Finite Group Databasebeta

← #29594124

Subgroups — #29594124

Order 15616.

272 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 65 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#21458788C211yesmaximal, characteristic
2#21448105C211yesmaximal, characteristic
3#21447972C211yesmaximal, characteristic
4#21445337C211yesmaximal, characteristic
5#21443870C211yesmaximal, characteristic
6#21443790C211yesmaximal, characteristic
7C61×#1338C211yesmaximal, characteristic
8#16840490—21no—
9#16840171—21no—
10#16840167C2211yescharacteristic
11#16840164C2211yescharacteristic
12#16840070—21no—
13#16840070—21no—
14#16840058—21no—
15#16839972—21no—
16#16839870—21no—
17C4×Dic244C2211yescharacteristic
18#16839590—21no—
19#16839588—21no—
20#16839588—21no—
21#16839567—21no—
22#16839513C2211yescharacteristic
23#16839507—21no—
24C61×#446C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#346C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28C2×#11758202—41no—
29#14519777—21no—
30#14519777—21no—
31#14519775—41no—
32#14519769—21no—
33#14519769—21no—
34#14519767—41no—
35#14519767—41no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39#14519742—41no—
40#14519711—21no—
41#14519711—21no—
42#14519711—21no—
43#14519711D411yescharacteristic
44#14519711D411yescharacteristic
45#14519711D411yescharacteristic
46#14519709—21no—
47#14519709—21no—
48C4⋊#92418—21no—
49#14519702—21no—
50#14519702—21no—
51#14519702—21no—
52#14519700—41no—
53C4×Q8×C61D411yescharacteristic
54C2×C16×C61—21no—
55C2×C16×C61—21no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61D411yescharacteristic
58#97×C61—21no—
59C4×C8×C61C2311yescharacteristic
60C2×Q8×C61D811yescharacteristic
61C2×Dic122—21no—
62C2×Dic122—41no—
63C2×Dic122—41no—
64C2×C8×C61—21no—
65C2×C8×C61C2×D411yescharacteristic
66C2×C8×C61C2×D411yescharacteristic
67C4⋊C4×C61—21no—
68C4⋊C4×C61D811yescharacteristic
69C42×C61—21no—
70C42×C61C2×D411yescharacteristic
71#11758202—82no—
72C4⋊Dic61—21no—
73C4⋊Dic61—21no—
74C4⋊Dic61—21no—
75C4⋊Dic61—41no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78#11758196—41no—
79#11758196—41no—
80#11758196—41no—
81#11758196—41no—
82#11758196—41no—
83#11758196—41no—
84#11758196—41no—
85C4×Dic61—41no—
86C4×Dic61—41no—
87C4×Dic61—41no—
88C2×#92418—41no—
89Dic244—21no—
90Dic244Q1612yescomplemented
91C16×C61—22no—
92C16×C61—41no—
93Q8×C61—41no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61#12011yescharacteristic
97C2×C4×C61C2×D811yescharacteristic
98C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
99C2×Dic61—41no—
100C2×Dic61—41no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61—81no—
104Dic122—22no—
105Dic122—41no—
106Dic122—82no—
107Dic122—81no—
108Dic122—81no—
109C8×C61—21no—
110C8×C61—41no—
111C8×C61C2×Q1611yescharacteristic
112C8×C61#13711yescharacteristic
113#92418—81no—
114#12415—611nomaximal, Sylow
115C22×C61#44711yescharacteristic
116C4×C61—21no—
117C4×C61—21no—
118C4×C61—41no—
119C4×C61—41no—
120C4×C61#45111yescharacteristic
121C4×C61#45611yescharacteristic
122Dic61—42no—
123Dic61—81no—
124Dic61—81no—
125Dic61—81no—
126Dic61—161no—
127#3390—611no—
128#2255—611no—
129#2227—611no—
130#1694—611no—
131#1363—611no—
132#1338D6111yescharacteristic
133#1334—611no—
134C2×C61#164911yescharacteristic
135C2×C61#219011yescharacteristic
136C2×C61#219511yescharacteristic
137#557—1221no—
138#501—1221no—
139#500—611no—
140#499—611no—
141#479—1221no—
142#479—1221no—
143#477—1221no—
144#462—1221no—
145#446C2×D6111yescharacteristic
146#441—1221no—
147C4×Q16—611no—
148#367—1221no—
149#366—1221no—
150#366—1221no—
151C4⋊C16C2×D6111yescharacteristic
152#358—1221no—
153#346C2×D6111yescharacteristic
154#334—611no—
155#332—1221no—
156C61#1241511yescharacteristic, complemented, Sylow
157C2×Q16—611no—
158C2×Q16—2441no—
159C4⋊Q8—1221no—
160C4⋊Q8—1221no—
161C4⋊Q8—2441no—
162#125—1221no—
163#125—1221no—
164#125—2441no—
165#125—2441no—
166C4×Q8—1221no—
167C4×Q8—1221no—
168C4×Q8—1221no—
169C4×Q8—2441no—
170C4×Q8D24411yescharacteristic
171C2×C16—21no—
172C2×C16—21no—
173#107—611no—
174#107—611no—
175#107—611no—
176#107—1221no—
177#107—1221no—
178#107—1221no—
179#106—1221no—
180#106—1221no—
181C4⋊C8—21no—
182C4⋊C8—1221no—
183C4⋊C8D24411yescharacteristic
184#103—1221no—
185#103—1221no—
186#103—1221no—
187#103—2441no—
188#97—21no—
189C4×C8C22×D6111yescharacteristic
190C2×Q8—1221no—
191C2×Q8—2441no—
192C2×Q8—2441no—
193C2×Q8D48811yescharacteristic
194Q16—612no—
195Q16—1221no—
196Q16—4882no—
197C2×C8—21no—
198C2×C8—2441no—
199C2×C8D4×D6111yescharacteristic
200C2×C8D4×D6111yescharacteristic
201C4⋊C4—21no—
202C4⋊C4—1221no—
203C4⋊C4—1221no—
204C4⋊C4—1221no—
205C4⋊C4—2441no—
206C4⋊C4—2441no—
207C4⋊C4—2441no—
208C4⋊C4—2441no—
209C4⋊C4—2441no—
210C4⋊C4—2441no—
211C4⋊C4—2441no—
212C4⋊C4—2441no—
213C4⋊C4—2441no—
214C4⋊C4—2441no—
215C4⋊C4D48811yescharacteristic
216C42—21no—
217C42—2441no—
218C42—2441no—
219C42—2441no—
220C42C2×D24411yescharacteristic
221C16—22no—
222C16—41no—
223Q8—41no—
224Q8—1222no—
225Q8—4881no—
226Q8—4881no—
227Q8—4882no—
228Q8—2441no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—4881no—
232C2×C4—2441no—
233C2×C4—2441no—
234C2×C4—2441no—
235C2×C4—2441no—
236C2×C4#1451974711yescharacteristic
237C2×C4C2×D48811yescharacteristic
238C2×C4#1451980511yescharacteristic
239C8—21no—
240C8—41no—
241C8—4881no—
242C8Q16×D6111yescharacteristic
243C8#1451980611yescharacteristic
244C22#1683989811yescharacteristic
245C4—21no—
246C4—21no—
247C4—41no—
248C4—41no—
249C4—9761no—
250C4—4881no—
251C4—4881no—
252C4—4881no—
253C4—2442no—
254C4#1683991911yescharacteristic
255C4#1683994611yescharacteristic
256C2#2144507011yescharacteristic
257C2#2144776711yescharacteristic
258C2#2144779911yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1338C2
socle, prime radicalC22×C61#447
hypercenter#1338D61
hypocenterC61#12415
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #446 ◁ #1338

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
#214587882
#214481052
#214479722
#214453372
#214438702
#214437902
C61×#13382
#1241561