Finite Group Databasebeta

← #30606050

Subgroups — #30606050

Order 15616.

204 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 60 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#21461465C211yesmaximal, characteristic
2#21461414C211yesmaximal, characteristic
3#21460845C211yesmaximal, characteristic
4#21460780C211yesmaximal, characteristic
5#21460780C211yesmaximal, characteristic
6#21460738C211yesmaximal, characteristic
7#21447689C211yesmaximal, characteristic
8#16840812—21no—
9#16840811—21no—
10#16840651C2211yescharacteristic
11#16840623C2211yescharacteristic
12#16840623C2211yescharacteristic
13#16840612—21no—
14#16840612—21no—
15#16840603C2211yescharacteristic
16C2×Dic488C411yescharacteristic
17#16839856C2211yescharacteristic
18#16839856C2211yescharacteristic
19#16839565C411yescharacteristic
20#16839565C411yescharacteristic
21#16839537C2211yescharacteristic
22C61×#367C411yescharacteristic
23C2×#11758187—21no—
24#14519844—41no—
25C4⋊#92420—21no—
26C4⋊#92420—21no—
27C4⋊#92420—41no—
28#14519832—41no—
29C4×#92420—41no—
30C4×#92420D411yescharacteristic
31C4×#92420D411yescharacteristic
32C2×Dic244C2×C411yescharacteristic
33C2×Dic244C2×C411yescharacteristic
34#14519742—21no—
35#14519742—21no—
36Dic488—22no—
37C2×#11758185C2×C411yescharacteristic
38#14519700—21no—
39#14519700—21no—
40C8×Dic61C2311yescharacteristic
41C2×C16×C61C2×C411yescharacteristic
42#107×C61C2×C411yescharacteristic
43#107×C61C2×C411yescharacteristic
44C2×Dic122—21no—
45C2×Dic122—21no—
46C2×#92420—21no—
47C2×#92420—21no—
48C2×#92420—41no—
49C2×#92420—41no—
50C2×C8×C61C22×C411yescharacteristic
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53#11758196—41no—
54#11758196—41no—
55C4×Dic61—41no—
56C4×Dic61—41no—
57C4×Dic61C2×D411yescharacteristic
58C2×#92418#4111yescharacteristic
59Dic244—21no—
60Dic244—21no—
61Dic244—21no—
62Dic244M1612yes—
63#11758187—22no—
64C16×C61—21no—
65#11758185—21no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61C4×D411yescharacteristic
69C2×Dic61—41no—
70C2×Dic61—41no—
71C2×Dic61AGL(1,ℤ/8)11yescharacteristic
72C2×Dic61AGL(1,ℤ/8)11yescharacteristic
73Dic122—22no—
74Dic122—41no—
75Dic122—41no—
76Dic122—41no—
77#92420—41no—
78#92420—41no—
79#92420—81no—
80#92420—81no—
81C8×C61C2×M1611yescharacteristic
82C8×C61#13111yescharacteristic
83#92418—21no—
84#12079—611nomaximal, Sylow
85C22×C61#44211yescharacteristic
86C4×C61—81no—
87C4×C61—81no—
88C4×C61#43511yescharacteristic
89C4×C61#44311yescharacteristic
90Dic61—21no—
91Dic61—21no—
92Dic61—42no—
93Dic61—81no—
94#2176—611no—
95#1593—611no—
96#1579—611no—
97#1368—611no—
98#1334—611no—
99#1334—611no—
100#1313—611no—
101C2×C61#158611yescharacteristic
102C2×C61#218011yescharacteristic
103C2×C61#218011yescharacteristic
104C2×Q32—611no—
105#446—1221no—
106C8×Q8—1221no—
107C4×Q16—611no—
108C4×Q16—611no—
109#367#692311yescharacteristic
110#358—611no—
111#358—611no—
112#346—611no—
113#346—611no—
114#334—611no—
115#334—611no—
116Q8⋊C8—1221no—
117Q8⋊C8—1221no—
118#322—611no—
119C61#1207911yescharacteristic, complemented, Sylow
120C2×Q16—611no—
121C2×Q16—611no—
122C4×Q8—1221no—
123C4×Q8—1221no—
124Q32—1222no—
125C2×C16—611no—
126C2×C16—1221no—
127C2×C16C2×#692311yescharacteristic
128#107C2×#692311yescharacteristic
129#107C2×#692311yescharacteristic
130C4⋊C8—1221no—
131C4⋊C8—1221no—
132C4⋊C8—2441no—
133C4⋊C8—2441no—
134#103—1221no—
135#103—1221no—
136#97—2441no—
137C4×C8—611no—
138C4×C8—611no—
139C4×C8—611no—
140C4×C8—2441no—
141C2×Q8—1221no—
142C2×Q8—1221no—
143Q16—612no—
144Q16—1221no—
145Q16—1221no—
146Q16—1221no—
147C2×C8—611no—
148C2×C8—1221no—
149C2×C8—1221no—
150C2×C8—2441no—
151C2×C8—2441no—
152C2×C8C22×#692311yescharacteristic
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—2441no—
156C4⋊C4—2441no—
157C42—611no—
158C42—2441no—
159C42—2441no—
160C16—21no—
161C16—1222no—
162C16—1221no—
163Q8—1222no—
164Q8—2441no—
165Q8—2441no—
166Q8—2441no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—611no—
170C2×C4—611no—
171C2×C4—2441no—
172C2×C4—2441no—
173C2×C4D4×#692311yescharacteristic
174C8—1221no—
175C8—4881no—
176C8—4881no—
177C8—2441no—
178C8—2441no—
179C8D61⋊M1611yescharacteristic
180C8#1451986511yescharacteristic
181C22#1684080311yescharacteristic
182C4—81no—
183C4—81no—
184C4—1221no—
185C4—1221no—
186C4—4881no—
187C4—2442no—
188C4#1684079211yescharacteristic
189C4#1684080611yescharacteristic
190C2#2146143911yescharacteristic
191C2#2146222411yescharacteristic
192C2#2146222511yescharacteristic
subgroupG/H
centerC22#16840803
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#367C4
socle, prime radicalC22×C61#442
cosocleC8×Dic61C23
hypercenter#367#6923
hypocenterC61#12079
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

Complements

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

NH ≅ G/Ntype
119. C61#12079semidirect

Maximal subgroups

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

subgroupindex
#214614652
#214614142
#214608452
#214607802
#214607382
#214476892
#1207961