Finite Group Databasebeta

← #30605356

Subgroups — #30605356

Order 15616.

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

normal subgroups only

This group has 300 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#21462183C211yesmaximal, characteristic
2#21461743C211yesmaximal, characteristic
3#21460812C212yesmaximal
4#21460811C212yesmaximal
5#21456402C211yesmaximal, characteristic
6#16840766—21no—
7C4⋊#11758187—21no—
8#16840657C2212yes—
9#16840651—21no—
10#16840638—21no—
11#16840638C2212yes—
12#16840316—21no—
13#16840166C411yescharacteristic
14#16840140C411yescharacteristic
15#16840111—21no—
16#16840004C2211yescharacteristic
17#16840002—21no—
18#16840000C2211yescharacteristic
19C4×Dic244C411yescharacteristic
20C4×#11758202—21no—
21C4×C8×D61C2211yescharacteristic
22C4×Q16×C61C411yescharacteristic
23C2×#11758213—22no—
24C2×#11758187—22no—
25C4⋊#92420—41no—
26C4⋊#92420—41no—
27C2×Dic244C2×C411yescharacteristic
28C2×#11758202—21no—
29C2×C8×D61D411yescharacteristic
30C2×C8×D61C2311yescharacteristic
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×Dic61C2×C411yescharacteristic
48C8×Dic61D411yescharacteristic
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×D61SD1611yescharacteristic
56C2×C4×D61SD1611yescharacteristic
57C2×C4×D61C2×D411yescharacteristic
58C2×Dic122—21no—
59C2×Dic122—41no—
60C2×#92420—42no—
61#11758213—42no—
62#11758213—42no—
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—42no—
71#11758198—41no—
72#11758198—41no—
73C4⋊Dic61—21no—
74C4⋊Dic61—41no—
75#11758196—41no—
76#11758196—41no—
77#11758196—41no—
78#11758196—41no—
79#11758196—41no—
80C4×Dic61—41no—
81C4×Dic61C22⋊C411yescharacteristic
82C4×Dic61D811yescharacteristic
83C4×Dic61D811yescharacteristic
84C2×#92418C22⋊C411yescharacteristic
85C2×#92418C2×D411yescharacteristic
86Dic244—41no—
87C8×D61—41no—
88C8×D61—41no—
89#11758187—42no—
90C22×D61C2×SD1611yescharacteristic
91Q8×C61—41no—
92Q8×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61#10211yescharacteristic
96C2×C4×C61#10211yescharacteristic
97C2×C4×C61C2×C22⋊C411yescharacteristic
98C2×Dic61—41no—
99C2×Dic61—41no—
100C2×Dic61#10211yescharacteristic
101C2×Dic61#10211yescharacteristic
102C2×Dic61C2×D811yescharacteristic
103C4×D61—22no—
104C4×D61—21no—
105C4×D61—21no—
106C4×D61—41no—
107Dic122—41no—
108Dic122—41no—
109Dic122—82no—
110#92420—82no—
111C8×C61—21no—
112C8×C61—21no—
113#92418—21no—
114#92418—21no—
115#11865—611nomaximal, Sylow
116C22×C61C2×#10211yescharacteristic
117C2×D61—21no—
118C2×D61—21no—
119C2×D61—21no—
120C4×C61—21no—
121C4×C61—81no—
122C4×C61—81no—
123C4×C61#36212yes—
124C4×C61#41011yescharacteristic
125C4×C61#42111yescharacteristic
126Dic61—21no—
127Dic61—21no—
128Dic61—21no—
129Dic61—81no—
130Dic61—81no—
131#3170—611no—
132#2163—611no—
133#1837—611no—
134#1350—612no—
135#1350—612no—
136C2×C61#151711yescharacteristic
137C2×C61#214311yescharacteristic
138C2×C61C2×#36211yescharacteristic
139D61—41no—
140#533—1221no—
141#500—611no—
142#494—611no—
143#487—1221no—
144#467—611no—
145#467—611no—
146#467—1221no—
147C4×Q16—611no—
148C4×Q16—1221no—
149C4×Q16#692311yescharacteristic
150#423—1221no—
151C2×C4×C8—611no—
152C4⋊C16—1221no—
153C22⋊C16—612no—
154#346—1221no—
155#341—612no—
156#341—1221no—
157C61#1186511yescharacteristic, complemented, Sylow
158C2×Q16—611no—
159C2×Q16—1221no—
160C2×Q16C2×#692311yescharacteristic
161C2×M16—1222no—
162C22×C8—611no—
163C22×C8—611no—
164C4⋊Q8—1221no—
165C4⋊Q8—1221no—
166#125—2441no—
167C22⋊Q8—1221no—
168C22⋊Q8—1221no—
169C22⋊Q8—2441no—
170C4×Q8—21no—
171C4×Q8—1221no—
172C4×Q8—2441no—
173#117—2441no—
174C2×C42—611no—
175C2×C16—1222no—
176#107—611no—
177#107—1221no—
178#107C2×#692311yescharacteristic
179C4⋊C8—2441no—
180C4⋊C8—2441no—
181#103—21no—
182#103—1221no—
183#103—1221no—
184#103—1221no—
185C4×C8—611no—
186C4×C8—611no—
187C4×C8—611no—
188C4×C8C2×#692311yescharacteristic
189C2×Q8—21no—
190C2×Q8—1221no—
191C2×Q8—2441no—
192C22×C4—611no—
193C22×C4—611no—
194C22×C4—611no—
195Q16—41no—
196Q16—2441no—
197Q16—2442no—
198M16—2442no—
199M16—2442no—
200C2×C8—611no—
201C2×C8—611no—
202C2×C8—2441no—
203C2×C8—2441no—
204C2×C8—2442no—
205C2×C8C22⋊#692311yescharacteristic
206C2×C8C22×#692311yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—41no—
209C4⋊C4—1221no—
210C4⋊C4—2441no—
211C4⋊C4—2441no—
212C4⋊C4—2441no—
213C4⋊C4—2441no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C22⋊C4—2441no—
217C22⋊C4—2441no—
218C42—41no—
219C42—611no—
220C42—611no—
221C42—611no—
222C42—2441no—
223C42C22⋊#692311yescharacteristic
224C16—2442no—
225C23—611no—
226Q8—41no—
227Q8—41no—
228Q8—4882no—
229Q8—2441no—
230Q8—2441no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—611no—
234C2×C4—611no—
235C2×C4—611no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—1222no—
239C2×C4—2441no—
240C2×C4—2441no—
241C2×C4—2441no—
242C2×C4#1451983911yescharacteristic
243C2×C4#1451983911yescharacteristic
244C2×C4C2×C22⋊#692311yescharacteristic
245C8—21no—
246C8—21no—
247C8—1221no—
248C8—1221no—
249C8—4882no—
250C22—1221no—
251C22—1221no—
252C22—1221no—
253C22C2×#1451983911yescharacteristic
254C4—21no—
255C4—81no—
256C4—81no—
257C4—1221no—
258C4—1221no—
259C4—1221no—
260C4—4881no—
261C4—4881no—
262C4#1684068112yes—
263C4#1684074111yescharacteristic
264C4#1684075911yescharacteristic
265C2—2441no—
266C2#2146124911yescharacteristic
267C2#2146213311yescharacteristic
268C2C2×#1684068111yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC4×Q16×C61C4
socleC22×C61C2×#102
prime radicalC22×D61C2×SD16
cosocleC2×C8×D61C23
hypercenterC4×Q16#6923
hypocenterC61#11865
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
157. C61#11865semidirect

Maximal subgroups

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

subgroupindex
#214621832
#214617432
#214608122
#214608112
#214564022
#1186561