Finite Group Databasebeta

← #30605715

Subgroups — #30605715

Order 15616.

308 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 80 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#21462152C211yesmaximal, characteristic
2#21461378C211yesmaximal, characteristic
3#21460837C212yesmaximal, complemented
4#21460834C212yesmaximal, complemented
5#21456402C211yesmaximal, characteristic
6C2×#14519852—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—
24#14519852—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—22no—
106C4×D61—21no—
107C4×D61—21no—
108C4×D61—21no—
109C4×D61—21no—
110Dic122—41no—
111Dic122—41no—
112Dic122—81no—
113Dic122—81no—
114#92420—82no—
115C8×C61—21no—
116C8×C61—21no—
117#92418—21no—
118#92418AGL(1,ℤ/8)11yescharacteristic
119#92418#13711yescharacteristic
120#11988—611nomaximal, Sylow
121C22×C61C2×#10211yescharacteristic
122C2×D61—21no—
123C2×D61—21no—
124C2×D61—21no—
125C4×C61—21no—
126C4×C61—81no—
127C4×C61—81no—
128C4×C61#36212yes—
129C4×C61#41311yescharacteristic
130C4×C61#41711yescharacteristic
131Dic61—21no—
132Dic61—21no—
133Dic61—81no—
134Dic61—81no—
135Dic61#50911yescharacteristic
136Dic61#51011yescharacteristic
137#3170—611no—
138#2150—611no—
139#1567—611no—
140#1364—612no—
141#1362—612no—
142C2×C61#154711yescharacteristic
143C2×C61#213911yescharacteristic
144C2×C61C2×#36211yescharacteristic
145D61—41no—
146#533—1221no—
147C2×M32—1221no—
148#500—611no—
149#494—611no—
150#487—1221no—
151#467—611no—
152#467—611no—
153#467—1221no—
154C4×Q16—611no—
155C4×Q16—1221no—
156C4×Q16#692311yescharacteristic
157#423—1221no—
158C2×C4×C8—611no—
159C4⋊C16—612no—
160C4⋊C16—1221no—
161#335—612no—
162#335—1221no—
163C61#1198811yescharacteristic, complemented, Sylow
164C2×Q16—611no—
165C2×Q16—1221no—
166C2×Q16C2×#692311yescharacteristic
167C2×M16—2441no—
168C22×C8—611no—
169C22×C8—611no—
170C4⋊Q8—1221no—
171C4⋊Q8—1221no—
172#125—2441no—
173C22⋊Q8—1221no—
174C22⋊Q8—1221no—
175C22⋊Q8—2441no—
176C4×Q8—21no—
177C4×Q8—1221no—
178C4×Q8—2441no—
179#117—2441no—
180C2×C42—611no—
181M32—2442no—
182C2×C16—1222no—
183#107—611no—
184#107—1221no—
185#107C2×#692311yescharacteristic
186C4⋊C8—1222no—
187C4⋊C8—2441no—
188#103—21no—
189#103—1221no—
190#103—1221no—
191#103—1221no—
192C4×C8—611no—
193C4×C8—611no—
194C4×C8—611no—
195C4×C8C2×#692311yescharacteristic
196C2×Q8—21no—
197C2×Q8—1221no—
198C2×Q8—2441no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—611no—
202Q16—41no—
203Q16—2441no—
204Q16—2441no—
205Q16—2441no—
206M16—4882no—
207C2×C8—611no—
208C2×C8—611no—
209C2×C8—1221no—
210C2×C8—1221no—
211C2×C8—2441no—
212C2×C8—2442no—
213C2×C8C22⋊#692311yescharacteristic
214C2×C8C22×#692311yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—41no—
217C4⋊C4—1221no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C22⋊C4—2441no—
225C22⋊C4—2441no—
226C42—41no—
227C42—611no—
228C42—611no—
229C42—611no—
230C42—2441no—
231C42C22⋊#692311yescharacteristic
232C16—2442no—
233C23—611no—
234Q8—41no—
235Q8—41no—
236Q8—4881no—
237Q8—4881no—
238Q8—2441no—
239Q8—2441no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—611no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1222no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4#1451983911yescharacteristic
253C2×C4#1451983911yescharacteristic
254C2×C4C2×C22⋊#692311yescharacteristic
255C8—21no—
256C8—21no—
257C8—611no—
258C8—611no—
259C8—1221no—
260C8—4882no—
261C22—1221no—
262C22—1221no—
263C22—1221no—
264C22C2×#1451983911yescharacteristic
265C4—21no—
266C4—81no—
267C4—81no—
268C4—611no—
269C4—611no—
270C4—1221no—
271C4—1221no—
272C4—4881no—
273C4—4881no—
274C4#1684068112yes—
275C4#1684074811yescharacteristic
276C4#1684075311yescharacteristic
277C2—2441no—
278C2#2146133011yescharacteristic
279C2#2146212711yescharacteristic
280C2C2×#1684068111yescharacteristic
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#11988
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. #21460837C2semidirect
4. #21460834C2semidirect
163. C61#11988semidirect

Maximal subgroups

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

subgroupindex
#214621522
#214613782
#214608372
#214608342
#214564022
#1198861