Finite Group Databasebeta

← #21445119

Subgroups — #21445119

Order 7808.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#16840516C211yesmaximal, characteristic, complemented
2#16840151C211yesmaximal, characteristic
3#16840128C211yesmaximal, characteristic, complemented
4#16840127C211yesmaximal, characteristic, complemented
5#16839503C211yesmaximal, characteristic, complemented
6#16839501C211yesmaximal, characteristic, complemented
7C61×#330C211yesmaximal, characteristic, complemented
8C2×#11758190—21no—
9C2×D488—21no—
10#14519776—21no—
11#14519774C2211yescharacteristic
12#14519772—21no—
13#14519772—21no—
14#14519769C2211yescharacteristic
15#14519765C2211yescharacteristic
16#14519762—21no—
17#14519757—21no—
18#14519755—21no—
19#14519699—21no—
20#14519699—21no—
21#14519697—21no—
22#14519697—21no—
23#14519688C2211yescharacteristic
24#125×C61C2211yescharacteristic
25#97×C61C2211yescharacteristic
26#97×C61C2211yescharacteristic
27C2×D244—21no—
28C2×D244—21no—
29C2×D244—21no—
30C2×D244D411yescharacteristic
31C2×C4×D61—21no—
32C2×Dic122—21no—
33C2×Dic122D411yescharacteristic
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61D411yescharacteristic
39C4⋊C4×C61D411yescharacteristic
40C42×C61C2311yescharacteristic
41#11758198—21no—
42#11758198—21no—
43#11758198—21no—
44#11758198—21no—
45#11758198—21no—
46C4⋊Dic61—21no—
47C4⋊Dic61D411yescharacteristic
48C4⋊Dic61D411yescharacteristic
49#11758196—21no—
50#11758196—21no—
51#11758196—21no—
52C4×Dic61—21no—
53C2×#92418—21no—
54D488—42no—
55#11758190—42no—
56C22×D61—21no—
57C22×D61—41no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×Dic61—21no—
64C2×Dic61—21no—
65C2×Dic61—21no—
66D244—41no—
67D244—41no—
68D244—41no—
69D244—42no—
70D244—42no—
71C4×D61—81no—
72Dic122—41no—
73Dic122—81no—
74C8×C61—22no—
75C8×C61—41no—
76#92418—41no—
77C22×C61#12011yescharacteristic
78C2×D61—41no—
79C2×D61—41no—
80C2×D61—41no—
81C2×D61—81no—
82C2×D61—81no—
83C2×D61—81no—
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—21no—
87C4×C61—41no—
88C4×C61—41no—
89Dic61—41no—
90Dic61—41no—
91Dic61—41no—
92#1657—611nomaximal, Sylow
93C2×C61#45311yescharacteristic
94C2×C61#45411yescharacteristic
95C2×C61#45411yescharacteristic
96D61—81no—
97D61—161no—
98#563—611no—
99#496—611no—
100#490—611no—
101#490—611no—
102#330—611no—
103#330D6111yescharacteristic, complemented
104#329—611no—
105C61#165711yescharacteristic, complemented, Sylow
106C2×SD16—1221no—
107C2×D8—1221no—
108C4⋊Q8—1221no—
109#127—611no—
110#126—1221no—
111#126—1221no—
112#125—611no—
113#125C2×D6111yescharacteristic
114#124—611no—
115#123—1221no—
116C22⋊Q8—1221no—
117C22⋊Q8—1221no—
118#102—1221no—
119#102—1221no—
120#102—1221no—
121#102—1221no—
122#97—611no—
123#97C2×D6111yescharacteristic
124#97C2×D6111yescharacteristic
125C2×Q8—611no—
126C2×Q8—1221no—
127C2×D4—611no—
128C2×D4—1221no—
129C2×D4—1221no—
130C2×D4—1221no—
131C22×C4—1221no—
132SD16—2442no—
133D8—2442no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1221no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—611no—
140C4⋊C4—611no—
141C4⋊C4—1221no—
142C4⋊C4—1221no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C4⋊C4D24411yescharacteristic
146C4⋊C4D24411yescharacteristic
147C22⋊C4—1221no—
148C22⋊C4—1221no—
149C22⋊C4—1221no—
150C22⋊C4—1221no—
151C22⋊C4—1221no—
152C42—1221no—
153C42C22×D6111yescharacteristic
154C23—1221no—
155C23—2441no—
156Q8—4881no—
157Q8—2441no—
158D4—2441no—
159D4—2441no—
160D4—2442no—
161D4—2442no—
162D4—2441no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—1221no—
166C2×C4—1221no—
167C2×C4—1221no—
168C2×C4—4881no—
169C2×C4C2×D24411yescharacteristic
170C2×C4D4×D6111yescharacteristic
171C2×C4D4×D6111yescharacteristic
172C8—22no—
173C8—41no—
174C8—2441no—
175C22—4881no—
176C22—4881no—
177C22—4881no—
178C22—2441no—
179C22—2441no—
180C22—2441no—
181C22#1451974711yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—2441no—
188C4—2441no—
189C4—2441no—
190C2—9761no—
191C2—4881no—
192C2#1683993111yescharacteristic
193C2#1683993611yescharacteristic
194C2#1683993711yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#330C2
socleC22×C61#120
hypercenter#330D61
hypocenterC61#1657
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #16840516C2semidirect
3. #16840128C2semidirect
4. #16840127C2semidirect
5. #16839503C2semidirect
6. #16839501C2semidirect
7. C61×#330C2semidirect
103. #330D61semidirect
105. C61#1657semidirect