Finite Group Databasebeta

← #30605705

Subgroups — #30605705

Order 15616.

314 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 86 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
1D61⋊(C4⋊C16)C211yesmaximal, characteristic
2#21461378C211yesmaximal, characteristic
3#21460838C212yesmaximal, complemented
4#21460834C212yesmaximal, complemented
5#21456402C211yesmaximal, characteristic
6C2×D61⋊C16—21no—
7#16840766—21no—
8#16840683C2212yes—
9C4⋊#11758187—21no—
10#16840626—21no—
11#16840626C2212yes—
12#16840316—21no—
13#16840166C2211yescharacteristic
14#16840140C2211yescharacteristic
15#16840111—21no—
16#16840004C411yescharacteristic
17#16840002—21no—
18#16840000C411yescharacteristic
19C4×Dic244C411yescharacteristic
20C4×#11758202—21no—
21C4×C8×D61C2211yescharacteristic
22C4×Q16×C61C411yescharacteristic
23C2×#11758213—41no—
24D61⋊C16—42no—
25C2×#11758187—22no—
26C4⋊#92420—22no—
27C4⋊#92420—41no—
28C2×Dic244C2×C411yescharacteristic
29C2×#11758202—21no—
30C2×C8×D61C2×C411yescharacteristic
31C2×C8×D61D411yescharacteristic
32#14519776—21no—
33#14519775—21no—
34#14519767—41no—
35#14519757—21no—
36#14519755—41no—
37#14519753—21no—
38C4×Dic122—21no—
39C4×Dic122—41no—
40#14519734—41no—
41C42×D61D411yescharacteristic
42#14519711C2×C411yescharacteristic
43#14519710—21no—
44#14519702—21no—
45#14519701—21no—
46#14519700—21no—
47C4×#92418D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61C2311yescharacteristic
50C2×Q16×C61C2×C411yescharacteristic
51C4×Q8×C61—21no—
52#107×C61C2×C411yescharacteristic
53#103×C61—21no—
54C4×C8×C61C2×C411yescharacteristic
55C2×Q8×C61—21no—
56C2×C4×D61C22⋊C411yescharacteristic
57C2×C4×D61D811yescharacteristic
58C2×C4×D61SD1611yescharacteristic
59C2×Dic122—21no—
60C2×Dic122—41no—
61C2×#92420—42no—
62#11758213—82no—
63Q16×C61—41no—
64C2×C8×C61C22⋊C411yescharacteristic
65C2×C8×C61C22×C411yescharacteristic
66C4⋊C4×C61—21no—
67C4⋊C4×C61—41no—
68C42×C61—41no—
69C42×C61C22⋊C411yescharacteristic
70#11758202—41no—
71#11758202—41no—
72#11758198—41no—
73#11758198—41no—
74C4⋊Dic61—21no—
75C4⋊Dic61—41no—
76#11758196—41no—
77#11758196—41no—
78#11758196—41no—
79#11758196—41no—
80#11758196—41no—
81C4×Dic61—41no—
82C4×Dic61D811yescharacteristic
83C4×Dic61SD1611yescharacteristic
84C4×Dic61C2×D411yescharacteristic
85C2×#92418C22⋊C411yescharacteristic
86C2×#92418C2×D411yescharacteristic
87Dic244—41no—
88C8×D61—21no—
89C8×D61—21no—
90C8×D61—41no—
91#11758187—42no—
92C22×D61#10211yescharacteristic
93Q8×C61—41no—
94Q8×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61#10211yescharacteristic
98C2×C4×C61#10211yescharacteristic
99C2×C4×C61C2×C22⋊C411yescharacteristic
100C2×Dic61—41no—
101C2×Dic61—41no—
102C2×Dic61#10211yescharacteristic
103C2×Dic61C2×D811yescharacteristic
104C2×Dic61C2×SD1611yescharacteristic
105C4×D61—21no—
106C4×D61—21no—
107C4×D61—41no—
108C4×D61SD3212yes—
109C4×D61Q3212yes—
110Dic122—41no—
111Dic122—41no—
112Dic122—82no—
113#92420—82no—
114C8×C61—21no—
115C8×C61—21no—
116#92418—21no—
117#92418AGL(1,ℤ/8)11yescharacteristic
118#92418#13711yescharacteristic
119#11983—611nomaximal, Sylow
120C22×C61C2×#10211yescharacteristic
121C2×D61—21no—
122C2×D61—21no—
123C2×D61#35812yes—
124C4×C61—21no—
125C4×C61—81no—
126C4×C61—81no—
127C4×C61#35812yes—
128C4×C61#41311yescharacteristic
129C4×C61#41711yescharacteristic
130Dic61—21no—
131Dic61—21no—
132Dic61—81no—
133Dic61—81no—
134Dic61C2×SD3211yescharacteristic
135Dic61C2×Q3211yescharacteristic
136#3170—611no—
137C2×C4⋊C16—611no—
138#1567—611no—
139#1365—612no—
140#1362—612no—
141C2×C61#154711yescharacteristic
142C2×C61C2×#35811yescharacteristic
143C2×C61#214811yescharacteristic
144D61—22no—
145#533—1221no—
146C22×C16—1221no—
147#500—611no—
148#494—611no—
149#487—1221no—
150#467—611no—
151#467—611no—
152#467—1221no—
153C4×Q16—611no—
154C4×Q16—1221no—
155C4×Q16#692311yescharacteristic
156#423—1221no—
157C2×C4×C8—611no—
158C4⋊C16—612no—
159C4⋊C16—1221no—
160#335—612no—
161#335—1221no—
162C61#1198311yescharacteristic, complemented, Sylow
163C2×Q16—611no—
164C2×Q16—1221no—
165C2×Q16C2×#692311yescharacteristic
166C2×M16—2441no—
167C22×C8—611no—
168C22×C8—611no—
169C4⋊Q8—1221no—
170C4⋊Q8—1221no—
171#125—2441no—
172C22⋊Q8—1221no—
173C22⋊Q8—1221no—
174C22⋊Q8—2441no—
175C4×Q8—21no—
176C4×Q8—1221no—
177C4×Q8—2441no—
178#117—2441no—
179C2×C42—611no—
180C2×C16—1222no—
181C2×C16—2442no—
182#107—611no—
183#107—1221no—
184#107C2×#692311yescharacteristic
185C4⋊C8—1222no—
186C4⋊C8—2441no—
187#103—21no—
188#103—1221no—
189#103—1221no—
190#103—1221no—
191C4×C8—611no—
192C4×C8—611no—
193C4×C8—611no—
194C4×C8C2×#692311yescharacteristic
195C2×Q8—21no—
196C2×Q8—1221no—
197C2×Q8—2441no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—611no—
201Q16—41no—
202Q16—2441no—
203Q16—2441no—
204Q16—2441no—
205M16—4882no—
206C2×C8—611no—
207C2×C8—611no—
208C2×C8—1221no—
209C2×C8—1221no—
210C2×C8—2441no—
211C2×C8—2442no—
212C2×C8C22⋊#692311yescharacteristic
213C2×C8C22×#692311yescharacteristic
214C4⋊C4—21no—
215C4⋊C4—41no—
216C4⋊C4—1221no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C22⋊C4—2441no—
224C22⋊C4—2441no—
225C42—41no—
226C42—611no—
227C42—611no—
228C42—611no—
229C42—2441no—
230C42C22⋊#692311yescharacteristic
231C16—2442no—
232C23—611no—
233Q8—41no—
234Q8—41no—
235Q8—4882no—
236Q8—2441no—
237Q8—2441no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—611no—
241C2×C4—612no—
242C2×C4—612no—
243C2×C4—611no—
244C2×C4—611no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4#1451983911yescharacteristic
251C2×C4#1451983911yescharacteristic
252C2×C4C2×C22⋊#692311yescharacteristic
253C8—21no—
254C8—21no—
255C8—611no—
256C8—611no—
257C8—1221no—
258C8—4882no—
259C22—612no—
260C22—1221no—
261C22—1221no—
262C22C2×#1451983911yescharacteristic
263C4—21no—
264C4—81no—
265C4—81no—
266C4—611no—
267C4—611no—
268C4—1221no—
269C4—1221no—
270C4—4881no—
271C4—4881no—
272C4#1684067512yes—
273C4#1684074811yescharacteristic
274C4#1684075311yescharacteristic
275C2—1222no—
276C2#2146133011yescharacteristic
277C2C2×#1684067511yescharacteristic
278C2#2146214711yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC4×Q16×C61C4
socleC22×C61C2×#102
prime radicalC22×D61#102
cosocleC8×Dic61C23
hypercenterC4×Q16#6923
hypocenterC61#11983
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. #21460838C2semidirect
4. #21460834C2semidirect
162. C61#11983semidirect

Maximal subgroups

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

subgroupindex
D61⋊(C4⋊C16)2
#214613782
#214608382
#214608342
#214564022
#1198361