Finite Group Databasebeta

← #30595155

Subgroups — #30595155

Order 15616.

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

normal subgroups only

This group has 270 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#21461322C211yesmaximal, characteristic
3#21446200C211yesmaximal, characteristic
4#16840779—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—
16#14519844—22no—
17#14519838—22no—
18#14519837—41no—
19C22⋊#92420—41no—
20C4×#92420—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—
52C2×#92420—42no—
53#11758213—81no—
54D61⋊C8—81no—
55C4⋊C4×C61—41no—
56C22⋊C4×C61—41no—
57C42×C61—41no—
58C22⋊Dic61—41no—
59#11758198—41no—
60#11758196—41no—
61C4×Dic61—21no—
62C4×Dic61C22⋊C411yescharacteristic
63C4×Dic61C4⋊C411yescharacteristic
64#11758194—22no—
65#11758194—42no—
66#11758194—41no—
67C2×#92418—41no—
68C2×#92418—42no—
69C23×C61—21no—
70C23×C61#9911yescharacteristic
71C22×D61—21no—
72Q8×C61—41no—
73D4×C61—41no—
74D4×C61—42no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61—81no—
81C2×C4×C61#9511yescharacteristic
82C2×C4×C61#9911yescharacteristic
83C22⋊D61—82no—
84C22⋊D61—81no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—42no—
89D244—41no—
90C4×D61—41no—
91C4×D61—41no—
92Dic122—41no—
93#92420—82no—
94#92420—82no—
95#92418—42no—
96#7488—611nomaximal, Sylow
97C22×C61—21no—
98C22×C61—41no—
99C22×C61—41no—
100C22×C61—81no—
101C22×C61#34211yescharacteristic
102C2×D61—41no—
103C2×D61—81no—
104C4×C61—21no—
105C4×C61—41no—
106C4×C61—161no—
107C4×C61AΣL(1,𝔽16)11yescharacteristic
108C4×C61#35211yescharacteristic
109Dic61—22no—
110Dic61—41no—
111Dic61—41no—
112#2132—611no—
113#1884—611no—
114#1543—611no—
115C2×C61—21no—
116C2×C61—41no—
117C2×C61—81no—
118C2×C61#139011yescharacteristic
119D61—81no—
120#568—611no—
121#532—611no—
122#431—1221no—
123#421—1221no—
124#413—1221no—
125#410#692311yescharacteristic
126#356—1221no—
127#355—612no—
128#339—1221no—
129#333—1221no—
130#331—612no—
131C61#748811yescharacteristic, complemented, Sylow
132C2×#41—611no—
133C2×#41C2×#692311yescharacteristic
134#131—2442no—
135C2×M16—1221no—
136C2×M16—2441no—
137C2×M16—2441no—
138C4⋊Q8—611no—
139#127—611no—
140#124—611no—
141#124—611no—
142#121—2441no—
143C4×D4—2441no—
144#117—21no—
145C2×C42—611no—
146C4⋊C8—1222no—
147#104—2442no—
148#101—1222no—
149#100—2441no—
150#99—41no—
151C22⋊C8—2441no—
152C4×C8—2441no—
153#41—41no—
154#41—41no—
155#41—2441no—
156#41—2441no—
157C2×Q8—611no—
158C2×Q8C4⋊#692311yescharacteristic
159C2×D4—21no—
160C2×D4—611no—
161C2×D4—1221no—
162C2×D4—2441no—
163C2×D4C4×#692311yescharacteristic
164C22×C4—21no—
165C22×C4—1221no—
166C22×C4—1221no—
167C22×C4C22⋊#692311yescharacteristic
168M16—1222no—
169M16—4881no—
170M16—2442no—
171M16—2442no—
172M16—2441no—
173C2×C8—4881no—
174C2×C8—2442no—
175C2×C8—2441no—
176C2×C8—2442no—
177C4⋊C4—41no—
178C4⋊C4—2441no—
179C22⋊C4—41no—
180C22⋊C4—2441no—
181C22⋊C4—2441no—
182C42—41no—
183C42—611no—
184C42—611no—
185C42—1221no—
186C23—21no—
187C23—1221no—
188C23#1451983511yescharacteristic
189Q8—41no—
190Q8—2441no—
191D4—41no—
192D4—42no—
193D4—4882no—
194D4—4881no—
195D4—2441no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—81no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—2442no—
206C2×C4—2441no—
207C2×C4—2441no—
208C2×C4(C2×#6923)⋊C411yescharacteristic
209C2×C4#1451983611yescharacteristic
210C8—4882no—
211C8—4882no—
212C8—2442no—
213C22—21no—
214C22—41no—
215C22—41no—
216C22—81no—
217C22—4881no—
218C22—2441no—
219C22#1684064011yescharacteristic
220C4—21no—
221C4—41no—
222C4—161no—
223C4—1222no—
224C4—2441no—
225C4—2441no—
226C4#1684066311yescharacteristic
227C4#1684066511yescharacteristic
228C2—21no—
229C2—41no—
230C2—81no—
231C2—4881no—
232C2#2146090411yescharacteristic
subgroupG/H
centerC4#16840663
commutatorC2×D4×C61C42
FrattiniC2×#41C2×#6923
FittingC61×#410C4
socleC2×C61#1390
prime radical, cosocle#16840308C22
hypercenter#410#6923
hypocenterC61#7488
LCSG ▷ C2×D4×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ 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
131. C61#7488semidirect

Maximal subgroups

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

subgroupindex
#214621102
#214613222
#214462002
#748861