Finite Group Databasebeta

← #22619905

Subgroups — #22619905

Order 9344.

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

normal subgroups only

This group has 398 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#17989070C211yesmaximal, characteristic, complemented
2#17988925C212yesmaximal, complemented
3#17988920C212yesmaximal, complemented
4#17988908C212yesmaximal, complemented
5#17988898C212yesmaximal, complemented
6#17988627C211yesmaximal, characteristic, complemented
7C2×#14556524C211yesmaximal, characteristic, complemented
8#17988588C211yesmaximal, characteristic, complemented
9#17988583C211yesmaximal, characteristic, complemented
10#17988554C211yesmaximal, characteristic, complemented
11#537×C73C211yesmaximal, characteristic
12C2×#11924012C2211yescharacteristic
13C22×#10596831C2211yescharacteristic
14Q8×Dic73—21no—
15D4×Dic73—22no—
16D4×Dic73—21no—
17#14556550C2211yescharacteristic
18#14556550C2212yes—
19C2×C4⋊Dic73C2211yescharacteristic
20C2×C4⋊Dic73C2212yes—
21#14556524C2212yes—
22#14556524C2212yes—
23#14556524C2212yes—
24#14556522C2212yes—
25#14556515C2211yescharacteristic
26#14556515C2212yes—
27#14556515C2211yescharacteristic
28#14556512C2211yescharacteristic
29#14556512C2212yes—
30#14556512C2211yescharacteristic
31C22⋊#10596831C2212yes—
32C22⋊#10596831C2212yes—
33C2×#41×C73C2211yescharacteristic
34C2×#41×C73C2211yescharacteristic
35C22⋊Q8×C73—21no—
36C22⋊Q8×C73C2212yes—
37#121×C73—21no—
38#121×C73—22no—
39#121×C73C2212yes—
40C2×C4⋊C4×C73C2211yescharacteristic
41C22×Dic73—22no—
42C22×Dic73—21no—
43#11924012—22no—
44C2×#10596831—22no—
45C2×#10596831C2312yes—
46C2×#10596831C2311yescharacteristic
47C2×#10596831C2311yescharacteristic
48C4⋊Dic73—22no—
49C4⋊Dic73—21no—
50C4⋊Dic73C2311yescharacteristic
51C4⋊Dic73C2311yescharacteristic
52C4⋊Dic73C2312yes—
53C22⋊Dic73—22no—
54C22⋊Dic73—21no—
55C4×Dic73—22no—
56C4×Dic73—21no—
57#41×C73—22no—
58#41×C73—22no—
59#41×C73—22no—
60#41×C73—22no—
61C2×Q8×C73D411yescharacteristic
62C2×Q8×C73C2311yescharacteristic
63C2×D4×C73—21no—
64C2×D4×C73—22no—
65C2×D4×C73D412yes—
66C2×D4×C73D411yescharacteristic
67C2×D4×C73C2311yescharacteristic
68C22×C4×C73—21no—
69C22×C4×C73—21no—
70C22×C4×C73C2312yes—
71C22×C4×C73C2311yescharacteristic
72C4⋊C4×C73—21no—
73C4⋊C4×C73—22no—
74C4⋊C4×C73C2312yes—
75C22⋊C4×C73—22no—
76C22⋊C4×C73—22no—
77C23×C73—21no—
78C23×C73C2×D412yes—
79C23×C73C2×D411yescharacteristic
80Q8×C73—22no—
81Q8×C73—21no—
82Q8×C73—21no—
83D4×C73—24no—
84D4×C73—22no—
85D4×C73—21no—
86D4×C73—21no—
87D4×C73—42no—
88D4×C73—82no—
89C2×C4×C73—22no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—21no—
93C2×C4×C73—42no—
94C2×C4×C73—81no—
95C2×C4×C73C2×D412yes—
96C2×C4×C73C2×D411yescharacteristic
97C2×C4×C73#4112yes—
98C2×C4×C73#4112yes—
99C2×C4×C73C2411yescharacteristic
100C2×Dic73—21no—
101C2×Dic73—22no—
102C2×Dic73—21no—
103C2×Dic73—81no—
104C2×Dic73—82no—
105#10596831—21no—
106#10596831—21no—
107#10596831—22no—
108C22×C73—21no—
109C22×C73—21no—
110C22×C73—22no—
111C22×C73—22no—
112C22×C73—22no—
113C22×C73—41no—
114C22×C73—41no—
115C22×C73—41no—
116C22×C73#12312yes—
117C22×C73C22×D411yescharacteristic
118C4×C73—22no—
119C4×C73—41no—
120C4×C73—42no—
121C4×C73#12312yes—
122C4×C73C2×#4111yescharacteristic
123C4×C73C2×#4111yescharacteristic
124Dic73—42no—
125Dic73—41no—
126Dic73—41no—
127C2×C73—22no—
128C2×C73—42no—
129C2×C73—81no—
130C2×C73C2×#12311yescharacteristic
131C2×C73#57611yescharacteristic
132C2×C73#57811yescharacteristic
133#3098—731nomaximal, Sylow
134C73#309811yescharacteristic, complemented, Sylow
135#537D7311yescharacteristic
136#520—731no—
137#485—732no—
138#484—732no—
139#482—732no—
140#480—732no—
141#428—731no—
142C2×#107—731no—
143#417—731no—
144#416—731no—
145#408—731no—
146C2×#41C2×D7311yescharacteristic
147C2×#41C2×D7311yescharacteristic
148C2×M16—731no—
149C22×C8—731no—
150C22⋊Q8—21no—
151C22⋊Q8C2×D7312yes—
152#121—21no—
153#121—22no—
154#121C2×D7312yes—
155C4×Q8—1461no—
156C4×D4—1462no—
157C4×D4—1461no—
158#117—731no—
159#117—732no—
160C2×C4⋊C4—731no—
161C2×C4⋊C4—732no—
162C2×C4⋊C4C2×D7311yescharacteristic
163#107—732no—
164#107—732no—
165#107—732no—
166#106—732no—
167#103—731no—
168#103—731no—
169#103—732no—
170#102—731no—
171#102—731no—
172#102—732no—
173C22⋊C8—732no—
174C22⋊C8—732no—
175#41—22no—
176#41—22no—
177#41—22no—
178#41—22no—
179C2×Q8C22⋊D7311yescharacteristic
180C2×Q8C22×D7311yescharacteristic
181C2×D4—21no—
182C2×D4—22no—
183C2×D4C22⋊D7312yes—
184C2×D4C22⋊D7311yescharacteristic
185C2×D4C22×D7311yescharacteristic
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—1462no—
189C22×C4—1461no—
190C22×C4C22×D7312yes—
191C22×C4C22×D7311yescharacteristic
192M16—1462no—
193C2×C8—732no—
194C2×C8—731no—
195C2×C8—731no—
196C2×C8—1462no—
197C4⋊C4—21no—
198C4⋊C4—22no—
199C4⋊C4—731no—
200C4⋊C4—731no—
201C4⋊C4—732no—
202C4⋊C4—1462no—
203C4⋊C4—1461no—
204C4⋊C4C22×D7312yes—
205C22⋊C4—22no—
206C22⋊C4—22no—
207C22⋊C4—1462no—
208C22⋊C4—1461no—
209C42—1462no—
210C42—1461no—
211C23—21no—
212C23C2×C22⋊D7312yes—
213C23C2×C22⋊D7311yescharacteristic
214Q8—22no—
215Q8—21no—
216Q8—21no—
217D4—24no—
218D4—22no—
219D4—21no—
220D4—21no—
221D4—42no—
222D4—82no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—81no—
229C2×C4—5841no—
230C2×C4—5842no—
231C2×C4—1461no—
232C2×C4—1462no—
233C2×C4—1461no—
234C2×C4C2×C22⋊D7312yes—
235C2×C4C2×C22⋊D7311yescharacteristic
236C2×C4#1192402712yes—
237C2×C4#1192402712yes—
238C2×C4C23×D7311yescharacteristic
239C8—1461no—
240C8—1461no—
241C8—1462no—
242C22—21no—
243C22—21no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22#1455657212yes—
251C22C22×C22⋊D7311yescharacteristic
252C4—22no—
253C4—42no—
254C4—41no—
255C4—2922no—
256C4—2921no—
257C4—2921no—
258C4#1455657212yes—
259C4C2×#1192402711yescharacteristic
260C4C2×#1192402711yescharacteristic
261C2—22no—
262C2—42no—
263C2—81no—
264C2C2×#1455657211yescharacteristic
265C2#1798939011yescharacteristic
266C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#537×C73C2
socleC22×C73C22×D4
hypercenter#537D73
hypocenterC73#3098
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #17989070C2semidirect
2. #17988925C2semidirect
3. #17988920C2semidirect
4. #17988908C2semidirect
5. #17988898C2semidirect
6. #17988627C2semidirect
7. C2×#14556524C2semidirect
8. #17988588C2semidirect
9. #17988583C2semidirect
10. #17988554C2semidirect
134. C73#3098semidirect