Finite Group Databasebeta

← #30595222

Subgroups — #30595222

Order 15616.

266 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 42 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#21462113C211yesmaximal, characteristic
2#21461956C211yesmaximal, characteristic
3#21447501C211yesmaximal, characteristic
4#16840766C411yescharacteristic
5C2×#14519842—21no—
6C2×#14519841—21no—
7#16840749—21no—
8#16840698C411yescharacteristic
9#16840672—21no—
10#16840671C412yescomplemented
11#16840311C2211yescharacteristic
12#16839745—21no—
13#16839560—21no—
14#16839559C411yescharacteristic, complemented
15C61×#355C411yescharacteristic, complemented
16C2×#11758213—21no—
17C2×#11758217—41no—
18C2×C4×#6923—21no—
19C4⋊#92420—41no—
20#14519842—42no—
21#14519841—42no—
22#14519838—22no—
23#14519837—41no—
24(C2×#6923)⋊C4—41no—
25C2×#11758226D411yescharacteristic
26C2×#11758224D411yescharacteristic
27M16×D61—41no—
28#14519775D411yescharacteristic
29#14519773Q811yescharacteristic
30#14519765C2×C411yescharacteristic
31#14519750—41no—
32#14519737—41no—
33C42×D61C2×C411yescharacteristic
34#14519696—21no—
35#14519693—41no—
36#124×C61C2×C411yescharacteristic
37#101×C61—21no—
38C22×#6923—41no—
39C2×Q8×C61C22⋊C411yescharacteristic
40C2×D4×C61C4⋊C411yescharacteristic
41C2×C22⋊D61—21no—
42C2×C22⋊D61—41no—
43C22×Dic61—21no—
44#11758226—41no—
45#11758226—41no—
46#11758224—41no—
47#11758224—41no—
48C2×D244—21no—
49C2×D244C4⋊C411yescharacteristic
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61C22⋊C411yescharacteristic
53C2×Dic122C22⋊C411yescharacteristic
54#11758217—42no—
55#11758217—81no—
56C2×#92420—41no—
57C2×#92420—81no—
58C4×#6923—22no—
59C4×#6923—41no—
60#11758213—41no—
61#11758213—41no—
62M16×C61—41no—
63C22⋊C4×C61—41no—
64C42×C61C4211yescharacteristic
65#11758198—41no—
66#11758196—41no—
67C4×Dic61—21no—
68C4×Dic61C4⋊C411yescharacteristic
69#11758194—41no—
70#11758189—81no—
71C8×D61—81no—
72C23×C61—21no—
73C22×D61—21no—
74C22×D61#9911yescharacteristic
75C2×#6923—42no—
76C2×#6923—82no—
77Q8×C61—41no—
78D4×C61—41no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61#9511yescharacteristic
82C22⋊D61—81no—
83C22⋊D61—82no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—41no—
87C2×Dic61—41no—
88C2×Dic61#9911yescharacteristic
89D244—41no—
90D244—81no—
91C4×D61—21no—
92C4×D61—21no—
93C4×D61—41no—
94C4×D61—41no—
95C4×D61—81no—
96Dic122—41no—
97#92420—82no—
98#92420—81no—
99C8×C61—81no—
100#92418—81no—
101#7507—611nomaximal, Sylow
102C22×C61—41no—
103C22×C61—81no—
104C22×C61#34211yescharacteristic
105C2×D61—21no—
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—81no—
109#6923—82no—
110C4×C61—21no—
111C4×C61—41no—
112C4×C61—41no—
113Dic61—41no—
114Dic61—41no—
115Dic61#35311yescharacteristic
116Dic61#35411yescharacteristic
117#2132—611no—
118#2132—611no—
119#1963—611no—
120C2×C61—21no—
121C2×C61—81no—
122C2×C61#139311yescharacteristic
123D61—41no—
124D61—81no—
125#532—611no—
126#423—611no—
127C2×#104—1221no—
128C2×#104—1221no—
129#413—1221no—
130#413—1221no—
131#376—611no—
132#356—1221no—
133#356—1221no—
134#355—612no—
135#355—611no—
136#355#692311yescharacteristic, complemented
137C61#750711yescharacteristic, complemented, Sylow
138C2×#41—611no—
139C2×#41—611no—
140C2×M16—1221no—
141C2×M16—2441no—
142C2×M16—2441no—
143C4⋊Q8—611no—
144#127—611no—
145#124—611no—
146#124C2×#692311yescharacteristic
147#121—2441no—
148C4×D4—2441no—
149C2×C42—611no—
150C2×C42—1221no—
151C4⋊C8—2441no—
152#104—2442no—
153#104—2442no—
154#101—21no—
155#101—1222no—
156#101—1221no—
157#100—2441no—
158#100—2441no—
159#95—2441no—
160#41—2441no—
161#41—2441no—
162#41—2441no—
163#41—2441no—
164C2×Q8—611no—
165C2×Q8C22⋊#692311yescharacteristic
166C2×D4—611no—
167C2×D4—1221no—
168C2×D4—1221no—
169C2×D4—2441no—
170C2×D4C4⋊#692311yescharacteristic
171C22×C4—611no—
172C22×C4—1221no—
173C22×C4—1221no—
174C22×C4—1221no—
175C22×C4—2441no—
176M16—41no—
177M16—4881no—
178M16—4881no—
179M16—2441no—
180M16—2442no—
181M16—2441no—
182M16—2441no—
183C2×C8—4881no—
184C2×C8—4881no—
185C2×C8—2441no—
186C4⋊C4—2441no—
187C22⋊C4—41no—
188C22⋊C4—2441no—
189C42—611no—
190C42—1221no—
191C42—1222no—
192C42—2441no—
193C42C4×#692311yescharacteristic
194C23—21no—
195C23—611no—
196C23—1221no—
197Q8—41no—
198Q8—2441no—
199D4—41no—
200D4—4881no—
201D4—4881no—
202D4—4882no—
203D4—2441no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—611no—
207C2×C4—1221no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—4881no—
212C2×C4—4882no—
213C2×C4—2441no—
214C2×C4—2441no—
215C2×C4—2441no—
216C2×C4—2441no—
217C2×C4—2442no—
218C2×C4(C2×#6923)⋊C411yescharacteristic
219C8—81no—
220C8—4881no—
221C8—4881no—
222C8—4882no—
223C22—41no—
224C22—81no—
225C22—1221no—
226C22—4881no—
227C22—2441no—
228C22—2441no—
229C22#1684063911yescharacteristic
230C4—21no—
231C4—41no—
232C4—41no—
233C4—611no—
234C4—611no—
235C4—4882no—
236C4—2441no—
237C4—2441no—
238C2—21no—
239C2—81no—
240C2—4881no—
241C2—2441no—
242C2#2146091211yescharacteristic
subgroupG/H
centerC2#21460912
commutatorC42×C61C42
Frattini#124C2×#6923
FittingC61×#355C4
socleC2×C61#1393
prime radical, cosocle#16840311C22
hypercenter#355#6923
hypocenterC61#7507
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #355

Complements

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

NH ≅ G/Ntype
10. #16840671C4semidirect
14. #16839559C4semidirect
15. C61×#355C4semidirect
136. #355#6923semidirect
137. C61#7507semidirect

Maximal subgroups

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

subgroupindex
#214621132
#214619562
#214475012
#750761