Finite Group Databasebeta

← #29593810

Subgroups — #29593810

Order 15616.

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

normal subgroups only

This group has 350 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#21448047C211yesmaximal, characteristic, complemented
3#21447961C211yesmaximal, characteristic, complemented
4#21445209C211yesmaximal, characteristic
5#21443867C211yesmaximal, characteristic, complemented
6#21443775C211yesmaximal, characteristic
7C61×#1332C211yesmaximal, characteristic, complemented
8C2×Q16×D61—21no—
9Q8×D244—21no—
10#16840167C2211yescharacteristic
11#16840142C2211yescharacteristic
12#16840004—21no—
13#16839972—21no—
14#16839968—21no—
15#16839919—22no—
16C8×D244C2211yescharacteristic
17#16839589—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839567—22no—
20#16839566—21no—
21#16839509—21no—
22C4×Q16×C61C2211yescharacteristic
23C4×C16×C61C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×Q8×D61—22no—
26C2×Dic244—21no—
27C2×Dic244D412yes—
28C2×#11758202—22no—
29Q16×D61—42no—
30Q16×D61—42no—
31C2×#11758190—41no—
32C2×C8×D61—21no—
33#14519777—21no—
34#14519777—21no—
35#14519777—41no—
36#14519757—22no—
37#14519757—42no—
38C4×D244—41no—
39C4×D244D411yescharacteristic
40C2×#11758185—21no—
41#14519711—21no—
42#14519711—21no—
43C4⋊#92418D411yescharacteristic
44#14519702—41no—
45#14519700—22no—
46#14519689—21no—
47C2×Q16×C61D411yescharacteristic
48C4×Q8×C61—21no—
49C2×C16×C61—21no—
50#107×C61D411yescharacteristic
51C4⋊C8×C61—21no—
52#103×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—21no—
55Q8×D61—44no—
56Q8×D61—82no—
57C2×D244D811yescharacteristic
58C2×C4×D61—21no—
59C2×C4×D61—42no—
60C2×Dic122—22no—
61C2×Dic122—42no—
62C2×Dic122—41no—
63Q16×C61—21no—
64Q16×C61SD1612yescomplemented
65C2×C8×C61—41no—
66C2×C8×C61C2×D411yescharacteristic
67C2×C8×C61C2×D411yescharacteristic
68C4⋊C4×C61—21no—
69C4⋊C4×C61—41no—
70C42×C61—41no—
71C42×C61C2×D411yescharacteristic
72#11758202—44no—
73#11758198—21no—
74#11758198—42no—
75C4⋊Dic61—42no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61D811yescharacteristic
81C2×#92418—21no—
82Dic244—42no—
83Dic244—41no—
84Dic244—41no—
85#11758190—82no—
86C8×D61—41no—
87C8×D61—41no—
88C16×C61—41no—
89#11758185—41no—
90C22×D61—21no—
91Q8×C61—22no—
92Q8×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61#12011yescharacteristic
96C2×C4×C61C2×D811yescharacteristic
97C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
98C2×Dic61—21no—
99C2×Dic61—42no—
100C2×Dic61—81no—
101D244—21no—
102D244SD3212yes—
103C4×D61—41no—
104C4×D61—41no—
105C4×D61—84no—
106Dic122—42no—
107Dic122—42no—
108Dic122—84no—
109Dic122—81no—
110Dic122—81no—
111C8×C61—21no—
112C8×C61—81no—
113C8×C61C2×SD1611yescharacteristic
114C8×C61AGL(1,ℤ/8)11yescharacteristic
115#92418—41no—
116#12370—611nomaximal, Sylow
117C22×C61#44711yescharacteristic
118C2×D61—22no—
119C2×D61—41no—
120C2×D61—41no—
121C4×C61—21no—
122C4×C61—42no—
123C4×C61—81no—
124C4×C61#45011yescharacteristic
125C4×C61#45511yescharacteristic
126C4×C61C2×SD3211yescharacteristic
127C4×C61#51011yescharacteristic
128Dic61—41no—
129Dic61—82no—
130Dic61—161no—
131D4×Q16—611no—
132#2241—611no—
133#2225—611no—
134#1673—611no—
135#1362—611no—
136#1332D6111yescharacteristic, complemented
137D4⋊C16—611no—
138C2×C61#163911yescharacteristic
139C2×C61#218511yescharacteristic
140C2×C61#219511yescharacteristic
141D61—42no—
142C22×Q16—1221no—
143D4×Q8—1221no—
144#500—611no—
145#494—611no—
146#467—1221no—
147#462—1221no—
148#461—1221no—
149#451—1222no—
150C4×Q16C2×D6111yescharacteristic
151C8×D4—611no—
152#367—1221no—
153C4⋊C16—611no—
154#358—1222no—
155#358—1221no—
156C4×C16C2×D6111yescharacteristic
157#335C2×D6111yescharacteristic
158#332—1221no—
159C61#1237011yescharacteristic, complemented, Sylow
160C22×Q8—1222no—
161C2×Q16—612no—
162C2×Q16—1222no—
163C2×Q16—1221no—
164C2×Q16—2442no—
165C2×Q16—2442no—
166C2×Q16D24411yescharacteristic
167C2×SD16—2441no—
168C22×C8—1221no—
169C4⋊Q8—1221no—
170C4⋊Q8—1221no—
171C4⋊Q8—2441no—
172C22⋊Q8—1222no—
173C22⋊Q8—2442no—
174C4×Q8—21no—
175C4×D4—611no—
176C4×D4—2441no—
177C2×C16—21no—
178C2×C16—1221no—
179#107—1221no—
180#107—1221no—
181#107D24411yescharacteristic
182C4⋊C8—21no—
183C4⋊C8—611no—
184#103—21no—
185#103—1222no—
186#103—2441no—
187C22⋊C8—1221no—
188C4×C8C22×D6111yescharacteristic
189C2×Q8—21no—
190C2×Q8—1222no—
191C2×Q8—4882no—
192C2×Q8—2442no—
193C2×Q8—2444no—
194C2×Q8—2441no—
195C2×D4—611no—
196C22×C4—1221no—
197C22×C4—2442no—
198Q16—21no—
199Q16—2442no—
200Q16—2444no—
201Q16—2441no—
202Q16—2441no—
203Q16#1175819012yescomplemented
204SD16—4882no—
205C2×C8—41no—
206C2×C8—1221no—
207C2×C8—2441no—
208C2×C8—2441no—
209C2×C8C2×D24411yescharacteristic
210C2×C8D4×D6111yescharacteristic
211C4⋊C4—21no—
212C4⋊C4—41no—
213C4⋊C4—611no—
214C4⋊C4—2442no—
215C4⋊C4—2441no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C22⋊C4—1221no—
220C22⋊C4—2442no—
221C42—41no—
222C42D4×D6111yescharacteristic
223C16—41no—
224C16—2441no—
225C23—1221no—
226Q8—22no—
227Q8—41no—
228Q8—4884no—
229Q8—4881no—
230Q8—4881no—
231Q8—2442no—
232Q8—2442no—
233D4—612no—
234D4—1221no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—1221no—
238C2×C4—4884no—
239C2×C4—4881no—
240C2×C4—2442no—
241C2×C4—2441no—
242C2×C4—2441no—
243C2×C4#1451974711yescharacteristic
244C2×C4D8×D6111yescharacteristic
245C2×C4#1451980411yescharacteristic
246C8—21no—
247C8—81no—
248C8—2441no—
249C8C2×#1175819011yescharacteristic
250C8#1451980511yescharacteristic
251C22—1222no—
252C22—2441no—
253C22—2441no—
254C22#1683989711yescharacteristic
255C4—21no—
256C4—42no—
257C4—81no—
258C4—9761no—
259C4—4882no—
260C4—2441no—
261C4#1683991511yescharacteristic
262C4#1683994111yescharacteristic
263C4SD32×D6111yescharacteristic
264C4#1684020411yescharacteristic
265C2—2442no—
266C2#2144500111yescharacteristic
267C2#2144773711yescharacteristic
268C2#2144779811yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1332C2
socleC22×C61#447
prime radicalC2×D244D8
hypercenter#1332D61
hypocenterC61#12370
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
2. #21448047C2semidirect
3. #21447961C2semidirect
5. #21443867C2semidirect
7. C61×#1332C2semidirect
64. Q16×C61SD16semidirect
136. #1332D61semidirect
159. C61#12370semidirect
203. Q16#11758190semidirect

Maximal subgroups

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

subgroupindex
Q16×D2442
#214480472
#214479612
#214452092
#214438672
#214437752
C61×#13322
#1237061