Finite Group Databasebeta

← #29574032

Subgroups — #29574032

Order 15616.

420 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 127 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#21454383C211yesmaximal, characteristic
2#21444593C212yesmaximal, complemented
3#21444133C211yesmaximal, characteristic
4#21443716C212yesmaximal, complemented
5C61×#1798C211yesmaximal, characteristic
6C22×#11758194—21no—
7#16839815C2212yes—
8#16839789—24no—
9#16839786—21no—
10#16839786C2212yes—
11#16839514—24no—
12#16839488C412yes—
13#16839486C412yes—
14C2×#117×C61C2211yescharacteristic
15C2×C4⋊C8×C61C2211yescharacteristic
16C2×C4⋊C8×C61C2211yescharacteristic
17C2×C22⋊C8×C61—21no—
18C61×#336—21no—
19C2×#11758194—22no—
20C2×#11758194—22no—
21C2×#11758194—42no—
22C2×#11758194—42no—
23C22×#92418—22no—
24C4⋊#92418—24no—
25C4⋊#92418—22no—
26C4⋊#92418—22no—
27C4⋊#92418D414yes—
28C22⋊#92418C2×C414yes—
29C4×#92418—22no—
30C23×C4×C61D411yescharacteristic
31C22×C8×C61—21no—
32C22×C8×C61—21no—
33#117×C61—22no—
34#117×C61—22no—
35C2×C4⋊C4×C61C2×C411yescharacteristic
36C2×C4⋊C4×C61Q811yescharacteristic
37C2×C22⋊C4×C61C2×C411yescharacteristic
38C2×C22⋊C4×C61Q811yescharacteristic
39C2×C42×C61D411yescharacteristic
40C2×C42×C61C2311yescharacteristic
41C4⋊C8×C61—22no—
42C4⋊C8×C61—22no—
43C22⋊C8×C61—42no—
44C24×C61C4⋊C411yescharacteristic
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61C4⋊C411yescharacteristic
50C22×C4×C61C4⋊C411yescharacteristic
51C22×C4×C61C4⋊C411yescharacteristic
52C22×C4×C61D812yes—
53C22×C4×C61Q1612yes—
54C22×C4×C61C22×C411yescharacteristic
55C22×C4×C61C2×D411yescharacteristic
56C22×C4×C61C2×Q811yescharacteristic
57C2×C8×C61—41no—
58C2×C8×C61—41no—
59C2×C8×C61—41no—
60C2×C8×C61—41no—
61C2×C8×C61—41no—
62C2×C8×C61—41no—
63C4⋊C4×C61—22no—
64C4⋊C4×C61—22no—
65C22⋊C4×C61—22no—
66C22⋊C4×C61—22no—
67C42×C61—21no—
68C42×C61—21no—
69C42×C61C2×D412yes—
70C42×C61#4112yes—
71#11758194—44no—
72#11758194—42no—
73#11758194—42no—
74C2×#92418—24no—
75C2×#92418—24no—
76C2×#92418—44no—
77C23×C61—21no—
78C23×C61—21no—
79C23×C61—41no—
80C23×C61—41no—
81C23×C61#10712yes—
82C23×C61C2×C4⋊C411yescharacteristic
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61#10712yes—
96C2×C4×C61C4×D412yes—
97C2×C4×C61#12011yescharacteristic
98C2×C4×C61C22⋊Q812yes—
99C2×C4×C61#12311yescharacteristic
100C2×C4×C61C2×D811yescharacteristic
101C2×C4×C61C2×Q1611yescharacteristic
102C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
103C2×C4×C61#13711yescharacteristic
104C8×C61—81no—
105C8×C61—81no—
106#92418—44no—
107#92418—44no—
108#8861—611nomaximal, Sylow
109C22×C61—21no—
110C22×C61—21no—
111C22×C61—22no—
112C22×C61—42no—
113C22×C61—41no—
114C22×C61—41no—
115C22×C61—81no—
116C22×C61#38511yescharacteristic
117C22×C61C2×#10711yescharacteristic
118C22×C61#42811yescharacteristic
119C4×C61—22no—
120C4×C61—22no—
121C4×C61—22no—
122C4×C61—41no—
123C4×C61—41no—
124C4×C61#44711yescharacteristic
125C4×C61#45111yescharacteristic
126C4×C61#48011yescharacteristic
127C4×C61#48411yescharacteristic
128#2905—611no—
129#1798D6111yescharacteristic
130#1571—612no—
131#1458—611no—
132#1301—612no—
133C2×C61—21no—
134C2×C61—21no—
135C2×C61—42no—
136C2×C61#185211yescharacteristic
137C2×C61#185811yescharacteristic
138C2×C61#186811yescharacteristic
139C22×M16—1221no—
140C2×#117C2×D6111yescharacteristic
141#431—612no—
142#424—1224no—
143#423—612no—
144#423—1221no—
145C2×C4⋊C8C2×D6111yescharacteristic
146C2×C4⋊C8C2×D6111yescharacteristic
147C2×C22⋊C8—21no—
148#336—21no—
149#335—1224no—
150#324—612no—
151#323—612no—
152C61#886111yescharacteristic, complemented, Sylow
153C23×C4C22⋊D6111yescharacteristic
154C2×M16—1222no—
155C2×M16—1222no—
156C2×M16—2442no—
157C2×M16—2442no—
158C22×C8—21no—
159C22×C8—21no—
160C22×C8—1222no—
161#117—22no—
162#117—22no—
163C2×C4⋊C4Dic12211yescharacteristic
164C2×C4⋊C4C4×D6111yescharacteristic
165C2×C22⋊C4Dic12211yescharacteristic
166C2×C22⋊C4C4×D6111yescharacteristic
167C2×C42C22⋊D6111yescharacteristic
168C2×C42C22×D6111yescharacteristic
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8—614no—
172C4⋊C8—1224no—
173C4⋊C8—1222no—
174C4⋊C8—1222no—
175C22⋊C8—42no—
176C22⋊C8—614no—
177C4×C8—1222no—
178C24#1175819611yescharacteristic
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4#1175819611yescharacteristic
184C22×C4#1175819611yescharacteristic
185C22×C4#1175819611yescharacteristic
186C22×C4#1175819912yes—
187C22×C4#1175820212yes—
188C22×C4C2×Dic12211yescharacteristic
189C22×C4C2×C4×D6111yescharacteristic
190C22×C4C2×C22⋊D6111yescharacteristic
191M16—2444no—
192M16—2442no—
193M16—2442no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—1224no—
201C2×C8—1224no—
202C2×C8—2444no—
203C4⋊C4—22no—
204C4⋊C4—22no—
205C22⋊C4—22no—
206C22⋊C4—22no—
207C42—21no—
208C42—21no—
209C42D4×D6112yes—
210C42#1175822412yes—
211C23—21no—
212C23—21no—
213C23—41no—
214C23—41no—
215C23#1451971012yes—
216C23C2×#1175819611yescharacteristic
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4#1451971012yes—
230C2×C4#1451973712yes—
231C2×C4#1451974511yescharacteristic
232C2×C4#1451975412yes—
233C2×C4#1451975811yescharacteristic
234C2×C4C2×#1175819911yescharacteristic
235C2×C4C2×#1175820211yescharacteristic
236C2×C4#1451980211yescharacteristic
237C2×C4#1451980711yescharacteristic
238C8—81no—
239C8—81no—
240C8—2444no—
241C8—2444no—
242C22—21no—
243C22—21no—
244C22—22no—
245C22—42no—
246C22—41no—
247C22—41no—
248C22—81no—
249C22#1683963411yescharacteristic
250C22C2×#1451971011yescharacteristic
251C22#1683980511yescharacteristic
252C4—22no—
253C4—22no—
254C4—22no—
255C4—41no—
256C4—41no—
257C4#1683989511yescharacteristic
258C4#1683991711yescharacteristic
259C4#1684007311yescharacteristic
260C4#1684009511yescharacteristic
261C2—21no—
262C2—21no—
263C2—42no—
264C2#2144600611yescharacteristic
265C2#2144603811yescharacteristic
266C2#2144610411yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1798C2
socleC22×C61#385
prime radicalC24×C61C4⋊C4
cosocleC2×C42×C61C23
hypercenter#1798D61
hypocenterC61#8861
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. #21444593C2semidirect
4. #21443716C2semidirect
152. C61#8861semidirect

Maximal subgroups

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

subgroupindex
#214543832
#214445932
#214441332
#214437162
C61×#17982
#886161