Finite Group Databasebeta

← #30594950

Subgroups — #30594950

Order 15616.

252 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 36 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#21460916C211yesmaximal, characteristic
2#21460750C211yesmaximal, characteristic
3#21446919C211yesmaximal, characteristic
4C2×#14519838—21no—
5#16840607—21no—
6C22×#11758202—21no—
7C2×#14519701—21no—
8#16839668C2211yescharacteristic
9#16839517C411yescharacteristic
10C2×C4⋊Q8×C61C411yescharacteristic
11C2×#11758217—41no—
12#14519838—22no—
13#14519838—41no—
14C22⋊#92420—41no—
15C22×Dic122D411yescharacteristic
16C2×#11758202—42no—
17C2×#11758202—42no—
18C2×#11758202—41no—
19C2×#11758202—41no—
20C22×#92418—21no—
21C2×C4⋊Dic61D411yescharacteristic
22#14519701—42no—
23#14519684—41no—
24C22×Q8×C61—21no—
25C4⋊Q8×C61—42no—
26C2×C4⋊C4×C61—41no—
27C2×C42×C61C2×C411yescharacteristic
28C2×Q8×C61—22no—
29C2×Q8×C61—41no—
30C2×Q8×C61—41no—
31C2×Q8×C61—41no—
32C2×Q8×C61—41no—
33C2×Q8×C61—41no—
34C22×C4×C61—21no—
35C22×C4×C61—41no—
36C22×C4×C61C22⋊C411yescharacteristic
37C22×Dic61—21no—
38C22×Dic61—21no—
39C2×Dic122—21no—
40C2×Dic122—41no—
41C2×Dic122—41no—
42C2×Dic122D811yescharacteristic
43C2×Dic122SD1611yescharacteristic
44#11758217—42no—
45#11758217—81no—
46C2×#92420—81no—
47C2×#92420—81no—
48C4⋊C4×C61—42no—
49C4⋊C4×C61—42no—
50C42×C61—41no—
51#11758202—44no—
52#11758202—44no—
53C4⋊Dic61—41no—
54C2×#92418—22no—
55C2×#92418—41no—
56C2×#92418—41no—
57C23×C61#9911yescharacteristic
58Q8×C61—42no—
59Q8×C61—42no—
60Q8×C61—81no—
61Q8×C61—81no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—22no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—42no—
68C2×C4×C61—81no—
69C2×C4×C61—81no—
70C2×C4×C61#10211yescharacteristic
71C2×C4×C61#10411yescharacteristic
72C2×Dic61—21no—
73C2×Dic61—21no—
74C2×Dic61—41no—
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61—81no—
78Dic122—41no—
79Dic122—41no—
80Dic122—81no—
81#92420—82no—
82#92420—161no—
83#92418—42no—
84#7405—611nomaximal, Sylow
85C22×C61—21no—
86C22×C61—21no—
87C22×C61#32711yescharacteristic
88C22×C61AΣL(1,𝔽16)11yescharacteristic
89C22×C61#35311yescharacteristic
90C4×C61—21no—
91C4×C61—21no—
92C4×C61—42no—
93C4×C61—82no—
94Dic61—41no—
95Dic61—41no—
96Dic61—81no—
97#2016—611no—
98#1394—611no—
99#1319—611no—
100C2×C61—21no—
101C2×C61—21no—
102C2×C61#134311yescharacteristic
103C2×C61#140711yescharacteristic
104C2×C61#141111yescharacteristic
105C22×Q16—1221no—
106C2×C4⋊Q8#692311yescharacteristic
107C2×#103—1221no—
108C2×#101—1221no—
109#391—611no—
110#336—611no—
111#324—1221no—
112C61#740511yescharacteristic, complemented, Sylow
113C22×Q8—21no—
114C22×Q8—611no—
115C2×Q16—2442no—
116C2×Q16—2442no—
117C2×Q16—2441no—
118C2×Q16—2441no—
119C2×M16—2441no—
120C22×C8—1221no—
121C4⋊Q8—42no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4—611no—
124C2×C42C2×#692311yescharacteristic
125#103—2442no—
126#101—1222no—
127#101—2441no—
128C22⋊C8—2441no—
129#95—2441no—
130C2×Q8—22no—
131C2×Q8—41no—
132C2×Q8—41no—
133C2×Q8—41no—
134C2×Q8—41no—
135C2×Q8—41no—
136C2×Q8—611no—
137C2×Q8—611no—
138C2×Q8—1221no—
139C2×Q8—2441no—
140C2×Q8—2441no—
141C22×C4—21no—
142C22×C4—41no—
143C22×C4—1221no—
144C22×C4—1221no—
145C22×C4C22⋊#692311yescharacteristic
146Q16—2444no—
147Q16—2444no—
148M16—4881no—
149M16—2442no—
150C2×C8—1222no—
151C2×C8—4881no—
152C2×C8—4881no—
153C2×C8—2441no—
154C2×C8—2441no—
155C4⋊C4—42no—
156C4⋊C4—42no—
157C4⋊C4—2441no—
158C42—41no—
159C23#1451983511yescharacteristic
160Q8—42no—
161Q8—42no—
162Q8—81no—
163Q8—81no—
164Q8—4881no—
165Q8—2441no—
166Q8—2441no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—42no—
173C2×C4—81no—
174C2×C4—81no—
175C2×C4—1221no—
176C2×C4—1221no—
177C2×C4—4881no—
178C2×C4—2441no—
179C2×C4—2441no—
180C2×C4—2441no—
181C2×C4#1451983911yescharacteristic
182C2×C4#1451984111yescharacteristic
183C8—9761no—
184C8—4882no—
185C8—2442no—
186C22—21no—
187C22—21no—
188C22#1684061311yescharacteristic
189C22#1684066211yescharacteristic
190C22#1684066611yescharacteristic
191C4—21no—
192C4—21no—
193C4—42no—
194C4—82no—
195C4—4881no—
196C4—2441no—
197C4—2441no—
198C2—21no—
199C2—21no—
200C2#2146079711yescharacteristic
201C2#2146094811yescharacteristic
202C2#2146095611yescharacteristic
subgroupG/H
centerC22#16840666
commutatorC2×C42×C61C2×C4
FrattiniC2×C42C2×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61#353
prime radicalC23×C61#99
cosocle#16839668C22
hypercenterC2×C4⋊Q8#6923
hypocenterC61#7405
LCSG ▷ C2×C42×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
112. C61#7405semidirect

Maximal subgroups

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

subgroupindex
#214609162
#214607502
#214469192
#740561