Finite Group Databasebeta

← #22611337

Subgroups — #22611337

Order 9344.

274 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14556512C211yesmaximal, characteristic
2#17988490C211yesmaximal, characteristic
3#17988456C211yesmaximal, characteristic, complemented
4#17988350C211yesmaximal, characteristic, complemented
5#17988349C211yesmaximal, characteristic, complemented
6#17988341C211yesmaximal, characteristic, complemented
7C2×#102×C73C211yesmaximal, characteristic
8C22×#10596831C2211yescharacteristic
9C2×C4⋊Dic73C2211yescharacteristic
10C2×C4⋊Dic73C2211yescharacteristic
11C2×#11924007—21no—
12C2×#11924007—21no—
13C2×C22⋊Dic73—21no—
14C2×C22⋊Dic73—21no—
15C2×C4×Dic73C2211yescharacteristic
16#14556512—22no—
17C22×D4×C73C2211yescharacteristic
18C22×C8×C73C2211yescharacteristic
19C2×C4⋊C4×C73C2211yescharacteristic
20#102×C73—22no—
21C22×Dic73—21no—
22C22×Dic73—21no—
23C22×Dic73D411yescharacteristic
24C22×Dic73D411yescharacteristic
25C2×#10596831—21no—
26C2×#10596831—21no—
27C2×#10596831—21no—
28C4⋊Dic73—21no—
29C4⋊Dic73—21no—
30C4⋊Dic73—21no—
31C4⋊Dic73—21no—
32#11924007—42no—
33#11924007—42no—
34C22⋊Dic73—42no—
35C22⋊Dic73—42no—
36C4×Dic73—21no—
37C4×Dic73—21no—
38C24×C73—21no—
39C2×D4×C73—21no—
40C2×D4×C73—21no—
41C2×D4×C73—21no—
42C2×D4×C73—21no—
43C2×D4×C73—21no—
44C2×D4×C73D412yes—
45C22×C4×C73—21no—
46C22×C4×C73C2311yescharacteristic
47C2×C8×C73—21no—
48C2×C8×C73—21no—
49C2×C8×C73—21no—
50C4⋊C4×C73—21no—
51C4⋊C4×C73—21no—
52C23×C73—22no—
53C23×C73—41no—
54C23×C73—41no—
55C23×C73—41no—
56C23×C73—41no—
57C23×C73—41no—
58C23×C73—41no—
59C23×C73C2×D411yescharacteristic
60D4×C73—22no—
61D4×C73—22no—
62D4×C73—41no—
63D4×C73—41no—
64C2×C4×C73—41no—
65C2×C4×C73—41no—
66C2×C4×C73—41no—
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73#4111yescharacteristic
69C2×C4×C73#4111yescharacteristic
70C2×C4×C73#4111yescharacteristic
71C2×C4×C73#4111yescharacteristic
72C2×C4×C73#4111yescharacteristic
73C2×Dic73—21no—
74C2×Dic73—21no—
75C2×Dic73—21no—
76C2×Dic73—21no—
77C2×Dic73—41no—
78C2×Dic73—41no—
79C2×Dic73—41no—
80C2×Dic73—41no—
81C2×Dic73—41no—
82C2×Dic73—41no—
83C2×Dic73D812yes—
84C2×Dic73SD1612yes—
85C8×C73—41no—
86#10596831—41no—
87C22×C73—42no—
88C22×C73—42no—
89C22×C73—42no—
90C22×C73—81no—
91C22×C73—81no—
92C22×C73—81no—
93C22×C73—81no—
94C22×C73#12111yescharacteristic
95C22×C73#12311yescharacteristic
96C22×C73#12411yescharacteristic
97C22×C73C2×D811yescharacteristic
98C22×C73C2×SD1611yescharacteristic
99C22×C73AGL(1,ℤ/8)11yescharacteristic
100C22×C73#13711yescharacteristic
101C4×C73—81no—
102C4×C73#12311yescharacteristic
103C4×C73#12311yescharacteristic
104C4×C73#12611yescharacteristic
105C4×C73#12611yescharacteristic
106Dic73—22no—
107Dic73—22no—
108Dic73—81no—
109Dic73—81no—
110C2×C73—82no—
111C2×C73#39711yescharacteristic
112C2×C73#45911yescharacteristic
113C2×C73#46111yescharacteristic
114C2×C73#48011yescharacteristic
115C2×C73#48111yescharacteristic
116C2×C73#48611yescharacteristic
117C2×C73#48911yescharacteristic
118#2071—731nomaximal, Sylow
119C73#207111yescharacteristic, complemented, Sylow
120C2×#102—731no—
121C2×#102D7311yescharacteristic
122#390—731no—
123#384—731no—
124#340—731no—
125#340—731no—
126#336—731no—
127C22×D4C2×D7311yescharacteristic
128C22×C8—731no—
129C22×C8C2×D7311yescharacteristic
130C2×C4⋊C4—731no—
131C2×C4⋊C4—731no—
132C2×C4⋊C4—1461no—
133C2×C4⋊C4—1461no—
134C2×C4⋊C4C2×D7311yescharacteristic
135C2×C22⋊C4—1461no—
136C2×C22⋊C4—1461no—
137C2×C42—731no—
138#102—22no—
139#102—1462no—
140C24—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4C22⋊D7312yes—
147C22×C4—21no—
148C22×C4—731no—
149C22×C4—731no—
150C22×C4—1461no—
151C22×C4—1461no—
152C22×C4C22×D7311yescharacteristic
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—1461no—
157C2×C8—1461no—
158C2×C8—1461no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—2922no—
162C4⋊C4—2922no—
163C4⋊C4—1461no—
164C4⋊C4—1461no—
165C4⋊C4—1461no—
166C4⋊C4—1461no—
167C22⋊C4—2922no—
168C22⋊C4—2922no—
169C42—1461no—
170C42—1461no—
171C23—22no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23D4×D7311yescharacteristic
179D4—22no—
180D4—22no—
181D4—41no—
182D4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—2921no—
187C2×C4—2921no—
188C2×C4—2921no—
189C2×C4—2921no—
190C2×C4—2921no—
191C2×C4—2921no—
192C2×C4—732no—
193C2×C4—732no—
194C2×C4—1461no—
195C2×C4—1461no—
196C2×C4—1461no—
197C2×C4—1461no—
198C2×C4C2×C22⋊D7311yescharacteristic
199C2×C4#1192402711yescharacteristic
200C2×C4#1192402711yescharacteristic
201C2×C4#1192402711yescharacteristic
202C2×C4#1192402811yescharacteristic
203C2×C4#1192402811yescharacteristic
204C8—41no—
205C8—2921no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22—81no—
213C22#1455656311yescharacteristic
214C22#1455657311yescharacteristic
215C22#1455657711yescharacteristic
216C22D8×D7311yescharacteristic
217C22SD16×D7311yescharacteristic
218C22#1455661511yescharacteristic
219C22#1455662011yescharacteristic
220C4—81no—
221C4—5841no—
222C4—5841no—
223C4—1462no—
224C4—1462no—
225C4#1455657211yescharacteristic
226C4#1455657411yescharacteristic
227C4#1455658411yescharacteristic
228C4#1455658411yescharacteristic
229C2—82no—
230C2#1798851511yescharacteristic
231C2#1798878011yescharacteristic
232C2#1798879011yescharacteristic
233C2#1798889911yescharacteristic
234C2#1798890411yescharacteristic
235C2#1798893211yescharacteristic
236C2#1798894511yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#102×C73C2
socleC23×C73C2×D4
hypercenterC2×#102D73
hypocenterC73#2071
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
3. #17988456C2semidirect
4. #17988350C2semidirect
5. #17988349C2semidirect
6. #17988341C2semidirect
119. C73#2071semidirect