Finite Group Databasebeta

← #21447553

Subgroups — #21447553

Order 7808.

224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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#135×D61C211yesmaximal, characteristic
2M32×D61C211yesmaximal, characteristic, complemented
3#16839797C211yesmaximal, characteristic, complemented
4#16839573C211yesmaximal, characteristic, complemented
5#16839572C211yesmaximal, characteristic, complemented
6#16839571C211yesmaximal, characteristic, complemented
7C61×#360C211yesmaximal, characteristic, complemented
8#41×D61—21no—
9#14519800C411yescharacteristic, complemented
10#14519799C2211yescharacteristic
11#14519798—21no—
12#14519797—21no—
13#14519796C411yescharacteristic, complemented
14Q16×D61C411yescharacteristic, complemented
15SD16×D61—21no—
16D8×D61C411yescharacteristic, complemented
17C2×C8×D61C2211yescharacteristic
18#14519735—21no—
19#14519717C2211yescharacteristic, complemented
20#14519716—21no—
21C16×D61—21no—
22#14519710—21no—
23#14519709C2211yescharacteristic, complemented
24#135×C61C2211yescharacteristic
25M32×C61C2211yescharacteristic, complemented
26#106×C61C2211yescharacteristic, complemented
27#41×C61—21no—
28#11758226—21no—
29Q8×D61—21no—
30#11758224—21no—
31#11758224—41no—
32D4×D61—21no—
33D4×D61—41no—
34#11758222—21no—
35#11758222—41no—
36C2×C4×D61—41no—
37C2×C4×D61D411yescharacteristic
38Q16×C61C2×C411yescharacteristic
39SD16×C61—21no—
40D8×C61C2×C411yescharacteristic
41C2×C8×C61C2311yescharacteristic
42C4⋊C4×C61—21no—
43#11758202—21no—
44#11758201—21no—
45#11758200—21no—
46#11758199—21no—
47#11758198—41no—
48C4⋊Dic61—21no—
49C4×Dic61—41no—
50C2×#92418D411yescharacteristic
51Dic244C2×C411yescharacteristic
52D488C2×C411yescharacteristic
53#11758190—21no—
54C8×D61C2×C411yescharacteristic
55C8×D61C2×C411yescharacteristic
56C8×D61D411yescharacteristic
57C8×D61D411yescharacteristic
58C16×C61—21no—
59#11758185—21no—
60C22×D61—41no—
61C22×D61D811yescharacteristic
62Q8×C61—21no—
63D4×C61—21no—
64D4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61C2×D411yescharacteristic
68C22⋊D61—41no—
69C22⋊D61—41no—
70C22⋊D61—41no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61D811yescharacteristic
74D244—21no—
75D244—41no—
76C4×D61—41no—
77C4×D61—41no—
78C4×D61—41no—
79C4×D61C22⋊C411yescharacteristic
80C4×D61C22⋊C411yescharacteristic
81C4×D61SD1611yescharacteristic
82C4×D61SD1611yescharacteristic
83Dic122—21no—
84Dic122—41no—
85C8×C61C22×C411yescharacteristic
86C8×C61C2×D411yescharacteristic
87#92418C22⋊C411yescharacteristic
88#92418C22⋊C411yescharacteristic
89C22×C61—41no—
90C22×C61C2×D811yescharacteristic
91C2×D61—41no—
92C2×D61—41no—
93C2×D61—82no—
94C2×D61#10211yescharacteristic
95C2×D61#10211yescharacteristic
96C4×C61—41no—
97C4×C61—81no—
98C4×C61C2×C22⋊C411yescharacteristic
99C4×C61C2×SD1611yescharacteristic
100Dic61—41no—
101Dic61—81no—
102Dic61#10211yescharacteristic
103Dic61#10211yescharacteristic
104#2145—611nomaximal, Sylow
105C2×C61—21no—
106C2×C61—81no—
107C2×C61C2×#10211yescharacteristic
108D61—21no—
109D61—21no—
110D61—81no—
111C2×#135—611no—
112C2×M32—611no—
113#427—611no—
114#360—611no—
115#360—611no—
116#360—611no—
117#360D6111yescharacteristic, complemented
118C61#214511yescharacteristic, complemented, Sylow
119C2×#41—1221no—
120#135—611no—
121#135—611no—
122#135—611no—
123#135—1221no—
124#135—1221no—
125#135C2×D6111yescharacteristic
126C2×Q16—611no—
127C2×SD16—1221no—
128C2×D8—611no—
129C22×C8—611no—
130#117—1221no—
131M32—611no—
132M32—1221no—
133M32C2×D6111yescharacteristic, complemented
134C2×C16—1221no—
135#107—1221no—
136#106—611no—
137#106C2×D6111yescharacteristic, complemented
138#41—21no—
139#41—1221no—
140#41—1221no—
141#41—1221no—
142#41—2441no—
143#41—2441no—
144C2×Q8—1221no—
145C2×D4—1221no—
146C2×D4—2441no—
147C22×C4—611no—
148C22×C4—2441no—
149Q16—611no—
150Q16—1221no—
151Q16C4×D6111yescharacteristic
152SD16—21no—
153SD16—1221no—
154SD16—1221no—
155SD16—1221no—
156D8—611no—
157D8—1221no—
158D8C4×D6111yescharacteristic
159C2×C8—611no—
160C2×C8—611no—
161C2×C8—611no—
162C2×C8—611no—
163C2×C8—611no—
164C2×C8C22×D6111yescharacteristic
165C4⋊C4—21no—
166C4⋊C4—1221no—
167C22⋊C4—2441no—
168C42—2441no—
169C16—21no—
170C16—1221no—
171C23—611no—
172C23—2441no—
173Q8—21no—
174Q8—1221no—
175Q8—2441no—
176D4—21no—
177D4—41no—
178D4—1221no—
179D4—2441no—
180D4—2441no—
181D4—2441no—
182D4—2441no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—611no—
186C2×C4—611no—
187C2×C4—611no—
188C2×C4—611no—
189C2×C4—611no—
190C2×C4—2441no—
191C2×C4—2441no—
192C2×C4—2441no—
193C2×C4—2441no—
194C2×C4—2441no—
195C2×C4D4×D6111yescharacteristic
196C8—611no—
197C8—611no—
198C8C2×C4×D6111yescharacteristic
199C8D4×D6111yescharacteristic
200C22—41no—
201C22—611no—
202C22—611no—
203C22—4882no—
204C22—2441no—
205C22—2441no—
206C22D8×D6111yescharacteristic
207C4—41no—
208C4—81no—
209C4—611no—
210C4—611no—
211C4—4881no—
212C4—2441no—
213C4C22⋊C4×D6111yescharacteristic
214C4SD16×D6111yescharacteristic
215C2—21no—
216C2—81no—
217C2—1221no—
218C2—1221no—
219C2—4881no—
220C2#102×D6111yescharacteristic
subgroupG/H
centerC2#102×D61
commutatorC8×C61C22×C4
FrattiniC2×C8C22×D61
FittingC61×#360C2
socleC2×C61C2×#102
hypercenter#360D61
hypocenterC61#2145
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. M32×D61C2semidirect
3. #16839797C2semidirect
4. #16839573C2semidirect
5. #16839572C2semidirect
6. #16839571C2semidirect
7. C61×#360C2semidirect
9. #14519800C4semidirect
13. #14519796C4semidirect
14. Q16×D61C4semidirect
16. D8×D61C4semidirect
19. #14519717C22semidirect
23. #14519709C22semidirect
25. M32×C61C22semidirect
26. #106×C61C22semidirect
117. #360D61semidirect
118. C61#2145semidirect
133. M32C2×D61semidirect
137. #106C2×D61semidirect