Finite Group Databasebeta

← #29594025

Subgroups — #29594025

Order 15616.

274 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 61 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#21458392C211yesmaximal, characteristic
2#21448106C211yesmaximal, characteristic, complemented
3#21447962C211yesmaximal, characteristic, complemented
4#21445343C211yesmaximal, characteristic
5#21443788C211yesmaximal, characteristic, complemented
6#21443776C211yesmaximal, characteristic
7C61×#1363C211yesmaximal, characteristic, complemented
8#16840450—21no—
9#16840167C2211yescharacteristic
10#16840105—21no—
11#16840099—21no—
12#16840066—21no—
13#16840053—21no—
14#16840021—21no—
15C4×Dic244C2211yescharacteristic
16#16839841C2211yescharacteristic
17#16839801—21no—
18#16839590—21no—
19#16839589—21no—
20#16839587—21no—
21#16839567—21no—
22#16839538C2211yescharacteristic
23#16839510—21no—
24C61×#499C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#334C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28C2×#11758189—21no—
29#14519777—21no—
30#14519772—41no—
31#14519768—41no—
32#14519762—41no—
33#14519757—21no—
34#14519757—21no—
35C4×Dic122—21no—
36C4×D244D411yescharacteristic
37#14519735—21no—
38#14519735—41no—
39C4⋊C4×D61—21no—
40C2×#11758185—21no—
41#14519711—21no—
42#14519711—21no—
43#14519711D411yescharacteristic
44#14519710—21no—
45#14519709—41no—
46#14519708—21no—
47C4⋊#92418D411yescharacteristic
48#14519702—21no—
49#14519700—21no—
50#14519700—21no—
51#14519699—41no—
52#14519689—21no—
53#125×C61—21no—
54C2×C16×C61—21no—
55#107×C61D411yescharacteristic
56#107×C61D411yescharacteristic
57#106×C61—21no—
58C4⋊C8×C61—21no—
59C4×C8×C61C2311yescharacteristic
60C2×D244D811yescharacteristic
61C2×C4×D61—21no—
62C2×C4×D61—41no—
63C2×Dic122—21no—
64C2×Dic122—41no—
65C2×C8×C61—41no—
66C2×C8×C61C2×D411yescharacteristic
67C2×C8×C61C2×D411yescharacteristic
68C4⋊C4×C61—21no—
69C4⋊C4×C61—21no—
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C42×C61C2×D411yescharacteristic
73#11758198—21no—
74#11758198—41no—
75#11758198—41no—
76#11758198—41no—
77C4⋊Dic61—21no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C4⋊Dic61D811yescharacteristic
83#11758196—41no—
84#11758196—41no—
85C4×Dic61—41no—
86C4×Dic61—41no—
87C2×#92418—21no—
88Dic244—21no—
89Dic244—21no—
90#11758189—41no—
91#11758189—41no—
92C16×C61—41no—
93#11758185—22no—
94C22×D61—21no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61#12011yescharacteristic
98C2×C4×C61C2×D811yescharacteristic
99C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
100C2×Dic61—21no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61—81no—
104D244—41no—
105C4×D61—41no—
106C4×D61—41no—
107C4×D61—82no—
108Dic122—41no—
109Dic122—41no—
110Dic122—161no—
111C8×C61—21no—
112C8×C61—81no—
113C8×C61#13511yescharacteristic
114C8×C61#13711yescharacteristic
115#92418—41no—
116#12401—611nomaximal, Sylow
117C22×C61#44711yescharacteristic
118C2×D61—41no—
119C2×D61—41no—
120C2×D61—41no—
121C4×C61—21no—
122C4×C61—21no—
123C4×C61—81no—
124C4×C61—81no—
125C4×C61#45211yescharacteristic
126C4×C61#45611yescharacteristic
127Dic61—41no—
128Dic61—81no—
129Dic61—81no—
130Dic61—161no—
131#3352—611no—
132#2255—611no—
133#2225—611no—
134#1695—611no—
135#1363D6111yescharacteristic, complemented
136#1334—611no—
137#1330—611no—
138C2×C61#164711yescharacteristic
139C2×C61#219111yescharacteristic
140C2×C61#219311yescharacteristic
141D61—81no—
142#552—1221no—
143#500—611no—
144#499C2×D6111yescharacteristic
145#485—1221no—
146#484—1221no—
147#479—1221no—
148#476—1221no—
149#470—1221no—
150C4×Q16—611no—
151#436—611no—
152#428—1221no—
153#367—1221no—
154#367—1221no—
155#366—1221no—
156C4⋊C16C2×D6111yescharacteristic
157#358—1221no—
158#346—611no—
159#334C2×D6111yescharacteristic
160#333—1221no—
161C61#1240111yescharacteristic, complemented, Sylow
162C2×Q16—611no—
163C2×M16—1221no—
164C4⋊Q8—1221no—
165#126—2441no—
166#125—21no—
167#125—2441no—
168#123—2441no—
169C22⋊Q8—1221no—
170C22⋊Q8—1221no—
171C4×Q8—1221no—
172C4×D4—611no—
173#117—1221no—
174#117—2441no—
175C2×C4⋊C4—1221no—
176C2×C16—21no—
177C2×C16—1221no—
178#107—611no—
179#107—1221no—
180#107—1221no—
181#107—1221no—
182#107D24411yescharacteristic
183#107D24411yescharacteristic
184#106—21no—
185#106—1221no—
186#106—2441no—
187C4⋊C8—21no—
188C4⋊C8—611no—
189#103—1221no—
190#103—1221no—
191#103—1221no—
192#102—2441no—
193C22⋊C8—1221no—
194C4×C8C22×D6111yescharacteristic
195C2×Q8—1221no—
196C2×Q8—2441no—
197C2×D4—611no—
198C22×C4—1221no—
199C22×C4—2441no—
200Q16—1221no—
201Q16—1221no—
202M16—2441no—
203M16—2441no—
204C2×C8—41no—
205C2×C8—1221no—
206C2×C8C2×D24411yescharacteristic
207C2×C8D4×D6111yescharacteristic
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—611no—
213C4⋊C4—1221no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C22⋊C4—1221no—
221C22⋊C4—2441no—
222C22⋊C4—2441no—
223C22⋊C4—2441no—
224C42—2441no—
225C42—2441no—
226C42D4×D6111yescharacteristic
227C16—41no—
228C16—1222no—
229C23—1221no—
230Q8—9761no—
231Q8—2441no—
232Q8—2441no—
233D4—2441no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—1221no—
237C2×C4—4882no—
238C2×C4—4881no—
239C2×C4—2441no—
240C2×C4—2441no—
241C2×C4—2441no—
242C2×C4—2441no—
243C2×C4#1451974711yescharacteristic
244C2×C4D8×D6111yescharacteristic
245C2×C4#1451980411yescharacteristic
246C8—21no—
247C8—81no—
248C8—2441no—
249C8#1451979811yescharacteristic
250C8#1451980911yescharacteristic
251C22—2441no—
252C22—2441no—
253C22—2441no—
254C22#1683989711yescharacteristic
255C4—21no—
256C4—21no—
257C4—81no—
258C4—81no—
259C4—9761no—
260C4—4881no—
261C4—4881no—
262C4—2441no—
263C4#1683992711yescharacteristic
264C4#1683994711yescharacteristic
265C2—4881no—
266C2#2144505511yescharacteristic
267C2#2144777111yescharacteristic
268C2#2144778411yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1363C2
socleC22×C61#447
prime radicalC2×D244D8
hypercenter#1363D61
hypocenterC61#12401
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1363

Complements

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

NH ≅ G/Ntype
2. #21448106C2semidirect
3. #21447962C2semidirect
5. #21443788C2semidirect
7. C61×#1363C2semidirect
135. #1363D61semidirect
161. C61#12401semidirect

Maximal subgroups

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

subgroupindex
#214583922
#214481062
#214479622
#214453432
#214437882
#214437762
C61×#13632
#1240161