Finite Group Databasebeta

← #30595170

Subgroups — #30595170

Order 15616.

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

normal subgroups only

This group has 282 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#21461273C211yesmaximal, characteristic
3#21446202C211yesmaximal, characteristic
4#16840748—21no—
5C4×#11758217—21no—
6#16840672C412yescomplemented
7#16840670—21no—
8#16840618C412yescomplemented
9#16840617—21no—
10#16840308C2211yescharacteristic
11#16839778—21no—
12#16839736C411yescharacteristic
13#16839523—21no—
14C61×#568C411yescharacteristic
15D61⋊M16—41no—
16C2×#11758217—41no—
17#14519838—22no—
18#14519837—41no—
19#14519832—22no—
20C4×#92420—41no—
21C2×#11758222D411yescharacteristic
22#14519775C2×C411yescharacteristic
23#14519773Q811yescharacteristic
24#14519766C2×C411yescharacteristic
25#14519764D411yescharacteristic
26#14519749—41no—
27C4×C22⋊D61—41no—
28#14519736—21no—
29C2×C4×Dic61D411yescharacteristic
30#14519703—42no—
31#14519692—41no—
32C2×#41×C61C2×C411yescharacteristic
33#131×C61—42no—
34C2×M16×C61—21no—
35C2×M16×C61—41no—
36#41×C61—41no—
37#41×C61—41no—
38C2×Q8×C61C4211yescharacteristic
39C2×D4×C61—21no—
40C2×D4×C61C4⋊C411yescharacteristic
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—44no—
52#11758217—42no—
53C2×#92420—42no—
54#11758213—81no—
55D61⋊C8—81no—
56M16×C61—22no—
57M16×C61—41no—
58M16×C61—42no—
59C2×C8×C61—41no—
60C2×C8×C61—42no—
61C22⋊Dic61—41no—
62C22⋊Dic61—41no—
63#11758198—41no—
64C4⋊Dic61—41no—
65#11758196—41no—
66C4×Dic61—21no—
67C4×Dic61—41no—
68C4×Dic61C22⋊C411yescharacteristic
69C4×Dic61C4⋊C411yescharacteristic
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#9511yescharacteristic
82C2×C4×C61#9911yescharacteristic
83C22⋊D61—82no—
84C22⋊D61—81no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—42no—
89C2×Dic61—81no—
90D244—41no—
91C4×D61—41no—
92C4×D61—41no—
93Dic122—41no—
94#92420—44no—
95#92420—82no—
96C8×C61—42no—
97#7492—611nomaximal, Sylow
98C22×C61—21no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61—81no—
102C22×C61#34211yescharacteristic
103C2×D61—41no—
104C2×D61—81no—
105C4×C61—21no—
106C4×C61—41no—
107C4×C61AΣL(1,𝔽16)11yescharacteristic
108C4×C61#35211yescharacteristic
109Dic61—22no—
110Dic61—41no—
111Dic61—41no—
112Dic61—161no—
113#2132—611no—
114#1884—611no—
115#1525—611no—
116C2×C61—21no—
117C2×C61—41no—
118C2×C61—81no—
119C2×C61#139011yescharacteristic
120D61—81no—
121#568#692311yescharacteristic
122#532—611no—
123#421—1221no—
124#413—1221no—
125#410—611no—
126C4×M16—1221no—
127#356—612no—
128#355—1221no—
129#339—1221no—
130#329—612no—
131#329—1221no—
132C61#749211yescharacteristic, complemented, Sylow
133C2×#41—611no—
134C2×#41C2×#692311yescharacteristic
135#131—42no—
136C2×M16—21no—
137C2×M16—41no—
138C2×M16—2441no—
139C2×M16—2441no—
140C4⋊Q8—611no—
141#127—611no—
142#124—611no—
143#124—611no—
144#121—2441no—
145C4×D4—2441no—
146#117—1221no—
147C2×C42—611no—
148#104—2442no—
149#101—1222no—
150#100—2441no—
151#99—2441no—
152#97—1222no—
153C4×C8—2441no—
154#41—41no—
155#41—41no—
156#41—2441no—
157#41—2441no—
158C2×Q8—611no—
159C2×Q8C4×#692311yescharacteristic
160C2×D4—21no—
161C2×D4—611no—
162C2×D4—1221no—
163C2×D4—2441no—
164C2×D4C4⋊#692311yescharacteristic
165C22×C4—21no—
166C22×C4—1221no—
167C22×C4—1221no—
168C22×C4C22⋊#692311yescharacteristic
169M16—22no—
170M16—41no—
171M16—42no—
172M16—4881no—
173M16—2442no—
174M16—2444no—
175C2×C8—41no—
176C2×C8—42no—
177C2×C8—4881no—
178C2×C8—2442no—
179C4⋊C4—2441no—
180C4⋊C4—2441no—
181C22⋊C4—2441no—
182C22⋊C4—2441no—
183C22⋊C4—2441no—
184C42—611no—
185C42—611no—
186C42—1221no—
187C42—2441no—
188C23—21no—
189C23—1221no—
190C23#1451983611yescharacteristic
191Q8—41no—
192Q8—2441no—
193D4—41no—
194D4—42no—
195D4—4882no—
196D4—4881no—
197D4—2441no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—4881no—
207C2×C4—2442no—
208C2×C4—2441no—
209C2×C4—2441no—
210C2×C4(C2×#6923)⋊C411yescharacteristic
211C2×C4#1451983511yescharacteristic
212C8—42no—
213C8—4882no—
214C8—2444no—
215C22—21no—
216C22—41no—
217C22—41no—
218C22—81no—
219C22—4881no—
220C22—2441no—
221C22#1684064011yescharacteristic
222C4—21no—
223C4—41no—
224C4—1222no—
225C4—9761no—
226C4—2441no—
227C4—2441no—
228C4#1684066211yescharacteristic
229C4#1684066411yescharacteristic
230C2—21no—
231C2—41no—
232C2—81no—
233C2—4881no—
234C2#2146090311yescharacteristic
subgroupG/H
centerC4#16840662
commutatorC2×Q8×C61C42
FrattiniC2×#41C2×#6923
FittingC61×#568C4
socleC2×C61#1390
prime radical, cosocle#16840308C22
hypercenter#568#6923
hypocenterC61#7492
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41 ◁ #568

Complements

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

NH ≅ G/Ntype
6. #16840672C4semidirect
8. #16840618C4semidirect
132. C61#7492semidirect

Maximal subgroups

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

subgroupindex
#214621102
#214612732
#214462022
#749261