Finite Group Databasebeta

← #30605684

Subgroups — #30605684

Order 15616.

292 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 78 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#21461378C211yesmaximal, characteristic
3#21460838C212yesmaximal, complemented
4#21460837C212yesmaximal, complemented
5#21456332C211yesmaximal, characteristic
6#16840766—21no—
7#16840683C2212yes—
8#16840657—21no—
9#16840650—21no—
10#16840626—21no—
11#16840626C2212yes—
12#16840318—21no—
13#16840166C2211yescharacteristic
14#16840166C2211yescharacteristic
15#16840164C411yescharacteristic
16#16840161—21no—
17#16840159—21no—
18#16839799C411yescharacteristic
19#16839799C411yescharacteristic
20#16839797—21no—
21C4×C8×D61C2211yescharacteristic
22C61×#499C411yescharacteristic
23C2×#11758213—41no—
24C2×#11758187—22no—
25C4⋊#92420—22no—
26C4⋊#92420—41no—
27C2×C8×D61C2×C411yescharacteristic
28C2×C8×D61D411yescharacteristic
29#14519776—21no—
30#14519776—21no—
31#14519769—21no—
32#14519755—41no—
33#14519755—41no—
34#14519742—41no—
35#14519742—41no—
36#14519735—21no—
37#14519735—21no—
38C42×D61D411yescharacteristic
39#14519711C2×C411yescharacteristic
40#14519711C2×C411yescharacteristic
41#14519710—21no—
42#14519710—21no—
43#14519709—21no—
44#14519708—21no—
45#14519708—21no—
46C4×#92418D411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61C2311yescharacteristic
49#125×C61—21no—
50#107×C61C2×C411yescharacteristic
51#107×C61C2×C411yescharacteristic
52#106×C61—21no—
53C4×C8×C61C2×C411yescharacteristic
54C2×C4×D61C22⋊C411yescharacteristic
55C2×C4×D61D811yescharacteristic
56C2×C4×D61SD1611yescharacteristic
57C2×Dic122—41no—
58C2×Dic122—41no—
59C2×#92420—42no—
60#11758213—82no—
61C2×C8×C61C22⋊C411yescharacteristic
62C2×C8×C61C22×C411yescharacteristic
63C4⋊C4×C61—21no—
64C4⋊C4×C61—21no—
65C4⋊C4×C61—41no—
66C4⋊C4×C61—41no—
67C42×C61C22⋊C411yescharacteristic
68#11758198—41no—
69#11758198—41no—
70C4⋊Dic61—21no—
71C4⋊Dic61—21no—
72#11758196—41no—
73#11758196—41no—
74#11758196—41no—
75#11758196—41no—
76C4×Dic61—41no—
77C4×Dic61—41no—
78C4×Dic61D811yescharacteristic
79C4×Dic61SD1611yescharacteristic
80C4×Dic61C2×D411yescharacteristic
81C2×#92418C22⋊C411yescharacteristic
82C2×#92418C2×D411yescharacteristic
83C8×D61—22no—
84C8×D61—22no—
85#11758187—42no—
86C22×D61#10211yescharacteristic
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61#10211yescharacteristic
90C2×C4×C61#10211yescharacteristic
91C2×C4×C61C2×C22⋊C411yescharacteristic
92C2×Dic61—41no—
93C2×Dic61—41no—
94C2×Dic61#10211yescharacteristic
95C2×Dic61C2×D811yescharacteristic
96C2×Dic61C2×SD1611yescharacteristic
97C4×D61—21no—
98C4×D61—21no—
99C4×D61—21no—
100C4×D61—21no—
101C4×D61—41no—
102Dic122—82no—
103Dic122—81no—
104Dic122—81no—
105#92420—82no—
106C8×C61—21no—
107C8×C61—21no—
108#92418#10112yes—
109#92418#13712yes—
110#11976—611nomaximal, Sylow
111C22×C61C2×#10211yescharacteristic
112C2×D61—21no—
113C2×D61—21no—
114C2×D61—21no—
115C4×C61—21no—
116C4×C61—21no—
117C4×C61—81no—
118C4×C61—81no—
119C4×C61C2×#10111yescharacteristic
120C4×C61#41911yescharacteristic
121Dic61—21no—
122Dic61—21no—
123Dic61—81no—
124Dic61—81no—
125Dic61#50911yescharacteristic
126Dic61#51011yescharacteristic
127#3160—611no—
128#2163—611no—
129#1567—611no—
130#1365—612no—
131#1364—612no—
132C2×C61#154611yescharacteristic
133C2×C61#213911yescharacteristic
134C2×C61#214811yescharacteristic
135D61—41no—
136#533—1221no—
137#500—611no—
138#500—611no—
139#499—611no—
140#499—1221no—
141#499#692311yescharacteristic
142#498—1221no—
143#427—611no—
144#427—611no—
145#427—1221no—
146#423—1221no—
147C2×C4×C8—611no—
148C4⋊C16—612no—
149C22⋊C16—1221no—
150#346—1221no—
151#335—612no—
152#335—1221no—
153C61#1197611yescharacteristic, complemented, Sylow
154C2×M16—2441no—
155C22×C8—611no—
156C22×C8—611no—
157C4⋊Q8—1221no—
158C4⋊Q8—1221no—
159#125—21no—
160#125—1221no—
161C22⋊Q8—2441no—
162C22⋊Q8—2441no—
163C4×Q8—2441no—
164C4×Q8—2441no—
165#117—1221no—
166#117—1221no—
167C2×C42—611no—
168C2×C16—1222no—
169#107—611no—
170#107—611no—
171#107—1221no—
172#107—1221no—
173#107C2×#692311yescharacteristic
174#107C2×#692311yescharacteristic
175#106—21no—
176#106—1221no—
177#106—1221no—
178#106—1221no—
179C4⋊C8—1222no—
180C4⋊C8—2441no—
181C4×C8—611no—
182C4×C8—611no—
183C4×C8—611no—
184C4×C8C2×#692311yescharacteristic
185C2×Q8—2441no—
186C2×Q8—2441no—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—611no—
190M16—4882no—
191C2×C8—611no—
192C2×C8—611no—
193C2×C8—1222no—
194C2×C8—1222no—
195C2×C8—2442no—
196C2×C8C22⋊#692311yescharacteristic
197C2×C8C22×#692311yescharacteristic
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—1221no—
203C4⋊C4—1221no—
204C4⋊C4—2441no—
205C4⋊C4—2441no—
206C4⋊C4—2441no—
207C4⋊C4—2441no—
208C22⋊C4—2441no—
209C22⋊C4—2441no—
210C42—611no—
211C42—611no—
212C42—611no—
213C42—2441no—
214C42—2441no—
215C42C22⋊#692311yescharacteristic
216C16—2442no—
217C23—611no—
218Q8—4881no—
219Q8—4881no—
220Q8—4882no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—611no—
224C2×C4—611no—
225C2×C4—611no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—2441no—
231C2×C4—2441no—
232C2×C4—2441no—
233C2×C4#1451983911yescharacteristic
234C2×C4#1451983911yescharacteristic
235C2×C4C2×C22⋊#692311yescharacteristic
236C8—21no—
237C8—21no—
238C8—612no—
239C8—612no—
240C8—4882no—
241C22—1221no—
242C22—1221no—
243C22—1221no—
244C22C2×#1451983911yescharacteristic
245C4—21no—
246C4—21no—
247C4—81no—
248C4—81no—
249C4—611no—
250C4—611no—
251C4—1221no—
252C4—1221no—
253C4—4881no—
254C4—4881no—
255C4D61⋊#10111yescharacteristic
256C4#1684075511yescharacteristic
257C2—2441no—
258C2#2146132911yescharacteristic
259C2#2146212711yescharacteristic
260C2#2146214711yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#499C4
socleC22×C61C2×#102
prime radicalC22×D61#102
cosocleC8×Dic61C23
hypercenter#499#6923
hypocenterC61#11976
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
3. #21460838C2semidirect
4. #21460837C2semidirect
153. C61#11976semidirect

Maximal subgroups

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

subgroupindex
#214621822
#214613782
#214608382
#214608372
#214563322
#1197661