Finite Group Databasebeta

← #22620822

Subgroups — #22620822

Order 9344.

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

normal subgroups only

This group has 378 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#17989158C211yesmaximal, characteristic
2#17988928C212yesmaximal, complemented
3#17988925C212yesmaximal, complemented
4#17988843C212yesmaximal, complemented
5#17988826C212yesmaximal, complemented
6#17988743C212yesmaximal, complemented
7#17988742C212yesmaximal, complemented
8#17988554C211yesmaximal, characteristic
9#536×C73C211yesmaximal, characteristic
10C22×Dic146C2211yescharacteristic
11C2×#11924018C2212yes—
12C2×#11924018C2212yes—
13C2×#11924012C2211yescharacteristic
14C22×#10596831C2211yescharacteristic
15#14556589—21no—
16#14556578—21no—
17#14556572—21no—
18#14556572—21no—
19#14556570C2212yes—
20#14556570C2212yes—
21#14556550C2211yescharacteristic
22#14556524C2212yes—
23#14556522C2212yes—
24#14556515C2212yes—
25#14556515C2212yes—
26#14556514C2212yes—
27#14556514C2212yes—
28C22⋊#10596831C2212yes—
29C22⋊#10596831C2212yes—
30C2×#41×C73C2211yescharacteristic
31C22×Q8×C73C2211yescharacteristic
32C4⋊Q8×C73—21no—
33#124×C73—21no—
34#123×C73—21no—
35#123×C73—21no—
36C22⋊Q8×C73C2212yes—
37C22⋊Q8×C73C2212yes—
38#117×C73C2211yescharacteristic
39C2×Dic146—21no—
40C2×Dic146—41no—
41C2×Dic146—41no—
42C2×Dic146C2312yes—
43C22×Dic73—21no—
44#11924018—42no—
45#11924018—42no—
46#11924012—41no—
47C2×#10596831—41no—
48C2×#10596831C2312yes—
49C2×#10596831C2312yes—
50C4⋊Dic73C2312yes—
51#11924007—22no—
52#11924007—22no—
53C22⋊Dic73—21no—
54C22⋊Dic73—22no—
55C22⋊Dic73—22no—
56C4×Dic73—21no—
57#41×C73—41no—
58#41×C73—41no—
59C2×Q8×C73—21no—
60C2×Q8×C73—41no—
61C2×Q8×C73—41no—
62C2×Q8×C73D411yescharacteristic
63C2×Q8×C73C2312yes—
64C2×D4×C73D411yescharacteristic
65C2×D4×C73D411yescharacteristic
66C2×D4×C73D411yescharacteristic
67C22×C4×C73—21no—
68C22×C4×C73C2311yescharacteristic
69C22×C4×C73C2311yescharacteristic
70C22×C4×C73C2311yescharacteristic
71C4⋊C4×C73—22no—
72C4⋊C4×C73—22no—
73C4⋊C4×C73C2312yes—
74C22⋊C4×C73—21no—
75C22⋊C4×C73—22no—
76C22⋊C4×C73—22no—
77C42×C73—21no—
78C23×C73C2×D411yescharacteristic
79C23×C73C2×D411yescharacteristic
80C23×C73C2×D411yescharacteristic
81Q8×C73—22no—
82Q8×C73—22no—
83Q8×C73—41no—
84Q8×C73—42no—
85D4×C73—41no—
86D4×C73—41no—
87D4×C73—41no—
88C2×C4×C73—21no—
89C2×C4×C73—21no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—21no—
94C2×C4×C73—22no—
95C2×C4×C73—22no—
96C2×C4×C73—42no—
97C2×C4×C73C2×D411yescharacteristic
98C2×C4×C73C2×D411yescharacteristic
99C2×C4×C73C2×D411yescharacteristic
100C2×C4×C73C2411yescharacteristic
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—42no—
104Dic146—22no—
105Dic146—22no—
106Dic146—42no—
107#10596831—22no—
108#10596831—22no—
109C22×C73—21no—
110C22×C73—21no—
111C22×C73—21no—
112C22×C73—22no—
113C22×C73—22no—
114C22×C73—22no—
115C22×C73C22×D411yescharacteristic
116C4×C73—21no—
117C4×C73—21no—
118C4×C73—21no—
119C4×C73—42no—
120C4×C73—42no—
121C4×C73H(5,𝔽2)11yescharacteristic
122C4×C73H(5,𝔽2)11yescharacteristic
123Dic73—42no—
124Dic73—42no—
125C2×C73—41no—
126C2×C73—41no—
127C2×C73—41no—
128C2×C73#53411yescharacteristic
129C2×C73#57812yes—
130#3202—731nomaximal, Sylow
131C73#320211yescharacteristic, complemented, Sylow
132#536—731no—
133#536D7311yescharacteristic
134#485—732no—
135#485—732no—
136#470—732no—
137#467—732no—
138#451—732no—
139#451—732no—
140#408—731no—
141C2×#41C2×D7311yescharacteristic
142C22×Q8—731no—
143C22×Q8C2×D7311yescharacteristic
144C2×Q16—732no—
145C2×Q16—732no—
146C2×M16—731no—
147C22×C8—731no—
148C4⋊Q8—21no—
149C4⋊Q8—1461no—
150#124—21no—
151#124—1461no—
152#123—21no—
153#123—21no—
154#123—1461no—
155#123—1461no—
156C22⋊Q8—732no—
157C22⋊Q8—732no—
158C22⋊Q8C2×D7312yes—
159C22⋊Q8C2×D7312yes—
160#117—731no—
161#117C2×D7311yescharacteristic
162#107—732no—
163#106—732no—
164#103—732no—
165#103—732no—
166#103—732no—
167#103—732no—
168C22⋊C8—732no—
169C22⋊C8—732no—
170#41—41no—
171#41—41no—
172C2×Q8—21no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—2921no—
176C2×Q8—2921no—
177C2×Q8—732no—
178C2×Q8—1461no—
179C2×Q8C22⋊D7311yescharacteristic
180C2×Q8C22×D7312yes—
181C2×D4C22⋊D7311yescharacteristic
182C2×D4C22⋊D7311yescharacteristic
183C2×D4C22⋊D7311yescharacteristic
184C22×C4—21no—
185C22×C4—1461no—
186C22×C4C22×D7311yescharacteristic
187C22×C4C22×D7311yescharacteristic
188C22×C4C22×D7311yescharacteristic
189Q16—2922no—
190Q16—2922no—
191M16—2921no—
192C2×C8—2921no—
193C2×C8—732no—
194C2×C8—732no—
195C4⋊C4—22no—
196C4⋊C4—22no—
197C4⋊C4—732no—
198C4⋊C4—1462no—
199C4⋊C4—1462no—
200C4⋊C4C22×D7312yes—
201C22⋊C4—21no—
202C22⋊C4—22no—
203C22⋊C4—22no—
204C22⋊C4—1461no—
205C22⋊C4—1462no—
206C22⋊C4—1462no—
207C42—21no—
208C42—1461no—
209C23C2×C22⋊D7311yescharacteristic
210C23C2×C22⋊D7311yescharacteristic
211C23C2×C22⋊D7311yescharacteristic
212Q8—22no—
213Q8—22no—
214Q8—41no—
215Q8—42no—
216Q8—2922no—
217Q8—1462no—
218Q8—1462no—
219D4—41no—
220D4—41no—
221D4—41no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—42no—
231C2×C4—2922no—
232C2×C4—1462no—
233C2×C4—1462no—
234C2×C4C2×C22⋊D7311yescharacteristic
235C2×C4C2×C22⋊D7311yescharacteristic
236C2×C4C2×C22⋊D7311yescharacteristic
237C2×C4C23×D7311yescharacteristic
238C8—1462no—
239C8—1462no—
240C22—21no—
241C22—21no—
242C22—21no—
243C22—22no—
244C22—22no—
245C22—22no—
246C22C22×C22⋊D7311yescharacteristic
247C4—21no—
248C4—21no—
249C4—21no—
250C4—42no—
251C4—42no—
252C4—2922no—
253C4—2922no—
254C4#1455663611yescharacteristic
255C4#1455663611yescharacteristic
256C2—41no—
257C2—41no—
258C2—41no—
259C2#1798914611yescharacteristic
260C2#1798940212yes—
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#536×C73C2
socleC22×C73C22×D4
hypercenter#536D73
hypocenterC73#3202
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #17988928C2semidirect
3. #17988925C2semidirect
4. #17988843C2semidirect
5. #17988826C2semidirect
6. #17988743C2semidirect
7. #17988742C2semidirect
131. C73#3202semidirect