Finite Group Databasebeta

← #22614404

Subgroups — #22614404

Order 9344.

544 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 161 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×#14556569C211yesmaximal, characteristic
2C2×C4⋊C4×D73C211yesmaximal, characteristic
3#17988519C211yesmaximal, characteristic, complemented
4#17988518C211yesmaximal, characteristic, complemented
5#17988517C211yesmaximal, characteristic, complemented
6#17988491C212yesmaximal, complemented
7#17988461C212yesmaximal
8#17988458C212yesmaximal
9#17988456C212yesmaximal, complemented
10#17988434C211yesmaximal, characteristic
11#398×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C22×C4×D73C2211yescharacteristic
14C22×C4×D73C2212yes—
15#14556569—24no—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×C4⋊Dic73C2212yes—
18C2×#11924007C2211yescharacteristic
19C2×#11924007C2212yes—
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2212yes—
22C2×#11924007C2212yes—
23C4⋊C4×D73—24no—
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2212yes—
27C2×C4×Dic73C2212yes—
28#14556498C2211yescharacteristic
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C4⋊C4×C73C2212yes—
35#95×C73C2211yescharacteristic
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C2×Dic146—22no—
39C2×Dic146—24no—
40C22×Dic73C2311yescharacteristic
41C22×Dic73C2312yes—
42C22×Dic73C2311yescharacteristic
43C22×Dic73C2312yes—
44C22×Dic73C2311yescharacteristic
45C2×C4×D73—24no—
46C2×C4×D73—24no—
47C2×C4×D73—42no—
48C2×C4×D73—42no—
49C2×C4×D73D414yes—
50C4⋊Dic73—22no—
51C4⋊Dic73—42no—
52#11924007—22no—
53#11924007—24no—
54#11924007—22no—
55#11924007—42no—
56#11924007—42no—
57#11924005—22no—
58#11924005—22no—
59#11924005Q818yescomplemented
60C4×Dic73—24no—
61C22×C4×C73C2311yescharacteristic
62C22×C4×C73C2312yes—
63C22×C4×C73C2311yescharacteristic
64C22×C4×C73C2311yescharacteristic
65C22×C4×C73C2312yes—
66C4⋊C4×C73—22no—
67C4⋊C4×C73—22no—
68C4⋊C4×C73—42no—
69C23×C73C2411yescharacteristic
70C22×D73—22no—
71C22×D73—21no—
72C22×D73—21no—
73C22×D73C2×D412yes—
74C22×D73C2×Q814yes—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
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×C4×C73C2×Q814yes—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—21no—
91C2×Dic73—21no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—21no—
95C2×Dic73—22no—
96C2×Dic73—21no—
97C2×Dic73—22no—
98C2×Dic73C2×D412yes—
99C2×Dic73C2×Q814yes—
100C2×Dic73#4114yes—
101C4×D73—28no—
102C4×D73—48no—
103Dic146—44no—
104C22×C73C22×D411yescharacteristic
105C22×C73C22×Q812yes—
106C22×C73C2×#4112yes—
107C22×C73H(5,𝔽2)11yescharacteristic
108C22×C73H(5,𝔽2)11yescharacteristic
109C2×D73—22no—
110C2×D73—22no—
111C2×D73—24no—
112C2×D73—24no—
113C2×D73C4⋊Q814yes—
114C4×C73—22no—
115C4×C73—24no—
116C4×C73—41no—
117C4×C73—42no—
118C4×C73—41no—
119Dic73—24no—
120Dic73—41no—
121Dic73—42no—
122Dic73—41no—
123Dic73#12314yes—
124C2×C73C2×#12311yescharacteristic
125C2×C73C2×C4⋊Q811yescharacteristic
126C2×C73#53511yescharacteristic
127C2×C73#55412yes—
128C2×C73#55412yes—
129D73—24no—
130#2502—731nomaximal, Sylow
131C73#250211yescharacteristic, complemented, Sylow
132C2×C22⋊Q8—731no—
133C22×C4⋊C4—731no—
134#398—731no—
135#398—731no—
136#398—731no—
137#398D7311yescharacteristic, complemented
138#391—732no—
139#385—732no—
140#385—732no—
141#384—732no—
142C4×C22⋊C4—731no—
143C22×Q8—731no—
144C23×C4—732no—
145C23×C4—731no—
146C22⋊Q8—1464no—
147C2×C4⋊C4—732no—
148C2×C4⋊C4—732no—
149C2×C4⋊C4—732no—
150C2×C4⋊C4—732no—
151C2×C4⋊C4—731no—
152C2×C4⋊C4—731no—
153C2×C4⋊C4—731no—
154C2×C4⋊C4—1464no—
155C2×C4⋊C4C2×D7311yescharacteristic
156C2×C4⋊C4C2×D7311yescharacteristic
157C2×C4⋊C4C2×D7312yes—
158C2×C22⋊C4—732no—
159C2×C22⋊C4—731no—
160C2×C22⋊C4—731no—
161C2×C42—732no—
162#95—731no—
163#95—732no—
164#95—732no—
165#95—732no—
166#95C2×D7311yescharacteristic
167#95C2×D7312yes—
168C24—731no—
169C2×Q8—1462no—
170C2×Q8—1464no—
171C22×C4—2922no—
172C22×C4—2922no—
173C22×C4—731no—
174C22×C4—732no—
175C22×C4—734no—
176C22×C4—731no—
177C22×C4—732no—
178C22×C4—731no—
179C22×C4—1464no—
180C22×C4—1464no—
181C22×C4C22×D7311yescharacteristic
182C22×C4C22×D7312yes—
183C22×C4C22×D7311yescharacteristic
184C22×C4C22×D7311yescharacteristic
185C22×C4C22×D7312yes—
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—42no—
189C4⋊C4—2922no—
190C4⋊C4—2922no—
191C4⋊C4—2922no—
192C4⋊C4—1464no—
193C4⋊C4—1462no—
194C4⋊C4—1462no—
195C4⋊C4—1462no—
196C22⋊C4—738no—
197C22⋊C4—1462no—
198C22⋊C4—1462no—
199C42—1464no—
200C23—732no—
201C23—734no—
202C23—1462no—
203C23—1461no—
204C23—1461no—
205C23C23×D7311yescharacteristic
206Q8—2924no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—2928no—
219C2×C4—732no—
220C2×C4—734no—
221C2×C4—734no—
222C2×C4—1468no—
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×C4D4×D7312yes—
234C2×C4Q8×D7314yes—
235C22—734no—
236C22—1462no—
237C22—1464no—
238C22—1464no—
239C22—1462no—
240C22C2×D4×D7311yescharacteristic
241C22C2×Q8×D7312yes—
242C22#41×D7312yes—
243C22#1455663611yescharacteristic
244C22#1455663711yescharacteristic
245C4—24no—
246C4—22no—
247C4—42no—
248C4—41no—
249C4—41no—
250C4—2922no—
251C4—2921no—
252C4—2921no—
253C4—734no—
254C4—1464no—
255C2—1464no—
256C2#123×D7311yescharacteristic
257C2C4⋊Q8×D7311yescharacteristic
258C2#1798915311yescharacteristic
259C2#1798929112yes—
260C2#1798929312yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#398×C73C2
hypercenter#398D73
hypocenterC73#2502
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #17988519C2semidirect
4. #17988518C2semidirect
5. #17988517C2semidirect
6. #17988491C2semidirect
9. #17988456C2semidirect
11. #398×C73C2semidirect
59. #11924005Q8semidirect
131. C73#2502semidirect
137. #398D73semidirect