Finite Group Databasebeta

← #21444187

Subgroups — #21444187

Order 7808.

214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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×#14519772C211yesmaximal, characteristic
2#16839816C211yesmaximal, characteristic, complemented
3#16839812C211yesmaximal, characteristic, complemented
4#16839488C211yesmaximal, characteristic, complemented
5#16839485C211yesmaximal, characteristic
6#16839485C211yesmaximal, characteristic
7C61×#324C211yesmaximal, characteristic, complemented
8#14519772—21no—
9#14519772—21no—
10#14519772—21no—
11#14519772—21no—
12C2×C4⋊Dic61C411yescharacteristic
13C2×#11758196C411yescharacteristic
14C2×#11758198C411yescharacteristic
15C2×#11758198C411yescharacteristic
16C2×#11758198C2211yescharacteristic
17C2×C4×Dic61C2211yescharacteristic
18#14519706—21no—
19#14519706—21no—
20C22⋊#92418C2211yescharacteristic
21C22⋊#92418C2211yescharacteristic
22#14519687—21no—
23C8×Dic61—21no—
24C2×C4⋊C4×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26C22⋊C8×C61C2211yescharacteristic
27C23×D61C2×C411yescharacteristic
28C22×C4×C61C2×C411yescharacteristic
29C22×C4×C61C2×C411yescharacteristic
30C22×C4×C61C2311yescharacteristic
31C22×Dic61C2×C411yescharacteristic
32C22×Dic61C2×C411yescharacteristic
33C22×Dic61C2×C411yescharacteristic
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38#11758198—21no—
39#11758198—21no—
40#11758198—21no—
41#11758198—21no—
42#11758198—21no—
43#11758198—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61—21no—
46#11758196—21no—
47#11758196—21no—
48C4×Dic61D411yescharacteristic
49C4×Dic61D411yescharacteristic
50C4×Dic61D411yescharacteristic
51C4×Dic61D411yescharacteristic
52C2×#92418—21no—
53C2×#92418—21no—
54C23×C61C22×C411yescharacteristic
55C22×D61—21no—
56C22×D61—21no—
57C22×D61—21no—
58C22×D61—41no—
59C22×D61—41no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×Dic61—21no—
69C2×Dic61—21no—
70C2×Dic61—21no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61C22⋊C411yescharacteristic
74C2×Dic61C22⋊C411yescharacteristic
75C2×Dic61C22⋊C411yescharacteristic
76C2×Dic61C22⋊C411yescharacteristic
77C8×C61—41no—
78C8×C61—41no—
79#92418—41no—
80#92418—41no—
81C22×C61—21no—
82C22×C61—21no—
83C22×C61C2×C22⋊C411yescharacteristic
84C22×C61#13111yescharacteristic
85C22×C61#13111yescharacteristic
86C2×D61—41no—
87C2×D61—41no—
88C2×D61—41no—
89C2×D61—81no—
90C2×D61—81no—
91C4×C61—21no—
92C4×C61—21no—
93C4×C61—41no—
94C4×C61—41no—
95Dic61—21no—
96Dic61—21no—
97Dic61—21no—
98Dic61—21no—
99Dic61—41no—
100#1473—611nomaximal, Sylow
101C2×C61—21no—
102C2×C61—21no—
103C2×C61#40811yescharacteristic
104C2×C61#41011yescharacteristic
105C2×C61#41311yescharacteristic
106D61—81no—
107C2×#126—611no—
108#432—611no—
109#431—611no—
110#324—611no—
111#324D6111yescharacteristic, complemented
112#323—611no—
113#323—611no—
114C61#147311yescharacteristic, complemented, Sylow
115#126—1221no—
116#126—1221no—
117#126—1221no—
118#126—1221no—
119C2×C4⋊C4—611no—
120C2×C4⋊C4—611no—
121C2×C4⋊C4C2×D6111yescharacteristic
122C2×C22⋊C4—611no—
123C2×C22⋊C4—611no—
124C2×C22⋊C4—611no—
125C2×C42—611no—
126C4⋊C8—1221no—
127C4⋊C8—1221no—
128C22⋊C8—611no—
129C22⋊C8—611no—
130C22⋊C8C2×D6111yescharacteristic
131C22⋊C8C2×D6111yescharacteristic
132#97—1221no—
133C4×C8—1221no—
134C24—611no—
135C22×C4—611no—
136C22×C4—611no—
137C22×C4—611no—
138C22×C4C4×D6111yescharacteristic
139C22×C4C4×D6111yescharacteristic
140C22×C4C22×D6111yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—1221no—
144C2×C8—1221no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—1221no—
148C4⋊C4—1221no—
149C4⋊C4—1221no—
150C4⋊C4—1221no—
151C22⋊C4—1221no—
152C22⋊C4—1221no—
153C22⋊C4—1221no—
154C22⋊C4—1221no—
155C22⋊C4—1221no—
156C22⋊C4—1221no—
157C42—611no—
158C42—611no—
159C42—611no—
160C42—611no—
161C23—1221no—
162C23—1221no—
163C23—1221no—
164C23—2441no—
165C23—2441no—
166C23C2×C4×D6111yescharacteristic
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—611no—
174C2×C4—611no—
175C2×C4—611no—
176C2×C4—611no—
177C2×C4—1221no—
178C2×C4—1221no—
179C2×C4—1221no—
180C2×C4—2441no—
181C2×C4—2441no—
182C2×C4D4×D6111yescharacteristic
183C2×C4D4×D6111yescharacteristic
184C8—41no—
185C8—41no—
186C8—2441no—
187C8—2441no—
188C22—21no—
189C22—21no—
190C22—4881no—
191C22—4881no—
192C22—2441no—
193C22—2441no—
194C22—2441no—
195C22C22⋊C4×D6111yescharacteristic
196C22#1451978311yescharacteristic
197C22#1451978511yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—1221no—
203C4—1221no—
204C4—1221no—
205C4—1221no—
206C4—2441no—
207C2—21no—
208C2—21no—
209C2—4881no—
210C2#1683972711yescharacteristic
211C2#1683973411yescharacteristic
212C2#1683974511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#324C2
socleC22×C61C2×C22⋊C4
hypercenter#324D61
hypocenterC61#1473
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #16839816C2semidirect
3. #16839812C2semidirect
4. #16839488C2semidirect
7. C61×#324C2semidirect
111. #324D61semidirect
114. C61#1473semidirect