237C22#1455657614yes—
238C22C2×D4×D7311yescharacteristic
239C22C2×#1192402712yes—
240C22C2×#1192402811yescharacteristic
241C22C2×#1192402911yescharacteristic
242C22#1455663812yes—
243C4—24no—
244C4—41no—
245C4—42no—
246C4—41no—
247C4—2921no—
248C4—2922no—
249C4—2922no—
250C4—2921no—
251C4—1462no—
252C4—1462no—
253C2—24no—
254C2C2×#1455657611yescharacteristic
255C2#1798909311yescharacteristic
256C2#1798915911yescharacteristic
257C2#1798927712yes—
258C2#1798927912yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#385×C73C2
hypercenter#385D73
hypocenterC73#2484
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #17988529C2semidirect
4. #17988520C2semidirect
5. #17988474C2semidirect
6. #17988473C2semidirect
130. C73#2484semidirect