Finite Group Databasebeta

← #22608932

Subgroups — #22608932

Order 9344.

254 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 51 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
1#17989164C211yesmaximal, characteristic
2#17988900C211yesmaximal, characteristic, complemented
3#17988518C211yesmaximal, characteristic, complemented
4#17988322C211yesmaximal, characteristic, complemented
5#17988321C211yesmaximal, characteristic, complemented
6#17988312C211yesmaximal, characteristic, complemented
7#480×C73C211yesmaximal, characteristic, complemented
8C2×#11924027—21no—
9#14556569—21no—
10#14556568—21no—
11#14556565C2211yescharacteristic
12#14556564—21no—
13#14556563—21no—
14#14556563—21no—
15C2×#11924007—21no—
16C2×#11924007C2211yescharacteristic
17#14556524—21no—
18#14556511—21no—
19C22⋊#10596831C2211yescharacteristic
20#14556498—21no—
21#14556498C2211yescharacteristic
22#121×C73C2211yescharacteristic
23C2×C4⋊C4×C73C2211yescharacteristic
24#107×C73—21no—
25#102×C73—21no—
26C22⋊C8×C73C2211yescharacteristic
27#11924027—42no—
28#11924027—42no—
29C2×Dic146—21no—
30C2×D292D411yescharacteristic
31C2×C22⋊D73—21no—
32C2×C22⋊D73—21no—
33C2×C22⋊D73—21no—
34C22×Dic73—21no—
35C22×Dic73—21no—
36C22×Dic73D411yescharacteristic
37C22×Dic73D411yescharacteristic
38C2×C4×D73—21no—
39C2×#10596831—21no—
40C4⋊Dic73D411yescharacteristic
41#11924007—21no—
42#11924007—21no—
43#11924007—21no—
44#11924007—42no—
45C22⋊Dic73—21no—
46#11924005—21no—
47#11924005—21no—
48C2×D4×C73—21no—
49C2×D4×C73D411yescharacteristic
50C22×C4×C73—21no—
51C22×C4×C73C2311yescharacteristic
52C2×C8×C73—21no—
53C4⋊C4×C73—21no—
54C4⋊C4×C73—21no—
55C4⋊C4×C73D411yescharacteristic
56C22⋊C4×C73—21no—
57C23×C73—21no—
58C23×C73C2×D411yescharacteristic
59C22×D73—21no—
60D4×C73—41no—
61D4×C73—41no—
62D4×C73—41no—
63C2×C4×C73—21no—
64C2×C4×C73—41no—
65C2×C4×C73—41no—
66C2×C4×C73—41no—
67C2×C4×C73—41no—
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C22⋊D73—42no—
71C22⋊D73—41no—
72C22⋊D73—41no—
73C22⋊D73—81no—
74C2×Dic73—21no—
75C2×Dic73—21no—
76C2×Dic73—22no—
77C2×Dic73—21no—
78C2×Dic73—21no—
79C2×Dic73—42no—
80C2×Dic73—41no—
81C2×Dic73—41no—
82C2×Dic73—41no—
83C2×Dic73D812yes—
84D292—41no—
85C4×D73—42no—
86Dic146—42no—
87C8×C73—41no—
88#10596831—41no—
89C22×C73—21no—
90C22×C73—21no—
91C22×C73—41no—
92C22×C73—41no—
93C22×C73—41no—
94C22×C73#12011yescharacteristic
95C22×C73C2×D811yescharacteristic
96C22×C73AGL(1,ℤ/8)11yescharacteristic
97C2×D73—41no—
98C2×D73—41no—
99C2×D73—41no—
100C4×C73—21no—
101C4×C73—21no—
102C4×C73—41no—
103C4×C73—81no—
104Dic73—22no—
105Dic73—42no—
106Dic73—41no—
107Dic73—41no—
108C2×C73—21no—
109C2×C73—21no—
110C2×C73—81no—
111C2×C73#44711yescharacteristic
112C2×C73#45611yescharacteristic
113C2×C73#45811yescharacteristic
114D73—81no—
115#1610—731nomaximal, Sylow
116C73#161011yescharacteristic, complemented, Sylow
117#537—731no—
118#480—731no—
119#480D7311yescharacteristic, complemented
120#398—731no—
121#327—731no—
122#327—731no—
123#324—731no—
124C2×#41—1461no—
125C22⋊Q8—1461no—
126C22⋊Q8—1461no—
127#121—731no—
128#121—1461no—
129#121—1461no—
130#121—1461no—
131#121C2×D7311yescharacteristic
132C2×C4⋊C4—731no—
133C2×C4⋊C4—1461no—
134C2×C4⋊C4C2×D7311yescharacteristic
135#107—21no—
136#107—1461no—
137#102—21no—
138#102—1461no—
139C22⋊C8—731no—
140C22⋊C8C2×D7311yescharacteristic
141#95—731no—
142#95—1461no—
143#41—2922no—
144#41—2922no—
145C2×Q8—1461no—
146C2×D4—21no—
147C2×D4—731no—
148C2×D4—1461no—
149C2×D4—1461no—
150C2×D4—1461no—
151C2×D4C22⋊D7311yescharacteristic
152C22×C4—21no—
153C22×C4—731no—
154C22×C4—731no—
155C22×C4—1461no—
156C22×C4—1461no—
157C22×C4—1461no—
158C22×C4C22×D7311yescharacteristic
159C2×C8—21no—
160C2×C8—1461no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—2922no—
164C4⋊C4—731no—
165C4⋊C4—1461no—
166C4⋊C4—1461no—
167C4⋊C4—1461no—
168C4⋊C4C22⋊D7311yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—1461no—
171C22⋊C4—1461no—
172C22⋊C4—1461no—
173C23—21no—
174C23—1461no—
175C23D4×D7311yescharacteristic
176Q8—2922no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—2921no—
181D4—2921no—
182D4—2921no—
183D4—2922no—
184D4—5841no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—2922no—
191C2×C4—2921no—
192C2×C4—2921no—
193C2×C4—2922no—
194C2×C4—2921no—
195C2×C4—732no—
196C2×C4—1462no—
197C2×C4—1461no—
198C2×C4—1461no—
199C2×C4—1461no—
200C2×C4—1461no—
201C2×C4D4×D7311yescharacteristic
202C2×C4C2×C22⋊D7311yescharacteristic
203C8—41no—
204C8—2921no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—2921no—
211C22—2921no—
212C22—2921no—
213C22#1455655911yescharacteristic
214C22D8×D7311yescharacteristic
215C22#1455661511yescharacteristic
216C4—21no—
217C4—21no—
218C4—41no—
219C4—81no—
220C4—2922no—
221C4—2921no—
222C4—2921no—
223C4—1462no—
224C2—21no—
225C2—21no—
226C2—81no—
227C2—5841no—
228C2#1798871911yescharacteristic
229C2#1798876811yescharacteristic
230C2#1798877611yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#480×C73C2
socleC22×C73#120
hypercenter#480D73
hypocenterC73#1610
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #17988900C2semidirect
3. #17988518C2semidirect
4. #17988322C2semidirect
5. #17988321C2semidirect
6. #17988312C2semidirect
7. #480×C73C2semidirect
116. C73#1610semidirect
119. #480D73semidirect