Finite Group Databasebeta

← #30607793

Subgroups — #30607793

Order 15616.

270 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461925C211yesmaximal, characteristic
2#21461640C211yesmaximal, characteristic
3#21460895C211yesmaximal, characteristic
4#21460894C211yesmaximal, characteristic
5#21460883C211yesmaximal, characteristic
6#21460865C211yesmaximal, characteristic
7#365×D61C211yesmaximal, characteristic
8D61⋊M32C2211yescharacteristic
9D61⋊#108C2211yescharacteristic
10C2×#14519846C2211yescharacteristic
11M16×#6923—21no—
12C2×#14519831C2211yescharacteristic
13#16840713—21no—
14#16840637—21no—
15#16840635—21no—
16M32×D61C2211yescharacteristic
17#108×D61C2211yescharacteristic
18#106×D61C2211yescharacteristic
19#16839586C411yescharacteristic, complemented
20#16839585C411yescharacteristic, complemented
21#16839584C411yescharacteristic, complemented
22C61×#365C411yescharacteristic, complemented
23D61⋊M16—21no—
24C2×D61⋊C8D411yescharacteristic
25C2×C4⋊#6923—21no—
26C2×C4⋊#6923—41no—
27C2×C4×#6923D411yescharacteristic
28#14519852—21no—
29#14519851—21no—
30D61⋊C16—21no—
31#14519848—21no—
32#14519847Q812yes—
33#14519846—21no—
34#14519846—21no—
35#14519831—21no—
36#14519831—21no—
37#14519831—41no—
38C8×#6923—41no—
39(C2×#6923)⋊C4—41no—
40M16×D61—21no—
41C2×C8×D61C2311yescharacteristic
42C4⋊C4×D61—21no—
43#14519717C2×C411yescharacteristic
44#14519716—21no—
45C16×D61—21no—
46#14519713C2×C411yescharacteristic
47#14519712—21no—
48#14519709C2×C411yescharacteristic
49#14519708—21no—
50M32×C61C2×C411yescharacteristic
51#108×C61C2×C411yescharacteristic
52#106×C61C2×C411yescharacteristic
53C22×#6923—41no—
54C22×#6923SD1611yescharacteristic
55C22×#6923SD1611yescharacteristic
56C2×C4×D61—41no—
57C2×C4×D61C2×D411yescharacteristic
58#11758217—41no—
59C2×#92420—21no—
60C4⋊#6923—41no—
61C4⋊#6923—41no—
62C4⋊#6923—82no—
63C4×#6923—21no—
64C4×#6923—21no—
65#11758213—22no—
66D61⋊C8—21no—
67D61⋊C8—21no—
68D61⋊C8—41no—
69M16×C61—21no—
70C2×C8×C61C22×C411yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊Dic61—21no—
73#11758196—41no—
74#11758194—21no—
75C2×#92418#4111yescharacteristic
76#11758189—41no—
77C8×D61—41no—
78C8×D61C2×Q811yescharacteristic
79C8×D61#4111yescharacteristic
80C8×D61#4111yescharacteristic
81C8×D61#4111yescharacteristic
82#11758187—41no—
83C16×C61—21no—
84#11758185—21no—
85C22×D61C2×SD1611yescharacteristic
86C2×#6923—21no—
87C2×#6923—21no—
88C2×#6923—41no—
89C2×#6923—41no—
90C2×#6923—81no—
91C2×#6923—81no—
92C2×#6923—81no—
93C2×C4×C61—41no—
94C2×C4×C61C4×D411yescharacteristic
95C2×Dic61—41no—
96C2×Dic61#13511yescharacteristic
97C4×D61—81no—
98C4×D61—81no—
99C4×D61C22⋊Q811yescharacteristic
100C4×D61#12311yescharacteristic
101C4×D61AGL(1,ℤ/8)11yescharacteristic
102C4×D61#13711yescharacteristic
103#92420—42no—
104#92420—41no—
105C8×C61—41no—
106C8×C61#11711yescharacteristic
107C8×C61C4×Q811yescharacteristic
108#92418—41no—
109#92418#12511yescharacteristic
110#92418#12611yescharacteristic
111#13114—611nomaximal, Sylow
112C22×C61C4×SD1611yescharacteristic
113C2×D61—21no—
114C2×D61—21no—
115C2×D61#47511yescharacteristic
116C2×D61#48111yescharacteristic
117#6923—41no—
118#6923—41no—
119#6923—161no—
120C4×C61—81no—
121C4×C61#38711yescharacteristic
122C4×C61#44011yescharacteristic
123Dic61—81no—
124Dic61#47811yescharacteristic
125Dic61#48511yescharacteristic
126C2×#365—611no—
127#1944—611no—
128#1778—611no—
129#1387—611no—
130#1387—611no—
131#1383—611no—
132#1377—611no—
133C2×C61—21no—
134C2×C61#191911yescharacteristic
135D61—21no—
136D61#223811yescharacteristic
137D61#223911yescharacteristic
138C2×M32—611no—
139C2×M32—611no—
140C2×#108—611no—
141C2×#108—611no—
142C2×#107—611no—
143C2×#106—611no—
144C4×M16—1221no—
145C2×#97—611no—
146#389—1221no—
147#365—611no—
148#365—611no—
149#365—611no—
150#365#692311yescharacteristic, complemented
151#341—1221no—
152#340—1221no—
153C61#1311411yescharacteristic, complemented, Sylow
154C2×M16—1221no—
155C2×M16—1221no—
156C22×C8—611no—
157C22×C8—611no—
158C2×C4⋊C4—1221no—
159C2×C4⋊C4—1221no—
160C2×C4⋊C4—2441no—
161C2×C42—611no—
162M32—611no—
163M32—1221no—
164M32—1221no—
165M32—1221no—
166M32C2×#692311yescharacteristic
167C2×C16—1221no—
168C2×C16—1221no—
169#108—612no—
170#108—611no—
171#108—1221no—
172#108—1221no—
173#108C2×#692311yescharacteristic
174#107—1221no—
175#107—1221no—
176#106—611no—
177#106—1221no—
178#106C2×#692311yescharacteristic
179#97—1221no—
180#97—1221no—
181#97—2441no—
182C4×C8—2441no—
183#95—2441no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—611no—
187C22×C4—2441no—
188C22×C4—2441no—
189M16—21no—
190M16—1222no—
191M16—1221no—
192M16—2441no—
193M16—2441no—
194C2×C8—611no—
195C2×C8—611no—
196C2×C8—611no—
197C2×C8—611no—
198C2×C8—611no—
199C2×C8—1221no—
200C2×C8—1221no—
201C2×C8—1221no—
202C2×C8—2441no—
203C2×C8—2441no—
204C2×C8C22×#692311yescharacteristic
205C4⋊C4—21no—
206C4⋊C4—1221no—
207C4⋊C4—4882no—
208C4⋊C4—2441no—
209C4⋊C4—2441no—
210C4⋊C4—2441no—
211C42—1221no—
212C42—1221no—
213C16—21no—
214C16—1221no—
215C16—2441no—
216C23—611no—
217C2×C4—41no—
218C2×C4—611no—
219C2×C4—611no—
220C2×C4—611no—
221C2×C4—611no—
222C2×C4—611no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—4881no—
226C2×C4—4881no—
227C2×C4—4881no—
228C2×C4—4881no—
229C2×C4—4881no—
230C2×C4—2441no—
231C2×C4—2441no—
232C2×C4—2441no—
233C2×C4D4×#692311yescharacteristic
234C8—41no—
235C8—611no—
236C8—611no—
237C8—2441no—
238C8—2442no—
239C8—2441no—
240C8#1451985611yescharacteristic
241C8Q8×#692311yescharacteristic
242C22—611no—
243C22—611no—
244C22—1221no—
245C22—1221no—
246C22SD16×#692311yescharacteristic
247C4—81no—
248C4—611no—
249C4—611no—
250C4—9761no—
251C4—4881no—
252C4—2441no—
253C4—2441no—
254C4#1684071111yescharacteristic
255C4#1684080111yescharacteristic
256C2—21no—
257C2—611no—
258C2—611no—
259C2—1221no—
260C2#2146188111yescharacteristic
subgroupG/H
centerC2#21461881
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#365C4
socleC2×C61#1919
prime radicalC22×D61C2×SD16
cosocleC2×C8×D61C23
hypercenter#365#6923
hypocenterC61#13114
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #365

Complements

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

NH ≅ G/Ntype
19. #16839586C4semidirect
20. #16839585C4semidirect
21. #16839584C4semidirect
22. C61×#365C4semidirect
150. #365#6923semidirect
153. C61#13114semidirect

Maximal subgroups

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

subgroupindex
#214619252
#214616402
#214608952
#214608942
#214608832
#214608652
#365×D612
#1311461