Finite Group Databasebeta

← #29594119

Subgroups — #29594119

Order 15616.

272 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 63 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#21458789C211yesmaximal, characteristic
2#21447968C211yesmaximal, characteristic
3#21445334C211yesmaximal, characteristic
4#21443871C211yesmaximal, characteristic
5#21443802C211yesmaximal, characteristic
6#21443790C211yesmaximal, characteristic
7C61×#2255C211yesmaximal, characteristic
8#16840489—21no—
9#16840169—21no—
10#16840068—21no—
11#16840066—21no—
12#16840056—21no—
13#16839969—21no—
14#16839892C2211yescharacteristic
15#16839868—21no—
16C4×Dic244C2211yescharacteristic
17#16839587—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839565—21no—
20#16839513C2211yescharacteristic
21#16839508—21no—
22C61×#500C2211yescharacteristic
23C61×#499C2211yescharacteristic
24C61×#367—21no—
25C61×#366—21no—
26C61×#346C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28C2×#11758202—41no—
29#14519776—21no—
30#14519776—41no—
31#14519768—21no—
32#14519767—41no—
33#14519767—41no—
34C4×Dic122—21no—
35C4×Dic122D411yescharacteristic
36#14519742—21no—
37#14519742—21no—
38#14519742—41no—
39C2×#11758185—21no—
40#14519711D411yescharacteristic
41#14519710—21no—
42#14519708—21no—
43C4⋊#92418—21no—
44C4⋊#92418D411yescharacteristic
45#14519706—21no—
46#14519702—21no—
47#14519701—41no—
48#14519700—21no—
49#14519700—21no—
50#14519687—21no—
51C4⋊Q8×C61—21no—
52#125×C61—21no—
53C2×C16×C61—21no—
54#107×C61—21no—
55#107×C61—21no—
56#107×C61D411yescharacteristic
57#107×C61D411yescharacteristic
58#106×C61—21no—
59C4×C8×C61C2311yescharacteristic
60C2×Q8×C61—41no—
61C2×Dic122—21no—
62C2×Dic122—41no—
63C2×Dic122D811yescharacteristic
64C2×C8×C61C2×D411yescharacteristic
65C2×C8×C61C2×D411yescharacteristic
66C4⋊C4×C61—21no—
67C4⋊C4×C61—21no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C42×C61C2×D411yescharacteristic
73#11758202—82no—
74C4⋊Dic61—21no—
75C4⋊Dic61—41no—
76C4⋊Dic61D811yescharacteristic
77#11758196—21no—
78#11758196—41no—
79#11758196—41no—
80#11758196—41no—
81#11758196—41no—
82#11758196—41no—
83C4×Dic61—21no—
84C4×Dic61—41no—
85C4×Dic61—41no—
86C4×Dic61—41no—
87C2×#92418—21no—
88C2×#92418—41no—
89Dic244—21no—
90Dic244Q1612yescomplemented
91C16×C61—22no—
92#11758185—41no—
93Q8×C61—81no—
94Q8×C61—81no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—81no—
98C2×C4×C61#12011yescharacteristic
99C2×C4×C61C2×D811yescharacteristic
100C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105Dic122—22no—
106Dic122—41no—
107Dic122—41no—
108Dic122—82no—
109C8×C61—21no—
110C8×C61C2×Q1611yescharacteristic
111C8×C61#13711yescharacteristic
112#92418—41no—
113#92418—81no—
114#12415—611nomaximal, Sylow
115C22×C61#44711yescharacteristic
116C4×C61—21no—
117C4×C61—21no—
118C4×C61—81no—
119C4×C61—81no—
120C4×C61—161no—
121C4×C61#45111yescharacteristic
122C4×C61#45611yescharacteristic
123Dic61—42no—
124Dic61—41no—
125Dic61—41no—
126Dic61—81no—
127#3390—611no—
128#2255D6111yescharacteristic
129#2227—611no—
130#1694—611no—
131#1363—611no—
132#1338—611no—
133#1334—611no—
134C2×C61#164911yescharacteristic
135C2×C61#219011yescharacteristic
136C2×C61#219511yescharacteristic
137#557—1221no—
138#501—1221no—
139#500C2×D6111yescharacteristic
140#499C2×D6111yescharacteristic
141#479—1221no—
142#479—1221no—
143#477—1221no—
144#462—1221no—
145#446—611no—
146#441—1221no—
147C4×Q16—611no—
148#367—21no—
149#366—21no—
150#366—1221no—
151C4⋊C16—611no—
152#358—1221no—
153#346C2×D6111yescharacteristic
154#334—611no—
155#332—1221no—
156C61#1241511yescharacteristic, complemented, Sylow
157C2×Q16—611no—
158C2×Q16—2441no—
159C4⋊Q8—21no—
160C4⋊Q8—1221no—
161C4⋊Q8—2441no—
162#125—21no—
163#125—1221no—
164#125—2441no—
165#125—2441no—
166C4×Q8—611no—
167C4×Q8—1221no—
168C4×Q8—1221no—
169C4×Q8—1221no—
170C4×Q8—2441no—
171C2×C16—21no—
172C2×C16—1221no—
173#107—21no—
174#107—21no—
175#107—611no—
176#107—1221no—
177#107C22⋊D6111yescharacteristic
178#107C22⋊D6111yescharacteristic
179#106—21no—
180#106—1221no—
181C4⋊C8—611no—
182C4⋊C8—1221no—
183C4⋊C8—1221no—
184#103—1221no—
185#103—1221no—
186#103—1221no—
187#103—2441no—
188#97—1221no—
189C4×C8C22×D6111yescharacteristic
190C2×Q8—41no—
191C2×Q8—611no—
192C2×Q8—1221no—
193C2×Q8—2441no—
194Q16—612no—
195Q16—1221no—
196Q16—4882no—
197C2×C8—1221no—
198C2×C8—2441no—
199C2×C8D4×D6111yescharacteristic
200C2×C8C2×C22⋊D6111yescharacteristic
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—611no—
208C4⋊C4—1221no—
209C4⋊C4—1221no—
210C4⋊C4—2441no—
211C4⋊C4—2441no—
212C4⋊C4—2441no—
213C4⋊C4—2441no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C42—1221no—
217C42—2441no—
218C42—2441no—
219C42—2441no—
220C42D4×D6111yescharacteristic
221C16—22no—
222C16—2441no—
223Q8—81no—
224Q8—81no—
225Q8—1222no—
226Q8—4882no—
227Q8—2441no—
228Q8—2441no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—81no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—2441no—
235C2×C4—2441no—
236C2×C4#1451974511yescharacteristic
237C2×C4D8×D6111yescharacteristic
238C2×C4#1451980111yescharacteristic
239C8—21no—
240C8—4881no—
241C8—2441no—
242C8Q16×D6111yescharacteristic
243C8#1451980911yescharacteristic
244C22#1683989411yescharacteristic
245C4—21no—
246C4—21no—
247C4—81no—
248C4—81no—
249C4—161no—
250C4—4881no—
251C4—2441no—
252C4—2441no—
253C4—2442no—
254C4#1683991611yescharacteristic
255C4#1683994411yescharacteristic
256C2#2144506511yescharacteristic
257C2#2144776311yescharacteristic
258C2#2144779411yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2255C2
socle, prime radicalC22×C61#447
hypercenter#2255D61
hypocenterC61#12415
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2255

Complements

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

NH ≅ G/Ntype
90. Dic244Q16semidirect
156. C61#12415semidirect

Maximal subgroups

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

subgroupindex
#214587892
#214479682
#214453342
#214438712
#214438022
#214437902
C61×#22552
#1241561