Finite Group Databasebeta

← #22614524

Subgroups — #22614524

Order 9344.

440 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 137 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
1#17988516C212yesmaximal, complemented
2#17988514C212yesmaximal, complemented
3#17988489C211yesmaximal, characteristic
4#17988488C211yesmaximal, characteristic
5#17988488C211yesmaximal, characteristic
6#17988486C211yesmaximal, characteristic, complemented
7#17988479C212yesmaximal, complemented
8#17988476C212yesmaximal, complemented
9C4⋊C4×Dic73C211yesmaximal, characteristic, complemented
10C4×#11924007C211yesmaximal, characteristic, complemented
11#382×C73C211yesmaximal, characteristic, complemented
12C22×D292C2211yescharacteristic
13C2×C4⋊Dic73C2211yescharacteristic
14C2×C4⋊Dic73C2212yes—
15C2×#11924007C2211yescharacteristic
16C2×#11924007C2211yescharacteristic
17C2×#11924005C2212yes—
18C2×#11924005C2212yes—
19C2×#11924005C2212yes—
20C2×#11924005C2212yes—
21C2×#11924005C2212yes—
22C2×#11924005C2212yes—
23C2×C4×Dic73C2211yescharacteristic
24C2×C4×Dic73C2211yescharacteristic
25C2×C4×Dic73C2212yes—
26#14556498C2211yescharacteristic
27#14556498C2211yescharacteristic
28#14556498C2212yes—
29#14556498C2212yes—
30C2×C4⋊C4×C73C2211yescharacteristic
31C2×C4⋊C4×C73C2211yescharacteristic
32C2×C42×C73C2211yescharacteristic
33#95×C73C2212yes—
34#95×C73C2212yes—
35C23×D73C2312yes—
36C2×D292—22no—
37C2×D292—22no—
38C2×D292—22no—
39C22×Dic73C2311yescharacteristic
40C22×Dic73C2311yescharacteristic
41C22×Dic73C2312yes—
42C22×Dic73C2311yescharacteristic
43C22×Dic73C2311yescharacteristic
44C4⋊Dic73—22no—
45C4⋊Dic73—42no—
46#11924007—22no—
47#11924007—22no—
48#11924005—24no—
49#11924005—24no—
50#11924005—42no—
51#11924005—42no—
52#11924005—42no—
53#11924005—42no—
54C4×Dic73—22no—
55C4×Dic73—22no—
56C4×Dic73—42no—
57C22×C4×C73C2311yescharacteristic
58C22×C4×C73C2311yescharacteristic
59C22×C4×C73C2312yes—
60C22×C4×C73C2312yes—
61C22×C4×C73C2311yescharacteristic
62C4⋊C4×C73—22no—
63C4⋊C4×C73—22no—
64C42×C73—22no—
65C23×C73C2411yescharacteristic
66C22×D73—22no—
67C22×D73—22no—
68C22×D73—22no—
69C22×D73—22no—
70C22×D73—22no—
71C22×D73—22no—
72C22×D73—22no—
73C2×C4×C73—21no—
74C2×C4×C73—21no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—22no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—22no—
85C2×C4×C73#4112yes—
86C2×C4×C73#4112yes—
87C2×C4×C73#4112yes—
88C2×Dic73—21no—
89C2×Dic73—21no—
90C2×Dic73—21no—
91C2×Dic73—21no—
92C2×Dic73—21no—
93C2×Dic73—21no—
94C2×Dic73—21no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—21no—
98C2×Dic73—21no—
99C2×Dic73—22no—
100C2×Dic73—21no—
101C2×Dic73#4112yes—
102C2×Dic73#4112yes—
103D292—44no—
104C22×C73C2×#4111yescharacteristic
105C22×C73C2×#4111yescharacteristic
106C22×C73C2×#4111yescharacteristic
107C22×C73C2×#4111yescharacteristic
108C22×C73C2×#4111yescharacteristic
109C22×C73H(5,𝔽2)11yescharacteristic
110C22×C73H(5,𝔽2)11yescharacteristic
111C2×D73—42no—
112C2×D73—42no—
113C2×D73—42no—
114C2×D73—42no—
115C2×D73—42no—
116C2×D73—42no—
117C2×D73—42no—
118C4×C73—41no—
119C4×C73—41no—
120C4×C73—42no—
121C4×C73—42no—
122C4×C73#12614yes—
123Dic73—22no—
124Dic73—22no—
125Dic73—41no—
126Dic73—42no—
127Dic73—41no—
128C2×C73C2×#12611yescharacteristic
129C2×C73#52911yescharacteristic
130C2×C73#54011yescharacteristic
131C2×C73#55311yescharacteristic
132C2×C73#55511yescharacteristic
133C2×C73#55911yescharacteristic
134C2×C73#55911yescharacteristic
135D73—82no—
136#2513—731nomaximal, Sylow
137C73#251311yescharacteristic, complemented, Sylow
138#397—732no—
139#397—732no—
140#390—731no—
141#390—731no—
142#390—731no—
143#389—731no—
144#388—732no—
145#388—732no—
146#382D7311yescharacteristic, complemented
147C4×C4⋊C4—731no—
148C4×C4⋊C4—731no—
149C22×D4—731no—
150C2×C4⋊C4—732no—
151C2×C4⋊C4—731no—
152C2×C4⋊C4—731no—
153C2×C4⋊C4—731no—
154C2×C4⋊C4C2×D7311yescharacteristic
155C2×C4⋊C4C2×D7311yescharacteristic
156C2×C22⋊C4—732no—
157C2×C22⋊C4—732no—
158C2×C22⋊C4—732no—
159C2×C22⋊C4—732no—
160C2×C22⋊C4—732no—
161C2×C22⋊C4—732no—
162C2×C42—732no—
163C2×C42—731no—
164C2×C42—731no—
165C2×C42C2×D7311yescharacteristic
166#95—731no—
167#95—732no—
168#95—731no—
169#95—732no—
170#95C2×D7312yes—
171#95C2×D7312yes—
172C24—732no—
173C2×D4—1462no—
174C2×D4—1462no—
175C2×D4—1462no—
176C22×C4—731no—
177C22×C4—731no—
178C22×C4—731no—
179C22×C4—731no—
180C22×C4—732no—
181C22×C4C22×D7312yes—
182C22×C4C22×D7311yescharacteristic
183C22×C4C22×D7311yescharacteristic
184C22×C4C22×D7312yes—
185C22×C4C22×D7311yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—2922no—
189C4⋊C4—1462no—
190C4⋊C4—1462no—
191C4⋊C4—1462no—
192C22⋊C4—2922no—
193C22⋊C4—2922no—
194C22⋊C4—2922no—
195C22⋊C4—2922no—
196C22⋊C4—1464no—
197C22⋊C4—1464no—
198C42—22no—
199C42—2922no—
200C42—1462no—
201C42—1462no—
202C23—1462no—
203C23—1462no—
204C23—1462no—
205C23—1462no—
206C23—1462no—
207C23—1462no—
208C23—1462no—
209C23C23×D7311yescharacteristic
210D4—2924no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—732no—
224C2×C4—732no—
225C2×C4—1461no—
226C2×C4—1461no—
227C2×C4—1461no—
228C2×C4—1462no—
229C2×C4—1462no—
230C2×C4—1461no—
231C2×C4—1461no—
232C2×C4—1462no—
233C2×C4—1461no—
234C2×C4—1461no—
235C2×C4—1461no—
236C2×C4—1461no—
237C2×C4—1461no—
238C2×C4#1192402712yes—
239C2×C4#1192402812yes—
240C2×C4#1192402912yes—
241C22—2922no—
242C22—2922no—
243C22—2922no—
244C22—2922no—
245C22—2922no—
246C22—2922no—
247C22—2922no—
248C22#41×D7311yescharacteristic
249C22#41×D7311yescharacteristic
250C22C2×#1192402711yescharacteristic
251C22C2×#1192402811yescharacteristic
252C22C2×#1192402911yescharacteristic
253C22#1455663711yescharacteristic
254C22#1455663711yescharacteristic
255C4—41no—
256C4—41no—
257C4—42no—
258C4—42no—
259C4—2921no—
260C4—2922no—
261C4—2921no—
262C4—1462no—
263C4—1462no—
264C4#1455658614yes—
265C2—5842no—
266C2C2×#1455658611yescharacteristic
267C2#1798912211yescharacteristic
268C2#1798919311yescharacteristic
269C2#1798928111yescharacteristic
270C2#1798930011yescharacteristic
271C2#1798931911yescharacteristic
272C2#1798931911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#382×C73C2
hypercenter#382D73
hypocenterC73#2513
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. #17988516C2semidirect
2. #17988514C2semidirect
6. #17988486C2semidirect
7. #17988479C2semidirect
8. #17988476C2semidirect
9. C4⋊C4×Dic73C2semidirect
10. C4×#11924007C2semidirect
11. #382×C73C2semidirect
137. C73#2513semidirect
146. #382D73semidirect