Finite Group Databasebeta

← #29591340

Subgroups — #29591340

Order 15616.

344 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 85 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#21456396C211yesmaximal, characteristic
2#21447617C211yesmaximal, characteristic, complemented
3#21444566C211yesmaximal, characteristic, complemented
4#21443878C211yesmaximal, characteristic, complemented
5#21443876C211yesmaximal, characteristic, complemented
6#21443865C211yesmaximal, characteristic, complemented
7C61×#1361C211yesmaximal, characteristic, complemented
8#16840310—21no—
9#16840167C2211yescharacteristic
10#16840108—21no—
11#16839995—21no—
12#16839995C412yes—
13D8×Dic61—21no—
14D8×Dic61C412yes—
15#16839814—21no—
16C4×C8×D61C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic
18#16839541—21no—
19C16×Dic61—21no—
20#16839515C2211yescharacteristic
21#16839512—21no—
22C61×#493C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×#11758224—41no—
26C2×C8×D61C2×C411yescharacteristic
27C2×C8×D61D411yescharacteristic
28#14519777—21no—
29#14519764—41no—
30#14519748—22no—
31#14519748—41no—
32D4×Dic61—22no—
33D4×Dic61—41no—
34C42×D61D411yescharacteristic
35C2×#11758185—21no—
36#14519711—21no—
37#14519711C2×C412yes—
38C4⋊#92418—21no—
39#14519698—22no—
40#14519698—22no—
41#14519689—41no—
42C4×#92418D411yescharacteristic
43C8×Dic61—41no—
44C8×Dic61C2×C411yescharacteristic
45C8×Dic61D411yescharacteristic
46C2×D8×C61—21no—
47C2×D8×C61C2×C412yes—
48#127×C61—21no—
49C2×C16×C61—21no—
50C4⋊C8×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×D4×C61—22no—
53C2×D4×C61—41no—
54C2×D4×C61—41no—
55C2×C22⋊D61—42no—
56C22×Dic61—42no—
57#11758224—84no—
58C2×C4×D61C22⋊C411yescharacteristic
59C2×C4×D61D811yescharacteristic
60C2×C4×D61SD1611yescharacteristic
61C2×Dic122—41no—
62D8×C61—42no—
63D8×C61—41no—
64D8×C61—41no—
65C2×C8×C61—41no—
66C2×C8×C61C22×C411yescharacteristic
67C2×C8×C61C2×D411yescharacteristic
68C42×C61C2×D411yescharacteristic
69C22⋊Dic61—42no—
70C22⋊Dic61—42no—
71C4⋊Dic61—22no—
72C4⋊Dic61—41no—
73C4×Dic61C22⋊C411yescharacteristic
74C4×Dic61D811yescharacteristic
75C4×Dic61SD1611yescharacteristic
76C2×#92418—41no—
77C2×#92418C22⋊C411yescharacteristic
78C2×#92418C22⋊C411yescharacteristic
79C8×D61—21no—
80C8×D61—21no—
81C8×D61—41no—
82C16×C61—41no—
83#11758185—41no—
84C23×C61—42no—
85C22×D61#10211yescharacteristic
86D4×C61—42no—
87D4×C61—42no—
88D4×C61—82no—
89D4×C61—81no—
90D4×C61—81no—
91C2×C4×C61C2×C22⋊C411yescharacteristic
92C2×C4×C61C2×D811yescharacteristic
93C2×C4×C61C2×SD1611yescharacteristic
94C22⋊D61—84no—
95C2×Dic61—42no—
96C2×Dic61—84no—
97C2×Dic61#10211yescharacteristic
98C2×Dic61#10211yescharacteristic
99C2×Dic61#10211yescharacteristic
100C4×D61—21no—
101C4×D61—21no—
102C4×D61—21no—
103C4×D61—21no—
104C4×D61—22no—
105Dic122—82no—
106C8×C61—21no—
107C8×C61—81no—
108C8×C61#13511yescharacteristic
109C8×C61#13511yescharacteristic
110#92418—21no—
111#92418—21no—
112#92418—81no—
113#11948—611nomaximal, Sylow
114C22×C61—82no—
115C22×C61—82no—
116C22×C61—82no—
117C22×C61C2×#10211yescharacteristic
118C2×D61—21no—
119C2×D61—21no—
120C2×D61—21no—
121C4×C61—21no—
122C4×C61#41311yescharacteristic
123C4×C61#41611yescharacteristic
124C4×C61#50811yescharacteristic
125C4×C61#50811yescharacteristic
126Dic61—21no—
127Dic61—21no—
128Dic61—82no—
129Dic61#36112yes—
130#3169—611no—
131#2162—611no—
132#1564—611no—
133#1365—611no—
134#1365—611no—
135#1361—611no—
136#1361D6111yescharacteristic, complemented
137C2×C61—162no—
138C2×C61#154011yescharacteristic
139C2×C61#213811yescharacteristic
140C2×C61C2×#36111yescharacteristic
141D61—41no—
142#532—1221no—
143#500—611no—
144#493C2×D6111yescharacteristic
145#486—1221no—
146#466—612no—
147#466—1221no—
148C4×D8—612no—
149C4×D8—1221no—
150#431—1221no—
151C2×C4×C8—611no—
152C4⋊C16—611no—
153C4⋊C16C2×D6111yescharacteristic
154C22⋊C16—1221no—
155C4×C16—1221no—
156#335—611no—
157#335C2×D6111yescharacteristic
158#334—1221no—
159C61#1194811yescharacteristic, complemented, Sylow
160C2×#41—2441no—
161C2×D8—21no—
162C2×D8C4×D6112yes—
163C22×C8—611no—
164C22×C8—611no—
165C4⋊Q8—1221no—
166#127—21no—
167#124—2441no—
168#121—1222no—
169#121—2441no—
170C4×D4—1222no—
171C4×D4—2441no—
172C2×C42—611no—
173C2×C16—21no—
174C2×C16—1221no—
175#107—612no—
176#107—1221no—
177C4⋊C8—21no—
178C4⋊C8—1221no—
179#102—1222no—
180#102—1222no—
181C22⋊C8—2441no—
182C4×C8—611no—
183C4×C8—611no—
184C4×C8—611no—
185C4×C8—2441no—
186C4×C8C22×D6111yescharacteristic
187#41—4884no—
188C2×Q8—2441no—
189C2×D4—22no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—2442no—
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—2442no—
197D8—42no—
198D8—41no—
199D8—41no—
200C2×C8—41no—
201C2×C8—611no—
202C2×C8—611no—
203C2×C8—1221no—
204C2×C8—1221no—
205C2×C8—2441no—
206C2×C8—2441no—
207C2×C8C2×C4×D6111yescharacteristic
208C2×C8D4×D6111yescharacteristic
209C4⋊C4—1222no—
210C4⋊C4—2441no—
211C22⋊C4—2442no—
212C22⋊C4—2442no—
213C42—611no—
214C42—611no—
215C42—611no—
216C42D4×D6111yescharacteristic
217C16—41no—
218C16—2441no—
219C23—42no—
220C23—611no—
221Q8—4882no—
222D4—42no—
223D4—42no—
224D4—82no—
225D4—81no—
226D4—81no—
227D4—4884no—
228C2×C4—611no—
229C2×C4—611no—
230C2×C4—611no—
231C2×C4—1222no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—1221no—
235C2×C4—1221no—
236C2×C4—4884no—
237C2×C4—2442no—
238C2×C4C22⋊C4×D6111yescharacteristic
239C2×C4D8×D6111yescharacteristic
240C2×C4SD16×D6111yescharacteristic
241C8—21no—
242C8—81no—
243C8—1221no—
244C8—1221no—
245C8—4881no—
246C8#1451979611yescharacteristic
247C8#1451979811yescharacteristic
248C22—82no—
249C22—82no—
250C22—82no—
251C22—1221no—
252C22—1221no—
253C22—1221no—
254C22#102×D6111yescharacteristic
255C4—21no—
256C4—612no—
257C4—1221no—
258C4—1221no—
259C4—4882no—
260C4#1683974311yescharacteristic
261C4#1683975511yescharacteristic
262C4#1684019111yescharacteristic
263C4#1684019311yescharacteristic
264C2—162no—
265C2—2441no—
266C2#2144446511yescharacteristic
267C2#2144752311yescharacteristic
268C2#361×D6111yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1361C2
socleC22×C61C2×#102
prime radical#21456396C2
cosocleC4×C8×C61C23
hypercenter#1361D61
hypocenterC61#11948
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
2. #21447617C2semidirect
3. #21444566C2semidirect
4. #21443878C2semidirect
5. #21443876C2semidirect
6. #21443865C2semidirect
7. C61×#1361C2semidirect
136. #1361D61semidirect
159. C61#11948semidirect

Maximal subgroups

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

subgroupindex
#214563962
#214476172
#214445662
#214438782
#214438762
#214438652
C61×#13612
#1194861