Finite Group Databasebeta

← #21447141

Subgroups — #21447141

Order 7808.

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×#11758202C211yesmaximal, characteristic
2C2×C4⋊#92418C211yesmaximal, characteristic
3C2×#14519701C211yesmaximal, characteristic
4C2×#14519700C211yesmaximal, characteristic
5#16839668C211yesmaximal, characteristic
6#16839524C211yesmaximal, characteristic
7C61×#391C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758202—22no—
10C2×#11758202—22no—
11C2×#11758202—22no—
12C22×#92418C2211yescharacteristic
13C22×#92418C2211yescharacteristic
14C2×C4⋊Dic61C2211yescharacteristic
15C4⋊#92418—22no—
16#14519701—22no—
17#14519700—22no—
18#14519684—21no—
19#14519684—21no—
20C22×Q8×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22C2×C42×C61C2211yescharacteristic
23#95×C61—21no—
24#95×C61—21no—
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61D412yes—
31C22×C4×C61—21no—
32C22×C4×C61—21no—
33C22×C4×C61D411yescharacteristic
34C22×C4×C61D411yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×Dic61—21no—
37C22×Dic61—21no—
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122—21no—
42C2×Dic122—21no—
43C2×Dic122D412yes—
44C4⋊C4×C61—21no—
45C4⋊C4×C61—21no—
46C42×C61—21no—
47C42×C61—21no—
48#11758202—28no—
49C4⋊Dic61—21no—
50C4⋊Dic61—21no—
51C2×#92418—21no—
52C2×#92418—21no—
53C2×#92418—21no—
54C2×#92418—21no—
55C2×#92418—21no—
56C2×#92418D412yes—
57C23×C61C2×D411yescharacteristic
58Q8×C61—22no—
59Q8×C61—22no—
60Q8×C61—41no—
61Q8×C61—41no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—22no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61—41no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61Q1612yescomplemented
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61#4111yescharacteristic
78C2×C4×C61#4111yescharacteristic
79C2×C4×C61#4111yescharacteristic
80C2×Dic61—22no—
81C2×Dic61—41no—
82C2×Dic61—41no—
83C2×Dic61—41no—
84C2×Dic61—41no—
85C2×Dic61—41no—
86Dic122—22no—
87Dic122—22no—
88Dic122—41no—
89Dic122—41no—
90#92418—22no—
91#92418—41no—
92C22×C61#12111yescharacteristic
93C22×C61#12111yescharacteristic
94C22×C61#12111yescharacteristic
95C22×C61C2×Q1611yescharacteristic
96C22×C61#13511yescharacteristic
97C22×C61#13711yescharacteristic
98C22×C61#13711yescharacteristic
99C4×C61—22no—
100C4×C61—42no—
101C4×C61—41no—
102C4×C61—81no—
103C4×C61#12011yescharacteristic
104C4×C61#12311yescharacteristic
105C4×C61#12311yescharacteristic
106C4×C61#12411yescharacteristic
107Dic61—42no—
108Dic61—81no—
109#2056—611nomaximal, Sylow
110C2×C61#39411yescharacteristic
111C2×C61#46211yescharacteristic
112C2×C61#46211yescharacteristic
113C2×C61#46411yescharacteristic
114C2×C61#46411yescharacteristic
115C2×C61#46711yescharacteristic
116C2×C61#47011yescharacteristic
117C22×Q16—611no—
118C2×C4⋊C8—611no—
119C2×#103—611no—
120C2×#103—611no—
121#391—611no—
122#391D6111yescharacteristic
123#340—611no—
124C61#205611yescharacteristic, complemented, Sylow
125C22×Q8—611no—
126C22×Q8C2×D6111yescharacteristic
127C2×Q16—1222no—
128C2×Q16—1222no—
129C2×Q16—1222no—
130C22×C8—611no—
131C22×C8—611no—
132C2×C4⋊C4—611no—
133C2×C4⋊C4C2×D6111yescharacteristic
134C2×C42C2×D6111yescharacteristic
135C4⋊C8—1222no—
136#103—1222no—
137#103—1222no—
138#95—21no—
139#95—21no—
140#95—1221no—
141#95—1221no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—21no—
145C2×Q8—21no—
146C2×Q8—21no—
147C2×Q8—612no—
148C2×Q8—1221no—
149C2×Q8—1221no—
150C2×Q8—1221no—
151C2×Q8—1221no—
152C2×Q8—1221no—
153C2×Q8D24412yes—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—1221no—
157C22×C4—1221no—
158C22×C4C22⋊D6111yescharacteristic
159C22×C4C22⋊D6111yescharacteristic
160C22×C4C22×D6111yescharacteristic
161Q16—1228no—
162C2×C8—612no—
163C2×C8—1221no—
164C2×C8—1221no—
165C2×C8—1221no—
166C2×C8—1221no—
167C2×C8—1221no—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—1221no—
171C4⋊C4—1221no—
172C42—21no—
173C42—21no—
174C23C2×C22⋊D6111yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—41no—
178Q8—41no—
179Q8—1222no—
180Q8—1222no—
181Q8—2441no—
182Q8—2441no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—1222no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4—2441no—
200C2×C4#1175820212yescomplemented
201C2×C4C2×D24411yescharacteristic
202C2×C4#1175822211yescharacteristic
203C2×C4D4×D6111yescharacteristic
204C2×C4D4×D6111yescharacteristic
205C2×C4#1175822411yescharacteristic
206C2×C4#1175822411yescharacteristic
207C8—1222no—
208C8—2441no—
209C22#1451974811yescharacteristic
210C22#1451974911yescharacteristic
211C22#1451975111yescharacteristic
212C22C2×#1175820211yescharacteristic
213C22#1451979711yescharacteristic
214C22#1451980711yescharacteristic
215C22#1451980811yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—81no—
220C4—4881no—
221C4—2442no—
222C4#1451974711yescharacteristic
223C4#1451975911yescharacteristic
224C4#1451976111yescharacteristic
225C4#1451976311yescharacteristic
226C2#1683967811yescharacteristic
227C2#1683996911yescharacteristic
228C2#1683997211yescharacteristic
229C2#1683998111yescharacteristic
230C2#1683998411yescharacteristic
231C2#1684000111yescharacteristic
232C2#1684001811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#391C2
socleC23×C61C2×D4
hypercenter#391D61
hypocenterC61#2056
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
73. C2×C4×C61Q16semidirect
124. C61#2056semidirect
200. C2×C4#11758202semidirect