Finite Group Databasebeta

← #29593834

Subgroups — #29593834

Order 15616.

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

normal subgroups only

This group has 344 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#21448048C211yesmaximal, characteristic, complemented
3#21445215C211yesmaximal, characteristic
4#21443869C211yesmaximal, characteristic, complemented
5#21443783C211yesmaximal, characteristic, complemented
6#21443773C211yesmaximal, characteristic
7C61×#2227C211yesmaximal, characteristic, complemented
8C2×Q16×D61—21no—
9Q8×D244—21no—
10#16840142C2211yescharacteristic
11#16840049—21no—
12#16840004—21no—
13#16839972—21no—
14#16839919—22no—
15C8×D244C2211yescharacteristic
16#16839565—22no—
17C4×#11758185C2211yescharacteristic
18#16839515C2211yescharacteristic
19#16839511—21no—
20C61×#500C2211yescharacteristic
21C4×Q16×C61C2211yescharacteristic
22C61×#366—21no—
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
38C2×#11758185—21no—
39#14519708—41no—
40C4⋊#92418—21no—
41C4⋊#92418D411yescharacteristic
42#14519700—22no—
43#14519697—41no—
44#14519689—21no—
45C2×Q16×C61D411yescharacteristic
46C4⋊Q8×C61—21no—
47C4×Q8×C61—21no—
48C2×C16×C61—21no—
49#107×C61—21no—
50#107×C61—21no—
51#107×C61D411yescharacteristic
52#103×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—21no—
55C2×Q8×C61—41no—
56Q8×D61—44no—
57Q8×D61—82no—
58C2×D244D811yescharacteristic
59C2×C4×D61—21no—
60C2×C4×D61—42no—
61C2×Dic122—22no—
62C2×Dic122—42no—
63Q16×C61—21no—
64Q16×C61SD1612yes—
65C2×C8×C61C2×D411yescharacteristic
66C2×C8×C61C2×D411yescharacteristic
67C4⋊C4×C61—21no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C42×C61—41no—
72C42×C61C2×D411yescharacteristic
73#11758202—44no—
74#11758198—21no—
75#11758198—42no—
76C4⋊Dic61—42no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79C4⋊Dic61D811yescharacteristic
80C2×#92418—21no—
81C2×#92418—41no—
82Dic244—42no—
83Dic244—41no—
84Dic244—41no—
85C8×D61—41no—
86C8×D61—41no—
87C16×C61—41no—
88#11758185—41no—
89C22×D61—21no—
90Q8×C61—22no—
91Q8×C61—41no—
92Q8×C61—161no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—81no—
96C2×C4×C61#12011yescharacteristic
97C2×C4×C61C2×D811yescharacteristic
98C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
99C2×Dic61—21no—
100C2×Dic61—42no—
101D244—21no—
102D244Q3212yes—
103C4×D61—41no—
104C4×D61—41no—
105C4×D61—84no—
106Dic122—42no—
107Dic122—42no—
108Dic122—84no—
109C8×C61—21no—
110C8×C61C2×SD1611yescharacteristic
111C8×C61AGL(1,ℤ/8)11yescharacteristic
112#92418—41no—
113#92418—81no—
114#12374—611nomaximal, Sylow
115C22×C61#44711yescharacteristic
116C2×D61—22no—
117C2×D61—41no—
118C2×D61—41no—
119C4×C61—21no—
120C4×C61—42no—
121C4×C61—81no—
122C4×C61—161no—
123C4×C61#45011yescharacteristic
124C4×C61#45511yescharacteristic
125C4×C61C2×Q3211yescharacteristic
126C4×C61#51011yescharacteristic
127Dic61—41no—
128Dic61—82no—
129D4×Q16—611no—
130#2241—611no—
131#2227D6111yescharacteristic, complemented
132#1675—611no—
133#1362—611no—
134#1332—611no—
135D4⋊C16—611no—
136C2×C61#163911yescharacteristic
137C2×C61#218811yescharacteristic
138C2×C61#219311yescharacteristic
139D61—42no—
140C22×Q16—1221no—
141D4×Q8—1221no—
142#500C2×D6111yescharacteristic
143#494—611no—
144#476—1221no—
145#467—1221no—
146#462—1221no—
147#451—1222no—
148C4×Q16C2×D6111yescharacteristic
149C8×D4—611no—
150#366—21no—
151C4⋊C16C2×D6111yescharacteristic
152#358—21no—
153#358—1222no—
154C4×C16—611no—
155#335—611no—
156#333—1221no—
157C61#1237411yescharacteristic, complemented, Sylow
158C22×Q8—1222no—
159C2×Q16—612no—
160C2×Q16—1222no—
161C2×Q16—1221no—
162C2×Q16—2442no—
163C2×Q16—2442no—
164C2×Q16C22⋊D6111yescharacteristic
165C22×C8—1221no—
166C4⋊Q8—21no—
167C4⋊Q8—1221no—
168C4⋊Q8—2441no—
169C22⋊Q8—1222no—
170C22⋊Q8—2442no—
171C4×Q8—21no—
172C4×D4—611no—
173C4×D4—2441no—
174C2×C16—21no—
175C2×C16—1221no—
176#107—21no—
177#107—21no—
178#107C22⋊D6111yescharacteristic
179#106—2441no—
180C4⋊C8—611no—
181C4⋊C8—1221no—
182#103—21no—
183#103—1222no—
184#102—2441no—
185C22⋊C8—1221no—
186C4×C8C22×D6111yescharacteristic
187C2×Q8—21no—
188C2×Q8—41no—
189C2×Q8—1222no—
190C2×Q8—4882no—
191C2×Q8—2442no—
192C2×Q8—2444no—
193C2×D4—611no—
194C22×C4—1221no—
195C22×C4—2442no—
196Q16—21no—
197Q16—2442no—
198Q16—2444no—
199Q16—2441no—
200Q16—2441no—
201Q16#1175820112yes—
202C2×C8—1221no—
203C2×C8—2441no—
204C2×C8—2441no—
205C2×C8—2441no—
206C2×C8D4×D6111yescharacteristic
207C2×C8C2×C22⋊D6111yescharacteristic
208C4⋊C4—21no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—611no—
213C4⋊C4—2442no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C22⋊C4—1221no—
217C22⋊C4—2442no—
218C42—41no—
219C42D4×D6111yescharacteristic
220C16—41no—
221C16—2441no—
222C23—1221no—
223Q8—22no—
224Q8—41no—
225Q8—161no—
226Q8—4884no—
227Q8—2442no—
228Q8—2442no—
229D4—612no—
230D4—1221no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—81no—
234C2×C4—1221no—
235C2×C4—4884no—
236C2×C4—2442no—
237C2×C4—2441no—
238C2×C4—2441no—
239C2×C4#1451974511yescharacteristic
240C2×C4D8×D6111yescharacteristic
241C2×C4#1451980111yescharacteristic
242C8—21no—
243C8—4881no—
244C8—2441no—
245C8C2×#1175820111yescharacteristic
246C8#1451980211yescharacteristic
247C22—1222no—
248C22—2441no—
249C22—2441no—
250C22#1683989411yescharacteristic
251C4—21no—
252C4—42no—
253C4—81no—
254C4—161no—
255C4—4882no—
256C4—2441no—
257C4#1683991211yescharacteristic
258C4#1683993811yescharacteristic
259C4Q32×D6111yescharacteristic
260C4#1684020411yescharacteristic
261C2—2442no—
262C2#2144499711yescharacteristic
263C2#2144775111yescharacteristic
264C2#2144778011yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2227C2
socleC22×C61#447
prime radicalC2×D244D8
hypercenter#2227D61
hypocenterC61#12374
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2227

Complements

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

NH ≅ G/Ntype
2. #21448048C2semidirect
4. #21443869C2semidirect
5. #21443783C2semidirect
7. C61×#2227C2semidirect
131. #2227D61semidirect
157. C61#12374semidirect

Maximal subgroups

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

subgroupindex
Q16×D2442
#214480482
#214452152
#214438692
#214437832
#214437732
C61×#22272
#1237461