Finite Group Databasebeta

← #29589447

Subgroups — #29589447

Order 15616.

284 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 75 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#21454455C211yesmaximal, characteristic
2#21447631C211yesmaximal, characteristic, complemented
3#21443769C212yesmaximal, complemented
4#21443754C212yesmaximal
5C61×#2165C211yesmaximal, characteristic, complemented
6C2×#14519734C411yescharacteristic
7#16839824—21no—
8#16839824—21no—
9#16839821—21no—
10#16839821—21no—
11#16839785C411yescharacteristic
12#16839785C2211yescharacteristic
13#16839725C411yescharacteristic
14#16839725C2211yescharacteristic
15C4×#11758194C411yescharacteristic
16#16839583—21no—
17#16839544C2212yes—
18#16839540—21no—
19C4×M16×C61C2211yescharacteristic
20C61×#364—21no—
21C61×#349C2212yes—
22C61×#347—21no—
23C22×C4×D61C2×C411yescharacteristic
24C2×#11758194C2×C411yescharacteristic
25C2×#11758194C2×C411yescharacteristic
26#14519734—21no—
27#14519734—21no—
28#14519734—22no—
29C2×#11758196—21no—
30C2×#11758198—21no—
31C2×C4×Dic61C2×C411yescharacteristic
32#14519717—22no—
33#14519706—21no—
34#14519706—21no—
35#14519706—21no—
36#14519706—21no—
37#14519689—21no—
38#14519689—21no—
39#14519689—21no—
40#14519689—21no—
41#14519688—21no—
42C4×#92418—21no—
43C2×M16×C61C2×C411yescharacteristic
44C2×M16×C61C2311yescharacteristic
45C2×C42×C61C2×C411yescharacteristic
46M32×C61—22no—
47#97×C61D411yescharacteristic
48#97×C61D411yescharacteristic
49C4×C8×C61D411yescharacteristic
50C4×C8×C61D411yescharacteristic
51C23×D61M1611yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61C22×C411yescharacteristic
54C22×Dic61—21no—
55C22×Dic61M1611yescharacteristic
56C2×C4×D61—21no—
57C2×C4×D61—21no—
58C2×C4×D61—41no—
59C2×C4×D61—41no—
60M16×C61—41no—
61M16×C61—41no—
62C2×C8×C61C22⋊C411yescharacteristic
63C2×C8×C61C22⋊C411yescharacteristic
64C2×C8×C61C2×D411yescharacteristic
65C2×C8×C61C2×D411yescharacteristic
66C42×C61—21no—
67C42×C61C22⋊C411yescharacteristic
68C42×C61C22⋊C411yescharacteristic
69#11758198—22no—
70#11758198—22no—
71#11758196—22no—
72#11758196—22no—
73C4×Dic61—21no—
74C4×Dic61M1612yes—
75#11758194—41no—
76#11758194—41no—
77C2×#92418—21no—
78C2×#92418—21no—
79C16×C61—42no—
80#11758185—42no—
81C23×C61C2×M1611yescharacteristic
82C22×D61—21no—
83C22×D61—41no—
84C22×D61—81no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—81no—
90C2×C4×C61C2×C22⋊C411yescharacteristic
91C2×C4×C61C2×M1611yescharacteristic
92C2×Dic61—22no—
93C2×Dic61—21no—
94C2×Dic61—41no—
95C2×Dic61—81no—
96C4×D61—42no—
97C4×D61—41no—
98C4×D61—41no—
99C8×C61—21no—
100C8×C61—21no—
101C8×C61—21no—
102C8×C61—21no—
103#92418—41no—
104#92418—41no—
105#11522—611nomaximal, Sylow
106C22×C61—21no—
107C22×C61—41no—
108C22×C61#40711yescharacteristic
109C2×D61—42no—
110C2×D61—41no—
111C2×D61—82no—
112C4×C61—21no—
113C4×C61—41no—
114C4×C61—41no—
115C4×C61#41011yescharacteristic
116C4×C61#41311yescharacteristic
117Dic61—42no—
118Dic61—41no—
119#2921—611no—
120#2165—611no—
121#2165D6111yescharacteristic, complemented
122#1327—612no—
123#1320—612no—
124C2×C61—21no—
125C2×C61—41no—
126C2×C61#146411yescharacteristic
127D61—81no—
128C2×#117—611no—
129#433—1221no—
130#433—1221no—
131#433—1221no—
132#433—1221no—
133#423—611no—
134#423—611no—
135#407—611no—
136#407—611no—
137C4×M16—611no—
138C4×M16C2×D6111yescharacteristic
139#364—21no—
140#364—1221no—
141#349—612no—
142#349C2×D6112yes—
143#347—21no—
144#347—1221no—
145C61#1152211yescharacteristic, complemented, Sylow
146C23×C4—611no—
147C2×M16—611no—
148C2×M16—611no—
149C2×M16C4×D6111yescharacteristic
150C2×M16C22×D6111yescharacteristic
151#117—1222no—
152#117—1221no—
153#117—1221no—
154C2×C4⋊C4—1221no—
155C2×C22⋊C4—1221no—
156C2×C42—611no—
157C2×C42C4×D6111yescharacteristic
158M32—22no—
159M32—1222no—
160C4⋊C8—1221no—
161C4⋊C8—1221no—
162C4⋊C8—1221no—
163C4⋊C8—1221no—
164C22⋊C8—1221no—
165C22⋊C8—1221no—
166C22⋊C8—1221no—
167C22⋊C8—1221no—
168#97—1221no—
169#97D24411yescharacteristic
170#97C22⋊D6111yescharacteristic
171C4×C8—1221no—
172C4×C8D24411yescharacteristic
173C4×C8C22⋊D6111yescharacteristic
174C24—611no—
175C22×C4—21no—
176C22×C4—611no—
177C22×C4—1221no—
178C22×C4—1221no—
179C22×C4—1221no—
180C22×C4—2441no—
181C22×C4—2441no—
182C22×C4C2×C4×D6111yescharacteristic
183M16—41no—
184M16—41no—
185M16—2441no—
186M16—2441no—
187C2×C8—1221no—
188C2×C8—1221no—
189C2×C8#1175819811yescharacteristic
190C2×C8#1175819811yescharacteristic
191C2×C8C2×D24411yescharacteristic
192C2×C8C2×C22⋊D6111yescharacteristic
193C4⋊C4—1222no—
194C4⋊C4—1222no—
195C22⋊C4—1222no—
196C22⋊C4—1222no—
197C42—21no—
198C42—612no—
199C42—1221no—
200C42#1175819811yescharacteristic
201C42#1175819811yescharacteristic
202C16—42no—
203C16—2442no—
204C23—1221no—
205C23—4881no—
206C23—2441no—
207C23M16×D6111yescharacteristic
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—81no—
213C2×C4—1222no—
214C2×C4—1221no—
215C2×C4—4881no—
216C2×C4—2442no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4—2441no—
220C2×C4C2×#1175819811yescharacteristic
221C2×C4M16×D6111yescharacteristic
222C8—21no—
223C8—21no—
224C8—21no—
225C8—21no—
226C8—2441no—
227C8—2441no—
228C22—21no—
229C22—41no—
230C22—4882no—
231C22—2442no—
232C22—2441no—
233C22#1683972511yescharacteristic
234C4—21no—
235C4—41no—
236C4—41no—
237C4—2442no—
238C4—2441no—
239C4#1683973511yescharacteristic
240C4#1683974411yescharacteristic
241C2—21no—
242C2—41no—
243C2—4881no—
244C2#2144415111yescharacteristic
subgroupG/H
centerC4#16839735
commutatorC22×C4×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#2165C2
socleC2×C61#1464
prime radicalC23×D61M16
cosocleC2×M16×C61C23
hypercenter#2165D61
hypocenterC61#11522
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C42 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
2. #21447631C2semidirect
3. #21443769C2semidirect
5. C61×#2165C2semidirect
121. #2165D61semidirect
145. C61#11522semidirect

Maximal subgroups

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

subgroupindex
#214544552
#214476312
#214437692
#214437542
C61×#21652
#1152261