Finite Group Databasebeta

← #29589448

Subgroups — #29589448

Order 15616.

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

normal subgroups only

This group has 284 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#21454456C211yesmaximal, characteristic
2#21447628C212yesmaximal, complemented
3#21443770C211yesmaximal, characteristic, complemented
4#21443754C212yesmaximal
5C61×#1327C211yesmaximal, characteristic, complemented
6C2×#14519734C411yescharacteristic
7#16839822—22no—
8#16839822—22no—
9#16839786C411yescharacteristic
10#16839725C411yescharacteristic
11#16839725C2211yescharacteristic
12M16×Dic61C411yescharacteristic
13M16×Dic61C2211yescharacteristic
14#16839582—22no—
15#16839544C2212yes—
16#16839539—22no—
17C61×#423C2211yescharacteristic
18C61×#349C2212yes—
19C22×C4×D61C2×C411yescharacteristic
20C2×#11758194C2×C411yescharacteristic
21C2×#11758194C2×C411yescharacteristic
22#14519734—22no—
23#14519734—21no—
24#14519734—21no—
25C2×#11758196—21no—
26C2×#11758198—21no—
27C2×C4×Dic61C2×C411yescharacteristic
28#14519717—22no—
29C4⋊#92418—22no—
30#14519689—22no—
31#14519689—22no—
32#14519687—21no—
33#14519687D412yes—
34C8×Dic61—21no—
35C8×Dic61D412yes—
36C2×M16×C61C2×C411yescharacteristic
37C2×M16×C61C2311yescharacteristic
38C2×C42×C61C2×C411yescharacteristic
39M32×C61—22no—
40C4⋊C8×C61—22no—
41C23×D61M1611yescharacteristic
42C22×C4×C61—21no—
43C22×C4×C61C22×C411yescharacteristic
44C22×Dic61—21no—
45C22×Dic61M1611yescharacteristic
46C2×C4×D61—21no—
47C2×C4×D61—21no—
48C2×C4×D61—41no—
49C2×C4×D61—41no—
50M16×C61—41no—
51M16×C61—41no—
52C2×C8×C61—21no—
53C2×C8×C61C2×D412yes—
54C42×C61—21no—
55C42×C61M1612yes—
56#11758198—22no—
57#11758198—22no—
58#11758196—22no—
59#11758196—22no—
60C4×Dic61—21no—
61C4×Dic61C22⋊C411yescharacteristic
62C4×Dic61C22⋊C411yescharacteristic
63#11758194—41no—
64#11758194—41no—
65C2×#92418—21no—
66C2×#92418C22⋊C412yes—
67C16×C61—42no—
68#11758185—42no—
69C23×C61C2×M1611yescharacteristic
70C22×D61—21no—
71C22×D61—41no—
72C22×D61—81no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—22no—
76C2×C4×C61—81no—
77C2×C4×C61C2×C22⋊C411yescharacteristic
78C2×C4×C61C2×M1611yescharacteristic
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—41no—
83C2×Dic61—81no—
84C4×D61—42no—
85C4×D61—41no—
86C4×D61—41no—
87C8×C61—22no—
88C8×C61—41no—
89#92418—22no—
90#92418—41no—
91#11522—611nomaximal, Sylow
92C22×C61—21no—
93C22×C61—41no—
94C22×C61#40711yescharacteristic
95C2×D61—42no—
96C2×D61—41no—
97C2×D61—82no—
98C4×C61—21no—
99C4×C61—42no—
100C4×C61#41011yescharacteristic
101C4×C61#41311yescharacteristic
102Dic61—41no—
103Dic61—41no—
104Dic61—41no—
105#2921—611no—
106#2165—612no—
107#1327—611no—
108#1327D6111yescharacteristic, complemented
109#1320—612no—
110C2×C61—21no—
111C2×C61—41no—
112C2×C61#146411yescharacteristic
113D61—81no—
114C2×#117—611no—
115#433—1222no—
116#433—1222no—
117#423—611no—
118#423C2×D6111yescharacteristic
119#407—611no—
120#407—611no—
121C4×M16—611no—
122C4×M16—611no—
123#364—1222no—
124#349—612no—
125#349C2×D6112yes—
126#347—1222no—
127C61#1152211yescharacteristic, complemented, Sylow
128C23×C4—611no—
129C2×M16—611no—
130C2×M16—611no—
131C2×M16C4×D6111yescharacteristic
132C2×M16C22×D6111yescharacteristic
133#117—1221no—
134#117—1221no—
135#117—1222no—
136C2×C4⋊C4—1221no—
137C2×C22⋊C4—1221no—
138C2×C42—611no—
139C2×C42C4×D6111yescharacteristic
140M32—22no—
141M32—1222no—
142C4⋊C8—22no—
143C4⋊C8—1222no—
144C22⋊C8—1222no—
145C22⋊C8—1222no—
146#97—612no—
147#97—1221no—
148C4×C8—612no—
149C4×C8—1221no—
150C24—611no—
151C22×C4—21no—
152C22×C4—611no—
153C22×C4—1221no—
154C22×C4—1221no—
155C22×C4—1221no—
156C22×C4—2441no—
157C22×C4—2441no—
158C22×C4C2×C4×D6111yescharacteristic
159M16—41no—
160M16—41no—
161M16—2441no—
162M16—2441no—
163C2×C8—21no—
164C2×C8—612no—
165C2×C8—1221no—
166C2×C8D4×D6112yes—
167C4⋊C4—1222no—
168C4⋊C4—1222no—
169C22⋊C4—1222no—
170C22⋊C4—1222no—
171C42—21no—
172C42—611no—
173C42—611no—
174C42—1221no—
175C42#1175818912yes—
176C16—42no—
177C16—2442no—
178C23—1221no—
179C23—4881no—
180C23—2441no—
181C23M16×D6111yescharacteristic
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—81no—
186C2×C4—1221no—
187C2×C4—1221no—
188C2×C4—1221no—
189C2×C4—4881no—
190C2×C4—2442no—
191C2×C4—2441no—
192C2×C4—2441no—
193C2×C4—2441no—
194C2×C4C22⋊C4×D6111yescharacteristic
195C2×C4C2×#1175818911yescharacteristic
196C8—22no—
197C8—41no—
198C8—1222no—
199C8—2441no—
200C22—21no—
201C22—41no—
202C22—4882no—
203C22—2442no—
204C22—2441no—
205C22#1683972411yescharacteristic
206C4—21no—
207C4—42no—
208C4—2441no—
209C4—2441no—
210C4—2441no—
211C4#1683973411yescharacteristic
212C4#1683974511yescharacteristic
213C2—21no—
214C2—41no—
215C2—4881no—
216C2#2144415211yescharacteristic
subgroupG/H
centerC4#16839734
commutatorC22×C4×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#1327C2
socleC2×C61#1464
prime radicalC23×D61M16
cosocleC2×M16×C61C23
hypercenter#1327D61
hypocenterC61#11522
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
2. #21447628C2semidirect
3. #21443770C2semidirect
5. C61×#1327C2semidirect
108. #1327D61semidirect
127. C61#11522semidirect

Maximal subgroups

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

subgroupindex
#214544562
#214476282
#214437702
#214437542
C61×#13272
#1152261