Finite Group Databasebeta

← #30605722

Subgroups — #30605722

Order 15616.

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

normal subgroups only

This group has 268 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#21462195C211yesmaximal, characteristic
2#21462161C211yesmaximal, characteristic
3#21460840C211yesmaximal, characteristic, complemented
4#21460839C211yesmaximal, characteristic, complemented
5#21460828C211yesmaximal, characteristic, complemented
6#21460828C211yesmaximal, characteristic, complemented
7#21456477C211yesmaximal, characteristic
8D61⋊M32—21no—
9#16840685C2211yescharacteristic
10#16840685C2211yescharacteristic
11#16840685C2211yescharacteristic
12#16840685C2211yescharacteristic
13#16840684—21no—
14#16840659—21no—
15#16840655—21no—
16#16840375C411yescharacteristic
17#16840373C411yescharacteristic
18#16840161C2211yescharacteristic
19#16840141C2211yescharacteristic
20#16840131C411yescharacteristic
21#16840019—21no—
22#16840002—21no—
23#16839866—21no—
24#16839854—21no—
25#16839719C2211yescharacteristic
26C61×#491C411yescharacteristic
27#14519852—41no—
28#14519851—21no—
29#14519851—21no—
30#14519851—21no—
31#14519851—21no—
32D61⋊C16—41no—
33C2×#11758202—21no—
34C2×#11758202—21no—
35C2×#11758189D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37#14519777C2×C411yescharacteristic
38#14519772—41no—
39#14519772—41no—
40#14519769C2×C411yescharacteristic
41#14519768—41no—
42#14519767—41no—
43#14519757—21no—
44#14519753—21no—
45Q8×Dic61—21no—
46#14519742—21no—
47#14519734C2×C411yescharacteristic
48#14519710—21no—
49#14519708—21no—
50#14519702—21no—
51#14519702—21no—
52#14519687D411yescharacteristic
53C4×#92418C2311yescharacteristic
54C8×Dic61D411yescharacteristic
55C4⋊Q8×C61C2×C411yescharacteristic
56#125×C61C2×C411yescharacteristic
57#103×C61—21no—
58#103×C61—21no—
59#97×C61C2×C411yescharacteristic
60C2×Q8×C61—21no—
61C2×C4×D61C22⋊C411yescharacteristic
62C2×Dic122—21no—
63C2×C8×C61C22⋊C411yescharacteristic
64C2×C8×C61C22⋊C411yescharacteristic
65C4⋊C4×C61—21no—
66C4⋊C4×C61—41no—
67C4⋊C4×C61—41no—
68C42×C61C22×C411yescharacteristic
69#11758202—41no—
70#11758202—41no—
71#11758202—41no—
72#11758202—41no—
73#11758198—21no—
74#11758198—41no—
75#11758198—41no—
76C4⋊Dic61—21no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80#11758196—21no—
81#11758196—41no—
82#11758196—41no—
83#11758196—41no—
84C4×Dic61—41no—
85C4×Dic61—41no—
86C4×Dic61C22⋊C411yescharacteristic
87C2×#92418C2×D411yescharacteristic
88C2×#92418C2×D411yescharacteristic
89#11758189—21no—
90#11758189—21no—
91C8×D61—21no—
92C8×D61—21no—
93#11758187—41no—
94#11758187—41no—
95#11758187—41no—
96#11758187—41no—
97C22×D61#10011yescharacteristic
98Q8×C61—41no—
99Q8×C61—41no—
100C2×C4×C61—21no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61C2×C22⋊C411yescharacteristic
104C2×Dic61—21no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61#10011yescharacteristic
108C4×D61—21no—
109C4×D61—21no—
110Dic122—41no—
111Dic122—41no—
112C8×C61—21no—
113C8×C61—21no—
114#92418#13511yescharacteristic
115#92418#13511yescharacteristic
116#92418AGL(1,ℤ/8)11yescharacteristic
117#92418#13711yescharacteristic
118#11990—611nomaximal, Sylow
119C22×C61C2×#10011yescharacteristic
120C2×D61—21no—
121C2×D61—41no—
122C4×C61—41no—
123C4×C61—81no—
124C4×C61—81no—
125C4×C61#41611yescharacteristic
126C4×C61#41711yescharacteristic
127Dic61—21no—
128Dic61—41no—
129Dic61—81no—
130Dic61—81no—
131#3177—611no—
132#2166—611no—
133#2153—611no—
134#1366—611no—
135#1366—611no—
136#1358—611no—
137#1358—611no—
138C2×C61—21no—
139C2×C61#155111yescharacteristic
140D61—41no—
141#541—611no—
142#541—611no—
143C2×M32—1221no—
144#499—611no—
145#494—611no—
146#491—611no—
147#491#692311yescharacteristic
148#470—1221no—
149#467—1221no—
150#441—1221no—
151C4×Q16—1221no—
152#405—611no—
153#364—611no—
154#364—611no—
155#364—611no—
156#364—611no—
157#364—1221no—
158#349—1221no—
159#347—1221no—
160C61#1199011yescharacteristic, complemented, Sylow
161C2×Q16—1221no—
162C2×Q16—1221no—
163C2×M16—611no—
164C22×C8—611no—
165C4⋊Q8—611no—
166C4⋊Q8C2×#692311yescharacteristic
167#126—2441no—
168#126—2441no—
169#125—611no—
170#125—2441no—
171#125—2441no—
172#125C2×#692311yescharacteristic
173C22⋊Q8—1221no—
174C22⋊Q8—1221no—
175C4×Q8—1221no—
176C4×Q8—1221no—
177#117—611no—
178M32—1221no—
179M32—1221no—
180M32—1221no—
181M32—1221no—
182M32—2441no—
183C2×C16—2441no—
184#107—1221no—
185#106—1221no—
186#103—21no—
187#103—21no—
188#103—1221no—
189#103—1221no—
190#97—611no—
191#97C2×#692311yescharacteristic
192C4×C8—611no—
193C4×C8—611no—
194C2×Q8—21no—
195C2×Q8—1221no—
196C22×C4—611no—
197Q16—2441no—
198Q16—2441no—
199Q16—2441no—
200Q16—2441no—
201M16—1221no—
202M16—1221no—
203C2×C8—611no—
204C2×C8—611no—
205C2×C8—1221no—
206C2×C8—1221no—
207C2×C8C22⋊#692311yescharacteristic
208C2×C8C22⋊#692311yescharacteristic
209C4⋊C4—21no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—1221no—
213C4⋊C4—1221no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C22⋊C4—1221no—
221C22⋊C4—2441no—
222C22⋊C4—2441no—
223C42—611no—
224C42—2441no—
225C42—2441no—
226C42C22×#692311yescharacteristic
227C16—2441no—
228C16—2441no—
229C16—2441no—
230C16—2441no—
231C23—611no—
232Q8—41no—
233Q8—41no—
234Q8—2441no—
235Q8—2441no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—611no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4C2×C22⋊#692311yescharacteristic
246C8—21no—
247C8—21no—
248C8—611no—
249C8—611no—
250C8—611no—
251C8—611no—
252C22—1221no—
253C22—2441no—
254C22D61⋊#10011yescharacteristic
255C4—41no—
256C4—81no—
257C4—81no—
258C4—1221no—
259C4—4881no—
260C4—4881no—
261C4—2441no—
262C4#1684075211yescharacteristic
263C4#1684075311yescharacteristic
264C2—21no—
265C2—2441no—
266C2#2146133911yescharacteristic
subgroupG/H
centerC2#21461339
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#491C4
socleC2×C61#1551
prime radicalC22×D61#100
cosocleC4×#92418C23
hypercenter#491#6923
hypocenterC61#11990
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #491

Complements

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

NH ≅ G/Ntype
3. #21460840C2semidirect
4. #21460839C2semidirect
5. #21460828C2semidirect
6. #21460828C2semidirect
160. C61#11990semidirect

Maximal subgroups

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

subgroupindex
#214621952
#214621612
#214608402
#214608392
#214608282
#214564772
#1199061