Finite Group Databasebeta

← #22622515

Subgroups — #22622515

Order 9344.

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

normal subgroups only

This group has 374 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#17989307C211yesmaximal, characteristic, complemented
2#17988990C211yesmaximal, characteristic, complemented
3#17988922C212yesmaximal, complemented
4#17988908C212yesmaximal, complemented
5#17988869C211yesmaximal, characteristic, complemented
6#17988867C211yesmaximal, characteristic, complemented
7#17988831C212yesmaximal, complemented
8C4×#11924016C211yesmaximal, characteristic, complemented
9#17988665C211yesmaximal, characteristic, complemented
10#17988627C212yesmaximal, complemented
11#547×C73C211yesmaximal, characteristic
12C2×#11924016C2211yescharacteristic
13C2×#11924012C2212yes—
14#14556591C2211yescharacteristic
15#14556584—22no—
16#14556578—21no—
17#14556570C2212yes—
18C4×Dic146C2211yescharacteristic
19#14556556—21no—
20#14556550C2212yes—
21#14556524C2212yes—
22#14556524C2212yes—
23#14556524C2212yes—
24#14556522C2212yes—
25#14556522C2211yescharacteristic
26C4⋊#10596831C2211yescharacteristic
27#14556514C2212yes—
28#14556514C2211yescharacteristic
29#14556512C2212yes—
30#14556512C2211yescharacteristic
31C22⋊#10596831C2212yes—
32C4×#10596831C2211yescharacteristic
33C2×#41×C73—21no—
34C4⋊Q8×C73C2211yescharacteristic
35#123×C73—22no—
36C22⋊Q8×C73—21no—
37#121×C73C2212yes—
38C4×D4×C73C2211yescharacteristic
39C4×D4×C73C2211yescharacteristic
40C2×C4⋊C4×C73C2212yes—
41C2×Dic146—21no—
42C2×Dic146C2311yescharacteristic
43#11924016—22no—
44#11924012—24no—
45C2×#10596831C2311yescharacteristic
46C2×#10596831C2312yes—
47C2×#10596831C2311yescharacteristic
48C4⋊Dic73—21no—
49C4⋊Dic73C2311yescharacteristic
50C4⋊Dic73C2312yes—
51#11924007—22no—
52#11924007—21no—
53C22⋊Dic73—22no—
54C22⋊Dic73—22no—
55C4×Dic73—22no—
56C4×Dic73—21no—
57#41×C73—44no—
58C2×Q8×C73—21no—
59C2×D4×C73—22no—
60C2×D4×C73D411yescharacteristic
61C2×D4×C73C2311yescharacteristic
62C22×C4×C73—22no—
63C22×C4×C73—21no—
64C22×C4×C73C2312yes—
65C4⋊C4×C73—22no—
66C4⋊C4×C73—21no—
67C4⋊C4×C73D411yescharacteristic
68C4⋊C4×C73C2311yescharacteristic
69C4⋊C4×C73C2312yes—
70C22⋊C4×C73—21no—
71C22⋊C4×C73—22no—
72C22⋊C4×C73D412yes—
73C42×C73C2311yescharacteristic
74C23×C73—21no—
75C23×C73C2×D412yes—
76Q8×C73—42no—
77D4×C73—22no—
78D4×C73—21no—
79D4×C73—21no—
80D4×C73—44no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—21no—
84C2×C4×C73—22no—
85C2×C4×C73—44no—
86C2×C4×C73—42no—
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73C2×D412yes—
89C2×C4×C73C2×D411yescharacteristic
90C2×C4×C73C2411yescharacteristic
91C2×Dic73—21no—
92C2×Dic73—21no—
93C2×Dic73—22no—
94Dic146—21no—
95Dic146—21no—
96Dic146—42no—
97#10596831—22no—
98#10596831—21no—
99#10596831#4112yescomplemented
100C22×C73—22no—
101C22×C73—22no—
102C22×C73—22no—
103C22×C73—41no—
104C22×C73—41no—
105C22×C73—41no—
106C22×C73C22×D411yescharacteristic
107C4×C73—22no—
108C4×C73—21no—
109C4×C73—41no—
110C4×C73—42no—
111C4×C73AGL(1,ℤ/8)12yes—
112C4×C73C2×#4111yescharacteristic
113C4×C732−1+411yescharacteristic
114Dic73—41no—
115Dic73—42no—
116Dic73—41no—
117C2×C73—42no—
118C2×C73—81no—
119C2×C73#54711yescharacteristic
120C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C73#57811yescharacteristic
122#3353—731nomaximal, Sylow
123C73#335311yescharacteristic, complemented, Sylow
124#556—731no—
125#547D7311yescharacteristic
126#500—731no—
127#484—732no—
128#482—732no—
129#475—731no—
130#474—731no—
131#468—732no—
132C4×SD16—731no—
133#436—731no—
134#428—732no—
135C2×#41—21no—
136C2×SD16—731no—
137C2×M16—732no—
138C4⋊Q8—731no—
139C4⋊Q8C2×D7311yescharacteristic
140#126—1462no—
141#124—1461no—
142#123—22no—
143C22⋊Q8—21no—
144C22⋊Q8—732no—
145#121C2×D7312yes—
146C4×Q8—731no—
147C4×Q8—1461no—
148C4×D4C2×D7311yescharacteristic
149C4×D4C2×D7311yescharacteristic
150#117—732no—
151C2×C4⋊C4C2×D7312yes—
152#107—732no—
153#107—732no—
154#107—732no—
155#106—731no—
156#106—732no—
157C4⋊C8—731no—
158#103—731no—
159#103—732no—
160#102—731no—
161#102—732no—
162C22⋊C8—732no—
163C4×C8—731no—
164#41—44no—
165C2×Q8—21no—
166C2×Q8—731no—
167C2×Q8—1461no—
168C2×D4—22no—
169C2×D4C22⋊D7311yescharacteristic
170C2×D4C22×D7311yescharacteristic
171C22×C4—22no—
172C22×C4—21no—
173C22×C4C22×D7312yes—
174SD16—1462no—
175M16—1464no—
176C2×C8—731no—
177C2×C8—731no—
178C2×C8—732no—
179C4⋊C4—22no—
180C4⋊C4—21no—
181C4⋊C4—731no—
182C4⋊C4—732no—
183C4⋊C4—1461no—
184C4⋊C4—1462no—
185C4⋊C4—1461no—
186C4⋊C4C22⋊D7311yescharacteristic
187C4⋊C4C22×D7311yescharacteristic
188C4⋊C4C22×D7312yes—
189C22⋊C4—21no—
190C22⋊C4—22no—
191C22⋊C4—1462no—
192C22⋊C4—1462no—
193C22⋊C4C22⋊D7312yes—
194C42—1462no—
195C42—1461no—
196C42C22×D7311yescharacteristic
197C23—21no—
198C23C2×C22⋊D7312yes—
199Q8—42no—
200Q8—2922no—
201Q8—1461no—
202Q8—1461no—
203D4—22no—
204D4—21no—
205D4—21no—
206D4—44no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—44no—
212C2×C4—42no—
213C2×C4—1461no—
214C2×C4—1462no—
215C2×C4—1461no—
216C2×C4C2×C22⋊D7312yes—
217C2×C4C2×C22⋊D7311yescharacteristic
218C2×C4C2×C22⋊D7311yescharacteristic
219C2×C4C23×D7311yescharacteristic
220C8—732no—
221C8—1462no—
222C8—1461no—
223C22—22no—
224C22—22no—
225C22—22no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22C22×C22⋊D7311yescharacteristic
230C4—21no—
231C4—22no—
232C4—41no—
233C4—42no—
234C4—2921no—
235C4—2921no—
236C4—2922no—
237C4#1455661712yes—
238C4#41×D7311yescharacteristic
239C4#1455663811yescharacteristic
240C2—42no—
241C2—81no—
242C2#1798923611yescharacteristic
243C2C2×#1455661711yescharacteristic
244C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#547×C73C2
socleC22×C73C22×D4
hypercenter#547D73
hypocenterC73#3353
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #17989307C2semidirect
2. #17988990C2semidirect
3. #17988922C2semidirect
4. #17988908C2semidirect
5. #17988869C2semidirect
6. #17988867C2semidirect
7. #17988831C2semidirect
8. C4×#11924016C2semidirect
9. #17988665C2semidirect
10. #17988627C2semidirect
99. #10596831#41semidirect
123. C73#3353semidirect