Finite Group Databasebeta

← #22620008

Subgroups — #22620008

Order 9344.

390 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 119 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#17989118C211yesmaximal, characteristic
2C2×#14556556C211yesmaximal, characteristic, complemented
3#17988917C211yesmaximal, characteristic, complemented
4#17988893C212yesmaximal, complemented
5#17988808C212yesmaximal, complemented
6#17988745C211yesmaximal, characteristic, complemented
7#17988725C211yesmaximal, characteristic
8#17988681C212yesmaximal, complemented
9#17988678C212yesmaximal, complemented
10#17988637C211yesmaximal, characteristic, complemented
11#480×C73C211yesmaximal, characteristic
12C22×Dic146C2211yescharacteristic
13C2×Dic292C2212yes—
14C2×#11924016C2212yes—
15#14556584—21no—
16#14556582C2211yescharacteristic
17#14556578C2211yescharacteristic
18#14556572—21no—
19#14556570C2211yescharacteristic
20#14556556—21no—
21#14556556—21no—
22#14556556C2212yes—
23#14556556C2212yes—
24#14556556C2211yescharacteristic
25D4×Dic73—21no—
26D4×Dic73C2211yescharacteristic
27#14556547—21no—
28C2×#11924007—21no—
29C2×C4×Dic73—21no—
30C2×C4×Dic73C2211yescharacteristic
31#14556522C2212yes—
32#14556520C2212yes—
33#14556516C2212yes—
34#14556514C2212yes—
35#14556514C2212yes—
36C22⋊#10596831C2211yescharacteristic
37C8×Dic73C2212yes—
38#121×C73C2211yescharacteristic
39C2×C4⋊C4×C73C2211yescharacteristic
40#107×C73C2212yes—
41#102×C73C2212yes—
42C22⋊C8×C73C2211yescharacteristic
43C2×Dic146—21no—
44C2×Dic146—24no—
45C2×Dic146C2311yescharacteristic
46C2×Dic146C2312yes—
47C22×Dic73—21no—
48C22×Dic73—21no—
49C22×Dic73D411yescharacteristic
50C22×Dic73D411yescharacteristic
51Dic292—24no—
52#11924016—24no—
53C2×#10596831C2312yes—
54C4⋊Dic73—21no—
55C4⋊Dic73C2311yescharacteristic
56#11924007—21no—
57#11924007—22no—
58#11924007—22no—
59#11924007—21no—
60#11924007—21no—
61C22⋊Dic73—21no—
62C22⋊Dic73—21no—
63C22⋊Dic73—21no—
64C22⋊Dic73—21no—
65C4×Dic73—22no—
66C4×Dic73—22no—
67C4×Dic73—21no—
68C4×Dic73D411yescharacteristic
69C4×Dic73D411yescharacteristic
70C4×Dic73C2311yescharacteristic
71C4×Dic73C2311yescharacteristic
72C2×D4×C73—21no—
73C2×D4×C73C2311yescharacteristic
74C22×C4×C73—21no—
75C22×C4×C73C2311yescharacteristic
76C2×C8×C73C2312yes—
77C4⋊C4×C73—21no—
78C4⋊C4×C73C2312yes—
79C4⋊C4×C73C2311yescharacteristic
80C22⋊C4×C73—21no—
81C23×C73—21no—
82C23×C73C2×D411yescharacteristic
83D4×C73—22no—
84D4×C73—42no—
85C2×C4×C73—22no—
86C2×C4×C73—21no—
87C2×C4×C73—22no—
88C2×C4×C73—42no—
89C2×C4×C73C2×D411yescharacteristic
90C2×C4×C73C2411yescharacteristic
91C2×Dic73—24no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—21no—
96C2×Dic73—21no—
97C2×Dic73—42no—
98C2×Dic73C2×D411yescharacteristic
99C2×Dic73C2×D411yescharacteristic
100C2×Dic73C2×D411yescharacteristic
101C2×Dic73C2×D411yescharacteristic
102Dic146—24no—
103Dic146—22no—
104Dic146—22no—
105Dic146#4114yes—
106C8×C73—22no—
107#10596831—22no—
108C22×C73—21no—
109C22×C73—21no—
110C22×C73—41no—
111C22×C73—41no—
112C22×C73—41no—
113C22×C73#13512yes—
114C22×C73C22×D411yescharacteristic
115C4×C73—21no—
116C4×C73—42no—
117C4×C73—41no—
118C4×C73C2×#4112yes—
119Dic73—24no—
120Dic73—21no—
121Dic73—21no—
122Dic73—21no—
123Dic73—41no—
124Dic73—41no—
125Dic73#13712yes—
126C2×C73—22no—
127C2×C73—81no—
128C2×C73#52511yescharacteristic
129C2×C73C2×#13511yescharacteristic
130C2×C73C2×#13711yescharacteristic
131#3108—731nomaximal, Sylow
132C73#310811yescharacteristic, complemented, Sylow
133#529—731no—
134C2×C4×Q8—731no—
135#483—731no—
136#480D7311yescharacteristic
137#479—732no—
138#464—732no—
139#451—731no—
140#448—731no—
141C4×Q16—732no—
142C4×SD16—732no—
143#431—731no—
144C22×Q8—731no—
145C2×Q16—732no—
146C2×SD16—732no—
147#126—1461no—
148#125—731no—
149#124—731no—
150#123—1461no—
151C22⋊Q8—731no—
152#121C2×D7311yescharacteristic
153C4×Q8—732no—
154C4×Q8—732no—
155C4×Q8—731no—
156C4×Q8—1461no—
157C4×Q8—1461no—
158C4×D4—731no—
159C4×D4—1461no—
160#117—1461no—
161C2×C4⋊C4—1461no—
162C2×C4⋊C4C2×D7311yescharacteristic
163C2×C42—731no—
164C2×C42—1461no—
165#107C2×D7312yes—
166#106—732no—
167C4⋊C8—732no—
168#103—732no—
169#103—732no—
170#103—732no—
171#102C2×D7312yes—
172C22⋊C8—731no—
173C22⋊C8C2×D7311yescharacteristic
174C4×C8—732no—
175C2×Q8—732no—
176C2×Q8—731no—
177C2×Q8—1464no—
178C2×Q8—1461no—
179C2×D4—21no—
180C2×D4C22×D7311yescharacteristic
181C22×C4—21no—
182C22×C4—731no—
183C22×C4—731no—
184C22×C4—1461no—
185C22×C4—1461no—
186C22×C4C22×D7311yescharacteristic
187Q16—1464no—
188SD16—1464no—
189C2×C8—732no—
190C2×C8C22×D7312yes—
191C4⋊C4—21no—
192C4⋊C4—731no—
193C4⋊C4—1462no—
194C4⋊C4—1462no—
195C4⋊C4—1461no—
196C4⋊C4—1461no—
197C4⋊C4—1461no—
198C4⋊C4—1461no—
199C4⋊C4C22×D7312yes—
200C4⋊C4C22×D7311yescharacteristic
201C22⋊C4—21no—
202C22⋊C4—1461no—
203C22⋊C4—1461no—
204C22⋊C4—1461no—
205C22⋊C4—1461no—
206C42—731no—
207C42—731no—
208C42—731no—
209C42—731no—
210C42—1462no—
211C42—1462no—
212C42—1461no—
213C23—21no—
214C23D4×D7311yescharacteristic
215Q8—734no—
216Q8—1464no—
217Q8—1462no—
218Q8—1462no—
219D4—22no—
220D4—42no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—42no—
225C2×C4—2922no—
226C2×C4—731no—
227C2×C4—731no—
228C2×C4—731no—
229C2×C4—731no—
230C2×C4—1461no—
231C2×C4—1461no—
232C2×C4—1462no—
233C2×C4—1464no—
234C2×C4—1462no—
235C2×C4—1462no—
236C2×C4D4×D7311yescharacteristic
237C2×C4C23×D7311yescharacteristic
238C8—22no—
239C8—1462no—
240C22—21no—
241C22—21no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22#1455661012yes—
246C22C2×D4×D7311yescharacteristic
247C4—21no—
248C4—42no—
249C4—41no—
250C4—2921no—
251C4—2921no—
252C4—732no—
253C4—1461no—
254C4—1464no—
255C4—1461no—
256C4—1461no—
257C4#41×D7312yes—
258C2—22no—
259C2—81no—
260C2#1798909511yescharacteristic
261C2C2×#1455661011yescharacteristic
262C2#137×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#480×C73C2
socleC22×C73C22×D4
hypercenter#480D73
hypocenterC73#3108
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#14556556C2semidirect
3. #17988917C2semidirect
4. #17988893C2semidirect
5. #17988808C2semidirect
6. #17988745C2semidirect
8. #17988681C2semidirect
9. #17988678C2semidirect
10. #17988637C2semidirect
132. C73#3108semidirect