Finite Group Databasebeta

← #29567397

Subgroups — #29567397

Order 15616.

216 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 43 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#21446620C211yesmaximal, characteristic
2#21443765C211yesmaximal, characteristic
3C61×#1325C211yesmaximal, characteristic
4C2×#14519777C411yescharacteristic
5C2×#14519700—21no—
6C2×#14519700—21no—
7C2×C4×#92418C411yescharacteristic
8#16839488—21no—
9C61×#384C2211yescharacteristic
10C61×#324—21no—
11C22×Dic122—21no—
12C22×#92418—21no—
13#14519777—21no—
14#14519777—41no—
15#14519777C812yescomplemented
16C2×C4⋊Dic61—41no—
17#14519700—42no—
18#14519700—42no—
19C22⋊#92418—41no—
20C4×#92418—41no—
21C2×C4⋊C4×C61—41no—
22C2×C4⋊C4×C61D411yescharacteristic
23C2×C4⋊C4×C61D411yescharacteristic
24C2×C42×C61C2×C411yescharacteristic
25C22⋊C8×C61—41no—
26C22×C4×C61—21no—
27C22×C4×C61—21no—
28C22×C4×C61—21no—
29C22×C4×C61C22⋊C411yescharacteristic
30C22×Dic61—41no—
31C2×Dic122—22no—
32C2×Dic122—41no—
33C2×Dic122—41no—
34C2×Dic122—41no—
35C2×Dic122—41no—
36C2×Dic122—41no—
37C2×C8×C61—81no—
38C4⋊C4×C61—41no—
39C4⋊C4×C61—41no—
40C4⋊C4×C61—82no—
41C42×C61—21no—
42C42×C61C2×C811yescharacteristic
43C42×C61M1611yescharacteristic
44C4⋊Dic61—42no—
45C4⋊Dic61—42no—
46C2×#92418—22no—
47C2×#92418—41no—
48C2×#92418—41no—
49C2×#92418—81no—
50C23×C61#9911yescharacteristic
51C2×C4×C61—22no—
52C2×C4×C61—22no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—41no—
58C2×C4×C61—41no—
59C2×C4×C61—81no—
60C2×C4×C61—81no—
61C2×C4×C61C22⋊C811yescharacteristic
62C2×C4×C61#10011yescharacteristic
63C2×Dic61—42no—
64C2×Dic61—81no—
65C2×Dic61—81no—
66Dic122—42no—
67Dic122—42no—
68Dic122—81no—
69Dic122—81no—
70C8×C61—161no—
71#92418—42no—
72#92418—161no—
73#7355—611nomaximal, Sylow
74C22×C61—21no—
75C22×C61—21no—
76C22×C61#32311yescharacteristic
77C22×C61#35311yescharacteristic
78C22×C61#35511yescharacteristic
79C4×C61—22no—
80C4×C61—22no—
81C4×C61—21no—
82C4×C61—21no—
83C4×C61—81no—
84C4×C61—81no—
85Dic61—82no—
86#1956—611no—
87#1325—611no—
88#1325D6111yescharacteristic
89C2×C61—21no—
90C2×C61—21no—
91C2×C61#131811yescharacteristic
92C2×C61#140911yescharacteristic
93C2×C61#141111yescharacteristic
94C2×C4⋊Q8—611no—
95C2×#103—1221no—
96C2×#103—1221no—
97C2×C4×C8—611no—
98#384C2×D6111yescharacteristic
99#324—21no—
100#324—1221no—
101C61#735511yescharacteristic, complemented, Sylow
102C22×Q8—1221no—
103C22×C8—1221no—
104C4⋊Q8—612no—
105C4⋊Q8—1221no—
106C4⋊Q8—2441no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—2441no—
109C2×C4⋊C4D24411yescharacteristic
110C2×C4⋊C4C22⋊D6111yescharacteristic
111C2×C42C4×D6111yescharacteristic
112#103—2442no—
113#103—2442no—
114C22⋊C8—41no—
115C22⋊C8—2441no—
116C4×C8—2441no—
117C2×Q8—1222no—
118C2×Q8—2441no—
119C2×Q8—2441no—
120C2×Q8—2441no—
121C2×Q8—2441no—
122C2×Q8—2441no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—2441no—
127C22×C4#1175819811yescharacteristic
128C2×C8—81no—
129C2×C8—1222no—
130C2×C8—4881no—
131C2×C8—2441no—
132C2×C8—2441no—
133C4⋊C4—41no—
134C4⋊C4—41no—
135C4⋊C4—82no—
136C4⋊C4—2442no—
137C4⋊C4—2442no—
138C42—21no—
139C42C8×D6111yescharacteristic
140C42#1175818911yescharacteristic
141C23#1451969111yescharacteristic
142Q8—4881no—
143Q8—4881no—
144Q8—2442no—
145Q8—2442no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—81no—
155C2×C4—81no—
156C2×C4—4881no—
157C2×C4—4881no—
158C2×C4—2442no—
159C2×C4#1451968911yescharacteristic
160C2×C4#1451969311yescharacteristic
161C8—161no—
162C8—9761no—
163C8—2442no—
164C22—21no—
165C22—21no—
166C22#1683948511yescharacteristic
167C22#1683955411yescharacteristic
168C22#1683955811yescharacteristic
169C4—22no—
170C4—22no—
171C4—21no—
172C4—21no—
173C4—81no—
174C4—81no—
175C4—4882no—
176C2—21no—
177C2—21no—
178C2#2144375011yescharacteristic
179C2#2144398311yescharacteristic
180C2#2144398711yescharacteristic
subgroupG/H
centerC22#16839554
commutatorC42×C61C2×C8
Frattini#384C2×D61
FittingC61×#1325C2
socleC22×C61#353
prime radicalC23×C61#99
cosocleC61×#384C22
hypercenter#1325D61
hypocenterC61#7355
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #1325

Complements

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

NH ≅ G/Ntype
15. #14519777C8semidirect
101. C61#7355semidirect

Maximal subgroups

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

subgroupindex
#214466202
#214437652
C61×#13252
#735561