Finite Group Databasebeta

← #22620301

Subgroups — #22620301

Order 9344.

372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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#17989163C211yesmaximal, characteristic
2#17988957C212yesmaximal, complemented
3#17988949C212yesmaximal, complemented
4#17988944C212yesmaximal, complemented
5#17988939C212yesmaximal, complemented
6#17988595C211yesmaximal, characteristic, complemented
7#17988586C211yesmaximal, characteristic
8#17988581C211yesmaximal, characteristic
9C2×#14556514C211yesmaximal, characteristic, complemented
10#17988543C211yesmaximal, characteristic, complemented
11#544×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C22×Dic146C2211yescharacteristic
14C2×#11924012C2211yescharacteristic
15C22×#10596831C2211yescharacteristic
16#14556591C2212yes—
17#14556579C2212yes—
18#14556575—22no—
19#14556571—21no—
20#14556571—21no—
21#14556514C2211yescharacteristic
22#14556514C2212yes—
23#14556514C2212yes—
24#14556514C2212yes—
25#14556514C2212yes—
26#14556514C2212yes—
27#14556514C2211yescharacteristic
28#14556511C2211yescharacteristic
29#14556511C2212yes—
30#14556511C2211yescharacteristic
31#14556502C2212yes—
32C4×#10596831C2212yes—
33C4⋊Q8×C73—21no—
34C4⋊Q8×C73C2212yes—
35#125×C73—21no—
36#125×C73C2212yes—
37C22⋊Q8×C73—22no—
38#117×C73C2211yescharacteristic
39#117×C73C2211yescharacteristic
40C2×C4⋊C4×C73C2211yescharacteristic
41#11924028—22no—
42#11924028—22no—
43C2×Dic146—22no—
44C2×Dic146—22no—
45C2×Dic146—21no—
46C2×Dic146C2312yes—
47C2×Dic146C2311yescharacteristic
48C2×D292C2311yescharacteristic
49C2×C22⋊D73—21no—
50C22×Dic73—21no—
51C2×C4×D73—21no—
52#11924012—22no—
53C2×#10596831—22no—
54C2×#10596831C2311yescharacteristic
55C2×#10596831C2312yes—
56C2×#10596831C2311yescharacteristic
57C4⋊Dic73—22no—
58C4⋊Dic73—22no—
59#11924005—22no—
60#11924005—22no—
61C2×Q8×C73—22no—
62C22×C4×C73—21no—
63C22×C4×C73C2311yescharacteristic
64C4⋊C4×C73—21no—
65C4⋊C4×C73—22no—
66C4⋊C4×C73—22no—
67C4⋊C4×C73—22no—
68C4⋊C4×C73D411yescharacteristic
69C4⋊C4×C73D411yescharacteristic
70C4⋊C4×C73C2312yes—
71C4⋊C4×C73C2311yescharacteristic
72C4⋊C4×C73C2311yescharacteristic
73C22⋊C4×C73—21no—
74C22⋊C4×C73D412yes—
75C42×C73—21no—
76C42×C73C2312yes—
77C23×C73C2×D411yescharacteristic
78C22×D73—21no—
79Q8×C73—82no—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—22no—
83C2×C4×C73—81no—
84C2×C4×C73C2×D412yes—
85C2×C4×C73C2×D412yes—
86C2×C4×C73C2×D411yescharacteristic
87C2×C4×C73#4112yes—
88C2×C4×C73#4112yes—
89C2×C4×C73C2411yescharacteristic
90C22⋊D73—42no—
91C2×Dic73—22no—
92C2×Dic73—21no—
93C2×Dic73—42no—
94D292—21no—
95D292—21no—
96C4×D73—42no—
97Dic146—22no—
98Dic146—22no—
99Dic146—21no—
100Dic146—21no—
101Dic146—42no—
102#10596831—21no—
103#10596831—21no—
104#10596831—22no—
105C22×C73—21no—
106C22×C73—21no—
107C22×C73#12412yes—
108C22×C73C22×D411yescharacteristic
109C2×D73—41no—
110C2×D73—41no—
111C2×D73—41no—
112C4×C73—22no—
113C4×C73—22no—
114C4×C73—42no—
115C4×C73—41no—
116C4×C73—41no—
117C4×C73#12412yes—
118C4×C73C2×#4111yescharacteristic
119C4×C73C2×#4111yescharacteristic
120Dic73—42no—
121Dic73—41no—
122C2×C73—22no—
123C2×C73C2×#12411yescharacteristic
124C2×C73#57711yescharacteristic
125C2×C73#57811yescharacteristic
126D73—81no—
127#3137—731nomaximal, Sylow
128C73#313711yescharacteristic, complemented, Sylow
129#544D7311yescharacteristic, complemented
130#536—731no—
131#491—732no—
132#489—732no—
133#488—732no—
134#487—732no—
135#419—731no—
136#417—731no—
137#416—731no—
138C2×#103—731no—
139#405—731no—
140C2×#41—731no—
141C22×Q8—731no—
142C2×M16—731no—
143C22×C8—731no—
144C4⋊Q8—21no—
145C4⋊Q8—732no—
146C4⋊Q8C2×D7312yes—
147#125—21no—
148#125C2×D7312yes—
149#124—732no—
150#123—1462no—
151C22⋊Q8—22no—
152C22⋊Q8—1461no—
153C22⋊Q8—1461no—
154#117C2×D7311yescharacteristic
155#117C2×D7311yescharacteristic
156C2×C4⋊C4C2×D7311yescharacteristic
157#103—732no—
158#103—732no—
159#103—731no—
160#103—731no—
161#103—732no—
162#103—732no—
163#103—732no—
164#102—731no—
165#102—731no—
166#102—732no—
167#97—732no—
168C4×C8—732no—
169#41—1462no—
170#41—1462no—
171C2×Q8—22no—
172C2×Q8—732no—
173C2×Q8—731no—
174C2×Q8—1462no—
175C2×Q8—1462no—
176C2×Q8—1461no—
177C2×D4—731no—
178C2×D4—1461no—
179C22×C4—21no—
180C22×C4—1461no—
181C22×C4—1461no—
182C22×C4C22×D7311yescharacteristic
183M16—1462no—
184C2×C8—731no—
185C2×C8—732no—
186C2×C8—731no—
187C2×C8—1462no—
188C4⋊C4—21no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—1462no—
193C4⋊C4—1462no—
194C4⋊C4C22⋊D7311yescharacteristic
195C4⋊C4C22⋊D7311yescharacteristic
196C4⋊C4C22×D7312yes—
197C4⋊C4C22×D7311yescharacteristic
198C4⋊C4C22×D7311yescharacteristic
199C22⋊C4—21no—
200C22⋊C4—1462no—
201C22⋊C4—1462no—
202C22⋊C4C22⋊D7312yes—
203C42—21no—
204C42C22×D7312yes—
205C23—1461no—
206C23C2×C22⋊D7311yescharacteristic
207Q8—82no—
208Q8—2922no—
209Q8—1462no—
210Q8—1462no—
211Q8—1461no—
212Q8—1461no—
213D4—2922no—
214D4—1461no—
215D4—1461no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—81no—
220C2×C4—2922no—
221C2×C4—2922no—
222C2×C4—1462no—
223C2×C4—1461no—
224C2×C4C2×C22⋊D7312yes—
225C2×C4C2×C22⋊D7312yes—
226C2×C4C2×C22⋊D7311yescharacteristic
227C2×C4#1192402912yes—
228C2×C4#1192402912yes—
229C2×C4C23×D7311yescharacteristic
230C8—1461no—
231C8—1461no—
232C8—1462no—
233C22—21no—
234C22—21no—
235C22—2921no—
236C22—2921no—
237C22—2921no—
238C22#1455658012yes—
239C22C22×C22⋊D7311yescharacteristic
240C4—22no—
241C4—22no—
242C4—42no—
243C4—41no—
244C4—41no—
245C4—2921no—
246C4—2922no—
247C4#1455658012yes—
248C4C2×#1192402911yescharacteristic
249C4C2×#1192402911yescharacteristic
250C2—22no—
251C2—5841no—
252C2C2×#1455658011yescharacteristic
253C2#1798939811yescharacteristic
254C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#544×C73C2
socleC22×C73C22×D4
hypercenter#544D73
hypocenterC73#3137
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
2. #17988957C2semidirect
3. #17988949C2semidirect
4. #17988944C2semidirect
5. #17988939C2semidirect
6. #17988595C2semidirect
9. C2×#14556514C2semidirect
10. #17988543C2semidirect
11. #544×C73C2semidirect
128. C73#3137semidirect
129. #544D73semidirect