Finite Group Databasebeta

← #22615804

Subgroups — #22615804

Order 9344.

512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14556582C211yesmaximal, characteristic, complemented
2C2×#14556551C211yesmaximal, characteristic
3#17988524C211yesmaximal, characteristic, complemented
4#17988523C211yesmaximal, characteristic, complemented
5#17988521C212yesmaximal, complemented
6#17988513C211yesmaximal, characteristic, complemented
7#17988502C212yesmaximal
8#17988462C212yesmaximal, complemented
9#17988461C212yesmaximal, complemented
10#17988454C211yesmaximal, characteristic, complemented
11#397×C73C211yesmaximal, characteristic, complemented
12C22×C22⋊D73C2211yescharacteristic
13C23×Dic73C2211yescharacteristic
14C22×C4×D73C2211yescharacteristic
15#14556582—24no—
16#14556551—24no—
17C2×C4⋊Dic73C2212yes—
18C2×C4⋊Dic73C2211yescharacteristic
19C2×C4⋊Dic73C2212yes—
20C2×#11924007C2212yes—
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2212yes—
23C2×C22⋊Dic73C2212yes—
24C2×#11924005C2212yes—
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2212yes—
27C2×C4×Dic73C2211yescharacteristic
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2211yescharacteristic
31#14556498C2212yes—
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C22⋊C4×C73C2212yes—
34C2×C22⋊C4×C73C2211yescharacteristic
35#95×C73C2211yescharacteristic
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C2×C22⋊D73—22no—
39C2×C22⋊D73—22no—
40C2×C22⋊D73—22no—
41C22×Dic73—22no—
42C22×Dic73—42no—
43C22×Dic73C2312yes—
44C22×Dic73C2311yescharacteristic
45C22×Dic73C2312yes—
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2311yescharacteristic
48C2×C4×D73—22no—
49C2×C4×D73—42no—
50C4⋊Dic73—22no—
51C4⋊Dic73—24no—
52C4⋊Dic73—42no—
53#11924007—22no—
54#11924007—24no—
55#11924007—42no—
56C22⋊Dic73—42no—
57#11924005—24no—
58#11924005—22no—
59#11924005—42no—
60C4×Dic73D414yes—
61C24×C73C2311yescharacteristic
62C22×C4×C73C2312yes—
63C22×C4×C73C2311yescharacteristic
64C22×C4×C73C2312yes—
65C22×C4×C73C2311yescharacteristic
66C4⋊C4×C73—22no—
67C22⋊C4×C73—24no—
68C22⋊C4×C73—22no—
69C23×C73—21no—
70C23×C73—21no—
71C23×C73—22no—
72C23×C73—22no—
73C23×C73#4112yes—
74C23×C73C2411yescharacteristic
75C22×D73—21no—
76C22×D73—21no—
77C22×D73—22no—
78C22×D73—22no—
79C22×D73#4112yes—
80C2×C4×C73—22no—
81C2×C4×C73—21no—
82C2×C4×C73—22no—
83C2×C4×C73—22no—
84C2×C4×C73—22no—
85C2×C4×C73—22no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73C2×D412yes—
90C22⋊D73—28no—
91C2×Dic73—21no—
92C2×Dic73—21no—
93C2×Dic73—22no—
94C2×Dic73—21no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—22no—
100C2×Dic73—22no—
101C2×Dic73—22no—
102C2×Dic73—44no—
103C2×Dic73C2×D412yes—
104C2×Dic73C2×D412yes—
105C4×D73—44no—
106C22×C73—22no—
107C22×C73—24no—
108C22×C73—41no—
109C22×C73—41no—
110C22×C73—42no—
111C22×C73C22×D411yescharacteristic
112C22×C73C2×#4111yescharacteristic
113C22×C73C2×#4111yescharacteristic
114C22×C73H(5,𝔽2)12yes—
115C22×C732−1+412yes—
116C2×D73—22no—
117C2×D73—24no—
118C2×D73—41no—
119C2×D73—41no—
120C2×D73—42no—
121C4×C73—22no—
122C4×C73—42no—
123C4×C73—41no—
124C4×C73—42no—
125Dic73—22no—
126Dic73—22no—
127Dic73—42no—
128Dic73—41no—
129Dic73—42no—
130C2×C73—42no—
131C2×C73#52511yescharacteristic
132C2×C73#53511yescharacteristic
133C2×C73#53611yescharacteristic
134C2×C73#53912yes—
135C2×C73#53912yes—
136D73—42no—
137#2633—731nomaximal, Sylow
138C73#263311yescharacteristic, complemented, Sylow
139C2×#125—731no—
140C2×C4×D4—731no—
141#399—731no—
142#399—731no—
143#398—732no—
144#397—731no—
145#397D7311yescharacteristic, complemented
146#394—732no—
147#385—732no—
148#385—732no—
149#383—731no—
150C22×D4—731no—
151C23×C4—731no—
152C23×C4—731no—
153#125—1464no—
154C4×D4—1464no—
155C2×C4⋊C4—732no—
156C2×C4⋊C4—732no—
157C2×C4⋊C4—731no—
158C2×C4⋊C4—732no—
159C2×C4⋊C4—732no—
160C2×C4⋊C4—731no—
161C2×C4⋊C4C2×D7311yescharacteristic
162C2×C22⋊C4—732no—
163C2×C22⋊C4—732no—
164C2×C22⋊C4—731no—
165C2×C22⋊C4—732no—
166C2×C22⋊C4C2×D7311yescharacteristic
167C2×C22⋊C4C2×D7312yes—
168C2×C42—731no—
169#95—732no—
170#95—732no—
171#95—731no—
172#95—732no—
173#95C2×D7311yescharacteristic
174#95C2×D7312yes—
175C24—731no—
176C24C22×D7311yescharacteristic
177C2×D4—1462no—
178C2×D4—1462no—
179C2×D4—1462no—
180C22×C4—2922no—
181C22×C4—2922no—
182C22×C4—731no—
183C22×C4—731no—
184C22×C4—732no—
185C22×C4—731no—
186C22×C4—732no—
187C22×C4—1462no—
188C22×C4—1462no—
189C22×C4C22×D7312yes—
190C22×C4C22×D7312yes—
191C22×C4C22×D7311yescharacteristic
192C22×C4C22×D7311yescharacteristic
193C4⋊C4—22no—
194C4⋊C4—2922no—
195C4⋊C4—2922no—
196C4⋊C4—1462no—
197C4⋊C4—1464no—
198C4⋊C4—1464no—
199C4⋊C4—1462no—
200C22⋊C4—24no—
201C22⋊C4—22no—
202C22⋊C4—2922no—
203C22⋊C4—2922no—
204C22⋊C4—1464no—
205C22⋊C4—1462no—
206C42—734no—
207C23—21no—
208C23—21no—
209C23—22no—
210C23—22no—
211C23—732no—
212C23—1461no—
213C23—1461no—
214C23—1462no—
215C23—1462no—
216C23#1192402712yes—
217C23C23×D7311yescharacteristic
218D4—1468no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—2924no—
229C2×C4—2924no—
230C2×C4—732no—
231C2×C4—732no—
232C2×C4—1461no—
233C2×C4—1462no—
234C2×C4—1462no—
235C2×C4—1462no—
236C2×C4—1462no—
237C2×C4—1462no—
238C2×C4—1462no—
239C2×C4—1462no—
240C2×C4—1461no—
241C2×C4—1461no—
242C2×C4—1462no—
243C2×C4D4×D7312yes—
244C22—24no—
245C22—22no—
246C22—41no—
247C22—41no—
248C22—42no—
249C22—2921no—
250C22—2921no—
251C22—2922no—
252C22—1464no—
253C22—1462no—
254C22C2×D4×D7311yescharacteristic
255C22#41×D7311yescharacteristic
256C22C2×#1192402711yescharacteristic
257C22#1455663712yes—
258C22#1455663812yes—
259C4—22no—
260C4—41no—
261C4—42no—
262C4—42no—
263C4—2921no—
264C4—2922no—
265C4—2922no—
266C4—1462no—
267C4—1462no—
268C2—42no—
269C2—2922no—
270C2#1798909711yescharacteristic
271C2#1798915511yescharacteristic
272C2#1798915911yescharacteristic
273C2#1798917812yes—
274C2#1798918112yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#397×C73C2
hypercenter#397D73
hypocenterC73#2633
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14556582C2semidirect
3. #17988524C2semidirect
4. #17988523C2semidirect
5. #17988521C2semidirect
6. #17988513C2semidirect
8. #17988462C2semidirect
9. #17988461C2semidirect
10. #17988454C2semidirect
11. #397×C73C2semidirect
138. C73#2633semidirect
145. #397D73semidirect