Finite Group Databasebeta

← #22615798

Subgroups — #22615798

Order 9344.

512 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 133 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, complemented
2C2×D4×Dic73C211yesmaximal, characteristic
3#17988523C212yesmaximal, complemented
4#17988519C211yesmaximal, characteristic, complemented
5#17988517C211yesmaximal, characteristic, complemented
6#17988515C212yesmaximal, complemented
7#17988501C211yesmaximal, characteristic
8#17988462C212yesmaximal, complemented
9#17988459C212yesmaximal, complemented
10#17988454C211yesmaximal, characteristic, complemented
11#394×C73C211yesmaximal, characteristic
12C23×Dic73C2212yes—
13#14556581—24no—
14D4×Dic73—24no—
15C2×C4⋊Dic73C2211yescharacteristic
16C2×C4⋊Dic73C2211yescharacteristic
17C2×C4⋊Dic73C2212yes—
18C2×#11924007C2211yescharacteristic
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2212yes—
23C2×C22⋊Dic73C2212yes—
24C2×C22⋊Dic73C2212yes—
25C2×C22⋊Dic73C2212yes—
26C2×C4×Dic73C2211yescharacteristic
27#14556498C2212yes—
28#14556498C2211yescharacteristic
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C22×D4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C22⋊C4×C73C2212yes—
35C2×C22⋊C4×C73C2212yes—
36#95×C73C2211yescharacteristic
37C22×Dic73—24no—
38C22×Dic73—42no—
39C22×Dic73—42no—
40C22×Dic73C2312yes—
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2312yes—
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2311yescharacteristic
45C22×Dic73C2311yescharacteristic
46C4⋊Dic73—22no—
47C4⋊Dic73—22no—
48C4⋊Dic73—42no—
49#11924007—22no—
50#11924007—22no—
51#11924007—22no—
52#11924007—22no—
53#11924007—42no—
54C22⋊Dic73—24no—
55C22⋊Dic73—24no—
56C22⋊Dic73—42no—
57C4×Dic73D414yes—
58C24×C73C2312yes—
59C2×D4×C73—24no—
60C2×D4×C73—22no—
61C22×C4×C73C2312yes—
62C22×C4×C73C2311yescharacteristic
63C22×C4×C73C2311yescharacteristic
64C22×C4×C73C2311yescharacteristic
65C4⋊C4×C73—22no—
66C22⋊C4×C73—24no—
67C22⋊C4×C73—42no—
68C23×C73—22no—
69C23×C73—22no—
70C23×C73—22no—
71C23×C73—22no—
72C23×C73—22no—
73C23×C73—22no—
74C23×C73#4114yes—
75C23×C73C2411yescharacteristic
76D4×C73—28no—
77C2×C4×C73—22no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—21no—
83C2×C4×C73—22no—
84C2×C4×C73—21no—
85C2×C4×C73—22no—
86C2×C4×C73C2×D412yes—
87C2×Dic73—21no—
88C2×Dic73—21no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—21no—
92C2×Dic73—21no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—21no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73—21no—
99C2×Dic73—22no—
100C2×Dic73—22no—
101C2×Dic73—48no—
102C2×Dic73C2×D412yes—
103C2×Dic73C2×D412yes—
104C22×C73—24no—
105C22×C73—24no—
106C22×C73—24no—
107C22×C73—42no—
108C22×C73—42no—
109C22×C73—42no—
110C22×C73—42no—
111C22×C73C22×D411yescharacteristic
112C22×C73C2×#4112yes—
113C22×C73H(5,𝔽2)11yescharacteristic
114C22×C73H(5,𝔽2)11yescharacteristic
115C22×C732−1+412yes—
116C4×C73—22no—
117C4×C73—41no—
118C4×C73—41no—
119C4×C73—42no—
120Dic73—22no—
121Dic73—22no—
122Dic73—41no—
123Dic73—41no—
124Dic73—42no—
125Dic73—42no—
126C2×C73—44no—
127C2×C73#52511yescharacteristic
128C2×C73#53511yescharacteristic
129C2×C73#53611yescharacteristic
130C2×C73#53912yes—
131C2×C73#53912yes—
132#2633—731nomaximal, Sylow
133C73#263311yescharacteristic, complemented, Sylow
134C2×#125—731no—
135C2×C4×D4—731no—
136#399—732no—
137#398—731no—
138#398—731no—
139#397—732no—
140#394—731no—
141#394D7311yescharacteristic
142#385—732no—
143#385—732no—
144#383—731no—
145C22×D4C2×D7311yescharacteristic
146C23×C4—732no—
147#125—1464no—
148C4×D4—1464no—
149C2×C4⋊C4—732no—
150C2×C4⋊C4—732no—
151C2×C4⋊C4—731no—
152C2×C4⋊C4—731no—
153C2×C4⋊C4—731no—
154C2×C4⋊C4—731no—
155C2×C4⋊C4—731no—
156C2×C4⋊C4—731no—
157C2×C4⋊C4C2×D7311yescharacteristic
158C2×C22⋊C4—732no—
159C2×C22⋊C4—732no—
160C2×C22⋊C4—732no—
161C2×C22⋊C4C2×D7312yes—
162C2×C22⋊C4C2×D7312yes—
163C2×C42—731no—
164#95—732no—
165#95—731no—
166#95—732no—
167#95—732no—
168#95—732no—
169#95C2×D7311yescharacteristic
170C24C22×D7312yes—
171C2×D4—24no—
172C2×D4—22no—
173C22×C4—2922no—
174C22×C4—2922no—
175C22×C4—731no—
176C22×C4—731no—
177C22×C4—732no—
178C22×C4—731no—
179C22×C4—732no—
180C22×C4—731no—
181C22×C4—1464no—
182C22×C4C22×D7312yes—
183C22×C4C22×D7311yescharacteristic
184C22×C4C22×D7311yescharacteristic
185C22×C4C22×D7311yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—2922no—
188C4⋊C4—2922no—
189C4⋊C4—1462no—
190C4⋊C4—1462no—
191C4⋊C4—1462no—
192C4⋊C4—1462no—
193C4⋊C4—1462no—
194C4⋊C4—1462no—
195C22⋊C4—24no—
196C22⋊C4—42no—
197C22⋊C4—2922no—
198C22⋊C4—1464no—
199C22⋊C4—1464no—
200C42—734no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23#1192402714yes—
208C23C23×D7311yescharacteristic
209D4—28no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—2928no—
220C2×C4—732no—
221C2×C4—732no—
222C2×C4—1462no—
223C2×C4—1461no—
224C2×C4—1461no—
225C2×C4—1462no—
226C2×C4—1462no—
227C2×C4—1461no—
228C2×C4—1462no—
229C2×C4—1461no—
230C2×C4—1462no—
231C2×C4—1462no—
232C2×C4—1462no—
233C2×C4—1461no—
234C2×C4—1461no—
235C2×C4—1462no—
236C2×C4D4×D7312yes—
237C22—24no—
238C22—24no—
239C22—24no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22C2×D4×D7311yescharacteristic
245C22C2×#1192402712yes—
246C22#1455663611yescharacteristic
247C22#1455663711yescharacteristic
248C22#1455663812yes—
249C4—22no—
250C4—41no—
251C4—42no—
252C4—41no—
253C4—2922no—
254C4—2921no—
255C4—2922no—
256C4—2921no—
257C4—1462no—
258C4—1462no—
259C2—44no—
260C2#1798909311yescharacteristic
261C2#1798915311yescharacteristic
262C2#1798915711yescharacteristic
263C2#1798918112yes—
264C2#1798918212yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#394×C73C2
hypercenter#394D73
hypocenterC73#2633
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14556581C2semidirect
3. #17988523C2semidirect
4. #17988519C2semidirect
5. #17988517C2semidirect
6. #17988515C2semidirect
8. #17988462C2semidirect
9. #17988459C2semidirect
10. #17988454C2semidirect
133. C73#2633semidirect