Finite Group Databasebeta

← #30605373

Subgroups — #30605373

Order 15616.

392 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 72 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#21462056C211yesmaximal, characteristic, complemented
2#21461703C211yesmaximal, characteristic, complemented
3#21460793C214yesmaximal, complemented
4#21455463C211yesmaximal, characteristic
5D61⋊M32—21no—
6D61⋊#108—21no—
7#16840748—21no—
8#16840659C2212yescomplemented
9#16840658—21no—
10#16840631C2212yescomplemented
11C2×#14519783C2211yescharacteristic
12#16840329—21no—
13#16840012C412yes—
14#16840012C2212yes—
15#16839995—21no—
16#16839995—21no—
17#16839800C411yescharacteristic
18#16839767—21no—
19C22×D8×C61C411yescharacteristic
20D61⋊M16—22no—
21#14519852—41no—
22#14519851—22no—
23D61⋊C16—41no—
24#14519848—41no—
25#14519847—41no—
26#14519838—41no—
27#14519837—41no—
28C2×#11758222D411yescharacteristic
29#14519783—41no—
30#14519783—41no—
31C2×#11758194D411yescharacteristic
32C2×#11758189C2×C411yescharacteristic
33C2×#11758189C2311yescharacteristic
34C2×C8×D61D411yescharacteristic
35C2×C8×D61D411yescharacteristic
36#14519773—41no—
37#14519764—41no—
38#14519748—22no—
39#14519748—22no—
40#14519746—41no—
41#14519746—41no—
42#14519736—21no—
43#14519711—21no—
44#14519709C2×C412yes—
45#14519698—22no—
46#14519698—22no—
47C22×D4×C61—21no—
48C2×D8×C61—21no—
49C2×D8×C61—41no—
50C2×D8×C61—41no—
51C2×D8×C61C2×C412yes—
52C22×C8×C61C2×C411yescharacteristic
53C24×C61—41no—
54C2×D4×C61—22no—
55C2×D4×C61—42no—
56C2×D4×C61—42no—
57C2×D4×C61—41no—
58C22×C4×C61C22⋊C411yescharacteristic
59C2×C22⋊D61—42no—
60C2×C22⋊D61—42no—
61C2×C22⋊D61D811yescharacteristic
62C2×C22⋊D61SD1611yescharacteristic
63#11758222—41no—
64#11758222—41no—
65C2×D244SD1611yescharacteristic
66C2×C4×D61C22⋊C411yescharacteristic
67C2×C4×D61C2×D411yescharacteristic
68C2×Dic122D811yescharacteristic
69#11758217—42no—
70#11758213—42no—
71D61⋊C8—42no—
72D8×C61—42no—
73D8×C61—41no—
74D8×C61—41no—
75C2×C8×C61—21no—
76C2×C8×C61—21no—
77C2×C8×C61C22⋊C411yescharacteristic
78C2×C8×C61C22×C411yescharacteristic
79C22⋊Dic61—41no—
80C22⋊Dic61—42no—
81C22⋊Dic61—42no—
82C4⋊Dic61—22no—
83C4×Dic61—41no—
84#11758194—41no—
85C2×#92418C22⋊C411yescharacteristic
86C2×#92418C2×D411yescharacteristic
87#11758189—41no—
88#11758189—41no—
89C8×D61—21no—
90C8×D61—21no—
91C8×D61—21no—
92C8×D61—21no—
93#11758187—42no—
94C23×C61—42no—
95C23×C61—82no—
96C23×C61—162no—
97C23×C61#10211yescharacteristic
98C22×D61#10211yescharacteristic
99C22×D61C2×SD1611yescharacteristic
100D4×C61—42no—
101D4×C61—42no—
102D4×C61—82no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61#10211yescharacteristic
106C2×C4×C61C2×C22⋊C411yescharacteristic
107C22⋊D61—41no—
108C22⋊D61—41no—
109C22⋊D61—162no—
110C22⋊D61—162no—
111C2×Dic61—42no—
112C2×Dic61#10211yescharacteristic
113C2×Dic61C2×D811yescharacteristic
114D244—41no—
115C4×D61—21no—
116C4×D61—21no—
117C4×D61—21no—
118C4×D61—21no—
119Dic122—41no—
120#92420—82no—
121C8×C61—21no—
122C8×C61#9911yescharacteristic
123C8×C61#9911yescharacteristic
124#92418—21no—
125#92418—21no—
126#11870—611nomaximal, Sylow
127C22×C61—21no—
128C22×C61—41no—
129C22×C61—82no—
130C22×C61—82no—
131C22×C61—82no—
132C22×C61—164no—
133C22×C61C2×#10211yescharacteristic
134C2×D61—21no—
135C2×D61—21no—
136C2×D61—41no—
137C2×D61—41no—
138C4×C61—21no—
139C4×C61C2×#9911yescharacteristic
140C4×C61#42111yescharacteristic
141Dic61—21no—
142Dic61—21no—
143Dic61—82no—
144#3058—611no—
145#2115—611no—
146#1813—611no—
147#1341—614no—
148C2×C61—21no—
149C2×C61—41no—
150C2×C61—162no—
151C2×C61#151911yescharacteristic
152D61—41no—
153D61—41no—
154C22×D8#692311yescharacteristic
155C2×#131—611no—
156#535—1221no—
157C2×M32—1221no—
158#469—612no—
159#469—612no—
160#466—1221no—
161#466—1221no—
162C2×#108—1221no—
163#427—611no—
164#418—1221no—
165#413—1221no—
166#349—612no—
167#349—1221no—
168#338—612no—
169C61#1187011yescharacteristic, complemented, Sylow
170C2×#41—611no—
171C22×D4—21no—
172C2×D8—21no—
173C2×D8—41no—
174C2×D8—41no—
175C2×D8C2×#692312yes—
176#131—2441no—
177#131—2441no—
178C2×M16—611no—
179C2×M16—611no—
180C2×M16—611no—
181C2×M16—1222no—
182C22×C8—611no—
183C22×C8—611no—
184C22×C8C2×#692311yescharacteristic
185#127—2441no—
186#124—2441no—
187#121—1222no—
188#121—1222no—
189#120—2441no—
190#120—2441no—
191#117—1221no—
192M32—1222no—
193M32—2441no—
194C2×C16—2441no—
195#108—2441no—
196#108—2441no—
197#107—1221no—
198#106—612no—
199#102—1222no—
200#102—1222no—
201#101—2441no—
202#100—2441no—
203C24—41no—
204#41—2441no—
205#41—2441no—
206C2×Q8—611no—
207C2×D4—22no—
208C2×D4—42no—
209C2×D4—42no—
210C2×D4—41no—
211C2×D4—611no—
212C2×D4—611no—
213C2×D4—611no—
214C2×D4—2442no—
215C2×D4—2442no—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4C22⋊#692311yescharacteristic
219D8—42no—
220D8—41no—
221D8—41no—
222M16—2441no—
223M16—2441no—
224M16—2441no—
225M16—2442no—
226M16—2442no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—611no—
230C2×C8—611no—
231C2×C8—1221no—
232C2×C8—1221no—
233C2×C8—1221no—
234C2×C8—1221no—
235C2×C8—2442no—
236C2×C8C22⋊#692311yescharacteristic
237C2×C8C22×#692311yescharacteristic
238C4⋊C4—1222no—
239C22⋊C4—2442no—
240C22⋊C4—2442no—
241C22⋊C4—2441no—
242C42—2441no—
243C16—2442no—
244C23—42no—
245C23—82no—
246C23—162no—
247C23—611no—
248C23—611no—
249C23#1451983911yescharacteristic
250Q8—2441no—
251D4—42no—
252D4—42no—
253D4—82no—
254D4—9762no—
255D4—9762no—
256D4—2441no—
257D4—2441no—
258D4—2441no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—611no—
262C2×C4—611no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—2442no—
268C2×C4#1451983911yescharacteristic
269C2×C4C2×C22⋊#692311yescharacteristic
270C8—21no—
271C8—1221no—
272C8—1221no—
273C8—4882no—
274C8#1451983511yescharacteristic
275C8#1451983511yescharacteristic
276C22—21no—
277C22—41no—
278C22—82no—
279C22—82no—
280C22—82no—
281C22—164no—
282C22—1221no—
283C22—1221no—
284C22—2441no—
285C22—2441no—
286C22C2×#1451983911yescharacteristic
287C4—21no—
288C4—1221no—
289C4—1221no—
290C4—4882no—
291C4C2×#1451983511yescharacteristic
292C4#1684076011yescharacteristic
293C2—21no—
294C2—41no—
295C2—162no—
296C2—2441no—
297C2—2441no—
298C2#2146125511yescharacteristic
subgroupG/H
centerC2#21461255
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC22×D8×C61C4
socleC2×C61#1519
prime radical#21455463C2
cosocleC2×#11758189C23
hypercenterC22×D8#6923
hypocenterC61#11870
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. #21462056C2semidirect
2. #21461703C2semidirect
3. #21460793C2semidirect
8. #16840659C22semidirect
10. #16840631C22semidirect
169. C61#11870semidirect

Maximal subgroups

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

subgroupindex
#214620562
#214617032
#214607932
#214554632
#1187061