Finite Group Databasebeta

← #22611303

Subgroups — #22611303

Order 9344.

284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14556523C211yesmaximal, characteristic, complemented
2C2×#14556520C211yesmaximal, characteristic, complemented
3C2×#14556512C211yesmaximal, characteristic
4#17988490C211yesmaximal, characteristic
5#17988483C211yesmaximal, characteristic, complemented
6#17988349C211yesmaximal, characteristic, complemented
7C2×#102×C73C211yesmaximal, characteristic
8C22×#10596831C2211yescharacteristic
9C2×C4⋊Dic73C2211yescharacteristic
10C2×C4⋊Dic73C2211yescharacteristic
11C2×#11924007—21no—
12C2×C22⋊Dic73—21no—
13C2×C22⋊Dic73—21no—
14C2×C4×Dic73C2211yescharacteristic
15#14556523—22no—
16#14556520—22no—
17#14556512—22no—
18#14556498—21no—
19C22×D4×C73C2211yescharacteristic
20C22×C8×C73C2211yescharacteristic
21C2×C4⋊C4×C73C2211yescharacteristic
22#102×C73—22no—
23C22×Dic73—21no—
24C22×Dic73—21no—
25C22×Dic73D411yescharacteristic
26C22×Dic73D411yescharacteristic
27C2×#10596831—21no—
28C2×#10596831—21no—
29C2×#10596831—21no—
30C4⋊Dic73—21no—
31C4⋊Dic73—21no—
32C4⋊Dic73—21no—
33C4⋊Dic73D412yes—
34#11924007—42no—
35C22⋊Dic73—42no—
36C22⋊Dic73—42no—
37C4×Dic73—21no—
38C4×Dic73—21no—
39C24×C73—21no—
40C2×D4×C73—21no—
41C2×D4×C73—21no—
42C2×D4×C73—21no—
43C2×D4×C73—21no—
44C2×D4×C73—21no—
45C2×D4×C73Q812yes—
46C22×C4×C73—21no—
47C22×C4×C73C2311yescharacteristic
48C2×C8×C73—21no—
49C2×C8×C73—21no—
50C2×C8×C73D412yes—
51C4⋊C4×C73—21no—
52C4⋊C4×C73—21no—
53C23×C73—22no—
54C23×C73—41no—
55C23×C73—41no—
56C23×C73—41no—
57C23×C73—41no—
58C23×C73—41no—
59C23×C73—41no—
60C23×C73C2×D411yescharacteristic
61D4×C73—22no—
62D4×C73—22no—
63D4×C73—41no—
64D4×C73—41no—
65C2×C4×C73—41no—
66C2×C4×C73—41no—
67C2×C4×C73—41no—
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2×Q811yescharacteristic
71C2×C4×C73#4111yescharacteristic
72C2×C4×C73#4111yescharacteristic
73C2×C4×C73#4111yescharacteristic
74C2×Dic73—21no—
75C2×Dic73—21no—
76C2×Dic73—21no—
77C2×Dic73—22no—
78C2×Dic73—21no—
79C2×Dic73—21no—
80C2×Dic73—41no—
81C2×Dic73—41no—
82C2×Dic73—41no—
83C2×Dic73—41no—
84C2×Dic73—41no—
85C2×Dic73SD1612yes—
86C8×C73—22no—
87#10596831—41no—
88C22×C73—42no—
89C22×C73—42no—
90C22×C73—42no—
91C22×C73—81no—
92C22×C73—81no—
93C22×C73—81no—
94C22×C73—81no—
95C22×C73#12111yescharacteristic
96C22×C73#12111yescharacteristic
97C22×C73C22⋊Q811yescharacteristic
98C22×C73C2×SD1611yescharacteristic
99C22×C73#13511yescharacteristic
100C22×C73AGL(1,ℤ/8)11yescharacteristic
101C22×C73AGL(1,ℤ/8)11yescharacteristic
102C4×C73—81no—
103C4×C73#12111yescharacteristic
104C4×C73C22⋊Q811yescharacteristic
105C4×C73C22⋊Q811yescharacteristic
106C4×C73#12611yescharacteristic
107Dic73—22no—
108Dic73—42no—
109Dic73—41no—
110Dic73—81no—
111C2×C73—82no—
112C2×C73#39611yescharacteristic
113C2×C73#46011yescharacteristic
114C2×C73#46311yescharacteristic
115C2×C73#46511yescharacteristic
116C2×C73#46911yescharacteristic
117C2×C73#47611yescharacteristic
118C2×C73#47811yescharacteristic
119#2065—731nomaximal, Sylow
120C73#206511yescharacteristic, complemented, Sylow
121C2×#106—731no—
122C2×C4⋊C8—731no—
123C2×#102—731no—
124C2×#102D7311yescharacteristic
125#390—731no—
126#389—731no—
127#340—731no—
128C22×D4C2×D7311yescharacteristic
129C22×C8—731no—
130C22×C8C2×D7311yescharacteristic
131C2×C4⋊C4—731no—
132C2×C4⋊C4—731no—
133C2×C4⋊C4—1461no—
134C2×C4⋊C4C2×D7311yescharacteristic
135C2×C22⋊C4—1461no—
136C2×C22⋊C4—1461no—
137C2×C42—731no—
138#106—1462no—
139C4⋊C8—1462no—
140#102—22no—
141#102—1462no—
142#95—1461no—
143C24—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4Dic14612yes—
150C22×C4—21no—
151C22×C4—731no—
152C22×C4—731no—
153C22×C4—1461no—
154C22×C4—1461no—
155C22×C4C22×D7311yescharacteristic
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—1461no—
159C2×C8—1461no—
160C2×C8—1461no—
161C2×C8C22⋊D7312yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—2922no—
165C4⋊C4—732no—
166C4⋊C4—1461no—
167C4⋊C4—1461no—
168C4⋊C4—1461no—
169C22⋊C4—2922no—
170C22⋊C4—2922no—
171C42—1461no—
172C42—1461no—
173C23—22no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23—41no—
179C23—41no—
180C23D4×D7311yescharacteristic
181D4—22no—
182D4—22no—
183D4—41no—
184D4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—2921no—
189C2×C4—2921no—
190C2×C4—2921no—
191C2×C4—2921no—
192C2×C4—2921no—
193C2×C4—732no—
194C2×C4—1461no—
195C2×C4—1462no—
196C2×C4—1461no—
197C2×C4—1461no—
198C2×C4—1461no—
199C2×C4—1461no—
200C2×C4D4×D7311yescharacteristic
201C2×C4C2×C22⋊D7311yescharacteristic
202C2×C4C2×Dic14611yescharacteristic
203C2×C4#1192402711yescharacteristic
204C2×C4#1192402711yescharacteristic
205C2×C4#1192402811yescharacteristic
206C8—22no—
207C8—2921no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—81no—
212C22—81no—
213C22—81no—
214C22—81no—
215C22#1455656211yescharacteristic
216C22#1455656411yescharacteristic
217C22#1455656811yescharacteristic
218C22SD16×D7311yescharacteristic
219C22#1455661211yescharacteristic
220C22#1455661511yescharacteristic
221C22#1455661511yescharacteristic
222C4—81no—
223C4—2922no—
224C4—2921no—
225C4—5841no—
226C4—1462no—
227C4#1455656311yescharacteristic
228C4#1455656811yescharacteristic
229C4#1455657011yescharacteristic
230C4#1455658411yescharacteristic
231C2—82no—
232C2#1798851011yescharacteristic
233C2#1798878611yescharacteristic
234C2#1798880111yescharacteristic
235C2#1798881311yescharacteristic
236C2#1798883711yescharacteristic
237C2#1798887511yescharacteristic
238C2#1798888911yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#102×C73C2
socleC23×C73C2×D4
hypercenterC2×#102D73
hypocenterC73#2065
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#14556523C2semidirect
2. C2×#14556520C2semidirect
5. #17988483C2semidirect
6. #17988349C2semidirect
120. C73#2065semidirect