Finite Group Databasebeta

← #22611252

Subgroups — #22611252

Order 9344.

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

normal subgroups only

This group has 288 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×#11924018C211yesmaximal, characteristic
2C2×#14556520C211yesmaximal, characteristic
3C2×#14556516C211yesmaximal, characteristic
4#17988494C211yesmaximal, characteristic
5#17988492C211yesmaximal, characteristic
6#17988349C211yesmaximal, characteristic
7C2×#103×C73C211yesmaximal, characteristic
8C22×Dic146C2211yescharacteristic
9C2×#11924018—22no—
10C2×#11924018—22no—
11C2×#11924018—22no—
12C22×#10596831C2211yescharacteristic
13C2×C4⋊Dic73C2211yescharacteristic
14C2×C4×Dic73C2211yescharacteristic
15#14556520—22no—
16#14556516—22no—
17#14556498—21no—
18#14556498—21no—
19#14556498—21no—
20#14556498—21no—
21C22×Q8×C73C2211yescharacteristic
22C22×C8×C73C2211yescharacteristic
23C2×C4⋊C4×C73C2211yescharacteristic
24#103×C73—22no—
25C2×Dic146—21no—
26C2×Dic146—21no—
27C2×Dic146—21no—
28C2×Dic146—21no—
29C2×Dic146—21no—
30C2×Dic146D412yes—
31C22×Dic73—21no—
32C22×Dic73—21no—
33C22×Dic73D411yescharacteristic
34C22×Dic73D411yescharacteristic
35#11924018—28no—
36C2×#10596831—21no—
37C2×#10596831—21no—
38C2×#10596831D412yes—
39C4⋊Dic73—21no—
40C4⋊Dic73—21no—
41C4×Dic73—21no—
42C4×Dic73—21no—
43C2×Q8×C73—21no—
44C2×Q8×C73—21no—
45C2×Q8×C73—21no—
46C2×Q8×C73—21no—
47C2×Q8×C73—21no—
48C2×Q8×C73D412yes—
49C22×C4×C73—21no—
50C22×C4×C73—21no—
51C22×C4×C73C2311yescharacteristic
52C2×C8×C73—21no—
53C2×C8×C73—21no—
54C2×C8×C73—21no—
55C4⋊C4×C73—21no—
56C4⋊C4×C73—21no—
57C23×C73C2×D411yescharacteristic
58Q8×C73—22no—
59Q8×C73—22no—
60Q8×C73—41no—
61Q8×C73—41no—
62C2×C4×C73—22no—
63C2×C4×C73—41no—
64C2×C4×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×D411yescharacteristic
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×Dic73Q1612yescomplemented
86Dic146—22no—
87Dic146—22no—
88Dic146—41no—
89Dic146—41no—
90C8×C73—41no—
91#10596831—22no—
92C22×C73#12111yescharacteristic
93C22×C73#12111yescharacteristic
94C22×C73#12111yescharacteristic
95C22×C73C2×Q1611yescharacteristic
96C22×C73#13511yescharacteristic
97C22×C73#13711yescharacteristic
98C22×C73#13711yescharacteristic
99C4×C73—42no—
100C4×C73—81no—
101C4×C73#12011yescharacteristic
102C4×C73#12311yescharacteristic
103C4×C73#12311yescharacteristic
104C4×C73#12411yescharacteristic
105Dic73—22no—
106Dic73—42no—
107Dic73—41no—
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×#103D7311yescharacteristic
122#391—731no—
123#391—731no—
124#340—731no—
125C22×Q8—731no—
126C22×Q8C2×D7311yescharacteristic
127C2×Q16—1462no—
128C2×Q16—1462no—
129C2×Q16—1462no—
130C22×C8—731no—
131C22×C8C2×D7311yescharacteristic
132C2×C4⋊C4—731no—
133C2×C4⋊C4C2×D7311yescharacteristic
134C2×C42—731no—
135C4⋊C8—1462no—
136#103—22no—
137#103—1462no—
138#95—1461no—
139#95—1461no—
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×Q8C22⋊D7312yes—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—731no—
157C22×C4—731no—
158C22×C4—1461no—
159C22×C4—1461no—
160C22×C4C22×D7311yescharacteristic
161Q16—1468no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—732no—
166C2×C8—1461no—
167C2×C8—1461no—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—1461no—
171C4⋊C4—1461no—
172C42—1461no—
173C42—1461no—
174C23D4×D7311yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—41no—
178Q8—41no—
179Q8—2921no—
180Q8—2921no—
181Q8—1462no—
182Q8—1462no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—2921no—
190C2×C4—2921no—
191C2×C4—2921no—
192C2×C4—2921no—
193C2×C4—2921no—
194C2×C4—732no—
195C2×C4—1461no—
196C2×C4—1462no—
197C2×C4—1461no—
198C2×C4—1461no—
199C2×C4—1461no—
200C2×C4—1461no—
201C2×C4D4×D7311yescharacteristic
202C2×C4D4×D7311yescharacteristic
203C2×C4C2×C22⋊D7311yescharacteristic
204C2×C4#1192402711yescharacteristic
205C2×C4#1192402811yescharacteristic
206C2×C4#1192402811yescharacteristic
207C8—41no—
208C8—1462no—
209C22#1455656311yescharacteristic
210C22#1455656411yescharacteristic
211C22#1455656411yescharacteristic
212C22Q16×D7311yescharacteristic
213C22#1455661211yescharacteristic
214C22#1455662011yescharacteristic
215C22#1455662311yescharacteristic
216C4—42no—
217C4—81no—
218C4—2922no—
219C4—2921no—
220C4—5841no—
221C4—1462no—
222C4#1455655911yescharacteristic
223C4#1455657311yescharacteristic
224C4#1455657411yescharacteristic
225C4#1455657711yescharacteristic
226C2#1798850211yescharacteristic
227C2#1798879511yescharacteristic
228C2#1798879611yescharacteristic
229C2#1798880711yescharacteristic
230C2#1798881211yescharacteristic
231C2#1798882711yescharacteristic
232C2#1798884411yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#103×C73C2
socleC23×C73C2×D4
hypercenterC2×#103D73
hypocenterC73#2056
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
85. C2×Dic73Q16semidirect
117. C73#2056semidirect