Finite Group Databasebeta

← #22616700

Subgroups — #22616700

Order 9344.

556 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14556577C212yesmaximal, complemented
2#17988505C212yesmaximal, complemented
3#17988500C212yesmaximal, complemented
4#17988496C211yesmaximal, characteristic
5#17988491C212yesmaximal, complemented
6#17988477C212yesmaximal, complemented
7#17988464C212yesmaximal, complemented
8#17988459C211yesmaximal, characteristic, complemented
9#397×C73C211yesmaximal, characteristic, complemented
10C22×Dic146C2212yes—
11C22×D292C2211yescharacteristic
12C22×C22⋊D73C2212yes—
13C23×Dic73C2211yescharacteristic
14#14556577—28no—
15C2×#11924007C2212yes—
16C2×C22⋊Dic73C2211yescharacteristic
17C2×#11924005C2212yes—
18C2×#11924005C2212yes—
19C2×#11924005C2212yes—
20C2×#11924005C2212yes—
21C2×#11924005C2212yes—
22C2×C4×Dic73C2212yes—
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2212yes—
26#14556498C2211yescharacteristic
27C2×C4⋊C4×C73C2211yescharacteristic
28C2×C22⋊C4×C73C2212yes—
29C2×C22⋊C4×C73C2211yescharacteristic
30#95×C73C2212yes—
31#95×C73C2211yescharacteristic
32C23×D73C2312yes—
33C2×Dic146—24no—
34C2×Dic146—24no—
35C2×Dic146—42no—
36C2×D292—41no—
37C2×D292—42no—
38C2×C22⋊D73—24no—
39C2×C22⋊D73—24no—
40C2×C22⋊D73—42no—
41C22×Dic73—41no—
42C22×Dic73—42no—
43C22×Dic73C2312yes—
44C22×Dic73C2312yes—
45C22×Dic73C2312yes—
46#11924007—42no—
47C22⋊Dic73D414yescomplemented
48#11924005—24no—
49#11924005—24no—
50#11924005—24no—
51#11924005—42no—
52#11924005—42no—
53C4×Dic73—24no—
54C24×C73C2311yescharacteristic
55C22×C4×C73C2312yes—
56C22×C4×C73C2311yescharacteristic
57C22×C4×C73C2311yescharacteristic
58C22×C4×C73C2312yes—
59C4⋊C4×C73—41no—
60C22⋊C4×C73—24no—
61C22⋊C4×C73—41no—
62C23×C73—22no—
63C23×C73—21no—
64C23×C73—22no—
65C23×C73—21no—
66C23×C73C2×D412yes—
67C23×C73C2411yescharacteristic
68C22×D73—22no—
69C22×D73—22no—
70C22×D73—22no—
71C22×D73—22no—
72C22×D73—22no—
73C22×D73—22no—
74C22×D73—22no—
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—22no—
83C2×C4×C73—22no—
84C2×C4×C73—22no—
85C22⋊D73—48no—
86C2×Dic73—22no—
87C2×Dic73—22no—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—44no—
94C2×Dic73C2×D414yes—
95C2×Dic73#4114yes—
96D292—44no—
97Dic146—48no—
98C22×C73—22no—
99C22×C73—24no—
100C22×C73—42no—
101C22×C73—41no—
102C22×C73—41no—
103C22×C73C22×D411yescharacteristic
104C22×C73C2×#4112yes—
105C22×C73H(5,𝔽2)11yescharacteristic
106C22×C73H(5,𝔽2)12yes—
107C22×C732−1+411yescharacteristic
108C2×D73—42no—
109C2×D73—42no—
110C2×D73—42no—
111C2×D73—42no—
112C2×D73—42no—
113C2×D73—42no—
114C2×D73—42no—
115C4×C73—42no—
116C4×C73—42no—
117C4×C73—41no—
118C4×C73—41no—
119Dic73—24no—
120Dic73—24no—
121Dic73—42no—
122C2×C73—42no—
123C2×C73#53711yescharacteristic
124C2×C73#54212yes—
125C2×C73#54612yes—
126C2×C73#55911yescharacteristic
127C2×C73H(3,𝔽4)11yescharacteristic
128D73—82no—
129#2712—731nomaximal, Sylow
130C73#271211yescharacteristic, complemented, Sylow
131C2×#124—732no—
132#397D7311yescharacteristic, complemented
133#394—732no—
134#393—732no—
135#392—731no—
136#391—732no—
137#388—732no—
138#386—732no—
139#385—731no—
140C22×Q8—732no—
141C22×D4—732no—
142C22×D4—731no—
143C23×C4—731no—
144#124—1468no—
145C2×C4⋊C4—732no—
146C2×C4⋊C4C2×D7311yescharacteristic
147C2×C22⋊C4—732no—
148C2×C22⋊C4—732no—
149C2×C22⋊C4—731no—
150C2×C22⋊C4—732no—
151C2×C22⋊C4—732no—
152C2×C22⋊C4—732no—
153C2×C22⋊C4C2×D7312yes—
154C2×C22⋊C4C2×D7311yescharacteristic
155C2×C42—732no—
156#95—732no—
157#95—732no—
158#95—732no—
159#95—731no—
160#95C2×D7312yes—
161#95C2×D7311yescharacteristic
162C24—732no—
163C24C22×D7311yescharacteristic
164C2×Q8—2922no—
165C2×Q8—1464no—
166C2×Q8—1464no—
167C2×D4—2921no—
168C2×D4—2922no—
169C2×D4—2922no—
170C2×D4—1464no—
171C2×D4—1464no—
172C22×C4—2921no—
173C22×C4—2922no—
174C22×C4—732no—
175C22×C4—732no—
176C22×C4—732no—
177C22×C4C22×D7311yescharacteristic
178C22×C4C22×D7312yes—
179C22×C4C22×D7311yescharacteristic
180C22×C4C22×D7312yes—
181C4⋊C4—41no—
182C4⋊C4—2922no—
183C22⋊C4—24no—
184C22⋊C4—41no—
185C22⋊C4—2922no—
186C22⋊C4—2922no—
187C22⋊C4—734no—
188C22⋊C4—1464no—
189C22⋊C4—1464no—
190C22⋊C4—1464no—
191C42—1464no—
192C23—22no—
193C23—21no—
194C23—22no—
195C23—21no—
196C23—1462no—
197C23—1462no—
198C23—1462no—
199C23—1462no—
200C23—1462no—
201C23—1462no—
202C23—1462no—
203C23D4×D7312yes—
204C23C23×D7311yescharacteristic
205Q8—2928no—
206D4—2924no—
207D4—2928no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—2924no—
219C2×C4—734no—
220C2×C4—734no—
221C2×C4—1462no—
222C2×C4—1462no—
223C2×C4—1462no—
224C2×C4—1462no—
225C2×C4—1462no—
226C2×C4—1462no—
227C2×C4—1462no—
228C22—22no—
229C22—24no—
230C22—42no—
231C22—41no—
232C22—41no—
233C22—2922no—
234C22—2922no—
235C22—2922no—
236C22—2922no—
237C22—2922no—
238C22—2922no—
239C22—2922no—
240C22C2×D4×D7311yescharacteristic
241C22#41×D7312yes—
242C22#1455663611yescharacteristic
243C22#1455663712yes—
244C22#1455663811yescharacteristic
245C4—42no—
246C4—42no—
247C4—41no—
248C4—41no—
249C4—2922no—
250C4—1464no—
251C4—1464no—
252C2—42no—
253C2—5842no—
254C2#1798916411yescharacteristic
255C2#1798920312yes—
256C2#1798922912yes—
257C2#1798932111yescharacteristic
258C2#1798932911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#397×C73C2
hypercenter#397D73
hypocenterC73#2712
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14556577C2semidirect
2. #17988505C2semidirect
3. #17988500C2semidirect
5. #17988491C2semidirect
6. #17988477C2semidirect
7. #17988464C2semidirect
8. #17988459C2semidirect
9. #397×C73C2semidirect
47. C22⋊Dic73D4semidirect
130. C73#2712semidirect
132. #397D73semidirect