Finite Group Databasebeta

← #30607796

Subgroups — #30607796

Order 15616.

254 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 72 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#21461926C211yesmaximal, characteristic
2#108×#6923C211yesmaximal, characteristic
3#21460901C211yesmaximal, characteristic
4#21460897C211yesmaximal, characteristic
5#21460888C211yesmaximal, characteristic
6#21460862C211yesmaximal, characteristic
7#21447590C211yesmaximal, characteristic
8D61⋊M32C2211yescharacteristic
9D61⋊#108C2211yescharacteristic
10C2×#14519847C2211yescharacteristic
11#16840769—21no—
12M16×#6923—21no—
13C2×C8×#6923C2211yescharacteristic
14#16840637—21no—
15#16840632—21no—
16M32×D61C2211yescharacteristic
17#108×D61C2211yescharacteristic
18#16839797C2211yescharacteristic
19#16839586C411yescharacteristic, complemented
20#16839585C411yescharacteristic, complemented
21#16839584C411yescharacteristic, complemented
22C61×#365C411yescharacteristic, complemented
23C2×#11758213—21no—
24D61⋊M16—21no—
25C2×D61⋊C8D411yescharacteristic
26C2×C4×#6923D411yescharacteristic
27#14519852—21no—
28#14519851—21no—
29D61⋊C16—21no—
30#14519848Q812yes—
31#14519847—21no—
32#14519847—21no—
33#14519847—21no—
34#14519844—41no—
35C4⋊#92420—41no—
36#14519831—41no—
37C8×#6923—21no—
38C8×#6923—21no—
39C8×#6923—41no—
40M16×D61—21no—
41C2×C8×D61C2311yescharacteristic
42#14519735—21no—
43#14519717C2×C411yescharacteristic
44#14519716—21no—
45C16×D61—21no—
46#14519713C2×C411yescharacteristic
47#14519712—21no—
48#14519710—21no—
49#14519709C2×C411yescharacteristic
50M32×C61C2×C411yescharacteristic
51#108×C61C2×C411yescharacteristic
52#106×C61C2×C411yescharacteristic
53C22×#6923—21no—
54C2×C4×D61C2×D411yescharacteristic
55#11758217—41no—
56C2×#92420—21no—
57C2×#92420—41no—
58C4×#6923—21no—
59C4×#6923SD1611yescharacteristic
60C4×#6923SD1611yescharacteristic
61#11758213—22no—
62#11758213—41no—
63#11758213—41no—
64D61⋊C8—21no—
65D61⋊C8—21no—
66D61⋊C8—41no—
67M16×C61—21no—
68C2×C8×C61C22×C411yescharacteristic
69C4⋊C4×C61—21no—
70#11758198—41no—
71C4⋊Dic61—21no—
72C4×Dic61—41no—
73#11758194—21no—
74C2×#92418#4111yescharacteristic
75#11758189—41no—
76C8×D61—41no—
77C8×D61C2×Q811yescharacteristic
78C8×D61#4111yescharacteristic
79C8×D61#4111yescharacteristic
80C8×D61#4111yescharacteristic
81#11758187—41no—
82C16×C61—21no—
83#11758185—21no—
84C22×D61#13711yescharacteristic
85C2×#6923—21no—
86C2×#6923—21no—
87C2×#6923—42no—
88C2×C4×C61—41no—
89C2×C4×C61C4×D411yescharacteristic
90C2×Dic61—41no—
91C2×Dic61AGL(1,ℤ/8)11yescharacteristic
92C4×D61C22⋊Q811yescharacteristic
93C4×D61#12311yescharacteristic
94C4×D61C2×SD1611yescharacteristic
95C4×D61#13511yescharacteristic
96#92420—42no—
97#92420—41no—
98#92420—81no—
99C8×C61—41no—
100C8×C61#11711yescharacteristic
101C8×C61C4×Q811yescharacteristic
102#92418—41no—
103#92418#12511yescharacteristic
104#92418#12611yescharacteristic
105#13117—611nomaximal, Sylow
106C22×C61#44011yescharacteristic
107C2×D61—41no—
108C2×D61#47911yescharacteristic
109C2×D61#48311yescharacteristic
110#6923—22no—
111#6923—41no—
112C4×C61—81no—
113C4×C61#38711yescharacteristic
114C4×C61C4×SD1611yescharacteristic
115Dic61—81no—
116Dic61#47611yescharacteristic
117Dic61#48211yescharacteristic
118#2155—611no—
119#1945—611no—
120C4×#108—611no—
121#1389—611no—
122#1388—611no—
123#1385—611no—
124#1376—611no—
125C2×C61—21no—
126C2×C61#192011yescharacteristic
127D61—21no—
128D61—21no—
129C2×M32—611no—
130C2×M32—611no—
131C2×#108—611no—
132C2×#108—611no—
133C2×#108—611no—
134#427—611no—
135#424—1221no—
136C4×M16—1221no—
137C2×C4×C8—611no—
138#365—611no—
139#365—611no—
140#365—611no—
141#365#692311yescharacteristic, complemented
142#341—1221no—
143#339—1221no—
144C61#1311711yescharacteristic, complemented, Sylow
145C2×M16—1221no—
146C2×M16—1221no—
147C2×M16—1221no—
148C22×C8—611no—
149C22×C8—611no—
150#117—1221no—
151C2×C42—611no—
152M32—611no—
153M32—1221no—
154M32—1221no—
155M32—1221no—
156M32C2×#692311yescharacteristic
157C2×C16—1221no—
158C2×C16—1221no—
159#108—612no—
160#108—611no—
161#108—1221no—
162#108—1221no—
163#108—1221no—
164#108—1221no—
165#108C2×#692311yescharacteristic
166#107—1221no—
167#106—611no—
168#106C2×#692311yescharacteristic
169C4⋊C8—2441no—
170C4⋊C8—2441no—
171#97—2441no—
172C4×C8—1221no—
173C4×C8—1221no—
174C4×C8—2441no—
175C22×C4—611no—
176C22×C4—1221no—
177M16—21no—
178M16—1222no—
179M16—1221no—
180M16—2441no—
181M16—2441no—
182M16—2441no—
183M16—2441no—
184C2×C8—611no—
185C2×C8—611no—
186C2×C8—611no—
187C2×C8—611no—
188C2×C8—611no—
189C2×C8—1221no—
190C2×C8—1221no—
191C2×C8—1221no—
192C2×C8—2441no—
193C2×C8—2441no—
194C2×C8—2441no—
195C2×C8C22×#692311yescharacteristic
196C4⋊C4—21no—
197C4⋊C4—1221no—
198C22⋊C4—2441no—
199C42—611no—
200C42—611no—
201C42—1221no—
202C42—2441no—
203C16—21no—
204C16—1221no—
205C16—2441no—
206C23—611no—
207C2×C4—41no—
208C2×C4—611no—
209C2×C4—611no—
210C2×C4—611no—
211C2×C4—611no—
212C2×C4—611no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—2442no—
216C2×C4—2441no—
217C2×C4D4×#692311yescharacteristic
218C8—41no—
219C8—611no—
220C8—611no—
221C8—4881no—
222C8—2441no—
223C8—2442no—
224C8—2441no—
225C8#1451985611yescharacteristic
226C8Q8×#692311yescharacteristic
227C22—611no—
228C22—611no—
229C22—2441no—
230C22#1684080111yescharacteristic
231C4—81no—
232C4—611no—
233C4—611no—
234C4—1222no—
235C4—4881no—
236C4—2441no—
237C4#1684071111yescharacteristic
238C4SD16×#692311yescharacteristic
239C2—21no—
240C2—1221no—
241C2—1221no—
242C2#2146188211yescharacteristic
subgroupG/H
centerC2#21461882
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#365C4
socleC2×C61#1920
prime radicalC22×D61#137
cosocleC2×C8×D61C23
hypercenter#365#6923
hypocenterC61#13117
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
141. #365#6923semidirect
144. C61#13117semidirect

Maximal subgroups

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

subgroupindex
#214619262
#108×#69232
#214609012
#214608972
#214608882
#214608622
#214475902
#1311761