Finite Group Databasebeta

← #29585018

Subgroups — #29585018

Order 15616.

334 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 91 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#21446652C211yesmaximal, characteristic
2#21445938C211yesmaximal, characteristic, complemented
3#21444593C211yesmaximal, characteristic, complemented
4#21444590C211yesmaximal, characteristic, complemented
5#21444218C211yesmaximal, characteristic
6#21443647C211yesmaximal, characteristic, complemented
7C61×#1480C211yesmaximal, characteristic
8#16839815C2211yescharacteristic
9#16839786C2211yescharacteristic
10C2×C4⋊#92418C2211yescharacteristic
11C2×#14519704—22no—
12#16839608C2211yescharacteristic
13#16839516—22no—
14#16839514—22no—
15#16839513—22no—
16D4⋊#92418—22no—
17C61×#532C2211yescharacteristic
18C61×#431C2211yescharacteristic
19C2×C4⋊C8×C61C2211yescharacteristic
20C61×D4⋊C8—22no—
21C2×#11758194—21no—
22C22×#92418—21no—
23C2×C4×Dic61D412yes—
24C4⋊#92418—21no—
25C4⋊#92418—21no—
26C4⋊#92418—21no—
27C4⋊#92418—21no—
28C4⋊#92418—21no—
29#14519704—44no—
30C22⋊#92418—21no—
31C4×#92418D412yes—
32#14519684—21no—
33#14519684—21no—
34C2×#41×C61—21no—
35C22×C8×C61—21no—
36C4⋊Q8×C61Q811yescharacteristic
37#127×C61Q811yescharacteristic
38#124×C61—21no—
39#121×C61—21no—
40#121×C61—21no—
41C4×D4×C61—21no—
42C4×D4×C61—21no—
43C2×C42×C61C2311yescharacteristic
44C4⋊C8×C61—21no—
45C4⋊C8×C61—21no—
46C4⋊C8×C61—21no—
47C22⋊C8×C61—21no—
48C4×C8×C61D412yes—
49#41×C61—42no—
50#41×C61—42no—
51C2×Q8×C61—21no—
52C2×D4×C61—21no—
53C2×D4×C61—21no—
54C2×D4×C61—21no—
55C2×D4×C61—41no—
56C22×C4×C61—41no—
57C22×C4×C61C2×D411yescharacteristic
58C22×C4×C61#4111yescharacteristic
59C22×C4×C61#4111yescharacteristic
60C22×Dic61—22no—
61C2×C8×C61—22no—
62C2×C8×C61—41no—
63C2×C8×C61—42no—
64C4⋊C4×C61—21no—
65C4⋊C4×C61—21no—
66C22⋊C4×C61—41no—
67C22⋊C4×C61—41no—
68C42×C61C2×D411yescharacteristic
69C42×C61C2×D411yescharacteristic
70C42×C61C2×Q811yescharacteristic
71C42×C61#4111yescharacteristic
72C4×Dic61—22no—
73C4×Dic61—22no—
74#11758194—42no—
75C2×#92418—22no—
76C2×#92418—41no—
77C2×#92418—41no—
78C2×#92418—42no—
79C23×C61—41no—
80C23×C61#12311yescharacteristic
81Q8×C61—42no—
82D4×C61—42no—
83D4×C61—42no—
84D4×C61—42no—
85D4×C61—82no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61—81no—
90C2×C4×C61—81no—
91C2×C4×C61C22⋊Q811yescharacteristic
92C2×C4×C61C22⋊Q811yescharacteristic
93C2×C4×C61C22⋊Q811yescharacteristic
94C2×C4×C61#12311yescharacteristic
95C2×C4×C61#12311yescharacteristic
96C2×C4×C61#12711yescharacteristic
97C2×C4×C61#13512yes—
98C2×C4×C61AGL(1,ℤ/8)12yes—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61—42no—
102C8×C61—42no—
103C8×C61—81no—
104#92418—42no—
105#92418—81no—
106#92418—81no—
107#10665—611nomaximal, Sylow
108C22×C61—21no—
109C22×C61—21no—
110C22×C61—81no—
111C22×C61—81no—
112C22×C61—81no—
113C22×C61#39911yescharacteristic
114C22×C61#48212yes—
115C4×C61—21no—
116C4×C61—21no—
117C4×C61—21no—
118C4×C61—21no—
119C4×C61—81no—
120C4×C61#47812yes—
121C4×C61#49511yescharacteristic
122C4×C61#49611yescharacteristic
123Dic61—82no—
124#1963—611no—
125#1832—611no—
126#1571—611no—
127#1570—611no—
128#1480—611no—
129#1480D6111yescharacteristic
130#1274—611no—
131C2×C61—22no—
132C2×C61—161no—
133C2×C61#209211yescharacteristic
134C2×C61#209811yescharacteristic
135C2×C61#209811yescharacteristic
136#532C2×D6111yescharacteristic
137#431—611no—
138#431C2×D6111yescharacteristic
139#423—611no—
140C2×C4⋊C8—611no—
141C2×C4⋊C8C2×D6111yescharacteristic
142C2×#104—1222no—
143#376—611no—
144#336—1222no—
145#335—1222no—
146#334—1222no—
147D4⋊C8—22no—
148D4⋊C8—1222no—
149C61#1066511yescharacteristic, complemented, Sylow
150C2×#41—21no—
151C2×M16—1221no—
152C22×C8—21no—
153C22×C8—1221no—
154C4⋊Q8Dic12211yescharacteristic
155#127Dic12211yescharacteristic
156#124—21no—
157#121—21no—
158#121—21no—
159C4×D4—21no—
160C4×D4—21no—
161C2×C42—612no—
162C2×C42C22×D6111yescharacteristic
163C4⋊C8—21no—
164C4⋊C8—21no—
165C4⋊C8—21no—
166C4⋊C8—1221no—
167C4⋊C8—1221no—
168C4⋊C8—1221no—
169C4⋊C8—1221no—
170C4⋊C8—1221no—
171#104—2444no—
172C22⋊C8—21no—
173C22⋊C8—1221no—
174C4×C8—612no—
175C4×C8C22⋊D6112yes—
176#95—1221no—
177#95—1221no—
178#41—42no—
179#41—42no—
180C2×Q8—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—41no—
185C22×C4—41no—
186C22×C4—1222no—
187C22×C4#1175822211yescharacteristic
188C22×C4D4×D6111yescharacteristic
189C22×C4#1175822411yescharacteristic
190M16—2442no—
191C2×C8—22no—
192C2×C8—41no—
193C2×C8—42no—
194C2×C8—1222no—
195C2×C8—2441no—
196C2×C8—2441no—
197C2×C8—2442no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C22⋊C4—41no—
201C22⋊C4—41no—
202C42—1222no—
203C42—1222no—
204C42C2×Dic12211yescharacteristic
205C42D4×D6111yescharacteristic
206C42#1175822411yescharacteristic
207C42C2×C22⋊D6111yescharacteristic
208C23—41no—
209C23#1451975911yescharacteristic
210Q8—42no—
211D4—42no—
212D4—42no—
213D4—42no—
214D4—82no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—2442no—
221C2×C4—2442no—
222C2×C4—2442no—
223C2×C4#1451975411yescharacteristic
224C2×C4#1451975411yescharacteristic
225C2×C4#1451975611yescharacteristic
226C2×C4#1451975811yescharacteristic
227C2×C4#1451975911yescharacteristic
228C2×C4#1451977311yescharacteristic
229C2×C4#1451979812yes—
230C2×C4#1451980112yes—
231C8—42no—
232C8—81no—
233C8—4881no—
234C8—4881no—
235C8—2442no—
236C22—21no—
237C22—21no—
238C22—81no—
239C22—81no—
240C22—81no—
241C22#1683969811yescharacteristic
242C22#1684008512yes—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—81no—
248C4—4882no—
249C4#1684006412yes—
250C4#1684014311yescharacteristic
251C4#1684015011yescharacteristic
252C2—22no—
253C2—161no—
254C2#2144734211yescharacteristic
255C2#2144737211yescharacteristic
256C2#2144737411yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1480C2
socleC22×C61#399
prime radicalC61×#532C22
hypercenter#1480D61
hypocenterC61#10665
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
2. #21445938C2semidirect
3. #21444593C2semidirect
4. #21444590C2semidirect
6. #21443647C2semidirect
149. C61#10665semidirect

Maximal subgroups

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

subgroupindex
#214466522
#214459382
#214445932
#214445902
#214442182
#214436472
C61×#14802
#1066561