Finite Group Databasebeta

← #29593478

Subgroups — #29593478

Order 15616.

368 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 71 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
1Q16×D244C211yesmaximal, characteristic
2#21448071C211yesmaximal, characteristic, complemented
3#21445181C211yesmaximal, characteristic
4#21443869C211yesmaximal, characteristic, complemented
5#21443783C211yesmaximal, characteristic, complemented
6#21443773C211yesmaximal, characteristic
7C61×#2209C211yesmaximal, characteristic, complemented
8C2×Q16×D61—21no—
9Q8×D244—21no—
10C2×#14519723—22no—
11#16840142C2211yescharacteristic
12#16840039—21no—
13#16840004—21no—
14#16839972—21no—
15#16839919—22no—
16C8×D244C2211yescharacteristic
17C4×#11758185C2211yescharacteristic
18#16839515C2211yescharacteristic
19#16839508—21no—
20C2×Q32×C61—21no—
21C61×#494C2211yescharacteristic
22C4×Q16×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#358—21no—
25C2×Q8×D61—22no—
26C2×Dic244—21no—
27C2×Dic244D412yes—
28C2×#11758202—22no—
29Q16×D61—42no—
30Q16×D61—42no—
31C2×C8×D61—21no—
32#14519777—21no—
33#14519777—41no—
34#14519757—22no—
35#14519757—42no—
36C4×D244—41no—
37C4×D244D411yescharacteristic
38#14519723—44no—
39C2×#11758185—21no—
40#14519710—41no—
41C4⋊#92418—21no—
42C4⋊#92418D411yescharacteristic
43#14519700—22no—
44#14519697—41no—
45#14519689—21no—
46C2×Q16×C61—21no—
47C2×Q16×C61—21no—
48C2×Q16×C61D411yescharacteristic
49C4⋊Q8×C61—21no—
50C4×Q8×C61—21no—
51Q32×C61—42no—
52C2×C16×C61—21no—
53#107×C61D411yescharacteristic
54#103×C61—21no—
55C4×C8×C61C2311yescharacteristic
56C2×Q8×C61—21no—
57C2×Q8×C61—41no—
58Q8×D61—44no—
59Q8×D61—82no—
60C2×D244D811yescharacteristic
61C2×C4×D61—21no—
62C2×C4×D61—42no—
63C2×Dic122—22no—
64C2×Dic122—42no—
65Q16×C61—21no—
66Q16×C61—42no—
67Q16×C61—41no—
68Q16×C61—41no—
69Q16×C61D812yes—
70C2×C8×C61C2×D411yescharacteristic
71C2×C8×C61C2×D411yescharacteristic
72C4⋊C4×C61—21no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C42×C61—41no—
77C42×C61C2×D411yescharacteristic
78#11758202—44no—
79#11758198—21no—
80#11758198—42no—
81C4⋊Dic61—42no—
82C4⋊Dic61—41no—
83C4⋊Dic61—41no—
84C4⋊Dic61D811yescharacteristic
85C2×#92418—21no—
86C2×#92418—41no—
87Dic244—42no—
88Dic244—41no—
89Dic244—41no—
90C8×D61—41no—
91C8×D61—41no—
92C16×C61—41no—
93#11758185—22no—
94C22×D61—21no—
95Q8×C61—22no—
96Q8×C61—41no—
97Q8×C61—81no—
98Q8×C61—81no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—81no—
102C2×C4×C61#12011yescharacteristic
103C2×C4×C61C2×D811yescharacteristic
104C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
105C2×Dic61—21no—
106C2×Dic61—42no—
107D244—21no—
108D244Q3212yescomplemented
109C4×D61—41no—
110C4×D61—41no—
111C4×D61—84no—
112Dic122—42no—
113Dic122—42no—
114Dic122—84no—
115C8×C61—21no—
116C8×C61C2×D811yescharacteristic
117C8×C61AGL(1,ℤ/8)11yescharacteristic
118#92418—41no—
119#92418—81no—
120#12322—611nomaximal, Sylow
121C22×C61#44711yescharacteristic
122C2×D61—22no—
123C2×D61—41no—
124C2×D61—41no—
125C4×C61—21no—
126C4×C61—42no—
127C4×C61—81no—
128C4×C61—161no—
129C4×C61#44711yescharacteristic
130C4×C61#45311yescharacteristic
131C4×C61C2×Q3211yescharacteristic
132C4×C61#51011yescharacteristic
133Dic61—41no—
134Dic61—82no—
135D4×Q16—611no—
136#2247—611no—
137#2209D6111yescharacteristic, complemented
138#1669—611no—
139#1362—611no—
140#1332—611no—
141D4⋊C16—611no—
142C2×C61#161911yescharacteristic
143C2×C61#218811yescharacteristic
144C2×C61#219511yescharacteristic
145D61—42no—
146C22×Q16—1221no—
147D4×Q8—1221no—
148C2×Q32—21no—
149C2×Q32—1222no—
150#494—611no—
151#494C2×D6111yescharacteristic
152#474—1221no—
153#467—1221no—
154#462—1221no—
155#451—1222no—
156C4×Q16C2×D6111yescharacteristic
157C8×D4—611no—
158C4⋊C16C2×D6111yescharacteristic
159#358—21no—
160C4×C16—611no—
161#335—611no—
162#332—1221no—
163C61#1232211yescharacteristic, complemented, Sylow
164C22×Q8—1222no—
165C2×Q16—21no—
166C2×Q16—21no—
167C2×Q16—612no—
168C2×Q16—1222no—
169C2×Q16—1221no—
170C2×Q16—2442no—
171C2×Q16—2442no—
172C2×Q16C22⋊D6111yescharacteristic
173C22×C8—1221no—
174C4⋊Q8—21no—
175C4⋊Q8—1221no—
176C4⋊Q8—2441no—
177C22⋊Q8—1222no—
178C22⋊Q8—2442no—
179C4×Q8—21no—
180C4×D4—611no—
181C4×D4—2441no—
182Q32—42no—
183Q32—2444no—
184C2×C16—21no—
185C2×C16—1221no—
186#107—2441no—
187#107C22⋊D6111yescharacteristic
188C4⋊C8—611no—
189C4⋊C8—1221no—
190#103—21no—
191#103—1222no—
192#102—2441no—
193C22⋊C8—1221no—
194C4×C8C22×D6111yescharacteristic
195C2×Q8—21no—
196C2×Q8—41no—
197C2×Q8—1222no—
198C2×Q8—4882no—
199C2×Q8—2442no—
200C2×Q8—2444no—
201C2×D4—611no—
202C22×C4—1221no—
203C22×C4—2442no—
204Q16—21no—
205Q16—42no—
206Q16—41no—
207Q16—41no—
208Q16—2442no—
209Q16—2444no—
210Q16—2441no—
211Q16—2441no—
212Q16#1175819912yes—
213C2×C8—1221no—
214C2×C8—2441no—
215C2×C8—2441no—
216C2×C8—2441no—
217C2×C8D4×D6111yescharacteristic
218C2×C8C2×C22⋊D6111yescharacteristic
219C4⋊C4—21no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—611no—
224C4⋊C4—2442no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C22⋊C4—1221no—
228C22⋊C4—2442no—
229C42—41no—
230C42D4×D6111yescharacteristic
231C16—41no—
232C16—1222no—
233C23—1221no—
234Q8—22no—
235Q8—41no—
236Q8—81no—
237Q8—81no—
238Q8—4884no—
239Q8—2442no—
240Q8—2442no—
241D4—612no—
242D4—1221no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—81no—
246C2×C4—1221no—
247C2×C4—4884no—
248C2×C4—2442no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4#1451974511yescharacteristic
252C2×C4D8×D6111yescharacteristic
253C2×C4#1451980111yescharacteristic
254C8—21no—
255C8—4881no—
256C8—2441no—
257C8C2×#1175819911yescharacteristic
258C8#1451980211yescharacteristic
259C22—1222no—
260C22—2441no—
261C22—2441no—
262C22#1683989411yescharacteristic
263C4—21no—
264C4—42no—
265C4—81no—
266C4—161no—
267C4—4882no—
268C4—2441no—
269C4#1683989511yescharacteristic
270C4#1683992811yescharacteristic
271C4Q32×D6111yescharacteristic
272C4#1684020411yescharacteristic
273C2—2442no—
274C2#2144487211yescharacteristic
275C2#2144775111yescharacteristic
276C2#2144779411yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2209C2
socleC22×C61#447
prime radicalC2×D244D8
hypercenter#2209D61
hypocenterC61#12322
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2209

Complements

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

NH ≅ G/Ntype
2. #21448071C2semidirect
4. #21443869C2semidirect
5. #21443783C2semidirect
7. C61×#2209C2semidirect
108. D244Q32semidirect
137. #2209D61semidirect
163. C61#12322semidirect

Maximal subgroups

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

subgroupindex
Q16×D2442
#214480712
#214451812
#214438692
#214437832
#214437732
C61×#22092
#1232261