Finite Group Databasebeta

← #22614213

Subgroups — #22614213

Order 9344.

512 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 139 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×#14556549C211yesmaximal, characteristic
2C2×C4⋊C4×D73C211yesmaximal, characteristic
3#17988527C211yesmaximal, characteristic, complemented
4#17988526C211yesmaximal, characteristic, complemented
5#17988518C211yesmaximal, characteristic, complemented
6#17988473C212yesmaximal, complemented
7#17988469C212yesmaximal, complemented
8#17988458C212yesmaximal
9#17988449C212yesmaximal
10#17988449C211yesmaximal, characteristic
11#398×C73C211yesmaximal, characteristic, complemented
12C22×C4×D73C2211yescharacteristic
13C22×C4×D73C2211yescharacteristic
14C22×C4×D73C2211yescharacteristic
15#14556549—24no—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×C4⋊Dic73C2211yescharacteristic
18C2×#11924007C2212yes—
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C4⋊C4×D73—24no—
22C2×#11924005C2212yes—
23C2×#11924005C2212yes—
24C2×C4×Dic73C2212yes—
25#14556498C2212yes—
26#14556498C2212yes—
27#14556498C2212yes—
28#14556498C2212yes—
29#14556498C2211yescharacteristic
30#14556498C2212yes—
31#14556498C2212yes—
32C2×C4⋊C4×C73C2212yes—
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C4⋊C4×C73C2211yescharacteristic
35#95×C73C2212yes—
36#95×C73C2211yescharacteristic
37C23×D73C2311yescharacteristic
38C22×Dic73C2312yes—
39C22×Dic73C2312yes—
40C22×Dic73C2311yescharacteristic
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2311yescharacteristic
43C2×C4×D73—22no—
44C2×C4×D73—24no—
45C2×C4×D73—22no—
46C2×C4×D73—22no—
47C2×C4×D73—22no—
48C2×C4×D73—24no—
49C2×C4×D73D414yes—
50C4⋊Dic73—22no—
51C4⋊Dic73—22no—
52#11924007—22no—
53#11924007—22no—
54#11924007—24no—
55#11924005—24no—
56#11924005—24no—
57C4×Dic73—24no—
58C22×C4×C73C2312yes—
59C22×C4×C73C2311yescharacteristic
60C22×C4×C73C2312yes—
61C22×C4×C73C2311yescharacteristic
62C22×C4×C73C2311yescharacteristic
63C4⋊C4×C73—22no—
64C4⋊C4×C73—22no—
65C4⋊C4×C73—24no—
66C23×C73C2411yescharacteristic
67C22×D73—21no—
68C22×D73—21no—
69C22×D73—22no—
70C22×D73C2×D412yes—
71C22×D73#4114yes—
72C2×C4×C73—21no—
73C2×C4×C73—22no—
74C2×C4×C73—21no—
75C2×C4×C73—22no—
76C2×C4×C73—21no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73C2×D412yes—
84C2×C4×C73#4112yes—
85C2×Dic73—21no—
86C2×Dic73—22no—
87C2×Dic73—21no—
88C2×Dic73—22no—
89C2×Dic73—21no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—24no—
94C2×Dic73—22no—
95C2×Dic73C2×D412yes—
96C2×Dic73#4112yes—
97C4×D73—28no—
98C4×D73—28no—
99C4×D73—44no—
100C22×C73C22×D411yescharacteristic
101C22×C73C2×#4112yes—
102C22×C73C2×#4111yescharacteristic
103C22×C73C2×#4111yescharacteristic
104C22×C732−1+412yes—
105C2×D73—22no—
106C2×D73—22no—
107C2×D73—24no—
108C2×D73—24no—
109C2×D73#12314yes—
110C4×C73—22no—
111C4×C73—22no—
112C4×C73—41no—
113C4×C73—42no—
114C4×C73—42no—
115Dic73—22no—
116Dic73—22no—
117Dic73—41no—
118Dic73—42no—
119Dic73—42no—
120C2×C73C2×#12311yescharacteristic
121C2×C73#52511yescharacteristic
122C2×C73#53611yescharacteristic
123C2×C73#55212yes—
124C2×C73#55212yes—
125D73—24no—
126#2484—731nomaximal, Sylow
127C73#248411yescharacteristic, complemented, Sylow
128C2×#117—731no—
129C22×C4⋊C4—731no—
130#400—731no—
131#400—731no—
132#398—731no—
133#398D7311yescharacteristic, complemented
134#387—732no—
135#387—732no—
136#385—732no—
137#381—731no—
138#381—732no—
139C23×C4—731no—
140C23×C4—731no—
141C23×C4—731no—
142#117—1464no—
143C2×C4⋊C4—731no—
144C2×C4⋊C4—731no—
145C2×C4⋊C4—731no—
146C2×C4⋊C4—731no—
147C2×C4⋊C4—732no—
148C2×C4⋊C4—1464no—
149C2×C4⋊C4C2×D7311yescharacteristic
150C2×C4⋊C4C2×D7311yescharacteristic
151C2×C4⋊C4C2×D7312yes—
152C2×C22⋊C4—732no—
153C2×C22⋊C4—732no—
154C2×C42—732no—
155#95—732no—
156#95—732no—
157#95—732no—
158#95—732no—
159#95—731no—
160#95—732no—
161#95—732no—
162#95C2×D7312yes—
163#95C2×D7311yescharacteristic
164C24—731no—
165C22×C4—731no—
166C22×C4—731no—
167C22×C4—734no—
168C22×C4—732no—
169C22×C4—732no—
170C22×C4—731no—
171C22×C4—1462no—
172C22×C4—1464no—
173C22×C4—1462no—
174C22×C4—1462no—
175C22×C4—1464no—
176C22×C4—1462no—
177C22×C4C22×D7312yes—
178C22×C4C22×D7311yescharacteristic
179C22×C4C22×D7312yes—
180C22×C4C22×D7311yescharacteristic
181C22×C4C22×D7311yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—24no—
185C4⋊C4—1464no—
186C4⋊C4—1462no—
187C4⋊C4—1462no—
188C4⋊C4—1462no—
189C4⋊C4—1462no—
190C22⋊C4—1464no—
191C22⋊C4—1464no—
192C42—1464no—
193C23—732no—
194C23—734no—
195C23—1461no—
196C23—1461no—
197C23—1462no—
198C23C23×D7311yescharacteristic
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—2924no—
211C2×C4—732no—
212C2×C4—732no—
213C2×C4—1468no—
214C2×C4—1468no—
215C2×C4—1462no—
216C2×C4—1461no—
217C2×C4—1462no—
218C2×C4—1462no—
219C2×C4—1462no—
220C2×C4—1464no—
221C2×C4—1462no—
222C2×C4—1461no—
223C2×C4—1462no—
224C2×C4—1461no—
225C2×C4D4×D7312yes—
226C2×C4#1192402712yes—
227C22—734no—
228C22—1462no—
229C22—1464no—
230C22—1464no—
231C22—1462no—
232C22C2×D4×D7311yescharacteristic
233C22#41×D7311yescharacteristic
234C22#41×D7312yes—
235C22C2×#1192402711yescharacteristic
236C22#1455663912yes—
237C4—22no—
238C4—22no—
239C4—42no—
240C4—41no—
241C4—42no—
242C4—2922no—
243C4—2922no—
244C4—2921no—
245C4—1462no—
246C4—1462no—
247C2—1464no—
248C2#123×D7311yescharacteristic
249C2#1798909711yescharacteristic
250C2#1798916211yescharacteristic
251C2#1798926912yes—
252C2#1798927112yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#398×C73C2
hypercenter#398D73
hypocenterC73#2484
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #17988527C2semidirect
4. #17988526C2semidirect
5. #17988518C2semidirect
6. #17988473C2semidirect
7. #17988469C2semidirect
11. #398×C73C2semidirect
127. C73#2484semidirect
133. #398D73semidirect