Finite Group Databasebeta

← #30595187

Subgroups — #30595187

Order 15616.

274 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 46 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#21462110C211yesmaximal, characteristic
2#21461356C211yesmaximal, characteristic
3#21446200C211yesmaximal, characteristic
4#16840765—21no—
5#16840748—21no—
6#16840672—21no—
7#16840670C412yescomplemented
8#16840622—21no—
9#16840620C412yescomplemented
10#16840529C411yescharacteristic
11#16840308C2211yescharacteristic
12#16839780—21no—
13#16839521—21no—
14C61×#410C411yescharacteristic
15D61⋊M16—41no—
16C2×#11758217—41no—
17#14519844—22no—
18C4⋊#92420—41no—
19#14519838—22no—
20#14519837—41no—
21C2×#11758222D411yescharacteristic
22#14519784—42no—
23C2×#11758194—21no—
24C2×#11758194—41no—
25#14519775D411yescharacteristic
26#14519773C2×C411yescharacteristic
27#14519766Q811yescharacteristic
28#14519764C2×C411yescharacteristic
29#14519749—41no—
30C4×C22⋊D61—41no—
31C2×C4×Dic61D411yescharacteristic
32#14519705—42no—
33C2×#41×C61C2×C411yescharacteristic
34#117×C61—21no—
35#99×C61—41no—
36#41×C61—41no—
37#41×C61—41no—
38C2×Q8×C61C4⋊C411yescharacteristic
39C2×D4×C61—21no—
40C2×D4×C61C4211yescharacteristic
41C22×C4×C61—21no—
42C22×C4×C61C22⋊C411yescharacteristic
43C2×C22⋊D61—21no—
44C2×C22⋊D61—41no—
45C22×Dic61—21no—
46#11758222—41no—
47#11758222—41no—
48C2×D244C4⋊C411yescharacteristic
49C2×C4×D61—21no—
50C2×Dic122C22⋊C411yescharacteristic
51#11758217—42no—
52#11758217—82no—
53C2×#92420—42no—
54#11758213—81no—
55D61⋊C8—81no—
56C4⋊C4×C61—41no—
57C22⋊C4×C61—41no—
58C42×C61—41no—
59C22⋊Dic61—41no—
60#11758198—41no—
61#11758196—41no—
62C4×Dic61—21no—
63C4×Dic61C22⋊C411yescharacteristic
64C4×Dic61C4⋊C411yescharacteristic
65#11758194—22no—
66#11758194—41no—
67#11758194—42no—
68C2×#92418—41no—
69C2×#92418—42no—
70C23×C61—21no—
71C23×C61#9911yescharacteristic
72C22×D61—21no—
73Q8×C61—41no—
74D4×C61—41no—
75D4×C61—42no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61—81no—
82C2×C4×C61#9511yescharacteristic
83C2×C4×C61#9911yescharacteristic
84C22⋊D61—81no—
85C22⋊D61—81no—
86C22⋊D61—81no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—41no—
91C2×Dic61—41no—
92D244—41no—
93C4×D61—41no—
94C4×D61—41no—
95Dic122—41no—
96#92420—82no—
97#92420—82no—
98#92418—42no—
99#7496—611nomaximal, Sylow
100C22×C61—21no—
101C22×C61—41no—
102C22×C61—41no—
103C22×C61—81no—
104C22×C61#34211yescharacteristic
105C2×D61—41no—
106C2×D61—81no—
107C4×C61—21no—
108C4×C61—41no—
109C4×C61—161no—
110C4×C61AΣL(1,𝔽16)11yescharacteristic
111C4×C61#35211yescharacteristic
112Dic61—21no—
113Dic61—21no—
114Dic61—41no—
115Dic61—41no—
116#2132—611no—
117#1884—611no—
118#1560—611no—
119C2×C61—21no—
120C2×C61—41no—
121C2×C61—81no—
122C2×C61#139011yescharacteristic
123D61—81no—
124#568—611no—
125#532—611no—
126#423—1221no—
127#421—1221no—
128#413—1221no—
129#410#692311yescharacteristic
130#356—1221no—
131#355—612no—
132#339—1221no—
133#333—1221no—
134#331—612no—
135C61#749611yescharacteristic, complemented, Sylow
136C2×#41—611no—
137C2×#41C2×#692311yescharacteristic
138#131—2442no—
139C2×M16—1221no—
140C2×M16—2441no—
141C2×M16—2441no—
142C2×M16—2441no—
143C4⋊Q8—611no—
144#127—611no—
145#124—611no—
146#124—611no—
147#121—2441no—
148C4×D4—2441no—
149#117—21no—
150C2×C42—611no—
151C4⋊C8—1222no—
152C4⋊C8—2441no—
153#104—2442no—
154#101—1222no—
155#100—2441no—
156#99—41no—
157#41—41no—
158#41—41no—
159#41—2441no—
160#41—2441no—
161C2×Q8—611no—
162C2×Q8C4⋊#692311yescharacteristic
163C2×D4—21no—
164C2×D4—611no—
165C2×D4—1221no—
166C2×D4—2441no—
167C2×D4C4×#692311yescharacteristic
168C22×C4—21no—
169C22×C4—1221no—
170C22×C4—1221no—
171C22×C4C22⋊#692311yescharacteristic
172M16—1222no—
173M16—4881no—
174M16—4882no—
175M16—2442no—
176M16—2441no—
177M16—2442no—
178C2×C8—4881no—
179C2×C8—2442no—
180C2×C8—2441no—
181C2×C8—2442no—
182C4⋊C4—41no—
183C4⋊C4—2441no—
184C22⋊C4—41no—
185C22⋊C4—2441no—
186C22⋊C4—2441no—
187C42—41no—
188C42—611no—
189C42—611no—
190C42—1221no—
191C23—21no—
192C23—1221no—
193C23#1451983511yescharacteristic
194Q8—41no—
195Q8—2441no—
196D4—41no—
197D4—42no—
198D4—4881no—
199D4—4881no—
200D4—4881no—
201D4—2441no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—81no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—2441no—
212C2×C4—2441no—
213C2×C4—2441no—
214C2×C4—2441no—
215C2×C4(C2×#6923)⋊C411yescharacteristic
216C2×C4#1451983611yescharacteristic
217C8—4882no—
218C8—4882no—
219C8—2442no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—81no—
224C22—4881no—
225C22—2441no—
226C22#1684064011yescharacteristic
227C4—21no—
228C4—41no—
229C4—161no—
230C4—1221no—
231C4—1221no—
232C4—2441no—
233C4—2441no—
234C4#1684066311yescharacteristic
235C4#1684066511yescharacteristic
236C2—21no—
237C2—41no—
238C2—81no—
239C2—4881no—
240C2#2146090411yescharacteristic
subgroupG/H
centerC2#21460904
commutatorC2×D4×C61C42
FrattiniC2×#41C2×#6923
FittingC61×#410C4
socleC2×C61#1390
prime radical, cosocle#16840308C22
hypercenter#410#6923
hypocenterC61#7496
LCSG ▷ C2×D4×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
7. #16840670C4semidirect
9. #16840620C4semidirect
135. C61#7496semidirect

Maximal subgroups

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

subgroupindex
#214621102
#214613562
#214462002
#749661