Finite Group Databasebeta

← #21447768

Subgroups — #21447768

Order 7808.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#16840559C211yesmaximal, characteristic
2#16840203C211yesmaximal, characteristic, complemented
3#16840017C211yesmaximal, characteristic, complemented
4#16839573C211yesmaximal, characteristic, complemented
5#16839572C211yesmaximal, characteristic, complemented
6#16839543C211yesmaximal, characteristic, complemented
7C61×#510C211yesmaximal, characteristic, complemented
8#41×D61—21no—
9#14519809—21no—
10#14519806—21no—
11#14519804—21no—
12#14519801—21no—
13#14519799C2211yescharacteristic
14#14519797—21no—
15C2×#11758189C2211yescharacteristic
16#14519753—21no—
17#14519723—21no—
18#14519720—21no—
19#14519717C2211yescharacteristic, complemented
20#14519709C2211yescharacteristic, complemented
21#14519701—21no—
22#135×C61C2211yescharacteristic
23C2×Q16×C61C2211yescharacteristic, complemented
24Q32×C61—21no—
25SD32×C61—21no—
26M32×C61C2211yescharacteristic, complemented
27#41×C61—21no—
28C2×Q8×C61—21no—
29#11758226—21no—
30Q8×D61—21no—
31#11758224—21no—
32#11758224—41no—
33D4×D61—21no—
34D4×D61—41no—
35#11758222—21no—
36#11758222—41no—
37C2×C4×D61—41no—
38C2×C4×D61D411yescharacteristic
39Q16×C61—21no—
40Q16×C61—21no—
41Q16×C61D411yescharacteristic
42SD16×C61—21no—
43D8×C61D411yescharacteristic
44C2×C8×C61C2311yescharacteristic
45#11758202—21no—
46#11758201—21no—
47#11758200—21no—
48#11758199—21no—
49#11758198—41no—
50C4⋊Dic61—21no—
51#11758196—41no—
52C2×#92418D411yescharacteristic
53Dic244D411yescharacteristic
54D488D411yescharacteristic
55#11758190—21no—
56#11758189—21no—
57#11758189—21no—
58C16×C61—21no—
59#11758185—21no—
60C22×D61—41no—
61C22×D61D811yescharacteristic
62Q8×C61—21no—
63Q8×C61—41no—
64Q8×C61—41no—
65D4×C61—21no—
66D4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61C2×D411yescharacteristic
70C22⋊D61—41no—
71C22⋊D61—41no—
72C22⋊D61—41no—
73C2×Dic61—41no—
74C2×Dic61—41no—
75C2×Dic61D811yescharacteristic
76D244—21no—
77D244—41no—
78C4×D61—21no—
79C4×D61—21no—
80C4×D61—41no—
81C4×D61—41no—
82C4×D61—41no—
83Dic122—21no—
84Dic122—41no—
85C8×C61C2×D411yescharacteristic
86C8×C61C2×D411yescharacteristic
87#92418—21no—
88C22×C61—41no—
89C22×C61C2×D811yescharacteristic
90C2×D61—21no—
91C2×D61—41no—
92C2×D61—41no—
93C2×D61—82no—
94C4×C61—41no—
95C4×C61—81no—
96C4×C61#12011yescharacteristic
97C4×C61AGL(1,ℤ/8)11yescharacteristic
98Dic61—21no—
99Dic61—41no—
100Dic61—81no—
101#2191—611nomaximal, Sylow
102C2×C61—21no—
103C2×C61—81no—
104C2×C61#44711yescharacteristic
105D61—41no—
106D61—81no—
107#575—611no—
108#510—611no—
109#510D6111yescharacteristic, complemented
110#470—611no—
111#360—611no—
112#360—611no—
113#349—611no—
114C61#219111yescharacteristic, complemented, Sylow
115C2×#41—1221no—
116#137—1221no—
117#137—1221no—
118AGL(1,ℤ/8)—1221no—
119AGL(1,ℤ/8)—1221no—
120#135—611no—
121#135—1221no—
122#135C2×D6111yescharacteristic
123C2×Q16C2×D6111yescharacteristic, complemented
124C2×M16—611no—
125C22⋊Q8—1221no—
126Q32—21no—
127Q32—1221no—
128SD32—21no—
129SD32—1221no—
130M32—611no—
131M32C2×D6111yescharacteristic, complemented
132#106—611no—
133#103—1221no—
134#41—21no—
135#41—1221no—
136#41—1221no—
137#41—1221no—
138#41—2441no—
139#41—2441no—
140C2×Q8—21no—
141C2×Q8—1221no—
142C2×D4—1221no—
143C2×D4—2441no—
144C22×C4—611no—
145C22×C4—2441no—
146Q16—21no—
147Q16—21no—
148Q16—611no—
149Q16—1221no—
150Q16C22⋊D6111yescharacteristic
151SD16—21no—
152SD16—1221no—
153SD16—1221no—
154SD16—1221no—
155D8—611no—
156D8—1221no—
157D8C22⋊D6111yescharacteristic
158M16—1221no—
159M16—1221no—
160C2×C8—611no—
161C2×C8C22×D6111yescharacteristic
162C4⋊C4—1221no—
163C4⋊C4—2441no—
164C22⋊C4—2441no—
165C16—21no—
166C16—1221no—
167C23—611no—
168C23—2441no—
169Q8—21no—
170Q8—41no—
171Q8—41no—
172Q8—1221no—
173Q8—2441no—
174D4—21no—
175D4—41no—
176D4—1221no—
177D4—2441no—
178D4—2441no—
179D4—2441no—
180D4—2441no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—611no—
184C2×C4—1221no—
185C2×C4—1221no—
186C2×C4—2441no—
187C2×C4—2441no—
188C2×C4—2441no—
189C2×C4—2441no—
190C2×C4—2441no—
191C2×C4D4×D6111yescharacteristic
192C8—1221no—
193C8D4×D6111yescharacteristic
194C8C2×C22⋊D6111yescharacteristic
195C22—41no—
196C22—1221no—
197C22—4882no—
198C22—2441no—
199C22—2441no—
200C22D8×D6111yescharacteristic
201C4—41no—
202C4—81no—
203C4—1221no—
204C4—4881no—
205C4—2441no—
206C4#1451974511yescharacteristic
207C4#1451980111yescharacteristic
208C2—21no—
209C2—81no—
210C2—4881no—
211C2—2441no—
212C2#1683989411yescharacteristic
subgroupG/H
centerC2#16839894
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#510C2
socleC2×C61#447
hypercenter#510D61
hypocenterC61#2191
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. #16840203C2semidirect
3. #16840017C2semidirect
4. #16839573C2semidirect
5. #16839572C2semidirect
6. #16839543C2semidirect
7. C61×#510C2semidirect
19. #14519717C22semidirect
20. #14519709C22semidirect
23. C2×Q16×C61C22semidirect
26. M32×C61C22semidirect
109. #510D61semidirect
114. C61#2191semidirect
123. C2×Q16C2×D61semidirect
131. M32C2×D61semidirect