Finite Group Databasebeta

← #21445127

Subgroups — #21445127

Order 7808.

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

normal subgroups only

This group has 228 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#16840504C211yesmaximal, characteristic
2#16840156C211yesmaximal, characteristic, complemented
3#16840122C211yesmaximal, characteristic, complemented
4#16840121C211yesmaximal, characteristic, complemented
5#16839501C211yesmaximal, characteristic, complemented
6#16839501C211yesmaximal, characteristic, complemented
7C61×#329C211yesmaximal, characteristic, complemented
8C2×Dic244—21no—
9C2×#11758190—21no—
10#14519777C2211yescharacteristic, complemented
11#14519766—21no—
12#14519765C2211yescharacteristic
13#14519765C2211yescharacteristic
14#14519763—21no—
15#14519763—21no—
16#14519747—21no—
17#14519747—21no—
18#14519745—21no—
19#14519702—21no—
20#14519701—21no—
21#14519699—21no—
22#14519698—21no—
23#14519688C2211yescharacteristic, complemented
24#124×C61C2211yescharacteristic
25#97×C61C2211yescharacteristic, complemented
26#97×C61C2211yescharacteristic, complemented
27C23×D61—21no—
28C2×Q8×C61D411yescharacteristic
29C2×D4×C61D411yescharacteristic
30C2×C22⋊D61—21no—
31C2×C22⋊D61—21no—
32C2×D244—21no—
33C2×D244D411yescharacteristic
34C2×D244D411yescharacteristic
35C2×Dic122—21no—
36C2×Dic122D411yescharacteristic
37C2×Dic122D411yescharacteristic
38C2×C8×C61—21no—
39C2×C8×C61—21no—
40C22⋊C4×C61—21no—
41C22⋊C4×C61—21no—
42C42×C61C2311yescharacteristic
43C22⋊Dic61—21no—
44#11758198—21no—
45#11758198—21no—
46#11758198—21no—
47#11758198—21no—
48#11758198—21no—
49#11758198—21no—
50C4⋊Dic61—21no—
51C4⋊Dic61—21no—
52C4×Dic61—21no—
53C2×#92418—21no—
54Dic244—42no—
55#11758190—42no—
56C23×C61—21no—
57C22×D61—21no—
58C22×D61—21no—
59C22×D61—81no—
60C22×D61—81no—
61C22×D61—81no—
62Q8×C61—41no—
63D4×C61—41no—
64C2×C4×C61—21no—
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C22⋊D61—81no—
69C22⋊D61—81no—
70C2×Dic61—21no—
71C2×Dic61—21no—
72C2×Dic61—41no—
73D244—41no—
74D244—41no—
75D244—81no—
76Dic122—41no—
77Dic122—41no—
78Dic122—41no—
79Dic122—41no—
80C8×C61—22no—
81C8×C61—41no—
82#92418—41no—
83C22×C61—41no—
84C22×C61—41no—
85C22×C61—41no—
86C22×C61#12011yescharacteristic
87C2×D61—41no—
88C2×D61—41no—
89C2×D61—41no—
90C2×D61—41no—
91C2×D61—41no—
92C2×D61—41no—
93C2×D61—84no—
94C4×C61—21no—
95C4×C61—21no—
96C4×C61—21no—
97C4×C61—41no—
98Dic61—41no—
99Dic61—41no—
100Dic61—81no—
101#1659—611nomaximal, Sylow
102C2×C61—81no—
103C2×C61#45311yescharacteristic
104C2×C61#45511yescharacteristic
105C2×C61#45511yescharacteristic
106D61—81no—
107D61—81no—
108H(3,𝔽4)—611no—
109#497—611no—
110#489—611no—
111#489—611no—
112#329—611no—
113#329—611no—
114#329D6111yescharacteristic, complemented
115C61#165911yescharacteristic, complemented, Sylow
116C2×Q16—1221no—
117C2×SD16—1221no—
118C4⋊Q8—611no—
119#124—611no—
120#124—611no—
121#124—1221no—
122#124—1221no—
123#124—1221no—
124#124C2×D6111yescharacteristic
125#120—1221no—
126#120—1221no—
127#120—1221no—
128#103—1221no—
129#103—1221no—
130#102—1221no—
131#102—1221no—
132#97—611no—
133#97C2×D6111yescharacteristic, complemented
134#97C2×D6111yescharacteristic, complemented
135C24—1221no—
136C2×Q8—611no—
137C2×Q8—611no—
138C2×Q8—1221no—
139C2×Q8D24411yescharacteristic
140C2×D4—611no—
141C2×D4—611no—
142C2×D4—1221no—
143C2×D4—1221no—
144C2×D4—1221no—
145C2×D4D24411yescharacteristic
146Q16—2442no—
147SD16—2442no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—1221no—
151C4⋊C4—1221no—
152C4⋊C4—1221no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—1221no—
156C22⋊C4—1221no—
157C22⋊C4—1221no—
158C22⋊C4—1221no—
159C22⋊C4—1221no—
160C22⋊C4—1221no—
161C22⋊C4—1221no—
162C42—1221no—
163C42C22×D6111yescharacteristic
164C23—21no—
165C23—1221no—
166C23—1221no—
167C23—4881no—
168C23—4881no—
169C23—4881no—
170Q8—41no—
171Q8—2441no—
172Q8—2441no—
173Q8—2441no—
174Q8—2441no—
175D4—41no—
176D4—4881no—
177D4—4881no—
178D4—4881no—
179D4—2441no—
180D4—2441no—
181C2×C4—21no—
182C2×C4—1221no—
183C2×C4—1221no—
184C2×C4—2441no—
185C2×C4C2×D24411yescharacteristic
186C2×C4D4×D6111yescharacteristic
187C2×C4D4×D6111yescharacteristic
188C8—22no—
189C8—41no—
190C8—2441no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—4884no—
195C22—2441no—
196C22—2441no—
197C22—2441no—
198C22—2441no—
199C22—2441no—
200C22—2441no—
201C22#1451974711yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—4881no—
207C4—2441no—
208C4—2441no—
209C2—81no—
210C2—4881no—
211C2—4881no—
212C2#1683993111yescharacteristic
213C2#1683994111yescharacteristic
214C2#1683994211yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#329C2
socleC22×C61#120
hypercenter#329D61
hypocenterC61#1659
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #16840156C2semidirect
3. #16840122C2semidirect
4. #16840121C2semidirect
5. #16839501C2semidirect
6. #16839501C2semidirect
7. C61×#329C2semidirect
10. #14519777C22semidirect
23. #14519688C22semidirect
25. #97×C61C22semidirect
26. #97×C61C22semidirect
114. #329D61semidirect
115. C61#1659semidirect
133. #97C2×D61semidirect
134. #97C2×D61semidirect