Finite Group Databasebeta

← #21445141

Subgroups — #21445141

Order 7808.

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

normal subgroups only

This group has 196 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#16840506C211yesmaximal, characteristic
2#16840130C211yesmaximal, characteristic, complemented
3#16840124C211yesmaximal, characteristic, complemented
4#16839503C211yesmaximal, characteristic, complemented
5#16839502C211yesmaximal, characteristic, complemented
6#16839501C211yesmaximal, characteristic, complemented
7C61×#489C211yesmaximal, characteristic, complemented
8#14519769C2211yescharacteristic
9#14519765C2211yescharacteristic
10#14519761—21no—
11#14519759—21no—
12#14519754—21no—
13#14519753—21no—
14#14519750—21no—
15#14519749—21no—
16#14519701—21no—
17#14519701—21no—
18#14519700—21no—
19#14519697—21no—
20#14519688C2211yescharacteristic
21#14519688C2211yescharacteristic
22C4⋊Q8×C61C2211yescharacteristic
23#124×C61C2211yescharacteristic
24#103×C61—21no—
25#102×C61—21no—
26#97×C61C2211yescharacteristic
27C2×Q8×C61—21no—
28C2×Q8×C61D411yescharacteristic
29C2×D4×C61D411yescharacteristic
30C2×C22⋊D61—21no—
31C2×C22⋊D61—21no—
32C22×Dic61—21no—
33C2×D244D411yescharacteristic
34C2×C4×D61—21no—
35C2×Dic122D411yescharacteristic
36C2×C8×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61—21no—
39C22⋊C4×C61—21no—
40C22⋊C4×C61—21no—
41C42×C61C2311yescharacteristic
42C22⋊Dic61—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—
52C2×#92418—21no—
53C2×#92418—21no—
54C23×C61—21no—
55C22×D61—21no—
56Q8×C61—41no—
57Q8×C61—42no—
58D4×C61—41no—
59C2×C4×C61—21no—
60C2×C4×C61—41no—
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C22⋊D61—81no—
65C22⋊D61—81no—
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—21no—
69C2×Dic61—81no—
70D244—41no—
71C4×D61—81no—
72Dic122—41no—
73C8×C61—41no—
74#92418—41no—
75#92418—41no—
76C22×C61—41no—
77C22×C61—41no—
78C22×C61—41no—
79C22×C61#12011yescharacteristic
80C2×D61—41no—
81C2×D61—41no—
82C2×D61—41no—
83C4×C61—21no—
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—41no—
87C4×C61—81no—
88Dic61—41no—
89Dic61—41no—
90Dic61—41no—
91#1662—611nomaximal, Sylow
92C2×C61—81no—
93C2×C61#45411yescharacteristic
94C2×C61#45511yescharacteristic
95C2×C61#45511yescharacteristic
96D61—81no—
97#562—611no—
98#491—611no—
99#489—611no—
100#489D6111yescharacteristic, complemented
101#330—611no—
102#329—611no—
103#329—611no—
104C61#166211yescharacteristic, complemented, Sylow
105C4⋊Q8C2×D6111yescharacteristic
106#125—611no—
107#124—611no—
108#124C2×D6111yescharacteristic
109#123—1221no—
110#123—1221no—
111C22⋊Q8—1221no—
112C22⋊Q8—1221no—
113#121—1221no—
114#121—1221no—
115#103—21no—
116#103—1221no—
117#103—1221no—
118#103—1221no—
119#102—21no—
120#102—1221no—
121#97—611no—
122#97—611no—
123#97C2×D6111yescharacteristic
124C2×Q8—21no—
125C2×Q8—611no—
126C2×Q8C22⋊D6111yescharacteristic
127C2×D4—611no—
128C2×D4—1221no—
129C2×D4—1221no—
130C2×D4C22⋊D6111yescharacteristic
131C22×C4—1221no—
132C22×C4—1221no—
133C2×C8—21no—
134C2×C8—1221no—
135C2×C8—1221no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—611no—
139C4⋊C4—611no—
140C4⋊C4—1221no—
141C4⋊C4—1221no—
142C4⋊C4—1221no—
143C4⋊C4—1221no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—1221no—
147C22⋊C4—1221no—
148C22⋊C4—1221no—
149C22⋊C4—1221no—
150C42C22×D6111yescharacteristic
151C23—21no—
152C23—1221no—
153Q8—41no—
154Q8—42no—
155Q8—2441no—
156D4—41no—
157D4—4881no—
158D4—4881no—
159D4—2441no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—1221no—
163C2×C4—1221no—
164C2×C4—1221no—
165C2×C4—4881no—
166C2×C4—4881no—
167C2×C4D4×D6111yescharacteristic
168C2×C4D4×D6111yescharacteristic
169C2×C4C2×C22⋊D6111yescharacteristic
170C8—41no—
171C8—2441no—
172C8—2441no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—2441no—
177C22—2441no—
178C22—2441no—
179C22#1451974511yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—81no—
185C4—2441no—
186C4—2441no—
187C4—2441no—
188C2—81no—
189C2—4881no—
190C2#1683993311yescharacteristic
191C2#1683993811yescharacteristic
192C2#1683993911yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#489C2
socleC22×C61#120
hypercenter#489D61
hypocenterC61#1662
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #16840130C2semidirect
3. #16840124C2semidirect
4. #16839503C2semidirect
5. #16839502C2semidirect
6. #16839501C2semidirect
7. C61×#489C2semidirect
100. #489D61semidirect
104. C61#1662semidirect