Finite Group Databasebeta

← #29593615

Subgroups — #29593615

Order 15616.

306 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 65 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#21458251C211yesmaximal, characteristic, complemented
2#21448043C211yesmaximal, characteristic, complemented
3#21447859C211yesmaximal, characteristic, complemented
4#21445175C211yesmaximal, characteristic
5#21443875C211yesmaximal, characteristic, complemented
6#21443775C211yesmaximal, characteristic, complemented
7C61×#1332C211yesmaximal, characteristic, complemented
8#16840485—21no—
9C2×#14519720—21no—
10#16840167C2211yescharacteristic
11#16840139C2211yescharacteristic
12#16840102—22no—
13#16840047—21no—
14#16840000—21no—
15#16839958—21no—
16C8×D244C2211yescharacteristic
17#16839799—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839564—22no—
20#16839562—21no—
21#16839505—21no—
22C4×Q16×C61C2211yescharacteristic
23C4×C16×C61C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×D488—21no—
26C2×D488—21no—
27C2×D488—41no—
28C2×C8×D61—21no—
29#14519777—21no—
30#14519774—21no—
31#14519772—42no—
32#14519765—41no—
33#14519753—22no—
34C4×Dic122—41no—
35C4×D244D411yescharacteristic
36#14519735—22no—
37#14519720—42no—
38C2×#11758185—21no—
39#14519711—21no—
40#14519711D412yes—
41#14519708—22no—
42C4⋊#92418D411yescharacteristic
43#14519701—22no—
44#14519699—41no—
45#14519689—21no—
46C2×Q16×C61D411yescharacteristic
47C4×Q8×C61—21no—
48C2×C16×C61—21no—
49#107×C61D411yescharacteristic
50C4⋊C8×C61—21no—
51#103×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61—21no—
54C2×D244—41no—
55C2×D244—41no—
56C2×D244—41no—
57C2×D244D811yescharacteristic
58C2×C4×D61—21no—
59C2×Dic122—41no—
60Q16×C61—21no—
61Q16×C61—21no—
62C2×C8×C61—41no—
63C2×C8×C61C2×D411yescharacteristic
64C2×C8×C61C2×D411yescharacteristic
65C4⋊C4×C61—21no—
66C4⋊C4×C61—41no—
67C42×C61—41no—
68C42×C61C2×D411yescharacteristic
69#11758198—21no—
70#11758198—42no—
71#11758198—42no—
72C4⋊Dic61—22no—
73C4⋊Dic61—41no—
74C4⋊Dic61D811yescharacteristic
75#11758196—42no—
76C4×Dic61—42no—
77C2×#92418—21no—
78D488—42no—
79D488—41no—
80D488—41no—
81D488—82no—
82C8×D61—41no—
83C8×D61—41no—
84C16×C61—41no—
85#11758185—41no—
86C22×D61—21no—
87C22×D61—81no—
88Q8×C61—41no—
89Q8×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61#12011yescharacteristic
93C2×C4×C61C2×D811yescharacteristic
94C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
95C2×Dic61—21no—
96C2×Dic61—42no—
97D244—21no—
98D244—21no—
99D244—81no—
100D244—81no—
101D244—81no—
102D244—81no—
103D244—161no—
104C4×D61—41no—
105C4×D61—41no—
106Dic122—81no—
107Dic122—81no—
108C8×C61—21no—
109C8×C61—81no—
110C8×C61#13511yescharacteristic
111C8×C61AGL(1,ℤ/8)11yescharacteristic
112#92418—41no—
113#12341—611nomaximal, Sylow
114C22×C61#44711yescharacteristic
115C2×D61—41no—
116C2×D61—41no—
117C2×D61—41no—
118C2×D61—161no—
119C2×D61—161no—
120C2×D61—161no—
121C4×C61—21no—
122C4×C61—81no—
123C4×C61—81no—
124C4×C61#44911yescharacteristic
125C4×C61#45411yescharacteristic
126C4×C61#50811yescharacteristic
127C4×C61#50911yescharacteristic
128Dic61—41no—
129Dic61—82no—
130#3342—611no—
131#2240—611no—
132#2207—611no—
133#1667—611no—
134#1364—611no—
135#1332D6111yescharacteristic, complemented
136D4⋊C16—611no—
137C2×C61#162511yescharacteristic
138C2×C61#218611yescharacteristic
139C2×C61#219311yescharacteristic
140D61—81no—
141D61—321no—
142#556—1221no—
143C2×SD32—1221no—
144#500—611no—
145#493—611no—
146#485—1222no—
147#475—1221no—
148#467—1221no—
149#459—1221no—
150C4×Q16C2×D6111yescharacteristic
151C8×D4—611no—
152#427—1221no—
153C4⋊C16—611no—
154#357—1222no—
155#357—1221no—
156C4×C16C2×D6111yescharacteristic
157#335C2×D6111yescharacteristic
158#331—1221no—
159C61#1234111yescharacteristic, complemented, Sylow
160C2×Q16D24411yescharacteristic
161C2×D8—1221no—
162C2×D8—1221no—
163C2×D8—2441no—
164C22×C8—1221no—
165C4⋊Q8—1221no—
166#127—1221no—
167#126—2442no—
168#124—2441no—
169C22⋊Q8—1222no—
170C4×Q8—21no—
171C4×Q8—2441no—
172C4×D4—611no—
173#117—1222no—
174SD32—2442no—
175C2×C16—21no—
176C2×C16—1221no—
177#107—612no—
178#107—1221no—
179#107D24411yescharacteristic
180#106—1222no—
181C4⋊C8—21no—
182C4⋊C8—611no—
183#103—21no—
184#103—1222no—
185#102—2441no—
186C22⋊C8—1221no—
187C4×C8C22×D6111yescharacteristic
188C2×Q8—21no—
189C2×Q8—2441no—
190C2×D4—611no—
191C2×D4—2441no—
192C2×D4—2441no—
193C2×D4—2441no—
194C22×C4—1221no—
195Q16—21no—
196Q16—21no—
197D8—4882no—
198D8—2442no—
199D8—2441no—
200D8—2441no—
201C2×C8—41no—
202C2×C8—1221no—
203C2×C8—2441no—
204C2×C8—2441no—
205C2×C8C2×D24411yescharacteristic
206C2×C8D4×D6111yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—41no—
209C4⋊C4—611no—
210C4⋊C4—1222no—
211C4⋊C4—2442no—
212C4⋊C4—2441no—
213C22⋊C4—1221no—
214C22⋊C4—2442no—
215C22⋊C4—2442no—
216C42—41no—
217C42—2442no—
218C42D4×D6111yescharacteristic
219C16—41no—
220C16—2441no—
221C23—1221no—
222C23—4881no—
223Q8—41no—
224Q8—41no—
225Q8—4881no—
226Q8—4881no—
227D4—1221no—
228D4—1221no—
229D4—9761no—
230D4—4881no—
231D4—4881no—
232D4—4881no—
233D4—4881no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—1221no—
237C2×C4—2442no—
238C2×C4—2441no—
239C2×C4—2441no—
240C2×C4#1451974711yescharacteristic
241C2×C4D8×D6111yescharacteristic
242C2×C4#1451980411yescharacteristic
243C8—21no—
244C8—81no—
245C8—2441no—
246C8#1451979911yescharacteristic
247C8#1451980511yescharacteristic
248C22—9761no—
249C22—9761no—
250C22—9761no—
251C22—2441no—
252C22—2441no—
253C22—2441no—
254C22#1683989711yescharacteristic
255C4—21no—
256C4—81no—
257C4—81no—
258C4—4882no—
259C4—2441no—
260C4#1683990911yescharacteristic
261C4#1683993611yescharacteristic
262C4#1684019511yescharacteristic
263C4#1684019911yescharacteristic
264C2—19521no—
265C2—4881no—
266C2#2144491111yescharacteristic
267C2#2144774511yescharacteristic
268C2#2144778411yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1332C2
socleC22×C61#447
prime radical#21445175C2
hypercenter#1332D61
hypocenterC61#12341
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1332

Complements

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

NH ≅ G/Ntype
1. #21458251C2semidirect
2. #21448043C2semidirect
3. #21447859C2semidirect
5. #21443875C2semidirect
6. #21443775C2semidirect
7. C61×#1332C2semidirect
135. #1332D61semidirect
159. C61#12341semidirect

Maximal subgroups

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

subgroupindex
#214582512
#214480432
#214478592
#214451752
#214438752
#214437752
C61×#13322
#1234161