Finite Group Databasebeta

← #21447231

Subgroups — #21447231

Order 7808.

238 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 81 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×#14519702C211yesmaximal, characteristic
2C2×#14519700C211yesmaximal, characteristic
3#16839667C211yesmaximal, characteristic
4#16839631C211yesmaximal, characteristic
5#16839524C211yesmaximal, characteristic
6#16839516C211yesmaximal, characteristic
7C61×#340C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×#11758196—21no—
12C2×#11758196—21no—
13C2×C4×Dic61C2211yescharacteristic
14#14519702—22no—
15#14519700—22no—
16#14519684—21no—
17#14519684—21no—
18C22×C8×C61C2211yescharacteristic
19C2×C4⋊C4×C61C2211yescharacteristic
20C2×C4⋊C4×C61C2211yescharacteristic
21C22×C4×C61—21no—
22C22×C4×C61—21no—
23C22×C4×C61C2311yescharacteristic
24C22×Dic61—21no—
25C22×Dic61—21no—
26C22×Dic61D411yescharacteristic
27C22×Dic61D411yescharacteristic
28C2×Dic122—21no—
29C2×Dic122—21no—
30C2×Dic122—21no—
31C2×Dic122—21no—
32C2×Dic122—21no—
33C2×Dic122D412yes—
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C2×C8×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43#11758196—42no—
44#11758196—42no—
45C4×Dic61—21no—
46C4×Dic61—21no—
47C2×#92418—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C23×C61C2×D411yescharacteristic
51C2×C4×C61—41no—
52C2×C4×C61—41no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61#4111yescharacteristic
59C2×C4×C61#4111yescharacteristic
60C2×C4×C61#4111yescharacteristic
61C2×C4×C61#4111yescharacteristic
62C2×C4×C61#4111yescharacteristic
63C2×Dic61—21no—
64C2×Dic61—21no—
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—22no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61SD1612yes—
74C2×Dic61Q1612yes—
75Dic122—22no—
76Dic122—22no—
77Dic122—41no—
78Dic122—41no—
79C8×C61—41no—
80#92418—41no—
81C22×C61#12111yescharacteristic
82C22×C61#12311yescharacteristic
83C22×C61#12411yescharacteristic
84C22×C61C2×SD1611yescharacteristic
85C22×C61C2×Q1611yescharacteristic
86C22×C61AGL(1,ℤ/8)11yescharacteristic
87C22×C61#13711yescharacteristic
88C4×C61—81no—
89C4×C61—81no—
90C4×C61#12311yescharacteristic
91C4×C61#12311yescharacteristic
92C4×C61#12611yescharacteristic
93C4×C61#12611yescharacteristic
94Dic61—22no—
95Dic61—22no—
96Dic61—42no—
97Dic61—81no—
98#2072—611nomaximal, Sylow
99C2×C61#39711yescharacteristic
100C2×C61#46011yescharacteristic
101C2×C61#46211yescharacteristic
102C2×C61#48311yescharacteristic
103C2×C61#48411yescharacteristic
104C2×C61#48711yescharacteristic
105C2×C61#48911yescharacteristic
106C2×#103—611no—
107C2×#103—611no—
108#391—611no—
109#384—611no—
110#340—611no—
111#340D6111yescharacteristic
112#336—611no—
113C61#207211yescharacteristic, complemented, Sylow
114C22×Q8—611no—
115C22×C8—611no—
116C22×C8C2×D6111yescharacteristic
117C2×C4⋊C4—611no—
118C2×C4⋊C4—1221no—
119C2×C4⋊C4—1221no—
120C2×C4⋊C4C2×D6111yescharacteristic
121C2×C4⋊C4C2×D6111yescharacteristic
122C2×C42—611no—
123#103—1222no—
124#103—1222no—
125#95—1221no—
126#95—1221no—
127C2×Q8—612no—
128C2×Q8—1221no—
129C2×Q8—1221no—
130C2×Q8—1221no—
131C2×Q8—1221no—
132C2×Q8—1221no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—611no—
136C22×C4—611no—
137C22×C4—1221no—
138C22×C4—1221no—
139C22×C4C22×D6111yescharacteristic
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—1221no—
144C2×C8—1221no—
145C2×C8—1221no—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—1221no—
151C4⋊C4—1221no—
152C4⋊C4—2442no—
153C4⋊C4—2442no—
154C42—1221no—
155C42—1221no—
156C23D4×D6111yescharacteristic
157Q8—1222no—
158Q8—1222no—
159Q8—2441no—
160Q8—2441no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—612no—
168C2×C4—612no—
169C2×C4—1221no—
170C2×C4—1221no—
171C2×C4—1221no—
172C2×C4—1221no—
173C2×C4—1222no—
174C2×C4—2441no—
175C2×C4—2441no—
176C2×C4—2441no—
177C2×C4—2441no—
178C2×C4—2441no—
179C2×C4#1175822211yescharacteristic
180C2×C4#1175822211yescharacteristic
181C2×C4#1175822211yescharacteristic
182C2×C4D4×D6111yescharacteristic
183C2×C4#1175822411yescharacteristic
184C2×C4#1175822611yescharacteristic
185C8—41no—
186C8—2441no—
187C22#1451975011yescharacteristic
188C22#1451976211yescharacteristic
189C22#1451976311yescharacteristic
190C22SD16×D6111yescharacteristic
191C22Q16×D6111yescharacteristic
192C22#1451980111yescharacteristic
193C22#1451980611yescharacteristic
194C4—81no—
195C4—81no—
196C4—1222no—
197C4—1222no—
198C4—4881no—
199C4—2442no—
200C4#1451975911yescharacteristic
201C4#1451976211yescharacteristic
202C4#1451977111yescharacteristic
203C4#1451977211yescharacteristic
204C2#1683969111yescharacteristic
205C2#1683996111yescharacteristic
206C2#1683997111yescharacteristic
207C2#1684009411yescharacteristic
208C2#1684009911yescharacteristic
209C2#1684011111yescharacteristic
210C2#1684012011yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#2072
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
113. C61#2072semidirect