Finite Group Databasebeta

← #22622551

Subgroups — #22622551

Order 9344.

354 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 123 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#17989294C211yesmaximal, characteristic, complemented
2#17988990C211yesmaximal, characteristic, complemented
3#17988928C212yesmaximal, complemented
4#17988898C212yesmaximal, complemented
5#17988879C211yesmaximal, characteristic, complemented
6#17988877C211yesmaximal, characteristic, complemented
7#17988831C212yesmaximal, complemented
8C4×#11924016C211yesmaximal, characteristic, complemented
9#17988665C211yesmaximal, characteristic, complemented
10#17988630C212yesmaximal, complemented
11#555×C73C211yesmaximal, characteristic
12C2×#11924016C2211yescharacteristic
13C2×#11924012C2212yes—
14#14556591C2211yescharacteristic
15#14556582—21no—
16#14556570C2212yes—
17#14556568—22no—
18C4×Dic146C2211yescharacteristic
19D4×Dic73—21no—
20C2×C4⋊Dic73C2212yes—
21#14556524C2212yes—
22#14556524C2212yes—
23#14556524C2212yes—
24#14556522C2212yes—
25#14556522C2211yescharacteristic
26C4⋊#10596831C2211yescharacteristic
27#14556514C2212yes—
28#14556514C2211yescharacteristic
29#14556512C2212yes—
30#14556512C2211yescharacteristic
31C22⋊#10596831C2212yes—
32C4×#10596831C2211yescharacteristic
33C4⋊Q8×C73C2211yescharacteristic
34#124×C73—22no—
35#121×C73—21no—
36#121×C73C2212yes—
37C4×D4×C73C2211yescharacteristic
38C4×D4×C73C2211yescharacteristic
39#117×C73—21no—
40#117×C73C2212yes—
41C2×Dic146—21no—
42C2×Dic146C2311yescharacteristic
43C22×Dic73—22no—
44#11924016—22no—
45#11924012—24no—
46C2×#10596831C2311yescharacteristic
47C2×#10596831C2312yes—
48C2×#10596831C2311yescharacteristic
49C4⋊Dic73—22no—
50C4⋊Dic73—21no—
51C4⋊Dic73C2311yescharacteristic
52C4⋊Dic73C2312yes—
53#11924007—21no—
54#11924007—22no—
55C22⋊Dic73—22no—
56C4×Dic73—21no—
57C2×Q8×C73—21no—
58C2×D4×C73—22no—
59C2×D4×C73D411yescharacteristic
60C2×D4×C73C2311yescharacteristic
61C22×C4×C73—21no—
62C22×C4×C73C2312yes—
63C4⋊C4×C73—21no—
64C4⋊C4×C73D411yescharacteristic
65C4⋊C4×C73C2311yescharacteristic
66C4⋊C4×C73C2312yes—
67C22⋊C4×C73—22no—
68C22⋊C4×C73—22no—
69C22⋊C4×C73—21no—
70C22⋊C4×C73D412yes—
71C42×C73—22no—
72C42×C73C2311yescharacteristic
73C23×C73—21no—
74C23×C73C2×D412yes—
75Q8×C73—81no—
76D4×C73—22no—
77D4×C73—21no—
78D4×C73—21no—
79D4×C73—82no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—21no—
83C2×C4×C73—22no—
84C2×C4×C73—42no—
85C2×C4×C73C2×D412yes—
86C2×C4×C73C2×D411yescharacteristic
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73C2411yescharacteristic
89C2×Dic73—21no—
90C2×Dic73—21no—
91C2×Dic73—22no—
92C2×Dic73—82no—
93Dic146—21no—
94Dic146—21no—
95Dic146—81no—
96#10596831—22no—
97#10596831—21no—
98#10596831#4112yes—
99C22×C73—22no—
100C22×C73—22no—
101C22×C73—22no—
102C22×C73—41no—
103C22×C73—41no—
104C22×C73—41no—
105C22×C73C22×D411yescharacteristic
106C4×C73—22no—
107C4×C73—21no—
108C4×C73—41no—
109C4×C73—42no—
110C4×C73#13712yes—
111C4×C73C2×#4111yescharacteristic
112C4×C732−1+411yescharacteristic
113Dic73—41no—
114Dic73—42no—
115Dic73—41no—
116C2×C73—42no—
117C2×C73—81no—
118C2×C73#54711yescharacteristic
119C2×C73C2×#13711yescharacteristic
120C2×C73#57611yescharacteristic
121#3357—731nomaximal, Sylow
122C73#335711yescharacteristic, complemented, Sylow
123#555D7311yescharacteristic
124#554—731no—
125#500—731no—
126#485—732no—
127#480—732no—
128#477—731no—
129#476—731no—
130#468—732no—
131C4×SD16—731no—
132#436—731no—
133#428—732no—
134C2×SD16—731no—
135C2×M16—732no—
136C4⋊Q8—731no—
137C4⋊Q8C2×D7311yescharacteristic
138#125—1461no—
139#124—22no—
140C22⋊Q8—732no—
141C22⋊Q8—1462no—
142#121—21no—
143#121C2×D7312yes—
144C4×Q8—731no—
145C4×D4—1461no—
146C4×D4C2×D7311yescharacteristic
147C4×D4C2×D7311yescharacteristic
148#117—21no—
149#117C2×D7312yes—
150C2×C4⋊C4—732no—
151#107—732no—
152#107—732no—
153#107—732no—
154#106—731no—
155#106—732no—
156C4⋊C8—731no—
157#103—731no—
158#103—732no—
159#102—731no—
160#102—732no—
161C22⋊C8—732no—
162C4×C8—731no—
163C2×Q8—21no—
164C2×Q8—731no—
165C2×Q8—1461no—
166C2×D4—22no—
167C2×D4C22⋊D7311yescharacteristic
168C2×D4C22×D7311yescharacteristic
169C22×C4—21no—
170C22×C4—1462no—
171C22×C4C22×D7312yes—
172SD16—1462no—
173M16—1464no—
174C2×C8—731no—
175C2×C8—731no—
176C2×C8—732no—
177C4⋊C4—21no—
178C4⋊C4—731no—
179C4⋊C4—732no—
180C4⋊C4—1461no—
181C4⋊C4—1462no—
182C4⋊C4—1462no—
183C4⋊C4—1461no—
184C4⋊C4C22⋊D7311yescharacteristic
185C4⋊C4C22×D7311yescharacteristic
186C4⋊C4C22×D7312yes—
187C22⋊C4—22no—
188C22⋊C4—22no—
189C22⋊C4—21no—
190C22⋊C4—1462no—
191C22⋊C4C22⋊D7312yes—
192C42—22no—
193C42—1461no—
194C42C22×D7311yescharacteristic
195C23—21no—
196C23C2×C22⋊D7312yes—
197Q8—81no—
198Q8—5841no—
199Q8—1461no—
200Q8—1461no—
201D4—22no—
202D4—21no—
203D4—21no—
204D4—82no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—42no—
210C2×C4—5842no—
211C2×C4—1461no—
212C2×C4—1461no—
213C2×C4—1462no—
214C2×C4C2×C22⋊D7312yes—
215C2×C4C2×C22⋊D7311yescharacteristic
216C2×C4C2×C22⋊D7311yescharacteristic
217C2×C4C23×D7311yescharacteristic
218C8—732no—
219C8—1462no—
220C8—1461no—
221C22—22no—
222C22—22no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22C22×C22⋊D7311yescharacteristic
228C4—21no—
229C4—22no—
230C4—41no—
231C4—42no—
232C4—2921no—
233C4—2922no—
234C4—2921no—
235C4#1455662112yes—
236C4#41×D7311yescharacteristic
237C4#1455663811yescharacteristic
238C2—42no—
239C2—81no—
240C2#1798923611yescharacteristic
241C2C2×#1455662111yescharacteristic
242C2#1798939011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#555×C73C2
socleC22×C73C22×D4
hypercenter#555D73
hypocenterC73#3357
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #17989294C2semidirect
2. #17988990C2semidirect
3. #17988928C2semidirect
4. #17988898C2semidirect
5. #17988879C2semidirect
6. #17988877C2semidirect
7. #17988831C2semidirect
8. C4×#11924016C2semidirect
9. #17988665C2semidirect
10. #17988630C2semidirect
122. C73#3357semidirect