Finite Group Databasebeta

← #22611246

Subgroups — #22611246

Order 9344.

324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C22×#11924015C211yesmaximal, characteristic
2C2×C4⋊#10596831C211yesmaximal, characteristic, complemented
3C2×#14556515C211yesmaximal, characteristic, complemented
4C2×#14556511C211yesmaximal, characteristic
5#17988489C211yesmaximal, characteristic
6#17988349C211yesmaximal, characteristic, complemented
7#391×C73C211yesmaximal, characteristic, complemented
8C22×D292C2211yescharacteristic
9C2×#11924015—22no—
10C2×#11924015—22no—
11C2×#11924015—22no—
12C22×#10596831C2211yescharacteristic
13C22×#10596831C2211yescharacteristic
14C2×C4⋊Dic73C2211yescharacteristic
15C2×#11924005—21no—
16C2×#11924005—21no—
17C4⋊#10596831—22no—
18#14556515—22no—
19#14556511—22no—
20C22×Q8×C73C2211yescharacteristic
21C2×C4⋊C4×C73C2211yescharacteristic
22C2×C42×C73C2211yescharacteristic
23#95×C73—21no—
24#95×C73—21no—
25C23×D73—21no—
26C2×D292—21no—
27C2×D292—21no—
28C2×D292—21no—
29C2×D292—21no—
30C2×D292—21no—
31C2×D292D412yes—
32C22×Dic73—21no—
33#11924015—28no—
34C2×#10596831—21no—
35C2×#10596831—21no—
36C2×#10596831—21no—
37C2×#10596831—21no—
38C2×#10596831—21no—
39C2×#10596831D412yes—
40C4⋊Dic73—21no—
41C4⋊Dic73—21no—
42#11924005—42no—
43#11924005—42no—
44C2×Q8×C73—21no—
45C2×Q8×C73—21no—
46C2×Q8×C73—21no—
47C2×Q8×C73—21no—
48C2×Q8×C73—21no—
49C2×Q8×C73D412yes—
50C22×C4×C73—21no—
51C22×C4×C73—21no—
52C22×C4×C73D411yescharacteristic
53C22×C4×C73D411yescharacteristic
54C22×C4×C73C2311yescharacteristic
55C4⋊C4×C73—21no—
56C4⋊C4×C73—21no—
57C42×C73—21no—
58C42×C73—21no—
59C23×C73C2×D411yescharacteristic
60C22×D73—22no—
61C22×D73—41no—
62C22×D73—41no—
63C22×D73—41no—
64C22×D73—41no—
65C22×D73—41no—
66C22×D73—41no—
67Q8×C73—22no—
68Q8×C73—22no—
69Q8×C73—41no—
70Q8×C73—41no—
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73—21no—
74C2×C4×C73—22no—
75C2×C4×C73—21no—
76C2×C4×C73—21no—
77C2×C4×C73—41no—
78C2×C4×C73—41no—
79C2×C4×C73—41no—
80C2×C4×C73—41no—
81C2×C4×C73—41no—
82C2×C4×C73SD1612yescomplemented
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73#4111yescharacteristic
87C2×C4×C73#4111yescharacteristic
88C2×C4×C73#4111yescharacteristic
89C2×Dic73—41no—
90C2×Dic73—41no—
91C2×Dic73—41no—
92D292—22no—
93D292—22no—
94D292—41no—
95D292—41no—
96#10596831—22no—
97#10596831—41no—
98C22×C73#12111yescharacteristic
99C22×C73#12111yescharacteristic
100C22×C73#12111yescharacteristic
101C22×C73C2×SD1611yescharacteristic
102C22×C73#13511yescharacteristic
103C22×C73AGL(1,ℤ/8)11yescharacteristic
104C22×C73#13711yescharacteristic
105C2×D73—42no—
106C2×D73—42no—
107C2×D73—42no—
108C2×D73—81no—
109C2×D73—81no—
110C2×D73—81no—
111C2×D73—81no—
112C4×C73—22no—
113C4×C73—42no—
114C4×C73—41no—
115C4×C73—81no—
116C4×C73#12011yescharacteristic
117C4×C73#12311yescharacteristic
118C4×C73#12311yescharacteristic
119C4×C73#12411yescharacteristic
120Dic73—81no—
121C2×C73#39411yescharacteristic
122C2×C73#46011yescharacteristic
123C2×C73#46111yescharacteristic
124C2×C73#46311yescharacteristic
125C2×C73#46411yescharacteristic
126C2×C73#46511yescharacteristic
127C2×C73#46811yescharacteristic
128D73—82no—
129#2055—731nomaximal, Sylow
130C73#205511yescharacteristic, complemented, Sylow
131C22×SD16—731no—
132C2×C4⋊C8—731no—
133C2×#103—731no—
134C2×#102—731no—
135#391D7311yescharacteristic, complemented
136#390—731no—
137#340—731no—
138C22×Q8C2×D7311yescharacteristic
139C22×D4—731no—
140C2×SD16—1462no—
141C2×SD16—1462no—
142C2×SD16—1462no—
143C22×C8—731no—
144C22×C8—731no—
145C2×C4⋊C4—731no—
146C2×C4⋊C4C2×D7311yescharacteristic
147C2×C22⋊C4—1461no—
148C2×C22⋊C4—1461no—
149C2×C42C2×D7311yescharacteristic
150C4⋊C8—1462no—
151#103—1462no—
152#102—1462no—
153#95—21no—
154#95—21no—
155C24—1461no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8D29212yes—
162C2×D4—732no—
163C2×D4—1461no—
164C2×D4—1461no—
165C2×D4—1461no—
166C2×D4—1461no—
167C2×D4—1461no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—1461no—
171C22×C4C22⋊D7311yescharacteristic
172C22×C4C22⋊D7311yescharacteristic
173C22×C4C22×D7311yescharacteristic
174SD16—1468no—
175C2×C8—732no—
176C2×C8—1461no—
177C2×C8—1461no—
178C2×C8—1461no—
179C2×C8—1461no—
180C2×C8—1461no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—1461no—
184C4⋊C4—1461no—
185C22⋊C4—2922no—
186C22⋊C4—2922no—
187C42—21no—
188C42—21no—
189C23—2921no—
190C23—2921no—
191C23—2921no—
192C23—2921no—
193C23—2921no—
194C23—2921no—
195C23—1462no—
196C23C2×C22⋊D7311yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—2921no—
202D4—2921no—
203D4—1462no—
204D4—1462no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—2921no—
217C2×C4—2921no—
218C2×C4—2921no—
219C2×C4#1192401512yescomplemented
220C2×C4D4×D7311yescharacteristic
221C2×C4D4×D7311yescharacteristic
222C2×C4C2×D29211yescharacteristic
223C2×C4#1192402711yescharacteristic
224C2×C4#1192402711yescharacteristic
225C2×C4#1192402811yescharacteristic
226C8—2921no—
227C8—1462no—
228C22—2922no—
229C22—2922no—
230C22—2922no—
231C22—5841no—
232C22—5841no—
233C22—5841no—
234C22—5841no—
235C22#1455656211yescharacteristic
236C22#1455656311yescharacteristic
237C22#1455656511yescharacteristic
238C22C2×#1192401511yescharacteristic
239C22#1455661111yescharacteristic
240C22#1455661611yescharacteristic
241C22#1455662211yescharacteristic
242C4—22no—
243C4—42no—
244C4—41no—
245C4—81no—
246C4—5841no—
247C4#1455656111yescharacteristic
248C4#1455657311yescharacteristic
249C4#1455657511yescharacteristic
250C4#1455657711yescharacteristic
251C2—5842no—
252C2#1798850311yescharacteristic
253C2#1798878711yescharacteristic
254C2#1798878911yescharacteristic
255C2#1798879911yescharacteristic
256C2#1798880911yescharacteristic
257C2#1798881811yescharacteristic
258C2#1798883511yescharacteristic
subgroupG/H
centerC23C2×C22⋊D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#391×C73C2
socleC23×C73C2×D4
hypercenter#391D73
hypocenterC73#2055
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊#10596831C2semidirect
3. C2×#14556515C2semidirect
6. #17988349C2semidirect
7. #391×C73C2semidirect
82. C2×C4×C73SD16semidirect
130. C73#2055semidirect
135. #391D73semidirect
219. C2×C4#11924015semidirect