Finite Group Databasebeta

← #29598562

Subgroups — #29598562

Order 15616.

316 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 115 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#21454751C211yesmaximal, characteristic
2#21447585C211yesmaximal, characteristic
3#21443906C212yesmaximal
4#21443900C212yesmaximal
5C61×#2110C211yesmaximal, characteristic
6#16840315C411yescharacteristic
7C2×#14519717C2212yes—
8#16839890—22no—
9C8×Dic122—22no—
10#16839790C411yescharacteristic
11#16839789C411yescharacteristic
12#16839785C411yescharacteristic
13#16839717C2211yescharacteristic
14C2×C8×Dic61C2211yescharacteristic
15#16839583—22no—
16C2×M32×C61C2212yes—
17C61×#405C2211yescharacteristic
18C61×#347—22no—
19C2×#11758194C2×C411yescharacteristic
20C22×#92418C2×C411yescharacteristic
21#14519776—21no—
22#14519768—21no—
23#14519754—22no—
24C4×Dic122—22no—
25#14519736C2×C411yescharacteristic
26C2×C4×Dic61C2×C411yescharacteristic
27#14519717—22no—
28#14519717—22no—
29C2×#11758185—22no—
30C4⋊#92418—22no—
31#14519706—22no—
32#14519706—22no—
33#14519687—21no—
34C8×Dic61—21no—
35C8×Dic61—21no—
36C8×Dic61—21no—
37C2×M16×C61C2×C411yescharacteristic
38C22×C8×C61C2311yescharacteristic
39#117×C61C2×C411yescharacteristic
40M32×C61—22no—
41M32×C61Q814yescomplemented
42C2×C16×C61—22no—
43#97×C61D412yes—
44C4×C8×C61D412yes—
45C22×C4×C61C22×C411yescharacteristic
46C22×Dic61—21no—
47C2×Dic122—22no—
48M16×C61—22no—
49C2×C8×C61C22⋊C412yes—
50C2×C8×C61C2×D411yescharacteristic
51C2×C8×C61C2×D411yescharacteristic
52C2×C8×C61C2×Q812yes—
53C2×C8×C61#4112yes—
54C4⋊C4×C61—21no—
55C22⋊C4×C61—21no—
56C42×C61C22⋊C412yes—
57C22⋊Dic61M1612yes—
58C4⋊Dic61—22no—
59C4⋊Dic61—21no—
60#11758196—22no—
61#11758196—22no—
62C4×Dic61—21no—
63C4×Dic61—21no—
64C4×Dic61M1611yescharacteristic
65C4×Dic61M1611yescharacteristic
66#11758194—22no—
67C2×#92418—21no—
68C2×#92418—21no—
69C2×#92418—22no—
70C16×C61—24no—
71#11758185—42no—
72C23×C61C2×M1611yescharacteristic
73C2×C4×C61—22no—
74C2×C4×C61C2×C22⋊C411yescharacteristic
75C2×C4×C61C4×Q812yes—
76C2×C4×C61C2×M1611yescharacteristic
77C2×C4×C61#13112yes—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—22no—
81C2×Dic61—42no—
82Dic122—44no—
83C8×C61—22no—
84C8×C61C22⋊Q812yes—
85C8×C61#12411yescharacteristic
86C8×C61C4⋊Q811yescharacteristic
87#92418—41no—
88#92418—41no—
89#13270—611nomaximal, Sylow
90C22×C61—41no—
91C22×C61#40711yescharacteristic
92C22×C61#44612yes—
93C4×C61—42no—
94C4×C61#39111yescharacteristic
95C4×C61#40811yescharacteristic
96C4×C61#44612yes—
97Dic61—22no—
98Dic61—42no—
99Dic61—41no—
100#2960—611no—
101#2153—611no—
102#2110D6111yescharacteristic
103#1378—612no—
104#1376—612no—
105C2×C61—21no—
106C2×C61—22no—
107C2×C61#198511yescharacteristic
108#533—611no—
109C2×M32—612no—
110C2×M32C2×D6112yes—
111#446—1222no—
112C8×Q8—1222no—
113#424—611no—
114#424—611no—
115#423—611no—
116#405—611no—
117#405C2×D6111yescharacteristic
118C2×C4×C8—611no—
119#364—1222no—
120#347—22no—
121C61#1327011yescharacteristic, complemented, Sylow
122C2×M16—611no—
123C2×M16C4×D6111yescharacteristic
124C22×C8—611no—
125C22×C8C22×D6111yescharacteristic
126C4⋊Q8—1221no—
127#125—1221no—
128C22⋊Q8—1222no—
129C4×Q8—1222no—
130#117—611no—
131#117C4×D6111yescharacteristic
132C2×C42—611no—
133M32—22no—
134M32—1222no—
135M32—1222no—
136M32Dic12214yescomplemented
137C2×C16—22no—
138C2×C16—1222no—
139C4⋊C8—1222no—
140C4⋊C8—1222no—
141C4⋊C8—1222no—
142#97—1221no—
143#97C22⋊D6112yes—
144C4×C8—1221no—
145C4×C8—1221no—
146C4×C8—1221no—
147C4×C8D24412yes—
148C2×Q8—1222no—
149C22×C4—1221no—
150C22×C4C2×C4×D6111yescharacteristic
151M16—22no—
152M16—1222no—
153C2×C8—1221no—
154C2×C8—1221no—
155C2×C8—1222no—
156C2×C8#1175819812yes—
157C2×C8C2×Dic12212yes—
158C2×C8C2×D24411yescharacteristic
159C2×C8#1175822212yes—
160C2×C8C2×C22⋊D6111yescharacteristic
161C4⋊C4—21no—
162C4⋊C4—1222no—
163C4⋊C4—1222no—
164C4⋊C4—1222no—
165C4⋊C4—1221no—
166C22⋊C4—21no—
167C22⋊C4—612no—
168C42—611no—
169C42—611no—
170C42—1221no—
171C42—1221no—
172C42#1175819812yes—
173C16—24no—
174C16—2442no—
175C23M16×D6111yescharacteristic
176Q8—2444no—
177C2×C4—22no—
178C2×C4—1221no—
179C2×C4—1221no—
180C2×C4—1222no—
181C2×C4—2442no—
182C2×C4C2×#1175819811yescharacteristic
183C2×C4C4×Dic12212yes—
184C2×C4M16×D6111yescharacteristic
185C2×C4#1451978512yes—
186C8—22no—
187C8—2441no—
188C8—2441no—
189C8#1451975612yes—
190C8#1451976511yescharacteristic
191C8#1451977711yescharacteristic
192C22—41no—
193C22#1683972511yescharacteristic
194C22#1683989012yes—
195C4—42no—
196C4—1222no—
197C4—2441no—
198C4—2442no—
199C4#1683966811yescharacteristic
200C4#1683973011yescharacteristic
201C4#1683989012yes—
202C2—21no—
203C2—22no—
204C2#2144675911yescharacteristic
subgroupG/H
centerC8#14519765
commutatorC22×C4×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#2110C2
socleC2×C61#1985
prime radicalC23×C61C2×M16
cosocleC22×C8×C61C23
hypercenter#2110D61
hypocenterC61#13270
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2110

Complements

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

NH ≅ G/Ntype
41. M32×C61Q8semidirect
121. C61#13270semidirect
136. M32Dic122semidirect

Maximal subgroups

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

subgroupindex
#214547512
#214475852
#214439062
#214439002
C61×#21102
#1327061