Finite Group Databasebeta

← #29591213

Subgroups — #29591213

Order 15616.

280 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 61 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#21456221C211yesmaximal, characteristic
2#21447629C212yesmaximal, complemented
3#21443854C211yesmaximal, characteristic, complemented
4#21443851C212yesmaximal, complemented
5C61×#1356C211yesmaximal, characteristic, complemented
6#16840313C411yescharacteristic
7#125×D61C411yescharacteristic
8#16840130C411yescharacteristic
9#16840128C411yescharacteristic
10#16840127C2211yescharacteristic
11#16840118—22no—
12#16839762—22no—
13#16839714C2211yescharacteristic
14#16839582—22no—
15#16839543—22no—
16#16839540C2212yes—
17C61×#491C2211yescharacteristic
18C61×#347C2212yes—
19C2×#11758226—21no—
20C2×#11758189D412yes—
21#14519774C2×C411yescharacteristic
22#14519769C2×C411yescharacteristic
23#14519768—21no—
24#14519767—41no—
25#14519766—21no—
26#14519752—41no—
27#14519739—41no—
28C4⋊C4×D61—21no—
29C4⋊C4×D61—41no—
30C42×D61C2×C411yescharacteristic
31#14519717—22no—
32#14519701—22no—
33#14519699—22no—
34#14519697—22no—
35#14519688C2×C411yescharacteristic
36C8×Dic61D412yes—
37C4⋊Q8×C61C2×C411yescharacteristic
38#125×C61C2×C411yescharacteristic
39M32×C61—22no—
40#103×C61—22no—
41#97×C61C2311yescharacteristic
42C2×Q8×C61—21no—
43#11758226—44no—
44C2×D244—21no—
45C2×D244—41no—
46C2×D244—41no—
47C2×C4×D61—21no—
48C2×C4×D61—41no—
49C2×C4×D61—41no—
50C2×C4×D61C22⋊C411yescharacteristic
51C2×C8×C61C2×D412yes—
52C4⋊C4×C61—21no—
53C4⋊C4×C61—41no—
54C4⋊C4×C61—41no—
55C42×C61C22×C411yescharacteristic
56#11758198—42no—
57C4⋊Dic61—21no—
58C4⋊Dic61—41no—
59#11758196—41no—
60#11758196—41no—
61#11758196—41no—
62C4×Dic61—21no—
63C4×Dic61C22⋊C411yescharacteristic
64C2×#92418C22⋊C412yes—
65#11758189—42no—
66C16×C61—42no—
67#11758185—42no—
68C22×D61—41no—
69C22×D61#10011yescharacteristic
70Q8×C61—42no—
71C2×C4×C61—21no—
72C2×C4×C61—41no—
73C2×C4×C61—41no—
74C2×C4×C61C2×C22⋊C411yescharacteristic
75C2×Dic61—21no—
76C2×Dic61—41no—
77C2×Dic61#10011yescharacteristic
78D244—42no—
79D244—82no—
80D244—82no—
81C4×D61—22no—
82C4×D61—82no—
83C4×D61—81no—
84C4×D61—82no—
85C8×C61—22no—
86#92418—22no—
87#11917—611nomaximal, Sylow
88C22×C61C2×#10011yescharacteristic
89C2×D61—21no—
90C2×D61—41no—
91C2×D61—82no—
92C2×D61—81no—
93C4×C61—41no—
94C4×C61—81no—
95C4×C61—81no—
96C4×C61#42112yes—
97Dic61—21no—
98Dic61—41no—
99Dic61—81no—
100#3142—611no—
101#2165—612no—
102#1356—611no—
103#1356D6111yescharacteristic, complemented
104#1355—612no—
105C2×C61—21no—
106C2×C61#153311yescharacteristic
107D61—41no—
108D61—161no—
109#532—611no—
110C2×#125—611no—
111#491—611no—
112#491C2×D6111yescharacteristic
113#490—611no—
114#490—611no—
115#488—1222no—
116#417—1222no—
117C4×M16—611no—
118#364—1222no—
119#349—1222no—
120#347—612no—
121#347C2×D6112yes—
122C61#1191711yescharacteristic, complemented, Sylow
123C2×#41—1221no—
124C2×M16—612no—
125C4⋊Q8C4×D6111yescharacteristic
126#127—611no—
127#125—611no—
128#125—1221no—
129#125—2441no—
130#125C4×D6111yescharacteristic
131#124—1221no—
132#121—2441no—
133C4×D4—2441no—
134C2×C4⋊C4—1221no—
135C2×C4⋊C4—2441no—
136C2×C42—611no—
137M32—22no—
138M32—1222no—
139#103—22no—
140#103—1222no—
141#102—1222no—
142#102—1222no—
143#97—611no—
144#97C22×D6111yescharacteristic
145C4×C8—612no—
146#41—2444no—
147C2×Q8—21no—
148C2×D4—1221no—
149C2×D4—2441no—
150C2×D4—2441no—
151C22×C4—611no—
152C22×C4—1221no—
153C22×C4—2441no—
154C22×C4—2441no—
155M16—2442no—
156C2×C8—612no—
157C2×C8D4×D6112yes—
158C4⋊C4—21no—
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—1221no—
162C4⋊C4—2441no—
163C4⋊C4—2441no—
164C4⋊C4—2441no—
165C4⋊C4—2441no—
166C22⋊C4—2442no—
167C42—611no—
168C42—1221no—
169C42C2×C4×D6111yescharacteristic
170C16—42no—
171C16—2442no—
172C23—611no—
173C23—2441no—
174Q8—42no—
175D4—4882no—
176D4—4882no—
177D4—2442no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—611no—
182C2×C4—1222no—
183C2×C4—1221no—
184C2×C4—4881no—
185C2×C4—4882no—
186C2×C4—4882no—
187C2×C4—2441no—
188C2×C4C22⋊C4×D6111yescharacteristic
189C8—22no—
190C8—1222no—
191C22—1221no—
192C22—4882no—
193C22—4881no—
194C22—2441no—
195C22#100×D6111yescharacteristic
196C4—41no—
197C4—81no—
198C4—81no—
199C4—1221no—
200C4—4881no—
201C4—2441no—
202C4#1683977712yes—
203C2—21no—
204C2—9761no—
205C2—2441no—
206C2#2144444111yescharacteristic
subgroupG/H
centerC2#21444441
commutatorC42×C61C22×C4
Frattini#97C22×D61
FittingC61×#1356C2
socleC2×C61#1533
prime radical#16840313C4
cosocle#97×C61C23
hypercenter#1356D61
hypocenterC61#11917
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1356

Complements

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

NH ≅ G/Ntype
2. #21447629C2semidirect
3. #21443854C2semidirect
4. #21443851C2semidirect
5. C61×#1356C2semidirect
103. #1356D61semidirect
122. C61#11917semidirect

Maximal subgroups

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

subgroupindex
#214562212
#214476292
#214438542
#214438512
C61×#13562
#1191761