Finite Group Databasebeta

← #30605739

Subgroups — #30605739

Order 15616.

258 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 62 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#21462191C211yesmaximal, characteristic
2#21462191C211yesmaximal, characteristic
3#21460840C211yesmaximal, characteristic, complemented
4#21460840C211yesmaximal, characteristic, complemented
5#21460839C211yesmaximal, characteristic, complemented
6#21460839C211yesmaximal, characteristic, complemented
7#21456367C211yesmaximal, characteristic
8#16840685C2211yescharacteristic
9#16840685C2211yescharacteristic
10#16840685C2211yescharacteristic
11#16840685C2211yescharacteristic
12#16840659—21no—
13#16840659—21no—
14#16840655—21no—
15#16840655—21no—
16#16840318C411yescharacteristic
17#125×D61C411yescharacteristic
18#16840170—21no—
19#16840169—21no—
20#16840164C411yescharacteristic
21#16840161C2211yescharacteristic
22#16840161C2211yescharacteristic
23#16839803—21no—
24#16839801—21no—
25C4×#11758189C2211yescharacteristic
26C61×#499C411yescharacteristic
27#14519851—21no—
28#14519851—21no—
29#14519851—21no—
30#14519851—21no—
31C2×#11758189D411yescharacteristic
32C2×#11758189D411yescharacteristic
33#14519776—21no—
34#14519769C2×C411yescharacteristic
35#14519769C2×C411yescharacteristic
36#14519768—21no—
37#14519767—41no—
38#14519755—41no—
39#14519742—41no—
40#14519735—21no—
41C4⋊C4×D61—21no—
42C4⋊C4×D61—41no—
43C42×D61C2×C411yescharacteristic
44#14519711—21no—
45#14519710—21no—
46#14519710—21no—
47#14519709—21no—
48#14519708—21no—
49#14519708—21no—
50#14519687D411yescharacteristic
51#14519687D411yescharacteristic
52C4×#92418C2311yescharacteristic
53#125×C61C2×C411yescharacteristic
54#125×C61C2×C411yescharacteristic
55#107×C61—21no—
56#106×C61—21no—
57C4×C8×C61C2×C411yescharacteristic
58C2×C4×D61—21no—
59C2×C4×D61—41no—
60C2×C4×D61C22⋊C411yescharacteristic
61C2×Dic122—41no—
62C2×C8×C61C22⋊C411yescharacteristic
63C2×C8×C61C22⋊C411yescharacteristic
64C4⋊C4×C61—21no—
65C4⋊C4×C61—21no—
66C4⋊C4×C61—41no—
67C4⋊C4×C61—41no—
68C42×C61C22×C411yescharacteristic
69#11758198—41no—
70C4⋊Dic61—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61—41no—
73#11758196—41no—
74#11758196—41no—
75#11758196—41no—
76#11758196—41no—
77#11758196—41no—
78C4×Dic61—21no—
79C4×Dic61—41no—
80C4×Dic61C22⋊C411yescharacteristic
81C2×#92418C2×D411yescharacteristic
82C2×#92418C2×D411yescharacteristic
83#11758189—21no—
84#11758189—21no—
85#11758189—21no—
86#11758189—21no—
87#11758187—41no—
88#11758187—41no—
89#11758187—41no—
90#11758187—41no—
91C22×D61#10011yescharacteristic
92C2×C4×C61—21no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61C2×C22⋊C411yescharacteristic
96C2×Dic61—21no—
97C2×Dic61—41no—
98C2×Dic61—41no—
99C2×Dic61#10011yescharacteristic
100C4×D61—21no—
101C4×D61—21no—
102C4×D61—81no—
103C4×D61—82no—
104Dic122—82no—
105C8×C61—21no—
106C8×C61—21no—
107#92418#13711yescharacteristic
108#92418#13711yescharacteristic
109#92418#13711yescharacteristic
110#92418#13711yescharacteristic
111#11994—611nomaximal, Sylow
112C22×C61C2×#10011yescharacteristic
113C2×D61—21no—
114C2×D61—41no—
115C4×C61—41no—
116C4×C61—81no—
117C4×C61—81no—
118C4×C61#41911yescharacteristic
119C4×C61#41911yescharacteristic
120Dic61—21no—
121Dic61—41no—
122Dic61—81no—
123Dic61—81no—
124#3166—611no—
125#2165—611no—
126#2165—611no—
127#1366—611no—
128#1366—611no—
129#1366—611no—
130#1366—611no—
131C2×C61—21no—
132C2×C61#155811yescharacteristic
133D61—41no—
134#533—611no—
135C2×#125—611no—
136#501—1221no—
137#501—1221no—
138#499—611no—
139#499—611no—
140#499—611no—
141#499#692311yescharacteristic
142#428—1221no—
143#428—1221no—
144C4×M16—611no—
145#364—611no—
146#364—611no—
147#364—611no—
148#364—611no—
149#349—1221no—
150#349—1221no—
151#347—1221no—
152#347—1221no—
153C61#1199411yescharacteristic, complemented, Sylow
154C2×M16—611no—
155C2×M16—611no—
156C4⋊Q8—1221no—
157#125—611no—
158#125—611no—
159#125—1221no—
160#125—2441no—
161#125C2×#692311yescharacteristic
162#125C2×#692311yescharacteristic
163C22⋊Q8—2441no—
164C4×Q8—2441no—
165#117—1221no—
166C2×C4⋊C4—1221no—
167C2×C4⋊C4—2441no—
168C2×C42—611no—
169M32—1221no—
170M32—1221no—
171M32—1221no—
172M32—1221no—
173#107—21no—
174#107—1221no—
175#107—1221no—
176#107—1221no—
177#106—21no—
178#106—1221no—
179#106—1221no—
180#106—1221no—
181#97—611no—
182#97—611no—
183C4×C8—611no—
184C4×C8C2×#692311yescharacteristic
185C2×Q8—2441no—
186C22×C4—611no—
187C22×C4—1221no—
188C22×C4—2441no—
189M16—1221no—
190M16—1221no—
191M16—1221no—
192M16—1221no—
193C2×C8—611no—
194C2×C8—611no—
195C2×C8C22⋊#692311yescharacteristic
196C2×C8C22⋊#692311yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—1221no—
202C4⋊C4—1221no—
203C4⋊C4—2441no—
204C4⋊C4—2441no—
205C4⋊C4—2441no—
206C4⋊C4—2441no—
207C4⋊C4—2441no—
208C4⋊C4—2441no—
209C22⋊C4—2441no—
210C42—611no—
211C42—1221no—
212C42—2441no—
213C42C22×#692311yescharacteristic
214C16—2441no—
215C16—2441no—
216C16—2441no—
217C16—2441no—
218C23—611no—
219Q8—4882no—
220C2×C4—21no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—611no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—4881no—
228C2×C4—4882no—
229C2×C4—2441no—
230C2×C4—2441no—
231C2×C4C2×C22⋊#692311yescharacteristic
232C8—21no—
233C8—21no—
234C8—611no—
235C8—611no—
236C8—611no—
237C8—611no—
238C22—1221no—
239C22—2441no—
240C22D61⋊#10011yescharacteristic
241C4—41no—
242C4—81no—
243C4—81no—
244C4—1221no—
245C4—4881no—
246C4—4881no—
247C4—2441no—
248C4#1684075511yescharacteristic
249C4#1684075511yescharacteristic
250C2—21no—
251C2—2441no—
252C2#2146135311yescharacteristic
subgroupG/H
centerC2#21461353
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#499C4
socleC2×C61#1558
prime radicalC22×D61#100
cosocleC4×#92418C23
hypercenter#499#6923
hypocenterC61#11994
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
3. #21460840C2semidirect
4. #21460840C2semidirect
5. #21460839C2semidirect
6. #21460839C2semidirect
153. C61#11994semidirect

Maximal subgroups

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

subgroupindex
#214621912
#214608402
#214608392
#214563672
#1199461