Finite Group Databasebeta

← #29593629

Subgroups — #29593629

Order 15616.

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

normal subgroups only

This group has 318 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#21458243C211yesmaximal, characteristic, complemented
2#21448043C211yesmaximal, characteristic, complemented
3#21447854C211yesmaximal, characteristic, complemented
4#21445175C211yesmaximal, characteristic, complemented
5#21443878C211yesmaximal, characteristic, complemented
6#21443775C211yesmaximal, characteristic, complemented
7C61×#1331C211yesmaximal, characteristic, complemented
8#16840477—21no—
9C2×#14519718—21no—
10#16840167C2211yescharacteristic
11#16840139C2211yescharacteristic
12#16840084—22no—
13#16840052—21no—
14#16839995—21no—
15#16839958—21no—
16C8×D244C2211yescharacteristic
17#16839799—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839564—22no—
20#16839562—21no—
21#16839505—21no—
22C4×D8×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#14519763—42no—
32#14519751—41no—
33#14519748—22no—
34C4×D244D411yescharacteristic
35#14519736—41no—
36#14519735—22no—
37#14519718—42no—
38C2×#11758185—21no—
39#14519711—21no—
40#14519711D412yes—
41#14519708—22no—
42C4⋊#92418D411yescharacteristic
43#14519699—41no—
44#14519698—22no—
45#14519689—21no—
46C2×D8×C61D411yescharacteristic
47C4×D4×C61—21no—
48C2×C16×C61—21no—
49#107×C61D411yescharacteristic
50C4⋊C8×C61—21no—
51#102×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×D4×C61—21no—
54C22×C4×C61—41no—
55C2×C22⋊D61—42no—
56C2×D244—41no—
57C2×D244—41no—
58C2×D244—41no—
59C2×D244D811yescharacteristic
60C2×C4×D61—21no—
61C2×Dic122—41no—
62D8×C61—21no—
63D8×C61—21no—
64C2×C8×C61—41no—
65C2×C8×C61C2×D411yescharacteristic
66C2×C8×C61C2×D411yescharacteristic
67C4⋊C4×C61—21no—
68C22⋊C4×C61—41no—
69C42×C61C2×D411yescharacteristic
70C22⋊Dic61—42no—
71#11758198—21no—
72#11758198—42no—
73C4⋊Dic61—22no—
74C4⋊Dic61—41no—
75C4⋊Dic61D811yescharacteristic
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—
86C23×C61—41no—
87C22×D61—21no—
88C22×D61—81no—
89D4×C61—41no—
90D4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—81no—
93C2×C4×C61—81no—
94C2×C4×C61#12011yescharacteristic
95C2×C4×C61C2×D811yescharacteristic
96C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
97C22⋊D61—162no—
98C2×Dic61—21no—
99C2×Dic61—42no—
100D244—21no—
101D244—21no—
102D244—81no—
103D244—81no—
104D244—81no—
105D244—81no—
106D244—161no—
107C4×D61—41no—
108C4×D61—41no—
109Dic122—161no—
110C8×C61—21no—
111C8×C61—81no—
112C8×C61#13511yescharacteristic
113C8×C61AGL(1,ℤ/8)11yescharacteristic
114#92418—41no—
115#12343—611nomaximal, Sylow
116C22×C61—81no—
117C22×C61—81no—
118C22×C61—81no—
119C22×C61#44711yescharacteristic
120C2×D61—41no—
121C2×D61—41no—
122C2×D61—41no—
123C2×D61—161no—
124C2×D61—161no—
125C2×D61—161no—
126C4×C61—21no—
127C4×C61—81no—
128C4×C61#44911yescharacteristic
129C4×C61#45411yescharacteristic
130C4×C61#50811yescharacteristic
131C4×C61#50911yescharacteristic
132Dic61—41no—
133Dic61—82no—
134#3341—611no—
135#2240—611no—
136#2206—611no—
137#1667—611no—
138#1365—611no—
139#1331D6111yescharacteristic, complemented
140D4⋊C16—611no—
141C2×C61—161no—
142C2×C61#162511yescharacteristic
143C2×C61#218611yescharacteristic
144C2×C61#219211yescharacteristic
145D61—81no—
146D61—321no—
147#555—1221no—
148C2×D16—1221no—
149#500—611no—
150#493—611no—
151#482—1222no—
152#476—1221no—
153#466—1221no—
154#459—1221no—
155C4×D8C2×D6111yescharacteristic
156C8×D4—611no—
157#427—1221no—
158C4⋊C16—611no—
159#357—1222no—
160#357—1221no—
161C4×C16C2×D6111yescharacteristic
162#335C2×D6111yescharacteristic
163#331—1221no—
164C61#1234311yescharacteristic, complemented, Sylow
165C2×D8—1221no—
166C2×D8—1221no—
167C2×D8—2441no—
168C2×D8D24411yescharacteristic
169C22×C8—1221no—
170C4⋊Q8—1221no—
171#127—1221no—
172#124—2442no—
173#121—1222no—
174#121—2441no—
175C4×D4—21no—
176C4×D4—611no—
177#117—1222no—
178#117—2441no—
179D16—2442no—
180C2×C16—21no—
181C2×C16—1221no—
182#107—612no—
183#107—1221no—
184#107D24411yescharacteristic
185#106—1222no—
186C4⋊C8—21no—
187C4⋊C8—611no—
188#102—21no—
189#102—1222no—
190#102—2441no—
191C22⋊C8—1221no—
192C4×C8C22×D6111yescharacteristic
193C2×Q8—2441no—
194C2×D4—21no—
195C2×D4—611no—
196C2×D4—2442no—
197C2×D4—2441no—
198C2×D4—2441no—
199C2×D4—2441no—
200C22×C4—41no—
201C22×C4—1221no—
202D8—21no—
203D8—21no—
204D8—4882no—
205D8—2442no—
206D8—2441no—
207D8—2441no—
208C2×C8—41no—
209C2×C8—1221no—
210C2×C8—2441no—
211C2×C8—2441no—
212C2×C8C2×D24411yescharacteristic
213C2×C8D4×D6111yescharacteristic
214C4⋊C4—21no—
215C4⋊C4—611no—
216C4⋊C4—1222no—
217C4⋊C4—2441no—
218C22⋊C4—41no—
219C22⋊C4—1221no—
220C22⋊C4—2442no—
221C22⋊C4—2442no—
222C42—2442no—
223C42D4×D6111yescharacteristic
224C16—41no—
225C16—2441no—
226C23—41no—
227C23—1221no—
228C23—4881no—
229Q8—9761no—
230D4—41no—
231D4—41no—
232D4—1221no—
233D4—1221no—
234D4—9761no—
235D4—9762no—
236D4—4881no—
237D4—4881no—
238D4—4881no—
239D4—4881no—
240C2×C4—41no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—1221no—
244C2×C4—2442no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4#1451974711yescharacteristic
248C2×C4D8×D6111yescharacteristic
249C2×C4#1451980411yescharacteristic
250C8—21no—
251C8—81no—
252C8—2441no—
253C8#1451979911yescharacteristic
254C8#1451980511yescharacteristic
255C22—81no—
256C22—81no—
257C22—81no—
258C22—9761no—
259C22—9761no—
260C22—9761no—
261C22—2441no—
262C22—2441no—
263C22—2441no—
264C22#1683989711yescharacteristic
265C4—21no—
266C4—81no—
267C4—4882no—
268C4—2441no—
269C4#1683990911yescharacteristic
270C4#1683993611yescharacteristic
271C4#1684019311yescharacteristic
272C4#1684019611yescharacteristic
273C2—161no—
274C2—19521no—
275C2—4881no—
276C2#2144491111yescharacteristic
277C2#2144774311yescharacteristic
278C2#2144777711yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1331C2
socleC22×C61#447
hypercenter#1331D61
hypocenterC61#12343
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
1. #21458243C2semidirect
2. #21448043C2semidirect
3. #21447854C2semidirect
4. #21445175C2semidirect
5. #21443878C2semidirect
6. #21443775C2semidirect
7. C61×#1331C2semidirect
139. #1331D61semidirect
164. C61#12343semidirect

Maximal subgroups

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

subgroupindex
#214582432
#214480432
#214478542
#214451752
#214438782
#214437752
C61×#13312
#1234361