Finite Group Databasebeta

← #30605628

Subgroups — #30605628

Order 15616.

296 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 76 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#21462182C211yesmaximal, characteristic
2#21461367C211yesmaximal, characteristic
3#21460838C212yesmaximal, complemented
4#21460834C212yesmaximal, complemented
5#21456402C211yesmaximal, characteristic
6#16840781—21no—
7#16840683C2212yes—
8#16840657—21no—
9#16840650—21no—
10#16840626C2212yes—
11#16840623—21no—
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×#11758187—22no—
24C4⋊#92420—22no—
25#14519834—41no—
26C4×#92420—41no—
27C2×Dic244C2×C411yescharacteristic
28C2×#11758202—21no—
29C2×C8×D61C2×C411yescharacteristic
30C2×C8×D61D411yescharacteristic
31#14519776—21no—
32#14519775—21no—
33#14519767—41no—
34#14519757—21no—
35#14519755—41no—
36#14519753—21no—
37C4×Dic122—21no—
38C4×Dic122—41no—
39#14519734—41no—
40C42×D61D411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519710—21no—
43#14519702—21no—
44#14519701—21no—
45#14519700—21no—
46C4×#92418D411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61C2311yescharacteristic
49C2×Q16×C61C2×C411yescharacteristic
50C4×Q8×C61—21no—
51#107×C61C2×C411yescharacteristic
52#103×C61—21no—
53C4×C8×C61C2×C411yescharacteristic
54C2×Q8×C61—21no—
55C2×C4×D61C22⋊C411yescharacteristic
56C2×C4×D61D811yescharacteristic
57C2×C4×D61SD1611yescharacteristic
58C2×Dic122—21no—
59C2×Dic122—41no—
60C2×#92420—42no—
61Q16×C61—41no—
62C2×C8×C61C22⋊C411yescharacteristic
63C2×C8×C61C22×C411yescharacteristic
64C4⋊C4×C61—21no—
65C4⋊C4×C61—41no—
66C42×C61—41no—
67C42×C61C22⋊C411yescharacteristic
68#11758202—42no—
69#11758198—41no—
70#11758198—41no—
71C4⋊Dic61—21no—
72C4⋊Dic61—41no—
73#11758196—41no—
74#11758196—41no—
75#11758196—41no—
76#11758196—41no—
77#11758196—41no—
78C4×Dic61—41no—
79C4×Dic61D811yescharacteristic
80C4×Dic61SD1611yescharacteristic
81C4×Dic61C2×D411yescharacteristic
82C2×#92418C22⋊C411yescharacteristic
83C2×#92418C2×D411yescharacteristic
84Dic244—41no—
85C8×D61—22no—
86C8×D61—41no—
87#11758187—42no—
88C22×D61#10211yescharacteristic
89Q8×C61—41no—
90Q8×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61#10211yescharacteristic
94C2×C4×C61#10211yescharacteristic
95C2×C4×C61C2×C22⋊C411yescharacteristic
96C2×Dic61—41no—
97C2×Dic61—41no—
98C2×Dic61#10211yescharacteristic
99C2×Dic61C2×D811yescharacteristic
100C2×Dic61C2×SD1611yescharacteristic
101C4×D61—21no—
102C4×D61—21no—
103C4×D61—22no—
104C4×D61—41no—
105Dic122—41no—
106Dic122—41no—
107Dic122—82no—
108#92420—82no—
109C8×C61—21no—
110C8×C61—21no—
111#92418—21no—
112#92418#13512yes—
113#11953—611nomaximal, Sylow
114C22×C61C2×#10211yescharacteristic
115C2×D61—21no—
116C2×D61—21no—
117C2×D61—21no—
118C4×C61—21no—
119C4×C61—21no—
120C4×C61—81no—
121C4×C61—81no—
122C4×C61#41311yescharacteristic
123C4×C61#41611yescharacteristic
124Dic61—21no—
125Dic61—21no—
126Dic61—81no—
127Dic61—81no—
128Dic61#51012yes—
129#3170—611no—
130#2163—611no—
131#1564—611no—
132#1365—612no—
133#1362—612no—
134C2×C61#154011yescharacteristic
135C2×C61#214111yescharacteristic
136C2×C61#214811yescharacteristic
137D61—41no—
138#533—1221no—
139#500—611no—
140#494—611no—
141#487—1221no—
142#467—611no—
143#467—611no—
144#467—1221no—
145C4×Q16—611no—
146C4×Q16—1221no—
147C4×Q16#692311yescharacteristic
148#431—1221no—
149C2×C4×C8—611no—
150C4⋊C16—612no—
151C22⋊C16—1221no—
152#346—1221no—
153#335—612no—
154#334—1221no—
155C61#1195311yescharacteristic, complemented, Sylow
156C2×Q16—611no—
157C2×Q16—1221no—
158C2×Q16C2×#692311yescharacteristic
159C22×C8—611no—
160C22×C8—611no—
161C4⋊Q8—1221no—
162C4⋊Q8—1221no—
163#125—2441no—
164C22⋊Q8—1221no—
165C22⋊Q8—1221no—
166C22⋊Q8—2441no—
167C4×Q8—21no—
168C4×Q8—1221no—
169C4×Q8—2441no—
170#117—2441no—
171C2×C42—611no—
172C2×C16—1222no—
173#107—611no—
174#107—1221no—
175#107C2×#692311yescharacteristic
176C4⋊C8—1222no—
177#103—21no—
178#103—1221no—
179#103—1221no—
180#103—1221no—
181C22⋊C8—2441no—
182C4×C8—611no—
183C4×C8—611no—
184C4×C8—611no—
185C4×C8—2441no—
186C4×C8C2×#692311yescharacteristic
187C2×Q8—21no—
188C2×Q8—1221no—
189C2×Q8—2441no—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—611no—
193Q16—41no—
194Q16—2441no—
195Q16—2442no—
196C2×C8—611no—
197C2×C8—611no—
198C2×C8—1222no—
199C2×C8—2441no—
200C2×C8—2442no—
201C2×C8C22⋊#692311yescharacteristic
202C2×C8C22×#692311yescharacteristic
203C4⋊C4—21no—
204C4⋊C4—41no—
205C4⋊C4—1221no—
206C4⋊C4—2441no—
207C4⋊C4—2441no—
208C4⋊C4—2441no—
209C4⋊C4—2441no—
210C4⋊C4—2441no—
211C4⋊C4—2441no—
212C22⋊C4—2441no—
213C22⋊C4—2441no—
214C42—41no—
215C42—611no—
216C42—611no—
217C42—611no—
218C42—2441no—
219C42C22⋊#692311yescharacteristic
220C16—2442no—
221C23—611no—
222Q8—41no—
223Q8—41no—
224Q8—4882no—
225Q8—2441no—
226Q8—2441no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—611no—
230C2×C4—611no—
231C2×C4—611no—
232C2×C4—1222no—
233C2×C4—1221no—
234C2×C4—1221no—
235C2×C4—2441no—
236C2×C4—2441no—
237C2×C4—2441no—
238C2×C4#1451983911yescharacteristic
239C2×C4#1451983911yescharacteristic
240C2×C4C2×C22⋊#692311yescharacteristic
241C8—21no—
242C8—21no—
243C8—612no—
244C8—1221no—
245C8—4882no—
246C22—1221no—
247C22—1221no—
248C22—1221no—
249C22C2×#1451983911yescharacteristic
250C4—21no—
251C4—21no—
252C4—81no—
253C4—81no—
254C4—612no—
255C4—1221no—
256C4—1221no—
257C4—4881no—
258C4—4881no—
259C4#1684074811yescharacteristic
260C4#1684075211yescharacteristic
261C2—2441no—
262C2#2146131611yescharacteristic
263C2#2146212911yescharacteristic
264C2#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#11953
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
155. C61#11953semidirect

Maximal subgroups

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

subgroupindex
#214621822
#214613672
#214608382
#214608342
#214564022
#1195361