Finite Group Databasebeta

← #30594762

Subgroups — #30594762

Order 15616.

256 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 56 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#21461685C211yesmaximal, characteristic
2#21461081C211yesmaximal, characteristic
3#21446758C211yesmaximal, characteristic
4#16840783—21no—
5#16840765—21no—
6C2×#14519838C412yes—
7#16840642—21no—
8#16840608—21no—
9#16840607C412yes—
10C2×C4×Dic122C2211yescharacteristic
11C2×#14519688C411yescharacteristic
12#16839516—21no—
13#16839516—21no—
14C2×C4⋊C8×C61C411yescharacteristic
15C2×#11758217—22no—
16#14519844—41no—
17C4⋊#92420—41no—
18C4⋊#92420—41no—
19#14519838—42no—
20C22⋊#92420—22no—
21#14519832—41no—
22C22×Dic122C2×C411yescharacteristic
23C22×#92418—21no—
24C4×Dic122—41no—
25C4×Dic122—41no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×#11758196D411yescharacteristic
28C2×#11758196Q811yescharacteristic
29C2×C4×Dic61D411yescharacteristic
30C2×C4×Dic61D411yescharacteristic
31#14519688—41no—
32C22×C8×C61—21no—
33C2×C42×C61C2×C411yescharacteristic
34C4⋊C8×C61—41no—
35C22×C4×C61C4211yescharacteristic
36C22×C4×C61C22⋊C411yescharacteristic
37C22×C4×C61C4⋊C411yescharacteristic
38C22×Dic61C22⋊C411yescharacteristic
39C22×Dic61C22⋊C411yescharacteristic
40C22×Dic61C4⋊C411yescharacteristic
41C22×Dic61C4⋊C411yescharacteristic
42C2×Dic122—21no—
43C2×Dic122—21no—
44C2×Dic122—41no—
45C2×Dic122—41no—
46#11758217—42no—
47#11758217—42no—
48C2×#92420—42no—
49C2×#92420—42no—
50C2×C8×C61—42no—
51C2×C8×C61—41no—
52C42×C61—21no—
53C42×C61—21no—
54C4⋊Dic61—41no—
55#11758196—41no—
56#11758196—41no—
57C4×Dic61—21no—
58C4×Dic61—21no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C2×#92418—22no—
62C2×#92418—41no—
63C2×#92418—41no—
64C23×C61#9511yescharacteristic
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—41no—
72C2×C4×C61#9911yescharacteristic
73C2×C4×C61#9911yescharacteristic
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—41no—
82C2×Dic61—41no—
83C2×Dic61#10011yescharacteristic
84C2×Dic61#10111yescharacteristic
85Dic122—42no—
86Dic122—42no—
87#92420—82no—
88#92420—82no—
89C8×C61—81no—
90#92418—42no—
91#7323—611nomaximal, Sylow
92C22×C61—21no—
93C22×C61—21no—
94C22×C61#34211yescharacteristic
95C22×C61#34311yescharacteristic
96C22×C61#34411yescharacteristic
97C4×C61—21no—
98C4×C61—41no—
99C4×C61—41no—
100C4×C61#35511yescharacteristic
101C4×C61#35611yescharacteristic
102Dic61—21no—
103Dic61—21no—
104Dic61—41no—
105Dic61—41no—
106Dic61—41no—
107#1985—611no—
108#1801—611no—
109#1467—611no—
110C2×C61—21no—
111C2×C61—21no—
112C2×C61#130511yescharacteristic
113C2×C61#139411yescharacteristic
114C2×C61#139511yescharacteristic
115C2×C4×Q8—611no—
116#432—1221no—
117#423—1221no—
118C2×C4⋊C8#692311yescharacteristic
119C2×#101—612no—
120C2×#97—611no—
121#343—1221no—
122#336—1221no—
123#336—1221no—
124#324—612no—
125#324—1221no—
126C61#732311yescharacteristic, complemented, Sylow
127C22×Q8—611no—
128C2×M16—1222no—
129C22×C8—21no—
130C22×C8—1221no—
131C4×Q8—2441no—
132C4×Q8—2441no—
133C2×C4⋊C4—611no—
134C2×C4⋊C4—611no—
135C2×C4⋊C4—611no—
136C2×C42—611no—
137C2×C42—611no—
138C2×C42C2×#692311yescharacteristic
139C4⋊C8—41no—
140C4⋊C8—2441no—
141C4⋊C8—2441no—
142C4⋊C8—2441no—
143#101—2442no—
144C22⋊C8—1222no—
145#97—2441no—
146#97—2441no—
147C2×Q8—1221no—
148C2×Q8—1221no—
149C2×Q8—2441no—
150C2×Q8—2441no—
151C22×C4—611no—
152C22×C4—611no—
153C22×C4—611no—
154C22×C4—611no—
155C22×C4C4×#692311yescharacteristic
156C22×C4C4⋊#692311yescharacteristic
157C22×C4C22⋊#692311yescharacteristic
158M16—2442no—
159M16—2442no—
160C2×C8—42no—
161C2×C8—41no—
162C2×C8—1222no—
163C2×C8—2442no—
164C2×C8—2442no—
165C2×C8—2441no—
166C2×C8—2441no—
167C4⋊C4—2441no—
168C4⋊C4—2441no—
169C4⋊C4—2441no—
170C42—21no—
171C42—21no—
172C42—1221no—
173C42—1221no—
174C42—1221no—
175C42—1221no—
176C23(C2×#6923)⋊C411yescharacteristic
177Q8—2442no—
178Q8—2442no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—611no—
187C2×C4—611no—
188C2×C4—1221no—
189C2×C4—1221no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4#1451983511yescharacteristic
198C2×C4#1451983611yescharacteristic
199C8—81no—
200C8—4882no—
201C8—4882no—
202C8—2442no—
203C22—21no—
204C22—21no—
205C22#1684064011yescharacteristic
206C22#1684064111yescharacteristic
207C22#1684064511yescharacteristic
208C4—21no—
209C4—41no—
210C4—41no—
211C4—1221no—
212C4—1221no—
213C4—2441no—
214C4—2441no—
215C4—2441no—
216C4#1684067011yescharacteristic
217C4#1684067211yescharacteristic
218C2—21no—
219C2—21no—
220C2#2146071911yescharacteristic
221C2#2146091711yescharacteristic
222C2#2146091911yescharacteristic
subgroupG/H
centerC22#16840640
commutatorC22×C4×C61C42
FrattiniC2×C42C2×#6923
FittingC2×C4⋊C8×C61C4
socleC22×C61#342
prime radicalC23×C61#95
cosocleC2×C4×Dic122C22
hypercenterC2×C4⋊C8#6923
hypocenterC61#7323
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
126. C61#7323semidirect

Maximal subgroups

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

subgroupindex
#214616852
#214610812
#214467582
#732361