Finite Group Databasebeta

← #29594153

Subgroups — #29594153

Order 15616.

240 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 63 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#21447968C211yesmaximal, characteristic, complemented
2#21447860C211yesmaximal, characteristic
3#21445412C211yesmaximal, characteristic
4#21444625C211yesmaximal, characteristic, complemented
5#21443882C211yesmaximal, characteristic, complemented
6#21443864C211yesmaximal, characteristic
7C61×#1365C211yesmaximal, characteristic, complemented
8C2×#14519722—21no—
9#16840139C2211yescharacteristic
10#16840136—21no—
11#16840110—21no—
12#16839886—21no—
13C4×Dic244C2211yescharacteristic
14#16839587—21no—
15C4⋊#11758185C2211yescharacteristic
16#16839565—21no—
17#16839564—21no—
18#16839492—21no—
19C8×#92418C2211yescharacteristic
20C61×#500C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×Dic244D411yescharacteristic
24C2×#11758201—42no—
25C2×D488—21no—
26C2×D488—21no—
27#14519774—21no—
28C4×Dic122—21no—
29#14519722—42no—
30C2×#11758185—21no—
31#14519711D411yescharacteristic
32#14519706—41no—
33#14519702—21no—
34#14519697—41no—
35#14519697—41no—
36C4×#92418D411yescharacteristic
37C4×#92418D411yescharacteristic
38C8×Dic61—41no—
39C4⋊Q8×C61—21no—
40C2×C16×C61—21no—
41#107×C61—21no—
42#107×C61—21no—
43C4⋊C8×C61—21no—
44C4×C8×C61C2311yescharacteristic
45C2×Q8×C61—41no—
46C2×D244—41no—
47C2×D244—41no—
48C2×D244—41no—
49C2×Dic122—21no—
50C2×C8×C61—41no—
51C2×C8×C61C2×D411yescharacteristic
52C2×C8×C61#4111yescharacteristic
53C4⋊C4×C61—41no—
54C4⋊C4×C61—41no—
55C42×C61C2×D411yescharacteristic
56#11758201—84no—
57C4⋊Dic61—21no—
58#11758196—41no—
59C4×Dic61—41no—
60C2×#92418—21no—
61C2×#92418D811yescharacteristic
62C2×#92418D811yescharacteristic
63Dic244—21no—
64Dic244SD1612yescomplemented
65D488—41no—
66D488—41no—
67D488—81no—
68C16×C61—41no—
69#11758185—41no—
70C22×D61—81no—
71Q8×C61—82no—
72C2×C4×C61—81no—
73C2×C4×C61#12111yescharacteristic
74C2×C4×C61C2×D811yescharacteristic
75C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
76C2×Dic61—41no—
77C2×Dic61—41no—
78D244—82no—
79D244—81no—
80D244—81no—
81D244—81no—
82D244—81no—
83Dic122—22no—
84Dic122—41no—
85C8×C61—21no—
86C8×C61—81no—
87C8×C61C2×SD1611yescharacteristic
88C8×C61#13511yescharacteristic
89#92418—22no—
90#92418—21no—
91#92418—21no—
92#12419—611nomaximal, Sylow
93C22×C61#45911yescharacteristic
94C2×D61—161no—
95C2×D61—161no—
96C2×D61—161no—
97C4×C61—21no—
98C4×C61—161no—
99C4×C61#46511yescharacteristic
100C4×C61#47111yescharacteristic
101C4×C61#50811yescharacteristic
102C4×C61#51011yescharacteristic
103Dic61—42no—
104Dic61—81no—
105#2227—611no—
106#2207—611no—
107#1706—611no—
108C8×Q16—611no—
109#1367—611no—
110#1365D6111yescharacteristic, complemented
111#1361—611no—
112C2×C61#166511yescharacteristic
113C2×C61#221111yescharacteristic
114C2×C61#221311yescharacteristic
115D61—321no—
116C2×SD32—1221no—
117#500C2×D6111yescharacteristic
118#493—611no—
119#492—1221no—
120#486—1221no—
121C8×Q8—1221no—
122C4×Q16—611no—
123#366—1221no—
124C4⋊C16—611no—
125C4⋊C16C2×D6111yescharacteristic
126#358—1221no—
127#357—1221no—
128#335C2×D6111yescharacteristic
129Q8⋊C8—1221no—
130C82—611no—
131C61#1241911yescharacteristic, complemented, Sylow
132C2×Q16—611no—
133C2×SD16—2442no—
134C2×D8—1221no—
135C2×D8—1221no—
136C4⋊Q8—21no—
137#127—1221no—
138C4×Q8—1221no—
139SD32—2442no—
140C2×C16—21no—
141C2×C16—1221no—
142#107—21no—
143#107—21no—
144#107—611no—
145C4⋊C8—21no—
146C4⋊C8—2441no—
147#103—1221no—
148#102—2441no—
149#102—2441no—
150C4×C8—611no—
151C4×C8—611no—
152C4×C8—2441no—
153C4×C8C22×D6111yescharacteristic
154C2×Q8—41no—
155C2×Q8—1221no—
156C2×D4—2441no—
157C2×D4—2441no—
158C2×D4—2441no—
159Q16—612no—
160Q16—1221no—
161SD16—4884no—
162D8—4881no—
163D8—2441no—
164D8—2441no—
165C2×C8—41no—
166C2×C8—611no—
167C2×C8—611no—
168C2×C8—1221no—
169C2×C8#1175822211yescharacteristic
170C2×C8D4×D6111yescharacteristic
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—1221no—
174C4⋊C4—2441no—
175C42—2441no—
176C42D4×D6111yescharacteristic
177C16—41no—
178C16—2441no—
179C23—4881no—
180Q8—82no—
181Q8—1222no—
182Q8—2441no—
183D4—4882no—
184D4—4881no—
185D4—4881no—
186D4—4881no—
187D4—4881no—
188C2×C4—81no—
189C2×C4—2441no—
190C2×C4—2441no—
191C2×C4#1451975011yescharacteristic
192C2×C4D8×D6111yescharacteristic
193C2×C4#1451980411yescharacteristic
194C8—21no—
195C8—81no—
196C8—1222no—
197C8—1221no—
198C8—1221no—
199C8SD16×D6111yescharacteristic
200C8#1451980011yescharacteristic
201C22—9761no—
202C22—9761no—
203C22—9761no—
204C22#1683995611yescharacteristic
205C4—21no—
206C4—161no—
207C4—4881no—
208C4—2442no—
209C4#1683999411yescharacteristic
210C4#1684002811yescharacteristic
211C4#1684019311yescharacteristic
212C4#1684020411yescharacteristic
213C2—19521no—
214C2#2144516311yescharacteristic
215C2#2144788411yescharacteristic
216C2#2144789411yescharacteristic
subgroupG/H
centerC22#16839956
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1365C2
socleC22×C61#459
prime radical#16840139C22
hypercenter#1365D61
hypocenterC61#12419
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1365

Complements

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

NH ≅ G/Ntype
1. #21447968C2semidirect
4. #21444625C2semidirect
5. #21443882C2semidirect
7. C61×#1365C2semidirect
64. Dic244SD16semidirect
110. #1365D61semidirect
131. C61#12419semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214479682
#214478602
#214454122
#214446252
#214438822
#214438642
C61×#13652
#1241961