Finite Group Databasebeta

← #22611245

Subgroups — #22611245

Order 9344.

324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14556520C211yesmaximal, characteristic, complemented
3C2×#14556513C211yesmaximal, characteristic
4#17988494C211yesmaximal, characteristic, complemented
5#17988488C211yesmaximal, characteristic
6#17988349C211yesmaximal, characteristic, complemented
7C2×#103×C73C211yesmaximal, characteristic, complemented
8C22×D292C2211yescharacteristic
9C2×#11924015—22no—
10C2×#11924015—22no—
11C2×#11924015—22no—
12C22×#10596831C2211yescharacteristic
13C2×C4⋊Dic73C2211yescharacteristic
14C2×#11924005—21no—
15C2×#11924005—21no—
16C2×C4×Dic73C2211yescharacteristic
17#14556520—22no—
18#14556513—22no—
19#14556498—21no—
20#14556498—21no—
21C22×Q8×C73C2211yescharacteristic
22C22×C8×C73C2211yescharacteristic
23C2×C4⋊C4×C73C2211yescharacteristic
24#103×C73—22no—
25C23×D73—21no—
26C2×D292—21no—
27C2×D292—21no—
28C2×D292—21no—
29C2×D292—21no—
30C2×D292—21no—
31C2×D292D412yes—
32C22×Dic73—21no—
33C22×Dic73D411yescharacteristic
34C22×Dic73D411yescharacteristic
35#11924015—28no—
36C2×#10596831—21no—
37C2×#10596831—21no—
38C2×#10596831D412yes—
39C4⋊Dic73—21no—
40C4⋊Dic73—21no—
41#11924005—42no—
42#11924005—42no—
43C4×Dic73—21no—
44C4×Dic73—21no—
45C2×Q8×C73—21no—
46C2×Q8×C73—21no—
47C2×Q8×C73—21no—
48C2×Q8×C73—21no—
49C2×Q8×C73—21no—
50C2×Q8×C73D412yes—
51C22×C4×C73—21no—
52C22×C4×C73—21no—
53C22×C4×C73C2311yescharacteristic
54C2×C8×C73—21no—
55C2×C8×C73—21no—
56C2×C8×C73—21no—
57C4⋊C4×C73—21no—
58C4⋊C4×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—22no—
72C2×C4×C73—41no—
73C2×C4×C73—41no—
74C2×C4×C73—41no—
75C2×C4×C73—41no—
76C2×C4×C73—41no—
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2×D411yescharacteristic
80C2×C4×C73#4111yescharacteristic
81C2×C4×C73#4111yescharacteristic
82C2×C4×C73#4111yescharacteristic
83C2×Dic73—21no—
84C2×Dic73—21no—
85C2×Dic73—21no—
86C2×Dic73—21no—
87C2×Dic73—21no—
88C2×Dic73—41no—
89C2×Dic73—41no—
90C2×Dic73—41no—
91C2×Dic73SD1612yescomplemented
92D292—22no—
93D292—22no—
94D292—41no—
95D292—41no—
96C8×C73—41no—
97#10596831—22no—
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—42no—
113C4×C73—81no—
114C4×C73#12011yescharacteristic
115C4×C73#12311yescharacteristic
116C4×C73#12311yescharacteristic
117C4×C73#12411yescharacteristic
118Dic73—22no—
119Dic73—41no—
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×#103D7311yescharacteristic, complemented
134C2×#102—731no—
135#391—731no—
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×C8C2×D7311yescharacteristic
145C2×C4⋊C4—731no—
146C2×C4⋊C4C2×D7311yescharacteristic
147C2×C22⋊C4—1461no—
148C2×C22⋊C4—1461no—
149C2×C42—731no—
150C4⋊C8—1462no—
151#103—22no—
152#102—1462no—
153#95—1461no—
154#95—1461no—
155C24—1461no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8C22⋊D7312yes—
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—731no—
171C22×C4—731no—
172C22×C4—1461no—
173C22×C4C22×D7311yescharacteristic
174SD16—1468no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—732no—
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—1461no—
188C42—1461no—
189C23—2921no—
190C23—2921no—
191C23—2921no—
192C23—2921no—
193C23—2921no—
194C23—2921no—
195C23—1462no—
196C23D4×D7311yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—2921no—
202D4—2921no—
203D4—1462no—
204D4—1462no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—2921no—
212C2×C4—2921no—
213C2×C4—2921no—
214C2×C4—732no—
215C2×C4—1461no—
216C2×C4—1461no—
217C2×C4—1461no—
218C2×C4—1461no—
219C2×C4—1461no—
220C2×C4D4×D7311yescharacteristic
221C2×C4D4×D7311yescharacteristic
222C2×C4C2×C22⋊D7311yescharacteristic
223C2×C4#1192402711yescharacteristic
224C2×C4#1192402811yescharacteristic
225C2×C4#1192402811yescharacteristic
226C8—41no—
227C8—1462no—
228C22—2922no—
229C22—2922no—
230C22—2922no—
231C22—5841no—
232C22—5841no—
233C22—5841no—
234C22—5841no—
235C22#1455656311yescharacteristic
236C22#1455656411yescharacteristic
237C22#1455656411yescharacteristic
238C22SD16×D7311yescharacteristic
239C22#1455661411yescharacteristic
240C22#1455661811yescharacteristic
241C22#1455662311yescharacteristic
242C4—42no—
243C4—81no—
244C4—2921no—
245C4—5841no—
246C4—1462no—
247C4#1455655911yescharacteristic
248C4#1455657311yescharacteristic
249C4#1455657411yescharacteristic
250C4#1455657711yescharacteristic
251C2—5842no—
252C2#1798850211yescharacteristic
253C2#1798878511yescharacteristic
254C2#1798879111yescharacteristic
255C2#1798880511yescharacteristic
256C2#1798881111yescharacteristic
257C2#1798881911yescharacteristic
258C2#1798883611yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#103×C73C2
socleC23×C73C2×D4
hypercenterC2×#103D73
hypocenterC73#2055
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×#14556520C2semidirect
4. #17988494C2semidirect
6. #17988349C2semidirect
7. C2×#103×C73C2semidirect
91. C2×Dic73SD16semidirect
130. C73#2055semidirect
133. C2×#103D73semidirect