Finite Group Databasebeta

← #29591532

Subgroups — #29591532

Order 15616.

268 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 69 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#21456475C211yesmaximal, characteristic
2#21447634C211yesmaximal, characteristic
3#21447583C211yesmaximal, characteristic
4#21443881C211yesmaximal, characteristic, complemented
5#21443879C211yesmaximal, characteristic, complemented
6#21443858C211yesmaximal, characteristic, complemented
7C61×#1358C211yesmaximal, characteristic, complemented
8#16840373C412yes—
9M32×D61—21no—
10#16840164C2211yescharacteristic
11#16840130C412yes—
12#16840017—21no—
13#16840000—21no—
14#16839869—21no—
15Q16×Dic61—21no—
16#16839716C2211yescharacteristic
17#16839583C2211yescharacteristic
18#16839583C2211yescharacteristic
19#16839582—21no—
20#16839543—21no—
21#16839539—21no—
22C61×#494C2211yescharacteristic
23C61×#364C2211yescharacteristic
24C61×#364C2211yescharacteristic
25C2×#11758189D411yescharacteristic
26C2×C8×D61D411yescharacteristic
27#14519772—42no—
28#14519769C2×C412yes—
29#14519767—42no—
30#14519753—22no—
31Q8×Dic61—22no—
32#14519734C2×C411yescharacteristic
33#14519717—21no—
34#14519717—21no—
35#14519716—41no—
36C16×D61—41no—
37#14519711—21no—
38#14519709—21no—
39#14519701—22no—
40#14519701—22no—
41#14519688C2×C411yescharacteristic
42#14519687D411yescharacteristic
43C8×Dic61D411yescharacteristic
44C2×Q16×C61—21no—
45C2×Q16×C61—21no—
46C4⋊Q8×C61C2×C412yes—
47M32×C61—21no—
48M32×C61—21no—
49C4×C8×C61C2311yescharacteristic
50C2×Q8×C61—22no—
51C2×C4×D61C22⋊C411yescharacteristic
52Q16×C61—41no—
53Q16×C61—41no—
54Q16×C61—41no—
55Q16×C61—41no—
56C2×C8×C61C2×D411yescharacteristic
57C2×C8×C61C2×D411yescharacteristic
58C4⋊C4×C61—42no—
59C42×C61C22×C411yescharacteristic
60#11758198—21no—
61#11758198—42no—
62C4⋊Dic61—22no—
63C4⋊Dic61—42no—
64#11758196—21no—
65#11758196—42no—
66#11758196—42no—
67C4×Dic61—42no—
68C4×Dic61C22⋊C411yescharacteristic
69C2×#92418C22⋊C411yescharacteristic
70C2×#92418C22⋊C411yescharacteristic
71#11758189—21no—
72#11758189—21no—
73C8×D61—21no—
74C8×D61—21no—
75C16×C61—41no—
76C16×C61—41no—
77#11758185—41no—
78#11758185—41no—
79C22×D61#10011yescharacteristic
80Q8×C61—42no—
81Q8×C61—42no—
82C2×C4×C61—21no—
83C2×C4×C61—42no—
84C2×C4×C61C2×C22⋊C411yescharacteristic
85C2×Dic61—21no—
86C2×Dic61—42no—
87C2×Dic61#10011yescharacteristic
88C4×D61—21no—
89C4×D61—21no—
90C8×C61#13511yescharacteristic
91C8×C61#13511yescharacteristic
92C8×C61AGL(1,ℤ/8)11yescharacteristic
93C8×C61#13711yescharacteristic
94#92418—21no—
95#92418—21no—
96#11990—611nomaximal, Sylow
97C22×C61C2×#10011yescharacteristic
98C2×D61—21no—
99C2×D61—41no—
100C4×C61—41no—
101C4×C61—82no—
102C4×C61#41611yescharacteristic
103C4×C61#41711yescharacteristic
104Dic61—21no—
105Dic61—41no—
106Dic61—82no—
107#3177—611no—
108#2166—611no—
109#2153—611no—
110#1366—611no—
111#1366—611no—
112#1358—611no—
113#1358D6111yescharacteristic, complemented
114C2×C61—21no—
115C2×C61#155111yescharacteristic
116D61—41no—
117#541—612no—
118C2×M32—1221no—
119#499—611no—
120#494C2×D6111yescharacteristic
121#491—612no—
122#470—1221no—
123#467—1221no—
124#441—1221no—
125C4×Q16—1221no—
126#405—611no—
127#364—611no—
128#364—611no—
129#364—1221no—
130#364C2×D6111yescharacteristic
131#364C2×D6111yescharacteristic
132#349—1221no—
133#347—1221no—
134C61#1199011yescharacteristic, complemented, Sylow
135C2×Q16—21no—
136C2×Q16—21no—
137C2×M16—611no—
138C22×C8—611no—
139C4⋊Q8C4×D6112yes—
140#126—2442no—
141#125—612no—
142#125—2442no—
143C22⋊Q8—1222no—
144C4×Q8—1222no—
145#117—611no—
146M32—21no—
147M32—21no—
148M32—1221no—
149M32—1221no—
150M32—2441no—
151C2×C16—2441no—
152#107—1221no—
153#106—1221no—
154#103—1222no—
155#103—1222no—
156#97—611no—
157#97—611no—
158C4×C8—611no—
159C4×C8C22×D6111yescharacteristic
160C2×Q8—22no—
161C22×C4—611no—
162Q16—41no—
163Q16—41no—
164Q16—41no—
165Q16—41no—
166M16—1221no—
167M16—1221no—
168C2×C8—611no—
169C2×C8—611no—
170C2×C8—1221no—
171C2×C8—1221no—
172C2×C8D4×D6111yescharacteristic
173C2×C8D4×D6111yescharacteristic
174C4⋊C4—42no—
175C4⋊C4—1221no—
176C4⋊C4—1222no—
177C4⋊C4—2442no—
178C4⋊C4—2442no—
179C4⋊C4—2442no—
180C22⋊C4—1221no—
181C22⋊C4—2442no—
182C42—611no—
183C42—2442no—
184C42C2×C4×D6111yescharacteristic
185C16—41no—
186C16—41no—
187C16—2441no—
188C16—2441no—
189C23—611no—
190Q8—42no—
191Q8—42no—
192C2×C4—21no—
193C2×C4—42no—
194C2×C4—611no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—2442no—
199C2×C4C22⋊C4×D6111yescharacteristic
200C8—1221no—
201C8—1221no—
202C8#1451979611yescharacteristic
203C8#1451979811yescharacteristic
204C8#1451980111yescharacteristic
205C8#1451980611yescharacteristic
206C22—1221no—
207C22—2441no—
208C22#100×D6111yescharacteristic
209C4—41no—
210C4—82no—
211C4—1221no—
212C4—4882no—
213C4—2441no—
214C4#1683975511yescharacteristic
215C4#1683976011yescharacteristic
216C2—21no—
217C2—2441no—
218C2#2144451111yescharacteristic
subgroupG/H
centerC2#21444511
commutatorC42×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1358C2
socleC2×C61#1551
prime radicalC22×D61#100
cosocleC4×C8×C61C23
hypercenter#1358D61
hypocenterC61#11990
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1358

Complements

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

NH ≅ G/Ntype
4. #21443881C2semidirect
5. #21443879C2semidirect
6. #21443858C2semidirect
7. C61×#1358C2semidirect
113. #1358D61semidirect
134. C61#11990semidirect

Maximal subgroups

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

subgroupindex
#214564752
#214476342
#214475832
#214438812
#214438792
#214438582
C61×#13582
#1199061