Finite Group Databasebeta

← #21444449

Subgroups — #21444449

Order 7808.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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
1#16840297C211yesmaximal, characteristic
2#16839817C211yesmaximal, characteristic, complemented
3#16839817C211yesmaximal, characteristic, complemented
4#16839504C211yesmaximal, characteristic, complemented
5#16839501C211yesmaximal, characteristic, complemented
6#16839501C211yesmaximal, characteristic, complemented
7C61×#330C211yesmaximal, characteristic, complemented
8#14519772—21no—
9#14519765C2211yescharacteristic
10#14519762—21no—
11#14519757C411yescharacteristic
12#14519752C411yescharacteristic
13#14519742C411yescharacteristic
14#14519739—21no—
15#14519739C411yescharacteristic
16#14519735—21no—
17C42×D61C2211yescharacteristic
18#14519706—21no—
19#14519706—21no—
20#14519689—21no—
21#14519689—21no—
22#14519688C2211yescharacteristic
23#14519688C2211yescharacteristic
24#125×C61C2211yescharacteristic
25#97×C61C2211yescharacteristic
26#97×C61C2211yescharacteristic
27C2×D244—21no—
28C2×D244C2×C411yescharacteristic
29C2×C4×D61—21no—
30C2×C4×D61C2×C411yescharacteristic
31C2×C4×D61D411yescharacteristic
32C2×C4×D61D411yescharacteristic
33C2×Dic122C2×C411yescharacteristic
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61C2×C411yescharacteristic
39C4⋊C4×C61C2×C411yescharacteristic
40C42×C61C2311yescharacteristic
41#11758198—21no—
42#11758198—21no—
43#11758198—21no—
44#11758198—21no—
45#11758198—21no—
46C4⋊Dic61—21no—
47#11758196—21no—
48C4×Dic61—21no—
49C4×Dic61C2×C411yescharacteristic
50C4×Dic61D411yescharacteristic
51C4×Dic61D411yescharacteristic
52C2×#92418—21no—
53C2×#92418—21no—
54C22×D61—21no—
55C22×D61C22⋊C411yescharacteristic
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61C22×C411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×Dic61—21no—
62C2×Dic61C22⋊C411yescharacteristic
63C2×Dic61C22⋊C411yescharacteristic
64C2×Dic61C22⋊C411yescharacteristic
65D244—41no—
66D244—42no—
67C4×D61—41no—
68C4×D61—41no—
69C4×D61—41no—
70C4×D61—42no—
71Dic122—41no—
72C8×C61—41no—
73C8×C61—41no—
74#92418—41no—
75#92418—41no—
76C22×C61C2×C22⋊C411yescharacteristic
77C2×D61—21no—
78C2×D61—21no—
79C2×D61—21no—
80C2×D61—41no—
81C2×D61—41no—
82C2×D61—41no—
83C4×C61—21no—
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—41no—
87C4×C61—41no—
88Dic61—21no—
89Dic61—21no—
90Dic61—21no—
91Dic61—41no—
92#1535—611nomaximal, Sylow
93C2×C61#41311yescharacteristic
94C2×C61#42111yescharacteristic
95C2×C61#42111yescharacteristic
96D61—41no—
97D61—81no—
98#529—611no—
99#432—611no—
100#432—611no—
101#330—611no—
102#330D6111yescharacteristic, complemented
103#329—611no—
104#329—611no—
105C61#153511yescharacteristic, complemented, Sylow
106#126—1221no—
107#125C2×D6111yescharacteristic
108#124—611no—
109#123—1221no—
110C22⋊Q8—611no—
111#121—611no—
112C4×Q8—611no—
113C4×D4—611no—
114C4×D4—1221no—
115#117—1221no—
116C2×C42—611no—
117C4⋊C8—1221no—
118C4⋊C8—1221no—
119C22⋊C8—1221no—
120C22⋊C8—1221no—
121#97—611no—
122#97—611no—
123#97C2×D6111yescharacteristic
124#97C2×D6111yescharacteristic
125C2×Q8—611no—
126C2×D4—611no—
127C2×D4—1221no—
128C22×C4—611no—
129C22×C4—611no—
130C22×C4—611no—
131C22×C4—1221no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—1221no—
135C2×C8—1221no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—1221no—
139C4⋊C4—1221no—
140C4⋊C4C4×D6111yescharacteristic
141C4⋊C4C4×D6111yescharacteristic
142C22⋊C4—1221no—
143C22⋊C4—1221no—
144C22⋊C4—1221no—
145C22⋊C4—1221no—
146C22⋊C4—1221no—
147C42—611no—
148C42—611no—
149C42—611no—
150C42—1221no—
151C42C22×D6111yescharacteristic
152C23—611no—
153C23—1221no—
154Q8—2441no—
155D4—2441no—
156D4—2442no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—611no—
160C2×C4—611no—
161C2×C4—611no—
162C2×C4—1221no—
163C2×C4—2441no—
164C2×C4—2441no—
165C2×C4—2441no—
166C2×C4—2442no—
167C2×C4C2×C4×D6111yescharacteristic
168C2×C4D4×D6111yescharacteristic
169C2×C4D4×D6111yescharacteristic
170C8—41no—
171C8—41no—
172C8—2441no—
173C8—2441no—
174C22—1221no—
175C22—1221no—
176C22—1221no—
177C22—2441no—
178C22—2441no—
179C22—2441no—
180C22C22⋊C4×D6111yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—1221no—
187C4—1221no—
188C4—1221no—
189C4—2441no—
190C2—4881no—
191C2—2441no—
192C2#1683974511yescharacteristic
193C2#1683977711yescharacteristic
194C2#1683977711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#330C2
socleC22×C61C2×C22⋊C4
hypercenter#330D61
hypocenterC61#1535
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #16839817C2semidirect
3. #16839817C2semidirect
4. #16839504C2semidirect
5. #16839501C2semidirect
6. #16839501C2semidirect
7. C61×#330C2semidirect
102. #330D61semidirect
105. C61#1535semidirect