Finite Group Databasebeta

← #22611253

Subgroups — #22611253

Order 9344.

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

normal subgroups only

This group has 288 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×#11924018C211yesmaximal, characteristic
2C2×C4⋊#10596831C211yesmaximal, characteristic
3C2×#14556515C211yesmaximal, characteristic
4C2×#14556514C211yesmaximal, characteristic
5#17988493C211yesmaximal, characteristic
6#17988349C211yesmaximal, characteristic
7#391×C73C211yesmaximal, characteristic
8C22×Dic146C2211yescharacteristic
9C2×#11924018—22no—
10C2×#11924018—22no—
11C2×#11924018—22no—
12C22×#10596831C2211yescharacteristic
13C22×#10596831C2211yescharacteristic
14C2×C4⋊Dic73C2211yescharacteristic
15C4⋊#10596831—22no—
16#14556515—22no—
17#14556514—22no—
18#14556498—21no—
19#14556498—21no—
20C22×Q8×C73C2211yescharacteristic
21C2×C4⋊C4×C73C2211yescharacteristic
22C2×C42×C73C2211yescharacteristic
23#95×C73—21no—
24#95×C73—21no—
25C2×Dic146—21no—
26C2×Dic146—21no—
27C2×Dic146—21no—
28C2×Dic146—21no—
29C2×Dic146—21no—
30C2×Dic146D412yes—
31C22×Dic73—21no—
32C22×Dic73—21no—
33#11924018—28no—
34C2×#10596831—21no—
35C2×#10596831—21no—
36C2×#10596831—21no—
37C2×#10596831—21no—
38C2×#10596831—21no—
39C2×#10596831D412yes—
40C4⋊Dic73—21no—
41C4⋊Dic73—21no—
42C2×Q8×C73—21no—
43C2×Q8×C73—21no—
44C2×Q8×C73—21no—
45C2×Q8×C73—21no—
46C2×Q8×C73—21no—
47C2×Q8×C73D412yes—
48C22×C4×C73—21no—
49C22×C4×C73—21no—
50C22×C4×C73D411yescharacteristic
51C22×C4×C73D411yescharacteristic
52C22×C4×C73C2311yescharacteristic
53C4⋊C4×C73—21no—
54C4⋊C4×C73—21no—
55C42×C73—21no—
56C42×C73—21no—
57C23×C73C2×D411yescharacteristic
58Q8×C73—22no—
59Q8×C73—22no—
60Q8×C73—41no—
61Q8×C73—41no—
62C2×C4×C73—21no—
63C2×C4×C73—21no—
64C2×C4×C73—21no—
65C2×C4×C73—22no—
66C2×C4×C73—21no—
67C2×C4×C73—21no—
68C2×C4×C73—41no—
69C2×C4×C73—41no—
70C2×C4×C73—41no—
71C2×C4×C73—41no—
72C2×C4×C73—41no—
73C2×C4×C73Q1612yescomplemented
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73C2×D411yescharacteristic
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73#4111yescharacteristic
78C2×C4×C73#4111yescharacteristic
79C2×C4×C73#4111yescharacteristic
80C2×Dic73—22no—
81C2×Dic73—41no—
82C2×Dic73—41no—
83C2×Dic73—41no—
84C2×Dic73—41no—
85C2×Dic73—41no—
86Dic146—22no—
87Dic146—22no—
88Dic146—41no—
89Dic146—41no—
90#10596831—22no—
91#10596831—41no—
92C22×C73#12111yescharacteristic
93C22×C73#12111yescharacteristic
94C22×C73#12111yescharacteristic
95C22×C73C2×Q1611yescharacteristic
96C22×C73#13511yescharacteristic
97C22×C73#13711yescharacteristic
98C22×C73#13711yescharacteristic
99C4×C73—22no—
100C4×C73—42no—
101C4×C73—41no—
102C4×C73—81no—
103C4×C73#12011yescharacteristic
104C4×C73#12311yescharacteristic
105C4×C73#12311yescharacteristic
106C4×C73#12411yescharacteristic
107Dic73—42no—
108Dic73—81no—
109C2×C73#39411yescharacteristic
110C2×C73#46211yescharacteristic
111C2×C73#46211yescharacteristic
112C2×C73#46411yescharacteristic
113C2×C73#46411yescharacteristic
114C2×C73#46711yescharacteristic
115C2×C73#47011yescharacteristic
116#2056—731nomaximal, Sylow
117C73#205611yescharacteristic, complemented, Sylow
118C22×Q16—731no—
119C2×C4⋊C8—731no—
120C2×#103—731no—
121C2×#103—731no—
122#391—731no—
123#391D7311yescharacteristic
124#340—731no—
125C22×Q8—731no—
126C22×Q8C2×D7311yescharacteristic
127C2×Q16—1462no—
128C2×Q16—1462no—
129C2×Q16—1462no—
130C22×C8—731no—
131C22×C8—731no—
132C2×C4⋊C4—731no—
133C2×C4⋊C4C2×D7311yescharacteristic
134C2×C42C2×D7311yescharacteristic
135C4⋊C8—1462no—
136#103—1462no—
137#103—1462no—
138#95—21no—
139#95—21no—
140#95—1461no—
141#95—1461no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—21no—
145C2×Q8—21no—
146C2×Q8—21no—
147C2×Q8—732no—
148C2×Q8—1461no—
149C2×Q8—1461no—
150C2×Q8—1461no—
151C2×Q8—1461no—
152C2×Q8—1461no—
153C2×Q8D29212yes—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—1461no—
157C22×C4—1461no—
158C22×C4C22⋊D7311yescharacteristic
159C22×C4C22⋊D7311yescharacteristic
160C22×C4C22×D7311yescharacteristic
161Q16—1468no—
162C2×C8—732no—
163C2×C8—1461no—
164C2×C8—1461no—
165C2×C8—1461no—
166C2×C8—1461no—
167C2×C8—1461no—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—1461no—
171C4⋊C4—1461no—
172C42—21no—
173C42—21no—
174C23C2×C22⋊D7311yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—41no—
178Q8—41no—
179Q8—2921no—
180Q8—2921no—
181Q8—1462no—
182Q8—1462no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—2921no—
195C2×C4—2921no—
196C2×C4—2921no—
197C2×C4—2921no—
198C2×C4—2921no—
199C2×C4—1462no—
200C2×C4#1192401812yescomplemented
201C2×C4D4×D7311yescharacteristic
202C2×C4D4×D7311yescharacteristic
203C2×C4C2×D29211yescharacteristic
204C2×C4#1192402711yescharacteristic
205C2×C4#1192402711yescharacteristic
206C2×C4#1192402811yescharacteristic
207C8—2921no—
208C8—1462no—
209C22#1455656211yescharacteristic
210C22#1455656311yescharacteristic
211C22#1455656511yescharacteristic
212C22C2×#1192401811yescharacteristic
213C22#1455661111yescharacteristic
214C22#1455662111yescharacteristic
215C22#1455662211yescharacteristic
216C4—22no—
217C4—42no—
218C4—41no—
219C4—81no—
220C4—2922no—
221C4—5841no—
222C4#1455656111yescharacteristic
223C4#1455657311yescharacteristic
224C4#1455657511yescharacteristic
225C4#1455657711yescharacteristic
226C2#1798850311yescharacteristic
227C2#1798879411yescharacteristic
228C2#1798879711yescharacteristic
229C2#1798880611yescharacteristic
230C2#1798880911yescharacteristic
231C2#1798882611yescharacteristic
232C2#1798884311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#391×C73C2
socleC23×C73C2×D4
hypercenter#391D73
hypocenterC73#2056
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
73. C2×C4×C73Q16semidirect
117. C73#2056semidirect
200. C2×C4#11924018semidirect