Finite Group Databasebeta

← #29593327

Subgroups — #29593327

Order 15616.

278 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 59 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#21457273C211yesmaximal, characteristic
2#21448022C211yesmaximal, characteristic
3#21448017C211yesmaximal, characteristic
4#21447324C211yesmaximal, characteristic
5#21443838C211yesmaximal, characteristic
6#21443838C211yesmaximal, characteristic
7C61×#1323C211yesmaximal, characteristic
8#16840374—21no—
9#16840070—21no—
10#16840070—21no—
11#16840020—21no—
12#16840003C2211yescharacteristic
13#16840003C2211yescharacteristic
14#16839973—21no—
15#16839973—21no—
16#16839805—21no—
17C2×#14519711C2211yescharacteristic
18#16839590—21no—
19#16839588—21no—
20#16839567—21no—
21#16839567—21no—
22#16839530—21no—
23#16839527C2211yescharacteristic
24C61×#424C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×C22⋊C16C2211yescharacteristic
27C2×Dic244—21no—
28C2×Dic244D411yescharacteristic
29C2×Dic244D411yescharacteristic
30C2×#11758194—21no—
31#14519777—21no—
32#14519770—41no—
33#14519770—41no—
34#14519769—21no—
35#14519767—41no—
36#14519767—41no—
37#14519756—21no—
38#14519756—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41C2×C4⋊Dic61—21no—
42#14519711—21no—
43#14519711—21no—
44#14519711D411yescharacteristic
45#14519711D411yescharacteristic
46#14519710—41no—
47#14519709—21no—
48#14519708—41no—
49#14519702—21no—
50#14519702—21no—
51#14519702—21no—
52#14519702—21no—
53C2×M16×C61D411yescharacteristic
54C22×C8×C61C2311yescharacteristic
55#117×C61D411yescharacteristic
56C2×C16×C61—21no—
57C2×C16×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C22×C4×C61C2×D411yescharacteristic
61C22×Dic61—41no—
62C2×Dic122—21no—
63C2×Dic122—21no—
64M16×C61—41no—
65C2×C8×C61—21no—
66C2×C8×C61—41no—
67C2×C8×C61C2×D411yescharacteristic
68C2×C8×C61C2×D411yescharacteristic
69C4⋊C4×C61D811yescharacteristic
70C4⋊C4×C61D811yescharacteristic
71C22⋊C4×C61—21no—
72C42×C61—21no—
73C22⋊Dic61—41no—
74C22⋊Dic61—41no—
75C4⋊Dic61—21no—
76C4⋊Dic61—21no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81#11758196—41no—
82#11758196—41no—
83#11758196—41no—
84#11758196—41no—
85#11758196—41no—
86#11758196—41no—
87C4×Dic61—41no—
88C4×Dic61—41no—
89#11758194—22no—
90#11758194—41no—
91C2×#92418—41no—
92Dic244—41no—
93Dic244—41no—
94Dic244—81no—
95C16×C61—41no—
96C16×C61—41no—
97C23×C61AGL(1,ℤ/8)11yescharacteristic
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61#12011yescharacteristic
103C2×C4×C61C2×D811yescharacteristic
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—81no—
109C2×Dic61—161no—
110Dic122—41no—
111Dic122—41no—
112Dic122—41no—
113Dic122—41no—
114C8×C61—21no—
115C8×C61—21no—
116C8×C61—41no—
117#92418—42no—
118#12296—611nomaximal, Sylow
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—21no—
122C22×C61#44711yescharacteristic
123C4×C61—21no—
124C4×C61—41no—
125C4×C61—41no—
126C4×C61#45611yescharacteristic
127C4×C61#45811yescharacteristic
128Dic61—81no—
129Dic61—81no—
130Dic61—81no—
131Dic61—81no—
132Dic61—161no—
133#3261—611no—
134#2236—611no—
135#2235—611no—
136#2089—611no—
137#1350—611no—
138#1350—611no—
139#1323D6111yescharacteristic
140C2×C61—41no—
141C2×C61#161011yescharacteristic
142C2×C61#219311yescharacteristic
143C2×C61#219511yescharacteristic
144#541—1221no—
145#479—1221no—
146#479—1221no—
147#470—1221no—
148#467—611no—
149#467—611no—
150#462—1221no—
151#462—1221no—
152#428—1221no—
153C2×#107—611no—
154#424C2×D6111yescharacteristic
155#367—1221no—
156#366—1221no—
157#358—1221no—
158#358—1221no—
159C22⋊C16C2×D6111yescharacteristic
160C22⋊C16C2×D6111yescharacteristic
161#343—1221no—
162#341—611no—
163C61#1229611yescharacteristic, complemented, Sylow
164C2×Q16—611no—
165C2×Q16—611no—
166C2×Q16—1221no—
167C2×M16—1221no—
168C2×M16D24411yescharacteristic
169C22×C8C22×D6111yescharacteristic
170C4⋊Q8—1221no—
171#126—2441no—
172#126—2441no—
173#125—1221no—
174#125—2441no—
175#125—2441no—
176C22⋊Q8—1221no—
177C22⋊Q8—1221no—
178C4×Q8—1221no—
179C4×Q8—1221no—
180#117D24411yescharacteristic
181C2×C4⋊C4—1221no—
182C2×C16—21no—
183C2×C16—21no—
184#107—611no—
185#107—611no—
186#107—1221no—
187#107—1221no—
188#107—2441no—
189#106—1221no—
190#106—2441no—
191C4⋊C8—21no—
192C4⋊C8—21no—
193#103—1221no—
194#103—1221no—
195#103—1221no—
196#103—1221no—
197C2×Q8—1221no—
198C2×Q8—1221no—
199C22×C4—2441no—
200C22×C4C2×D24411yescharacteristic
201Q16—4881no—
202Q16—2441no—
203Q16—2441no—
204M16—41no—
205M16—1222no—
206M16—2441no—
207C2×C8—21no—
208C2×C8—41no—
209C2×C8—2441no—
210C2×C8D4×D6111yescharacteristic
211C2×C8D4×D6111yescharacteristic
212C4⋊C4—1221no—
213C4⋊C4—1221no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C4⋊C4D48811yescharacteristic
225C4⋊C4D48811yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—2441no—
228C22⋊C4—2441no—
229C42—21no—
230C42—2441no—
231C42—2441no—
232C16—41no—
233C16—41no—
234C23#1451980511yescharacteristic
235Q8—2441no—
236Q8—2441no—
237Q8—2441no—
238Q8—2441no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—9761no—
244C2×C4—4881no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4#1451974711yescharacteristic
250C2×C4C2×D48811yescharacteristic
251C8—21no—
252C8—21no—
253C8—41no—
254C8—2442no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22#1683989811yescharacteristic
259C4—21no—
260C4—41no—
261C4—41no—
262C4—9761no—
263C4—4881no—
264C4—4881no—
265C4—4881no—
266C4—4881no—
267C4#1683994711yescharacteristic
268C4#1683995311yescharacteristic
269C2—41no—
270C2#2144482411yescharacteristic
271C2#2144778511yescharacteristic
272C2#2144779911yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1323C2
socleC22×C61#447
prime radicalC23×C61AGL(1,ℤ/8)
hypercenter#1323D61
hypocenterC61#12296
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #424 ◁ #1323

Complements

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

NH ≅ G/Ntype
163. C61#12296semidirect

Maximal subgroups

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

subgroupindex
#214572732
#214480222
#214480172
#214473242
#214438382
C61×#13232
#1229661