Finite Group Databasebeta

← #21447445

Subgroups — #21447445

Order 7808.

220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 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#131×D61C211yesmaximal, characteristic
2C2×#14519716C211yesmaximal, characteristic, complemented
3M32×D61C211yesmaximal, characteristic, complemented
4#16839547C211yesmaximal, characteristic, complemented
5#16839546C211yesmaximal, characteristic, complemented
6#16839545C211yesmaximal, characteristic, complemented
7C61×#350C211yesmaximal, characteristic, complemented
8#41×D61C411yescharacteristic
9#14519785—21no—
10#14519785C411yescharacteristic
11#14519784C411yescharacteristic
12#14519783—21no—
13#14519783C2211yescharacteristic
14M16×D61—21no—
15M16×D61C411yescharacteristic
16C2×C8×D61—21no—
17C2×C8×D61C2211yescharacteristic
18#14519717C2211yescharacteristic, complemented
19#14519716—21no—
20#14519716—21no—
21#14519716—21no—
22C2×#11758185C2211yescharacteristic, complemented
23C16×D61—21no—
24#131×C61C2211yescharacteristic
25M32×C61C2211yescharacteristic, complemented
26C2×C16×C61C2211yescharacteristic, complemented
27#41×C61C2×C411yescharacteristic
28#11758226C811yescharacteristic
29Q8×D61C811yescharacteristic
30#11758224—21no—
31#11758224C811yescharacteristic
32D4×D61—21no—
33D4×D61C811yescharacteristic
34#11758222—21no—
35#11758222C2×C411yescharacteristic
36C2×C4×D61—21no—
37C2×C4×D61C2×C411yescharacteristic
38M16×C61—21no—
39M16×C61C2×C411yescharacteristic
40C2×C8×C61—21no—
41C2×C8×C61C2311yescharacteristic
42#11758194—21no—
43#11758194C2×C411yescharacteristic
44C2×#92418—21no—
45C2×#92418C2×C411yescharacteristic
46#11758189—21no—
47#11758189—21no—
48#11758189—21no—
49C8×D61—21no—
50C8×D61—21no—
51C8×D61—21no—
52C8×D61D411yescharacteristic
53C8×D61D411yescharacteristic
54C8×D61D411yescharacteristic
55C8×D61D411yescharacteristic
56C16×C61—21no—
57C16×C61—21no—
58#11758185—21no—
59#11758185—21no—
60C22×D61—21no—
61C22×D61M1611yescharacteristic
62Q8×C61C2×C811yescharacteristic
63D4×C61—21no—
64D4×C61C2×C811yescharacteristic
65C2×C4×C61—21no—
66C2×C4×C61C22×C411yescharacteristic
67C22⋊D61—21no—
68C22⋊D61—21no—
69C22⋊D61—21no—
70C2×Dic61—21no—
71C2×Dic61M1611yescharacteristic
72D244—21no—
73D244C2×C811yescharacteristic
74C4×D61—21no—
75C4×D61—21no—
76C4×D61—21no—
77C4×D61C22⋊C411yescharacteristic
78C4×D61C22⋊C411yescharacteristic
79C4×D61C2×C811yescharacteristic
80C4×D61C2×C811yescharacteristic
81Dic122—21no—
82Dic122C2×C811yescharacteristic
83C8×C61—21no—
84C8×C61C2×D411yescharacteristic
85C8×C61C2×D411yescharacteristic
86#92418—21no—
87#92418C22⋊C411yescharacteristic
88#92418C22⋊C411yescharacteristic
89C22×C61—21no—
90C22×C61C2×M1611yescharacteristic
91C2×D61—21no—
92C2×D61—41no—
93C2×D61—42no—
94C2×D61C22⋊C811yescharacteristic
95C2×D61C22⋊C811yescharacteristic
96C4×C61—21no—
97C4×C61C2×C22⋊C411yescharacteristic
98C4×C61C22×C811yescharacteristic
99Dic61—21no—
100Dic61C22⋊C811yescharacteristic
101Dic61C22⋊C811yescharacteristic
102#2117—611nomaximal, Sylow
103C2×C61—21no—
104C2×C61—41no—
105C2×C61C2×C22⋊C811yescharacteristic
106D61—21no—
107D61—21no—
108D61—41no—
109C2×#131—611no—
110C2×M32—611no—
111C2×M32—611no—
112#350—611no—
113#350—611no—
114#350—611no—
115#350D6111yescharacteristic, complemented
116C61#211711yescharacteristic, complemented, Sylow
117C2×#41—611no—
118#131—611no—
119#131—611no—
120#131—611no—
121#131—1221no—
122#131—1221no—
123#131C2×D6111yescharacteristic
124C2×M16—611no—
125C2×M16—1221no—
126C22×C8—611no—
127C22×C8—1221no—
128M32—611no—
129M32—1221no—
130M32—1221no—
131M32—1221no—
132M32C2×D6111yescharacteristic, complemented
133C2×C16—611no—
134C2×C16—1221no—
135C2×C16C2×D6111yescharacteristic, complemented
136#41—611no—
137#41—611no—
138#41—611no—
139#41—1221no—
140#41—1221no—
141#41C4×D6111yescharacteristic
142C2×Q8—611no—
143C2×D4—611no—
144C2×D4—1221no—
145C22×C4—611no—
146C22×C4—1221no—
147M16—21no—
148M16—611no—
149M16—1221no—
150M16—1221no—
151M16—1221no—
152M16—1221no—
153M16C4×D6111yescharacteristic
154C2×C8—21no—
155C2×C8—611no—
156C2×C8—611no—
157C2×C8—611no—
158C2×C8—611no—
159C2×C8—611no—
160C2×C8—1221no—
161C2×C8—1221no—
162C2×C8—1221no—
163C2×C8—1221no—
164C2×C8C22×D6111yescharacteristic
165C16—21no—
166C16—21no—
167C16—1221no—
168C16—1221no—
169C23—611no—
170C23—1221no—
171Q8—611no—
172Q8—1221no—
173Q8C8×D6111yescharacteristic
174D4—21no—
175D4—611no—
176D4—1221no—
177D4—1221no—
178D4—1221no—
179D4—1221no—
180D4C8×D6111yescharacteristic
181C2×C4—21no—
182C2×C4—611no—
183C2×C4—611no—
184C2×C4—611no—
185C2×C4—611no—
186C2×C4—611no—
187C2×C4—1221no—
188C2×C4—1221no—
189C2×C4—1221no—
190C2×C4—1221no—
191C2×C4C2×C4×D6111yescharacteristic
192C8—21no—
193C8—611no—
194C8—611no—
195C8—1221no—
196C8D4×D6111yescharacteristic
197C8D4×D6111yescharacteristic
198C22—21no—
199C22—611no—
200C22—611no—
201C22—1221no—
202C22—2441no—
203C22—2442no—
204C22M16×D6111yescharacteristic
205C4—21no—
206C4—611no—
207C4—611no—
208C4—1221no—
209C4C22⋊C4×D6111yescharacteristic
210C4C2×C8×D6111yescharacteristic
211C2—21no—
212C2—41no—
213C2—1221no—
214C2—1221no—
215C2—2441no—
216C2C22⋊C8×D6111yescharacteristic
subgroupG/H
centerC8D4×D61
commutatorC4×C61C22×C8
FrattiniC2×C8C22×D61
FittingC61×#350C2
socleC2×C61C2×C22⋊C8
hypercenter#350D61
hypocenterC61#2117
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C8 ◁ C2×C8 ◁ #350

Complements

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

NH ≅ G/Ntype
2. C2×#14519716C2semidirect
3. M32×D61C2semidirect
4. #16839547C2semidirect
5. #16839546C2semidirect
6. #16839545C2semidirect
7. C61×#350C2semidirect
18. #14519717C22semidirect
22. C2×#11758185C22semidirect
25. M32×C61C22semidirect
26. C2×C16×C61C22semidirect
115. #350D61semidirect
116. C61#2117semidirect
132. M32C2×D61semidirect
135. C2×C16C2×D61semidirect