Finite Group Databasebeta

← #30605630

Subgroups — #30605630

Order 15616.

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

normal subgroups only

This group has 306 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
2D61⋊#335C211yesmaximal, characteristic
3#21460837C212yesmaximal, complemented
4#21460834C212yesmaximal, complemented
5#21456402C211yesmaximal, characteristic
6D61⋊(C4⋊C8)—21no—
7#16840683C2212yes—
8#16840657—21no—
9#16840650—21no—
10#16840626C2212yes—
11#16840625—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×D61⋊C8—41no—
24C2×#11758187—22no—
25#14519844—41no—
26C4⋊#92420—22no—
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—
61D61⋊C8—82no—
62Q16×C61—41no—
63C2×C8×C61C22⋊C411yescharacteristic
64C2×C8×C61C22×C411yescharacteristic
65C4⋊C4×C61—21no—
66C4⋊C4×C61—41no—
67C42×C61—41no—
68C42×C61C22⋊C411yescharacteristic
69#11758202—42no—
70#11758198—41no—
71#11758198—41no—
72C4⋊Dic61—21no—
73C4⋊Dic61—41no—
74#11758196—41no—
75#11758196—41no—
76#11758196—41no—
77#11758196—41no—
78#11758196—41no—
79C4×Dic61—41no—
80C4×Dic61D811yescharacteristic
81C4×Dic61SD1611yescharacteristic
82C4×Dic61C2×D411yescharacteristic
83C2×#92418C22⋊C411yescharacteristic
84C2×#92418C2×D411yescharacteristic
85Dic244—41no—
86C8×D61—22no—
87C8×D61—41no—
88#11758187—42no—
89C22×D61#10211yescharacteristic
90Q8×C61—41no—
91Q8×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61#10211yescharacteristic
95C2×C4×C61#10211yescharacteristic
96C2×C4×C61C2×C22⋊C411yescharacteristic
97C2×Dic61—41no—
98C2×Dic61—41no—
99C2×Dic61#10211yescharacteristic
100C2×Dic61C2×D811yescharacteristic
101C2×Dic61C2×SD1611yescharacteristic
102C4×D61—22no—
103C4×D61—21no—
104C4×D61—21no—
105C4×D61—21no—
106C4×D61—21no—
107Dic122—41no—
108Dic122—41no—
109Dic122—81no—
110Dic122—81no—
111#92420—82no—
112C8×C61—21no—
113C8×C61—21no—
114#92418—21no—
115#92418#13512yes—
116#11954—611nomaximal, Sylow
117C22×C61C2×#10211yescharacteristic
118C2×D61—21no—
119C2×D61—21no—
120C2×D61#36212yes—
121C4×C61—21no—
122C4×C61—21no—
123C4×C61—81no—
124C4×C61—81no—
125C4×C61#41311yescharacteristic
126C4×C61#41611yescharacteristic
127Dic61—21no—
128Dic61—21no—
129Dic61—81no—
130Dic61—81no—
131Dic61#50911yescharacteristic
132Dic61#51011yescharacteristic
133#3170—611no—
134#2163—611no—
135C2×#335—611no—
136#1364—612no—
137#1362—612no—
138C2×C61#154011yescharacteristic
139C2×C61#213911yescharacteristic
140C2×C61C2×#36211yescharacteristic
141D61—22no—
142#533—1221no—
143#500—611no—
144#494—611no—
145#487—1221no—
146#467—611no—
147#467—611no—
148#467—1221no—
149C4×Q16—611no—
150C4×Q16—1221no—
151C4×Q16#692311yescharacteristic
152C2×C4⋊C8—1221no—
153C2×C4×C8—611no—
154C4⋊C16—612no—
155C22⋊C16—1221no—
156#346—1221no—
157#335—612no—
158#335—1221no—
159C61#1195411yescharacteristic, complemented, Sylow
160C2×Q16—611no—
161C2×Q16—1221no—
162C2×Q16C2×#692311yescharacteristic
163C22×C8—611no—
164C22×C8—611no—
165C22×C8—2441no—
166C4⋊Q8—1221no—
167C4⋊Q8—1221no—
168#125—2441no—
169C22⋊Q8—1221no—
170C22⋊Q8—1221no—
171C22⋊Q8—2441no—
172C4×Q8—21no—
173C4×Q8—1221no—
174C4×Q8—2441no—
175#117—2441no—
176C2×C42—611no—
177C2×C16—1222no—
178#107—611no—
179#107—1221no—
180#107C2×#692311yescharacteristic
181C4⋊C8—1222no—
182C4⋊C8—2441no—
183#103—21no—
184#103—1221no—
185#103—1221no—
186#103—1221no—
187C4×C8—611no—
188C4×C8—611no—
189C4×C8—611no—
190C4×C8C2×#692311yescharacteristic
191C2×Q8—21no—
192C2×Q8—1221no—
193C2×Q8—2441no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—611no—
197Q16—41no—
198Q16—2441no—
199Q16—2442no—
200C2×C8—611no—
201C2×C8—611no—
202C2×C8—1222no—
203C2×C8—4882no—
204C2×C8—2441no—
205C2×C8—2442no—
206C2×C8C22⋊#692311yescharacteristic
207C2×C8C22×#692311yescharacteristic
208C4⋊C4—21no—
209C4⋊C4—41no—
210C4⋊C4—1221no—
211C4⋊C4—2441no—
212C4⋊C4—2441no—
213C4⋊C4—2441no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C4⋊C4—2441no—
217C22⋊C4—2441no—
218C22⋊C4—2441no—
219C42—41no—
220C42—611no—
221C42—611no—
222C42—611no—
223C42—2441no—
224C42C22⋊#692311yescharacteristic
225C16—2442no—
226C23—611no—
227Q8—41no—
228Q8—41no—
229Q8—4881no—
230Q8—4881no—
231Q8—2441no—
232Q8—2441no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—611no—
236C2×C4—611no—
237C2×C4—611no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1222no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4#1451983911yescharacteristic
246C2×C4#1451983911yescharacteristic
247C2×C4C2×C22⋊#692311yescharacteristic
248C8—21no—
249C8—21no—
250C8—612no—
251C8—1221no—
252C8—4882no—
253C22—612no—
254C22—1221no—
255C22—1221no—
256C22C2×#1451983911yescharacteristic
257C4—21no—
258C4—21no—
259C4—81no—
260C4—81no—
261C4—611no—
262C4—611no—
263C4—1221no—
264C4—1221no—
265C4—4881no—
266C4—4881no—
267C4#1684074811yescharacteristic
268C4#1684075211yescharacteristic
269C2—1222no—
270C2#2146131611yescharacteristic
271C2#2146212711yescharacteristic
272C2D61⋊#36211yescharacteristic
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#11954
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
159. C61#11954semidirect

Maximal subgroups

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

subgroupindex
#214621822
D61⋊#3352
#214608372
#214608342
#214564022
#1195461