Finite Group Databasebeta

← #30594959

Subgroups — #30594959

Order 15616.

268 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 36 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#21460917C211yesmaximal, characteristic, complemented
2#21460640C211yesmaximal, characteristic, complemented
3#21446868C211yesmaximal, characteristic
4C2×#14519838—21no—
5#16840628—21no—
6C2×#14519810—21no—
7#16840343C411yescharacteristic
8C2×#14519703—21no—
9#16839667C2211yescharacteristic
10C61×#343C411yescharacteristic
11C2×#11758217—41no—
12C22×#92420—41no—
13#14519838—22no—
14#14519838—41no—
15C2×#11758222—21no—
16C22×Dic122D411yescharacteristic
17#14519810—42no—
18#14519810—41no—
19#14519810—41no—
20C2×Dic244—41no—
21C2×#11758190—41no—
22#14519757—41no—
23#14519752—41no—
24#14519751—41no—
25C2×C4×Dic61D411yescharacteristic
26#14519703—42no—
27#14519684—41no—
28C2×M16×C61—21no—
29C2×C4⋊C4×C61C2×C411yescharacteristic
30C22×C4×C61—21no—
31C22×C4×C61C22⋊C411yescharacteristic
32C2×C22⋊D61—41no—
33C22×Dic61—21no—
34C22×Dic61—21no—
35#11758222—41no—
36#11758222—41no—
37#11758222—41no—
38#11758222—41no—
39C2×D244—21no—
40C2×D244—41no—
41C2×C4×D61—41no—
42C2×Dic122—21no—
43C2×Dic122—21no—
44C2×Dic122—41no—
45C2×Dic122—41no—
46C2×Dic122D811yescharacteristic
47C2×Dic122SD1611yescharacteristic
48#11758217—42no—
49#11758217—81no—
50C2×#92420—42no—
51C2×#92420—81no—
52C2×#92420—81no—
53C2×#92420—81no—
54M16×C61—22no—
55M16×C61—41no—
56C2×C8×C61—41no—
57C4⋊C4×C61—41no—
58#11758198—42no—
59C4⋊Dic61—41no—
60C4×Dic61—41no—
61Dic244—42no—
62Dic244—42no—
63#11758190—42no—
64#11758190—42no—
65C23×C61#9911yescharacteristic
66C22×D61—41no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—41no—
70C2×C4×C61—81no—
71C2×C4×C61#10211yescharacteristic
72C2×C4×C61#10411yescharacteristic
73C22⋊D61—81no—
74C22⋊D61—81no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—41no—
80C2×Dic61—41no—
81C2×Dic61—41no—
82C2×Dic61—41no—
83C2×Dic61—41no—
84D244—41no—
85D244—41no—
86D244—161no—
87C4×D61—81no—
88C4×D61—81no—
89Dic122—41no—
90Dic122—41no—
91Dic122—41no—
92Dic122—41no—
93Dic122—81no—
94#92420—82no—
95#92420—82no—
96C8×C61—42no—
97#7409—611nomaximal, Sylow
98C22×C61—21no—
99C22×C61—21no—
100C22×C61#32711yescharacteristic
101C22×C61AΣL(1,𝔽16)11yescharacteristic
102C22×C61#35311yescharacteristic
103C2×D61—81no—
104C2×D61—81no—
105C2×D61—81no—
106C4×C61—21no—
107C4×C61—21no—
108C4×C61—81no—
109Dic61—41no—
110Dic61—41no—
111Dic61—41no—
112Dic61—41no—
113Dic61—81no—
114#2007—611no—
115#1394—611no—
116#1272—611no—
117C2×C61—21no—
118C2×C61—21no—
119C2×C61#134311yescharacteristic
120C2×C61#140311yescharacteristic
121C2×C61#140511yescharacteristic
122D61—161no—
123C2×#137—1221no—
124#537—611no—
125C2×#104—1221no—
126C2×#101—1221no—
127#391—611no—
128#343#692311yescharacteristic
129#336—1221no—
130C61#740911yescharacteristic, complemented, Sylow
131C2×#41—1221no—
132C22×Q8—611no—
133#137—2442no—
134#137—2441no—
135#137—2441no—
136C2×Q16—2441no—
137C2×SD16—2441no—
138C2×M16—21no—
139C2×M16—2441no—
140C22×C8—2441no—
141C22⋊Q8—2441no—
142#121—2441no—
143#121—2441no—
144C2×C4⋊C4C2×#692311yescharacteristic
145C2×C42—611no—
146#104—2442no—
147#101—1222no—
148#101—2441no—
149#95—2441no—
150#41—2441no—
151#41—2441no—
152#41—2441no—
153#41—2441no—
154C2×Q8—611no—
155C2×Q8—611no—
156C2×Q8—1221no—
157C2×Q8—1221no—
158C2×Q8—2441no—
159C2×Q8—2441no—
160C2×D4—1221no—
161C2×D4—2441no—
162C2×D4—2441no—
163C22×C4—21no—
164C22×C4—1221no—
165C22×C4—1221no—
166C22×C4—2441no—
167C22×C4C22⋊#692311yescharacteristic
168Q16—2442no—
169Q16—2442no—
170SD16—2442no—
171SD16—2442no—
172M16—22no—
173M16—41no—
174M16—4881no—
175M16—2442no—
176C2×C8—41no—
177C2×C8—4881no—
178C2×C8—4881no—
179C2×C8—4881no—
180C2×C8—2442no—
181C4⋊C4—41no—
182C4⋊C4—2441no—
183C22⋊C4—2442no—
184C42—2441no—
185C23—2441no—
186C23#1451983611yescharacteristic
187Q8—4881no—
188Q8—2441no—
189Q8—2441no—
190Q8—2441no—
191Q8—2441no—
192D4—9761no—
193D4—4881no—
194D4—4881no—
195D4—2441no—
196D4—2441no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—81no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—4881no—
206C2×C4—4881no—
207C2×C4—2441no—
208C2×C4—2441no—
209C2×C4—2441no—
210C2×C4—2441no—
211C2×C4—2441no—
212C2×C4#1451983911yescharacteristic
213C2×C4#1451984211yescharacteristic
214C8—42no—
215C8—4882no—
216C8—4882no—
217C22—21no—
218C22—21no—
219C22—4881no—
220C22—4881no—
221C22—4881no—
222C22#1684061411yescharacteristic
223C22#1684066311yescharacteristic
224C22#1684066711yescharacteristic
225C4—21no—
226C4—21no—
227C4—81no—
228C4—4881no—
229C4—2441no—
230C4—2441no—
231C4—2441no—
232C4—2441no—
233C2—21no—
234C2—21no—
235C2—9761no—
236C2#2146079811yescharacteristic
237C2#2146094111yescharacteristic
238C2#2146094511yescharacteristic
subgroupG/H
centerC22#16840663
commutatorC2×C4⋊C4×C61C2×C4
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#343C4
socleC22×C61AΣL(1,𝔽16)
prime radical#16840343C4
cosocle#16839667C22
hypercenter#343#6923
hypocenterC61#7409
LCSG ▷ C2×C4⋊C4×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. #21460917C2semidirect
2. #21460640C2semidirect
130. C61#7409semidirect

Maximal subgroups

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

subgroupindex
#214609172
#214606402
#214468682
#740961