Finite Group Databasebeta

← #29593623

Subgroups — #29593623

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#21458241C211yesmaximal, characteristic, complemented
2#21447851C211yesmaximal, characteristic, complemented
3#21445171C211yesmaximal, characteristic, complemented
4#21443877C211yesmaximal, characteristic, complemented
5#21443781C211yesmaximal, characteristic, complemented
6#21443775C211yesmaximal, characteristic, complemented
7C61×#2240C211yesmaximal, characteristic, complemented
8#16840478—21no—
9C2×#14519718—21no—
10#16840089—22no—
11#16840049—21no—
12#16839999—21no—
13#16839954—21no—
14C4×D488C2211yescharacteristic
15C8×D244C2211yescharacteristic
16#16839799—21no—
17C4⋊#11758185C2211yescharacteristic
18#16839563—21no—
19#16839515C2211yescharacteristic
20#16839506—21no—
21C61×#500C2211yescharacteristic
22C61×#493C2211yescharacteristic
23C61×#357—22no—
24C4×C16×C61C2211yescharacteristic
25C2×D488D411yescharacteristic
26C2×#11758199—41no—
27C2×C8×D61—21no—
28#14519766—42no—
29#14519752—22no—
30#14519752—41no—
31C4×D244—21no—
32C4×D244D411yescharacteristic
33#14519735—22no—
34#14519735—41no—
35#14519718—42no—
36C2×#11758185—21no—
37#14519711D411yescharacteristic
38#14519708—22no—
39C4⋊#92418—21no—
40C4⋊#92418D411yescharacteristic
41#14519699—21no—
42#14519698—41no—
43#14519697—22no—
44#14519689—21no—
45C2×D8×C61—21no—
46C2×D8×C61—21no—
47C4⋊Q8×C61—21no—
48#127×C61—21no—
49C2×C16×C61—21no—
50#107×C61—21no—
51#107×C61D412yes—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61—41no—
54C2×D4×C61—41no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C2×D244—21no—
58C2×D244—42no—
59C2×D244D811yescharacteristic
60C2×C4×D61—21no—
61C2×C4×D61—41no—
62D8×C61—42no—
63D8×C61—41no—
64D8×C61—41no—
65C2×C8×C61C2×D411yescharacteristic
66C2×C8×C61C2×D411yescharacteristic
67C4⋊C4×C61—22no—
68C4⋊C4×C61—41no—
69C42×C61C2×D411yescharacteristic
70#11758199—82no—
71#11758198—21no—
72#11758198—42no—
73#11758198—42no—
74#11758198—41no—
75C4⋊Dic61—21no—
76C4⋊Dic61D811yescharacteristic
77C4×Dic61—42no—
78C2×#92418—21no—
79C2×#92418—41no—
80D488—21no—
81D488—21no—
82C8×D61—41no—
83C8×D61—41no—
84C16×C61—41no—
85#11758185—41no—
86C23×C61—81no—
87C22×D61—21no—
88C22×D61—41no—
89Q8×C61—161no—
90D4×C61—81no—
91D4×C61—81no—
92D4×C61—81no—
93D4×C61—81no—
94D4×C61—161no—
95C2×C4×C61—42no—
96C2×C4×C61#12011yescharacteristic
97C2×C4×C61C2×D811yescharacteristic
98C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
99C2×Dic61—21no—
100C2×Dic61—41no—
101D244—21no—
102D244—21no—
103D244—41no—
104D244—41no—
105D244—162no—
106C4×D61—41no—
107C4×D61—41no—
108C4×D61—81no—
109C4×D61—81no—
110C8×C61—21no—
111C8×C61#13511yescharacteristic
112C8×C61AGL(1,ℤ/8)11yescharacteristic
113#92418—41no—
114#92418—81no—
115#12343—611nomaximal, Sylow
116C22×C61—161no—
117C22×C61—161no—
118C22×C61—161no—
119C22×C61#44711yescharacteristic
120C2×D61—41no—
121C2×D61—41no—
122C2×D61—41no—
123C2×D61—81no—
124C2×D61—81no—
125C2×D61—81no—
126C4×C61—21no—
127C4×C61—82no—
128C4×C61#44911yescharacteristic
129C4×C61#45411yescharacteristic
130C4×C61#50811yescharacteristic
131C4×C61#50911yescharacteristic
132Dic61—41no—
133Dic61—81no—
134#3341—611no—
135#2240D6111yescharacteristic, complemented
136#2206—611no—
137#1667—611no—
138#1365—611no—
139#1331—611no—
140D4⋊C16—611no—
141C2×C61—321no—
142C2×C61#162511yescharacteristic
143C2×C61#218611yescharacteristic
144C2×C61#219211yescharacteristic
145D61—81no—
146D61—161no—
147#555—1221no—
148C2×D16—1221no—
149#500C2×D6111yescharacteristic
150#493C2×D6111yescharacteristic
151#482—1222no—
152#476—1221no—
153#466—1221no—
154#459—1221no—
155C4×D8—611no—
156C8×D4—611no—
157#427—1221no—
158C4⋊C16—611no—
159#357—22no—
160#357—1221no—
161C4×C16C2×D6111yescharacteristic
162#335—611no—
163#331—1221no—
164C61#1234311yescharacteristic, complemented, Sylow
165C2×D8—21no—
166C2×D8—21no—
167C2×D8—611no—
168C2×D8—2441no—
169C22×C8—1221no—
170C4⋊Q8—21no—
171#127—21no—
172#124—2442no—
173#121—1222no—
174#121—2441no—
175C4×D4—611no—
176C4×D4—1221no—
177#117—1222no—
178#117—2441no—
179D16—2442no—
180C2×C16—21no—
181C2×C16—1221no—
182#107—21no—
183#107—611no—
184#107C22⋊D6112yes—
185#106—1222no—
186C4⋊C8—611no—
187C4⋊C8—1221no—
188#102—1222no—
189#102—1221no—
190#102—2441no—
191C22⋊C8—1221no—
192C4×C8C22×D6111yescharacteristic
193C2×Q8—41no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4—41no—
197C2×D4—611no—
198C2×D4—1221no—
199C2×D4—2442no—
200C22×C4—1221no—
201C22×C4—2441no—
202D8—42no—
203D8—41no—
204D8—41no—
205D8—1221no—
206D8—1221no—
207D8—4882no—
208C2×C8—1221no—
209C2×C8—2441no—
210C2×C8—2441no—
211C2×C8—2441no—
212C2×C8D4×D6111yescharacteristic
213C2×C8C2×C22⋊D6111yescharacteristic
214C4⋊C4—22no—
215C4⋊C4—41no—
216C4⋊C4—611no—
217C4⋊C4—1221no—
218C22⋊C4—1221no—
219C22⋊C4—2442no—
220C22⋊C4—2442no—
221C22⋊C4—2441no—
222C42—2442no—
223C42D4×D6111yescharacteristic
224C16—41no—
225C16—2441no—
226C23—81no—
227C23—1221no—
228C23—2441no—
229Q8—161no—
230D4—81no—
231D4—81no—
232D4—81no—
233D4—81no—
234D4—161no—
235D4—1221no—
236D4—1221no—
237D4—9762no—
238D4—2441no—
239D4—2441no—
240C2×C4—42no—
241C2×C4—1221no—
242C2×C4—4881no—
243C2×C4—4881no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4#1451974511yescharacteristic
248C2×C4D8×D6111yescharacteristic
249C2×C4#1451980111yescharacteristic
250C8—21no—
251C8—4881no—
252C8—2441no—
253C8#1451979811yescharacteristic
254C8#1451980411yescharacteristic
255C22—161no—
256C22—161no—
257C22—161no—
258C22—4881no—
259C22—4881no—
260C22—4881no—
261C22—2441no—
262C22—2441no—
263C22—2441no—
264C22#1683989411yescharacteristic
265C4—21no—
266C4—82no—
267C4—4881no—
268C4—2441no—
269C4#1683990611yescharacteristic
270C4#1683993411yescharacteristic
271C4#1684019311yescharacteristic
272C4#1684019911yescharacteristic
273C2—321no—
274C2—9761no—
275C2—4881no—
276C2#2144490511yescharacteristic
277C2#2144774111yescharacteristic
278C2#2144777511yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2240C2
socleC22×C61#447
hypercenter#2240D61
hypocenterC61#12343
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
1. #21458241C2semidirect
2. #21447851C2semidirect
3. #21445171C2semidirect
4. #21443877C2semidirect
5. #21443781C2semidirect
6. #21443775C2semidirect
7. C61×#2240C2semidirect
135. #2240D61semidirect
164. C61#12343semidirect

Maximal subgroups

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

subgroupindex
#214582412
#214478512
#214451712
#214438772
#214437812
#214437752
C61×#22402
#1234361