Finite Group Databasebeta

← #30605374

Subgroups — #30605374

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#21460794C214yesmaximal, complemented
4#21455468C211yesmaximal, characteristic
5D61⋊M32—21no—
6D61⋊#108—21no—
7#16840748—21no—
8#16840659C2212yescomplemented
9#16840658—21no—
10#16840631C2212yescomplemented
11C22×D488C411yescharacteristic
12C2×#14519783C2211yescharacteristic
13#16840331—21no—
14#16840016C412yes—
15#16840016C2212yes—
16#16839999—21no—
17#16839999—21no—
18#16839766—21no—
19C61×#427C411yescharacteristic
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
29C22×D244—21no—
30C2×D488—21no—
31C2×D488—41no—
32C2×D488—41no—
33C2×D488C2×C412yes—
34#14519783—41no—
35#14519783—41no—
36C2×#11758194D411yescharacteristic
37C2×#11758189C2×C411yescharacteristic
38C2×#11758189C2311yescharacteristic
39C2×C8×D61D411yescharacteristic
40C2×C8×D61D411yescharacteristic
41#14519774—41no—
42#14519765—41no—
43#14519752—22no—
44#14519752—22no—
45#14519747—41no—
46#14519747—41no—
47#14519697—22no—
48#14519697—22no—
49C22×C8×C61C2×C411yescharacteristic
50#117×C61—21no—
51#107×C61—21no—
52#106×C61C2×C412yes—
53C23×D61—41no—
54C22×C4×C61C22⋊C411yescharacteristic
55C2×C22⋊D61D811yescharacteristic
56C2×C22⋊D61SD1611yescharacteristic
57#11758222—41no—
58#11758222—41no—
59C2×D244—22no—
60C2×D244—42no—
61C2×D244—42no—
62C2×D244—41no—
63C2×D244—42no—
64C2×D244—42no—
65C2×D244SD1611yescharacteristic
66C2×C4×D61C22⋊C411yescharacteristic
67C2×C4×D61C2×D411yescharacteristic
68C2×Dic122D811yescharacteristic
69#11758217—42no—
70#11758213—42no—
71D61⋊C8—42no—
72C2×C8×C61—21no—
73C2×C8×C61—21no—
74C2×C8×C61C22⋊C411yescharacteristic
75C2×C8×C61C22×C411yescharacteristic
76C4⋊C4×C61—22no—
77C22⋊C4×C61—41no—
78C42×C61—41no—
79#11758198—42no—
80#11758198—42no—
81#11758194—41no—
82C2×#92418C22⋊C411yescharacteristic
83C2×#92418C2×D411yescharacteristic
84D488—42no—
85D488—41no—
86D488—41no—
87#11758189—41no—
88#11758189—41no—
89C8×D61—21no—
90C8×D61—21no—
91C8×D61—21no—
92C8×D61—21no—
93#11758187—42no—
94C23×C61#10211yescharacteristic
95C22×D61—42no—
96C22×D61—82no—
97C22×D61—162no—
98C22×D61#10211yescharacteristic
99C22×D61C2×SD1611yescharacteristic
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—42no—
103C2×C4×C61#10211yescharacteristic
104C2×C4×C61C2×C22⋊C411yescharacteristic
105C22⋊D61—41no—
106C22⋊D61—41no—
107C2×Dic61#10211yescharacteristic
108C2×Dic61C2×D811yescharacteristic
109D244—41no—
110D244—42no—
111D244—42no—
112D244—82no—
113D244—162no—
114D244—162no—
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×C61C2×#10211yescharacteristic
130C2×D61—21no—
131C2×D61—21no—
132C2×D61—41no—
133C2×D61—41no—
134C2×D61—82no—
135C2×D61—82no—
136C2×D61—82no—
137C2×D61—164no—
138C4×C61—21no—
139C4×C61—82no—
140C4×C61C2×#9911yescharacteristic
141C4×C61#42111yescharacteristic
142Dic61—21no—
143Dic61—21no—
144#3058—611no—
145#2115—611no—
146#1813—611no—
147#1341—614no—
148C2×C61—21no—
149C2×C61—41no—
150C2×C61#151911yescharacteristic
151D61—41no—
152D61—41no—
153D61—162no—
154C22×D8—611no—
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#692311yescharacteristic
164#418—1221no—
165#413—1221no—
166#349—612no—
167#349—1221no—
168#338—612no—
169C61#1187011yescharacteristic, complemented, Sylow
170C2×#41—611no—
171C22×D4—1221no—
172C2×D8—612no—
173C2×D8—1221no—
174C2×D8—2441no—
175C2×D8—2441no—
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—21no—
192M32—1222no—
193M32—2441no—
194C2×C16—2441no—
195#108—2441no—
196#108—2441no—
197#107—21no—
198#106C2×#692312yes—
199#102—1222no—
200#102—1222no—
201#101—2441no—
202#100—2441no—
203C24—2441no—
204#41—2441no—
205#41—2441no—
206C2×Q8—611no—
207C2×D4—611no—
208C2×D4—611no—
209C2×D4—611no—
210C2×D4—1222no—
211C2×D4—2442no—
212C2×D4—2442no—
213C2×D4—2442no—
214C2×D4—2442no—
215C2×D4—2441no—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4C22⋊#692311yescharacteristic
219D8—2442no—
220D8—2441no—
221D8—2441no—
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—22no—
239C22⋊C4—41no—
240C22⋊C4—2442no—
241C22⋊C4—2442no—
242C42—41no—
243C16—2442no—
244C23—611no—
245C23—611no—
246C23—9762no—
247C23—4882no—
248C23—2442no—
249C23#1451983911yescharacteristic
250Q8—2441no—
251D4—9762no—
252D4—9762no—
253D4—4882no—
254D4—2441no—
255D4—2441no—
256D4—2441no—
257D4—2442no—
258D4—2442no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—611no—
263C2×C4—611no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4#1451983911yescharacteristic
269C2×C4C2×C22⋊#692311yescharacteristic
270C8—21no—
271C8—1221no—
272C8—1221no—
273C8—4882no—
274C8#1451983611yescharacteristic
275C8#1451983611yescharacteristic
276C22—21no—
277C22—41no—
278C22—1221no—
279C22—1221no—
280C22—9764no—
281C22—4882no—
282C22—4882no—
283C22—4882no—
284C22—2441no—
285C22—2441no—
286C22C2×#1451983911yescharacteristic
287C4—21no—
288C4—82no—
289C4—1221no—
290C4—1221no—
291C4C2×#1451983611yescharacteristic
292C4#1684076111yescharacteristic
293C2—21no—
294C2—41no—
295C2—9762no—
296C2—2441no—
297C2—2441no—
298C2#2146125611yescharacteristic
subgroupG/H
centerC2#21461256
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#427C4
socleC2×C61#1519
prime radical#21455468C2
cosocleC2×#11758189C23
hypercenter#427#6923
hypocenterC61#11870
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ #427

Complements

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

NH ≅ G/Ntype
1. #21462056C2semidirect
2. #21461703C2semidirect
3. #21460794C2semidirect
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
#214607942
#214554682
#1187061