Finite Group Databasebeta

← #22620105

Subgroups — #22620105

Order 9344.

386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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#17989123C211yesmaximal, characteristic
2C2×#14556556C211yesmaximal, characteristic, complemented
3#17988905C211yesmaximal, characteristic
4#17988893C212yesmaximal, complemented
5#17988812C212yesmaximal, complemented
6#17988742C211yesmaximal, characteristic, complemented
7#17988728C211yesmaximal, characteristic
8#17988691C212yesmaximal, complemented
9#17988686C212yesmaximal, complemented
10#17988641C211yesmaximal, characteristic, complemented
11#484×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C2×#11924018C2212yes—
14C2×#11924017C2212yes—
15#14556586—21no—
16#14556582C2211yescharacteristic
17#14556580C2211yescharacteristic
18#14556575—21no—
19#14556565C2211yescharacteristic
20Q8×Dic73C2211yescharacteristic
21#14556556—21no—
22#14556556—21no—
23#14556556C2212yes—
24#14556556C2212yes—
25#14556553C2211yescharacteristic
26#14556551—21no—
27#14556549—21no—
28C2×#11924007—21no—
29C2×C4×Dic73—21no—
30C2×C4×Dic73C2211yescharacteristic
31#14556522C2212yes—
32#14556520C2212yes—
33#14556516C2212yes—
34#14556514C2212yes—
35#14556511C2212yes—
36C22⋊#10596831C2211yescharacteristic
37#14556501C2212yes—
38C22⋊Q8×C73C2211yescharacteristic
39C2×C4⋊C4×C73C2211yescharacteristic
40#107×C73C2212yes—
41#103×C73C2212yes—
42C22⋊C8×C73C2211yescharacteristic
43C2×Dic146—21no—
44C2×Dic146—24no—
45C2×Dic146C2312yes—
46C2×D292C2311yescharacteristic
47C2×C22⋊D73—21no—
48C22×Dic73—21no—
49C22×Dic73D411yescharacteristic
50C22×Dic73D411yescharacteristic
51C2×C4×D73—21no—
52#11924018—24no—
53#11924017—24no—
54C2×#10596831C2312yes—
55C4⋊Dic73—21no—
56C4⋊Dic73—21no—
57C4⋊Dic73C2311yescharacteristic
58#11924007—22no—
59#11924007—22no—
60#11924007—21no—
61#11924005—21no—
62#11924005—21no—
63#11924005—21no—
64#11924005—21no—
65C4×Dic73—22no—
66C4×Dic73—22no—
67C4×Dic73—21no—
68C4×Dic73D411yescharacteristic
69C4×Dic73D411yescharacteristic
70C4×Dic73C2311yescharacteristic
71C4×Dic73C2311yescharacteristic
72C2×Q8×C73C2311yescharacteristic
73C22×C4×C73—21no—
74C22×C4×C73C2311yescharacteristic
75C2×C8×C73C2312yes—
76C4⋊C4×C73—21no—
77C4⋊C4×C73—21no—
78C4⋊C4×C73C2312yes—
79C4⋊C4×C73C2311yescharacteristic
80C22⋊C4×C73—21no—
81C23×C73C2×D411yescharacteristic
82C22×D73—21no—
83Q8×C73—22no—
84C2×C4×C73—22no—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73—22no—
88C2×C4×C73—42no—
89C2×C4×C73C2×D411yescharacteristic
90C2×C4×C73C2411yescharacteristic
91C22⋊D73—42no—
92C2×Dic73—24no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—21no—
96C2×Dic73—41no—
97C2×Dic73C2×D411yescharacteristic
98C2×Dic73C2×D411yescharacteristic
99C2×Dic73C2×D411yescharacteristic
100C2×Dic73C2×D411yescharacteristic
101D292—22no—
102C4×D73—42no—
103Dic146—24no—
104Dic146—22no—
105Dic146#4114yes—
106C8×C73—22no—
107#10596831—22no—
108C22×C73—21no—
109C22×C73—21no—
110C22×C73#13712yes—
111C22×C73C22×D411yescharacteristic
112C2×D73—41no—
113C2×D73—41no—
114C2×D73—41no—
115C4×C73—21no—
116C4×C73—41no—
117C4×C73—41no—
118C4×C73—42no—
119C4×C73C2×#4112yes—
120Dic73—24no—
121Dic73—21no—
122Dic73—21no—
123Dic73—21no—
124Dic73—21no—
125Dic73—41no—
126C2×C73—22no—
127C2×C73#52511yescharacteristic
128C2×C73C2×#13711yescharacteristic
129C2×C73#57511yescharacteristic
130D73—81no—
131#3117—731nomaximal, Sylow
132C73#311711yescharacteristic, complemented, Sylow
133#529—731no—
134C2×C4×Q8—731no—
135#484D7311yescharacteristic, complemented
136#481—731no—
137#479—732no—
138#464—732no—
139#451—731no—
140#448—731no—
141#441—732no—
142#440—732no—
143#432—731no—
144C22×Q8—731no—
145C2×Q16—732no—
146C2×SD16—732no—
147#126—1461no—
148#125—731no—
149#124—731no—
150#123—1461no—
151C22⋊Q8C2×D7311yescharacteristic
152#121—731no—
153C4×Q8—731no—
154C4×Q8—732no—
155C4×Q8—732no—
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#103C2×D7312yes—
171#102—732no—
172C22⋊C8—731no—
173C22⋊C8C2×D7311yescharacteristic
174#97—732no—
175C2×Q8—732no—
176C2×Q8—1464no—
177C2×Q8—1461no—
178C2×Q8C22×D7311yescharacteristic
179C2×D4—731no—
180C2×D4—1461no—
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—21no—
193C4⋊C4—731no—
194C4⋊C4—1462no—
195C4⋊C4—1462no—
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—1461no—
214C23D4×D7311yescharacteristic
215Q8—22no—
216Q8—734no—
217Q8—1464no—
218Q8—1462no—
219D4—2922no—
220D4—1462no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—42no—
226C2×C4—2922no—
227C2×C4—2921no—
228C2×C4—731no—
229C2×C4—731no—
230C2×C4—731no—
231C2×C4—731no—
232C2×C4—1461no—
233C2×C4—1464no—
234C2×C4—1462no—
235C2×C4—1462no—
236C2×C4D4×D7311yescharacteristic
237C2×C4C23×D7311yescharacteristic
238C8—22no—
239C8—1462no—
240C22—21no—
241C22—21no—
242C22—2921no—
243C22—2921no—
244C22—2921no—
245C22#1455662312yes—
246C22C2×D4×D7311yescharacteristic
247C4—21no—
248C4—42no—
249C4—41no—
250C4—41no—
251C4—2921no—
252C4—1461no—
253C4—1461no—
254C4—1461no—
255C4—1461no—
256C4—1464no—
257C4#41×D7312yes—
258C2—22no—
259C2—5841no—
260C2#1798909511yescharacteristic
261C2C2×#1455662311yescharacteristic
262C2#1798938311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#484×C73C2
socleC22×C73C22×D4
hypercenter#484D73
hypocenterC73#3117
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×#14556556C2semidirect
4. #17988893C2semidirect
5. #17988812C2semidirect
6. #17988742C2semidirect
8. #17988691C2semidirect
9. #17988686C2semidirect
10. #17988641C2semidirect
11. #484×C73C2semidirect
132. C73#3117semidirect
135. #484D73semidirect