Finite Group Databasebeta

← #30594409

Subgroups — #30594409

Order 15616.

248 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 60 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#21462051C211yesmaximal, characteristic
2#21461575C211yesmaximal, characteristic
3#21447438C211yesmaximal, characteristic
4C2×#14519851C411yescharacteristic, complemented
5C22×#11758187C411yescharacteristic, complemented
6#16840748C411yescharacteristic
7#16840741C411yescharacteristic
8#16840725—21no—
9#16840657—21no—
10#16840657—21no—
11#16840644—21no—
12C2×#14519785C2211yescharacteristic
13M32×D61—21no—
14#16839544C411yescharacteristic, complemented
15#16839543—21no—
16C61×#349C411yescharacteristic, complemented
17D61⋊M16—21no—
18#14519856—21no—
19#14519851—41no—
20C2×#11758187—21no—
21C2×#11758187—21no—
22C2×#11758187—41no—
23#14519838C812yes—
24#14519837—21no—
25#14519836C812yes—
26#14519835—21no—
27#14519831—41no—
28C8×#6923—41no—
29C2×#11758222C2×C411yescharacteristic
30#14519785—41no—
31#14519785—41no—
32C2×#11758189D411yescharacteristic
33C2×#11758189Q811yescharacteristic
34C22×#92418C2×C411yescharacteristic
35C2×C8×D61D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37#14519717—21no—
38#14519716—41no—
39C16×D61—41no—
40C2×M16×C61C2×C411yescharacteristic
41M32×C61—21no—
42C22×C4×C61C4211yescharacteristic
43C2×C22⋊D61M1611yescharacteristic
44C2×C22⋊D61M1611yescharacteristic
45#11758222—41no—
46#11758222—41no—
47C2×D244C2×C811yescharacteristic
48C2×C4×D61C22⋊C411yescharacteristic
49C2×C4×D61C4⋊C411yescharacteristic
50C2×Dic122C2×C811yescharacteristic
51C22⋊#6923—22no—
52#11758217—22no—
53C4⋊#6923—41no—
54C4×#6923—41no—
55#11758213—41no—
56D61⋊C8—41no—
57M16×C61—41no—
58C2×C8×C61C22⋊C411yescharacteristic
59C2×C8×C61C4⋊C411yescharacteristic
60C2×#92418—21no—
61C2×#92418—21no—
62C2×#92418C22⋊C411yescharacteristic
63C2×#92418C4⋊C411yescharacteristic
64#11758189—41no—
65#11758189—41no—
66C8×D61—21no—
67C8×D61—21no—
68C8×D61—21no—
69C8×D61—21no—
70#11758187—41no—
71#11758187—41no—
72C16×C61—41no—
73#11758185—41no—
74C23×C61#9711yescharacteristic
75C22×D61C22⋊C811yescharacteristic
76C22×D61C4⋊C811yescharacteristic
77C2×#6923—42no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61#9511yescharacteristic
81C2×C4×C61C4×C811yescharacteristic
82C22⋊D61—41no—
83C22⋊D61—41no—
84C2×Dic61C22⋊C811yescharacteristic
85C2×Dic61C4⋊C811yescharacteristic
86D244—41no—
87C4×D61—21no—
88C4×D61—21no—
89C4×D61—21no—
90C4×D61—21no—
91Dic122—41no—
92#92420—42no—
93C8×C61—21no—
94C8×C61—21no—
95#92418—21no—
96#92418#9911yescharacteristic
97#92418#9911yescharacteristic
98#7208—611nomaximal, Sylow
99C22×C61—21no—
100C22×C61—41no—
101C22×C61#33611yescharacteristic
102C2×D61—21no—
103C2×D61—21no—
104C2×D61—41no—
105C2×D61—41no—
106#6923—82no—
107C4×C61—21no—
108C4×C61#34211yescharacteristic
109C4×C61#34411yescharacteristic
110Dic61—21no—
111Dic61—21no—
112#2115—611no—
113#2113—611no—
114#1757—611no—
115C2×C61—21no—
116C2×C61—41no—
117C2×C61#128211yescharacteristic
118D61—41no—
119D61—41no—
120C2×#131—611no—
121C2×M32—611no—
122C2×M32—1221no—
123C22×C16—611no—
124#413—611no—
125#410—611no—
126#405—1221no—
127#349—611no—
128#349—1221no—
129#349#692311yescharacteristic, complemented
130C22⋊C16—1221no—
131C22⋊C16—1221no—
132#344—1221no—
133C61#720811yescharacteristic, complemented, Sylow
134C2×#41—611no—
135#131—2441no—
136#131—2441no—
137C2×M16—611no—
138C2×M16—611no—
139C2×M16—1221no—
140C2×M16C2×#692311yescharacteristic
141C22×C8—611no—
142C22×C8—611no—
143C22×C8—611no—
144#117—1221no—
145M32—21no—
146M32—1221no—
147M32—2441no—
148M32—2441no—
149C2×C16—1221no—
150C2×C16—1221no—
151C2×C16—2441no—
152C2×C16—2441no—
153#101—612no—
154#100—1221no—
155#99—612no—
156#99—1221no—
157#97—2441no—
158C4×C8—2441no—
159#41—2441no—
160#41—2441no—
161C2×Q8—611no—
162C2×D4—611no—
163C2×D4—611no—
164C2×D4—611no—
165C22×C4—611no—
166C22×C4—611no—
167C22×C4C4×#692311yescharacteristic
168M16—41no—
169M16—1222no—
170M16—2441no—
171M16—2441no—
172M16—2441no—
173C2×C8—611no—
174C2×C8—611no—
175C2×C8—1221no—
176C2×C8—1221no—
177C2×C8—1221no—
178C2×C8—1221no—
179C2×C8—1221no—
180C2×C8—1221no—
181C2×C8—2441no—
182C2×C8C4⋊#692311yescharacteristic
183C2×C8C22⋊#692311yescharacteristic
184C4⋊C4—2441no—
185C22⋊C4—1222no—
186C42—2441no—
187C16—41no—
188C16—2441no—
189C16—2441no—
190C16—2441no—
191C23—611no—
192C23—611no—
193C23#1451983111yescharacteristic
194Q8—2441no—
195D4—2441no—
196D4—2441no—
197D4—2441no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—611no—
201C2×C4—611no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—2442no—
207C2×C4(C2×#6923)⋊C411yescharacteristic
208C2×C4C8×#692311yescharacteristic
209C8—21no—
210C8—21no—
211C8—611no—
212C8—611no—
213C8—1221no—
214C8—2442no—
215C22—21no—
216C22—41no—
217C22—1221no—
218C22—1221no—
219C22—2441no—
220C22—2441no—
221C22(C2×#6923)⋊C811yescharacteristic
222C4—21no—
223C4—1221no—
224C4—1221no—
225C4—4882no—
226C4#1684063911yescharacteristic
227C4#1684064511yescharacteristic
228C2—21no—
229C2—41no—
230C2—2441no—
231C2—2441no—
232C2#2146066011yescharacteristic
subgroupG/H
centerC4#16840639
commutatorC2×C4×C61C4×C8
FrattiniC2×M16C2×#6923
FittingC61×#349C4
socleC2×C61#1282
prime radicalC2×#11758222C2×C4
cosocleC2×#14519785C22
hypercenter#349#6923
hypocenterC61#7208
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
4. C2×#14519851C4semidirect
5. C22×#11758187C4semidirect
14. #16839544C4semidirect
16. C61×#349C4semidirect
129. #349#6923semidirect
133. C61#7208semidirect

Maximal subgroups

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

subgroupindex
#214620512
#214615752
#214474382
#720861