Finite Group Databasebeta

← #30605683

Subgroups — #30605683

Order 15616.

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

normal subgroups only

This group has 292 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#21462181C211yesmaximal, characteristic
2#21461376C211yesmaximal, characteristic
3#21460838C212yesmaximal, complemented
4#21460837C212yesmaximal, complemented
5#21456331C211yesmaximal, characteristic
6#16840765—21no—
7#16840683C2212yes—
8C22⋊#11758187—21no—
9#16840651—21no—
10#16840626C2212yes—
11#16840625—21no—
12#16840315—21no—
13#16840166C2211yescharacteristic
14#16840166C2211yescharacteristic
15#16840163C411yescharacteristic
16#16840163C411yescharacteristic
17#16840162—21no—
18#16840159—21no—
19#16839800C411yescharacteristic
20#16839798—21no—
21C2×C8×Dic61C2211yescharacteristic
22C61×#427C411yescharacteristic
23C2×#11758217—41no—
24C2×#11758187—22no—
25#14519844—41no—
26C4⋊#92420—22no—
27C22×#92418D411yescharacteristic
28#14519776—21no—
29#14519776—21no—
30#14519768—21no—
31#14519768—21no—
32#14519754—41no—
33#14519754—41no—
34C4×Dic122—41no—
35C4×Dic122—41no—
36#14519736—21no—
37C2×C4×Dic61D411yescharacteristic
38#14519711C2×C411yescharacteristic
39#14519711C2×C411yescharacteristic
40#14519710—21no—
41#14519710—21no—
42#14519709—21no—
43#14519708—21no—
44#14519708—21no—
45C8×Dic61C2×C411yescharacteristic
46C8×Dic61D411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61C2311yescharacteristic
49C22×C8×C61C2×C411yescharacteristic
50#117×C61—21no—
51#107×C61C2×C411yescharacteristic
52#107×C61C2×C411yescharacteristic
53#106×C61—21no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×Dic61D811yescharacteristic
56C22×Dic61SD1611yescharacteristic
57C2×Dic122—41no—
58C2×Dic122—41no—
59#11758217—82no—
60C2×#92420—42no—
61C2×C8×C61—22no—
62C2×C8×C61C22⋊C411yescharacteristic
63C2×C8×C61C22×C411yescharacteristic
64C4⋊C4×C61—21no—
65C4⋊C4×C61—21no—
66C22⋊C4×C61—41no—
67C42×C61—41no—
68C22⋊Dic61—41no—
69C4⋊Dic61—21no—
70C4⋊Dic61—21no—
71C4⋊Dic61—41no—
72C4⋊Dic61—41no—
73#11758196—41no—
74#11758196—41no—
75#11758196—41no—
76#11758196—41no—
77C4×Dic61—41no—
78C4×Dic61C22⋊C411yescharacteristic
79C4×Dic61D811yescharacteristic
80C4×Dic61SD1611yescharacteristic
81C4×Dic61C2×D411yescharacteristic
82C2×#92418—22no—
83C2×#92418C22⋊C411yescharacteristic
84C2×#92418C2×D411yescharacteristic
85#11758187—42no—
86C23×C61#10211yescharacteristic
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61#10211yescharacteristic
92C2×C4×C61C2×C22⋊C411yescharacteristic
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—41no—
96C2×Dic61—41no—
97C2×Dic61—41no—
98C2×Dic61#10211yescharacteristic
99C2×Dic61#10211yescharacteristic
100C2×Dic61C2×D811yescharacteristic
101C2×Dic61C2×SD1611yescharacteristic
102Dic122—82no—
103Dic122—81no—
104Dic122—81no—
105#92420—82no—
106C8×C61—21no—
107C8×C61#10112yes—
108#92418—21no—
109#92418#13712yes—
110#11976—611nomaximal, Sylow
111C22×C61—21no—
112C22×C61—21no—
113C22×C61—21no—
114C22×C61C2×#10211yescharacteristic
115C4×C61—21no—
116C4×C61—81no—
117C4×C61—81no—
118C4×C61C2×#10111yescharacteristic
119C4×C61#41911yescharacteristic
120Dic61—21no—
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—41no—
133C2×C61#154611yescharacteristic
134C2×C61#213911yescharacteristic
135C2×C61#214811yescharacteristic
136#533—1221no—
137#500—611no—
138#500—611no—
139#499—611no—
140#499—611no—
141#499—1221no—
142#498—1221no—
143#427—611no—
144#427—1221no—
145#427#692311yescharacteristic
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×C8C2×#692311yescharacteristic
157C4⋊Q8—1221no—
158C4⋊Q8—1221no—
159#125—1221no—
160#125—1221no—
161C22⋊Q8—2441no—
162C22⋊Q8—2441no—
163C4×Q8—2441no—
164C4×Q8—2441no—
165#117—21no—
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×C8—611no—
185C2×Q8—2441no—
186C2×Q8—2441no—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4C22⋊#692311yescharacteristic
190M16—4882no—
191C2×C8—22no—
192C2×C8—611no—
193C2×C8—611no—
194C2×C8—1222no—
195C2×C8—2442no—
196C2×C8C22⋊#692311yescharacteristic
197C2×C8C22×#692311yescharacteristic
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—1221no—
201C4⋊C4—1221no—
202C4⋊C4—2441no—
203C4⋊C4—2441no—
204C4⋊C4—2441no—
205C4⋊C4—2441no—
206C4⋊C4—2441no—
207C4⋊C4—2441no—
208C22⋊C4—41no—
209C22⋊C4—2441no—
210C42—41no—
211C42—611no—
212C42—611no—
213C42—611no—
214C42—611no—
215C42—2441no—
216C16—2442no—
217C23#1451983911yescharacteristic
218Q8—4881no—
219Q8—4881no—
220Q8—4882no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—611no—
226C2×C4—611no—
227C2×C4—611no—
228C2×C4—611no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—2441no—
232C2×C4—2441no—
233C2×C4—2441no—
234C2×C4#1451983911yescharacteristic
235C2×C4C2×C22⋊#692311yescharacteristic
236C8—21no—
237C8—612no—
238C8—1221no—
239C8—4882no—
240C8#1451983812yes—
241C22—21no—
242C22—21no—
243C22—21no—
244C22C2×#1451983911yescharacteristic
245C4—21no—
246C4—81no—
247C4—81no—
248C4—611no—
249C4—611no—
250C4—1221no—
251C4—1221no—
252C4—1221no—
253C4—4881no—
254C4—4881no—
255C4C2×#1451983811yescharacteristic
256C4#1684075511yescharacteristic
257C2—41no—
258C2#2146132811yescharacteristic
259C2#2146212711yescharacteristic
260C2#2146214611yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#427C4
socleC22×C61C2×#102
prime radicalC23×C61#102
cosocleC8×Dic61C23
hypercenter#427#6923
hypocenterC61#11976
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #427

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
#214621812
#214613762
#214608382
#214608372
#214563312
#1197661