Finite Group Databasebeta

← #22610439

Subgroups — #22610439

Order 9344.

332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#14556616C211yesmaximal, characteristic
2#17988588C211yesmaximal, characteristic, complemented
3C2×#14556513C211yesmaximal, characteristic, complemented
4C2×#14556507C211yesmaximal, characteristic, complemented
5#17988355C211yesmaximal, characteristic, complemented
6#17988352C211yesmaximal, characteristic, complemented
7C2×#131×C73C211yesmaximal, characteristic, complemented
8C22×D292C2211yescharacteristic
9#14556616—22no—
10#14556616C414yescomplemented
11C2×#11924015—21no—
12C2×#11924013—21no—
13C2×#11924012C2211yescharacteristic
14C2×#11924012C2211yescharacteristic
15C2×C4⋊Dic73C2211yescharacteristic
16#14556515—21no—
17#14556513—21no—
18#14556513—21no—
19#14556512—21no—
20#14556507—22no—
21C2×#41×C73C2211yescharacteristic
22#131×C73—22no—
23#131×C73—22no—
24C2×M16×C73—21no—
25C2×M16×C73C2211yescharacteristic
26C22×C8×C73—21no—
27C22×C8×C73C2211yescharacteristic
28C23×D73—21no—
29C2×D292—21no—
30C2×D292—21no—
31C2×D292—21no—
32C2×D292—21no—
33C2×D292—21no—
34C2×D292C2×C412yes—
35C22×Dic73—21no—
36#11924015—24no—
37#11924013—24no—
38#11924012—21no—
39#11924012—21no—
40#11924012—21no—
41#11924012C2×C412yes—
42C2×#10596831—21no—
43C2×#10596831—21no—
44C4⋊Dic73—21no—
45C4⋊Dic73—21no—
46#41×C73—21no—
47#41×C73—21no—
48#41×C73C2×C412yes—
49#41×C73D412yes—
50C2×Q8×C73D411yescharacteristic
51C2×D4×C73—21no—
52C2×D4×C73D411yescharacteristic
53C22×C4×C73—21no—
54C22×C4×C73C2311yescharacteristic
55M16×C73—24no—
56M16×C73—21no—
57M16×C73D412yes—
58C2×C8×C73—24no—
59C2×C8×C73—21no—
60C2×C8×C73—21no—
61C2×C8×C73—21no—
62C2×C8×C73D411yescharacteristic
63C2×C8×C73D411yescharacteristic
64C23×C73—21no—
65C23×C73#4111yescharacteristic
66C22×D73—22no—
67C22×D73—41no—
68C22×D73—41no—
69C22×D73—81no—
70C22×D73—81no—
71Q8×C73—21no—
72Q8×C73C22⋊C412yes—
73D4×C73—22no—
74D4×C73—22no—
75D4×C73—21no—
76D4×C73C22⋊C412yes—
77C2×C4×C73—21no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73C22×C411yescharacteristic
81C2×C4×C73C2×D411yescharacteristic
82C2×C4×C73C2×D411yescharacteristic
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73#4111yescharacteristic
86C2×Dic73—41no—
87C2×Dic73—81no—
88D292—22no—
89D292—22no—
90D292—41no—
91D292—41no—
92C8×C73—21no—
93C8×C73—22no—
94C8×C73—21no—
95#10596831—22no—
96#10596831—41no—
97C22×C73—21no—
98C22×C73—21no—
99C22×C73—22no—
100C22×C73—41no—
101C22×C73—41no—
102C22×C73C4×D411yescharacteristic
103C22×C73#12111yescharacteristic
104C22×C73#12311yescharacteristic
105C2×D73—42no—
106C2×D73—82no—
107C2×D73—81no—
108C2×D73—81no—
109C2×D73—82no—
110C4×C73—22no—
111C4×C73C2×C22⋊C411yescharacteristic
112C4×C73C4×D411yescharacteristic
113C4×C73#12011yescharacteristic
114C4×C73#12111yescharacteristic
115Dic73—81no—
116C2×C73—21no—
117C2×C73—21no—
118C2×C73—42no—
119C2×C73#38611yescharacteristic
120C2×C73#47111yescharacteristic
121C2×C73#47211yescharacteristic
122D73—82no—
123#1907—731nomaximal, Sylow
124C73#190711yescharacteristic, complemented, Sylow
125C2×AGL(1,ℤ/8)—731no—
126C2×#131D7311yescharacteristic, complemented
127#417—731no—
128C2×#102—731no—
129C2×#100—731no—
130#343—731no—
131#341—731no—
132C2×#41C2×D7311yescharacteristic
133C22×D4—731no—
134AGL(1,ℤ/8)—734no—
135AGL(1,ℤ/8)—1462no—
136C2×SD16—1461no—
137C2×D8—1461no—
138#131—22no—
139#131—22no—
140C2×M16—21no—
141C2×M16—731no—
142C2×M16—731no—
143C2×M16C2×D7311yescharacteristic
144C22×C8—21no—
145C22×C8C2×D7311yescharacteristic
146C2×C4⋊C4—731no—
147#103—1461no—
148#102—1461no—
149#102—1461no—
150#102—1461no—
151#100—1462no—
152C24—1461no—
153#41—21no—
154#41—21no—
155#41C4×D7312yes—
156#41C22⋊D7312yes—
157C2×Q8D29211yescharacteristic
158C2×D4—21no—
159C2×D4—732no—
160C2×D4—1461no—
161C2×D4—1461no—
162C2×D4—1461no—
163C2×D4—1461no—
164C2×D4—1461no—
165C2×D4D29211yescharacteristic
166C22×C4—21no—
167C22×C4—1461no—
168C22×C4C22×D7311yescharacteristic
169SD16—1464no—
170D8—1464no—
171M16—24no—
172M16—21no—
173M16—732no—
174M16—1461no—
175M16—1461no—
176M16—1461no—
177M16C22⋊D7312yes—
178C2×C8—24no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—1461no—
183C2×C8—1461no—
184C2×C8C22⋊D7311yescharacteristic
185C2×C8C22⋊D7311yescharacteristic
186C4⋊C4—1461no—
187C4⋊C4—1461no—
188C23—21no—
189C23—2921no—
190C23—2921no—
191C23—5841no—
192C23—5841no—
193C23—1462no—
194C23#1192402811yescharacteristic
195Q8—21no—
196Q8#1192400512yes—
197D4—22no—
198D4—22no—
199D4—21no—
200D4—2921no—
201D4—2921no—
202D4—1462no—
203D4—1462no—
204D4#1192400512yes—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—2921no—
209C2×C4—5841no—
210C2×C4C2×C4×D7311yescharacteristic
211C2×C4C2×C22⋊D7311yescharacteristic
212C2×C4C2×C22⋊D7311yescharacteristic
213C2×C4C2×C22⋊D7311yescharacteristic
214C2×C4C2×D29211yescharacteristic
215C2×C4#1192402811yescharacteristic
216C8—21no—
217C8—22no—
218C8—21no—
219C8—2921no—
220C8—1462no—
221C22—21no—
222C22—21no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—2922no—
227C22—5842no—
228C22—5842no—
229C22—5841no—
230C22—5841no—
231C22C4×C22⋊D7311yescharacteristic
232C22#1455656511yescharacteristic
233C22#1455657411yescharacteristic
234C4—22no—
235C4—5841no—
236C4C2×#1192400511yescharacteristic
237C4C4×C22⋊D7311yescharacteristic
238C4#1455656011yescharacteristic
239C4#1455656511yescharacteristic
240C2—21no—
241C2—21no—
242C2—42no—
243C2—5842no—
244C2#1798846611yescharacteristic
245C2#1798885011yescharacteristic
246C2#1798885711yescharacteristic
subgroupG/H
centerC22#14556565
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
FittingC2×#131×C73C2
socleC22×C73#121
hypercenterC2×#131D73
hypocenterC73#1907
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
2. #17988588C2semidirect
3. C2×#14556513C2semidirect
4. C2×#14556507C2semidirect
5. #17988355C2semidirect
6. #17988352C2semidirect
7. C2×#131×C73C2semidirect
10. #14556616C4semidirect
124. C73#1907semidirect
126. C2×#131D73semidirect