Finite Group Databasebeta

← #29594105

Subgroups — #29594105

Order 15616.

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

normal subgroups only

This group has 266 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#21447958C211yesmaximal, characteristic
3#21445344C211yesmaximal, 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#16840054—21no—
14#16839892C2211yescharacteristic
15#16839868—21no—
16C4×Dic244C2211yescharacteristic
17#16839589—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839565—21no—
20#16839513C2211yescharacteristic
21#16839511—21no—
22C61×#500C2211yescharacteristic
23C61×#499C2211yescharacteristic
24C61×#367—21no—
25C61×#366—21no—
26C61×#346C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28#14519776—21no—
29#14519776—41no—
30#14519768—21no—
31#14519767—41no—
32#14519767—41no—
33C4×Dic122—21no—
34C4×Dic122D411yescharacteristic
35#14519742—21no—
36#14519742—21no—
37#14519742—41no—
38C2×#11758185—21no—
39#14519711D411yescharacteristic
40#14519710—21no—
41#14519710—41no—
42#14519708—21no—
43C4⋊#92418—21no—
44C4⋊#92418D411yescharacteristic
45#14519706—21no—
46#14519702—21no—
47#14519700—21no—
48#14519700—21no—
49#14519700—41no—
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
73C4⋊Dic61—21no—
74C4⋊Dic61—41no—
75C4⋊Dic61D811yescharacteristic
76#11758196—21no—
77#11758196—41no—
78#11758196—41no—
79#11758196—41no—
80#11758196—41no—
81#11758196—41no—
82C4×Dic61—21no—
83C4×Dic61—41no—
84C4×Dic61—41no—
85C4×Dic61—41no—
86C2×#92418—21no—
87C2×#92418—41no—
88Dic244—21no—
89Dic244Q1612yes—
90C16×C61—22no—
91#11758185—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—21no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103Dic122—22no—
104Dic122—41no—
105Dic122—41no—
106Dic122—82no—
107C8×C61—21no—
108C8×C61C2×Q1611yescharacteristic
109C8×C61#13711yescharacteristic
110#92418—41no—
111#92418—81no—
112#12413—611nomaximal, Sylow
113C22×C61#44711yescharacteristic
114C4×C61—21no—
115C4×C61—21no—
116C4×C61—81no—
117C4×C61—81no—
118C4×C61—161no—
119C4×C61#45111yescharacteristic
120C4×C61#45611yescharacteristic
121Dic61—42no—
122Dic61—41no—
123Dic61—41no—
124Dic61—81no—
125#3390—611no—
126#2255D6111yescharacteristic
127#2225—611no—
128#1696—611no—
129#1363—611no—
130#1338—611no—
131#1334—611no—
132C2×C61#164911yescharacteristic
133C2×C61#219111yescharacteristic
134C2×C61#219311yescharacteristic
135#557—1221no—
136#501—1221no—
137#500C2×D6111yescharacteristic
138#499C2×D6111yescharacteristic
139#479—1221no—
140#479—1221no—
141#477—1221no—
142#477—1221no—
143#446—611no—
144#441—1221no—
145C4×Q16—611no—
146#367—21no—
147#367—1221no—
148#366—21no—
149C4⋊C16—611no—
150#358—1221no—
151#346C2×D6111yescharacteristic
152#334—611no—
153#333—1221no—
154C61#1241311yescharacteristic, complemented, Sylow
155C2×Q16—611no—
156C4⋊Q8—21no—
157C4⋊Q8—1221no—
158C4⋊Q8—2441no—
159#125—21no—
160#125—1221no—
161#125—2441no—
162#125—2441no—
163C4×Q8—611no—
164C4×Q8—1221no—
165C4×Q8—1221no—
166C4×Q8—1221no—
167C4×Q8—2441no—
168C2×C16—21no—
169C2×C16—1221no—
170#107—21no—
171#107—21no—
172#107—611no—
173#107—1221no—
174#107—2441no—
175#107C22⋊D6111yescharacteristic
176#107C22⋊D6111yescharacteristic
177#106—21no—
178#106—1221no—
179C4⋊C8—611no—
180C4⋊C8—1221no—
181C4⋊C8—1221no—
182#103—1221no—
183#103—1221no—
184#103—1221no—
185#103—2441no—
186#97—1221no—
187C4×C8C22×D6111yescharacteristic
188C2×Q8—41no—
189C2×Q8—611no—
190C2×Q8—1221no—
191C2×Q8—2441no—
192Q16—612no—
193Q16—1221no—
194C2×C8—1221no—
195C2×C8—2441no—
196C2×C8D4×D6111yescharacteristic
197C2×C8C2×C22⋊D6111yescharacteristic
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—611no—
205C4⋊C4—1221no—
206C4⋊C4—1221no—
207C4⋊C4—2441no—
208C4⋊C4—2441no—
209C4⋊C4—2441no—
210C4⋊C4—2441no—
211C4⋊C4—2441no—
212C4⋊C4—2441no—
213C42—1221no—
214C42—2441no—
215C42—2441no—
216C42—2441no—
217C42D4×D6111yescharacteristic
218C16—22no—
219C16—2441no—
220Q8—161no—
221Q8—1222no—
222Q8—4882no—
223Q8—2441no—
224Q8—2441no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—81no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—2441no—
231C2×C4—2441no—
232C2×C4#1451974511yescharacteristic
233C2×C4D8×D6111yescharacteristic
234C2×C4#1451980111yescharacteristic
235C8—21no—
236C8—4881no—
237C8—2441no—
238C8Q16×D6111yescharacteristic
239C8#1451980911yescharacteristic
240C22#1683989411yescharacteristic
241C4—21no—
242C4—21no—
243C4—81no—
244C4—81no—
245C4—161no—
246C4—4881no—
247C4—2441no—
248C4—2441no—
249C4—2442no—
250C4#1683991611yescharacteristic
251C4#1683994411yescharacteristic
252C2#2144506511yescharacteristic
253C2#2144776811yescharacteristic
254C2#2144778011yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2255C2
socle, prime radicalC22×C61#447
hypercenter#2255D61
hypocenterC61#12413
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
154. C61#12413semidirect

Maximal subgroups

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

subgroupindex
#214587892
#214479582
#214453442
#214438712
#214438022
#214437902
C61×#22552
#1241361