Finite Group Databasebeta

← #29594111

Subgroups — #29594111

Order 15616.

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

normal subgroups only

This group has 266 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#21458784C211yesmaximal, characteristic
2#21448105C211yesmaximal, characteristic
3#21447961C211yesmaximal, characteristic
4#21445348C211yesmaximal, characteristic
5#21443872C211yesmaximal, characteristic
6#21443802C211yesmaximal, characteristic
7C61×#1334C211yesmaximal, characteristic
8#16840488—21no—
9#16840170—21no—
10#16840167C2211yescharacteristic
11#16840164C2211yescharacteristic
12#16840071—21no—
13#16840069—21no—
14#16840058—21no—
15#16840055—21no—
16#16839892C2211yescharacteristic
17#16839869—21no—
18#16839590—21no—
19#16839589—21no—
20#16839588—21no—
21C4⋊#11758185C2211yescharacteristic
22#16839566—21no—
23#16839510—21no—
24C4×Q16×C61C2211yescharacteristic
25C61×#346C2211yescharacteristic
26C61×#334C2211yescharacteristic
27#14519777—21no—
28#14519776—21no—
29#14519776—41no—
30#14519769—21no—
31#14519769—41no—
32#14519768—21no—
33#14519768—41no—
34Q8×Dic61—21no—
35Q8×Dic61—21no—
36C4×Dic122—41no—
37C4×Dic122D411yescharacteristic
38C2×#11758185—21no—
39#14519711—21no—
40#14519711—21no—
41#14519711—41no—
42#14519711D411yescharacteristic
43#14519711D411yescharacteristic
44#14519710—21no—
45#14519709—21no—
46#14519708—21no—
47C4⋊#92418D411yescharacteristic
48#14519706—21no—
49#14519702—41no—
50#14519701—21no—
51#14519701—21no—
52#14519687—21no—
53C2×Q16×C61D411yescharacteristic
54C4×Q8×C61—21no—
55C2×C16×C61—21no—
56#107×C61D411yescharacteristic
57C4⋊C8×C61—21no—
58#103×C61—21no—
59C4×C8×C61C2311yescharacteristic
60C2×Q8×C61—21no—
61C2×Dic122—41no—
62C2×Dic122—41no—
63C2×Dic122D811yescharacteristic
64Q16×C61—21no—
65Q16×C61Q1612yes—
66C2×C8×C61—41no—
67C2×C8×C61C2×D411yescharacteristic
68C2×C8×C61C2×D411yescharacteristic
69C4⋊C4×C61—21no—
70C4⋊C4×C61—41no—
71C42×C61—41no—
72C42×C61C2×D411yescharacteristic
73C4⋊Dic61—21no—
74C4⋊Dic61—21no—
75C4⋊Dic61—41no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61D811yescharacteristic
81#11758196—21no—
82#11758196—41no—
83#11758196—41no—
84#11758196—41no—
85#11758196—41no—
86C4×Dic61—21no—
87C4×Dic61—41no—
88C4×Dic61—41no—
89C2×#92418—21no—
90C16×C61—22no—
91#11758185—41no—
92Q8×C61—22no—
93Q8×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
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—
103C2×Dic61—81no—
104Dic122—41no—
105Dic122—82no—
106Dic122—161no—
107C8×C61—21no—
108C8×C61—81no—
109C8×C61C2×Q1611yescharacteristic
110C8×C61#13711yescharacteristic
111#92418—41no—
112#12413—611nomaximal, Sylow
113C22×C61#44711yescharacteristic
114C4×C61—21no—
115C4×C61—21no—
116C4×C61—42no—
117C4×C61—81no—
118C4×C61#45111yescharacteristic
119C4×C61#45611yescharacteristic
120Dic61—41no—
121Dic61—41no—
122Dic61—81no—
123Dic61—81no—
124Dic61—161no—
125#3390—611no—
126#2255—611no—
127#2225—611no—
128#1696—611no—
129#1363—611no—
130#1338—611no—
131#1334D6111yescharacteristic
132C2×C61#164911yescharacteristic
133C2×C61#219111yescharacteristic
134C2×C61#219311yescharacteristic
135#557—1221no—
136#501—1221no—
137#500—611no—
138#499—611no—
139#479—1221no—
140#479—1221no—
141#477—1221no—
142#477—1221no—
143#446—611no—
144#441—1221no—
145C4×Q16C2×D6111yescharacteristic
146#367—1221no—
147#367—1221no—
148#366—1221no—
149C4⋊C16—611no—
150#358—1221no—
151#346C2×D6111yescharacteristic
152#334C2×D6111yescharacteristic
153#333—1221no—
154C61#1241311yescharacteristic, complemented, Sylow
155C2×Q16D24411yescharacteristic
156C4⋊Q8—1221no—
157C4⋊Q8—1221no—
158C4⋊Q8—2441no—
159#125—1221no—
160#125—1221no—
161#125—2441no—
162#125—2441no—
163C4×Q8—21no—
164C4×Q8—611no—
165C4×Q8—1221no—
166C4×Q8—1221no—
167C4×Q8—2441no—
168C2×C16—21no—
169C2×C16—1221no—
170#107—611no—
171#107—611no—
172#107—1221no—
173#107—1221no—
174#107—1221no—
175#107—2441no—
176#107D24411yescharacteristic
177#106—1221no—
178#106—1221no—
179C4⋊C8—21no—
180C4⋊C8—611no—
181C4⋊C8—1221no—
182#103—21no—
183#103—1221no—
184#103—1221no—
185#103—2441no—
186#97—1221no—
187C4×C8C22×D6111yescharacteristic
188C2×Q8—21no—
189C2×Q8—611no—
190C2×Q8—2441no—
191C2×Q8—2441no—
192Q16—21no—
193Q16Dic24412yes—
194C2×C8—41no—
195C2×C8—1221no—
196C2×C8C2×D24411yescharacteristic
197C2×C8D4×D6111yescharacteristic
198C4⋊C4—21no—
199C4⋊C4—41no—
200C4⋊C4—611no—
201C4⋊C4—1221no—
202C4⋊C4—1221no—
203C4⋊C4—1221no—
204C4⋊C4—2441no—
205C4⋊C4—2441no—
206C4⋊C4—2441no—
207C4⋊C4—2441no—
208C4⋊C4—2441no—
209C4⋊C4—2441no—
210C4⋊C4—2441no—
211C4⋊C4—2441no—
212C4⋊C4—2441no—
213C42—41no—
214C42—1221no—
215C42—2441no—
216C42—2441no—
217C42D4×D6111yescharacteristic
218C16—22no—
219C16—2441no—
220Q8—22no—
221Q8—41no—
222Q8—9761no—
223Q8—4882no—
224Q8—2441no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—4881no—
230C2×C4—2441no—
231C2×C4—2441no—
232C2×C4#1451974711yescharacteristic
233C2×C4D8×D6111yescharacteristic
234C2×C4#1451980411yescharacteristic
235C8—21no—
236C8—81no—
237C8—2441no—
238C8C2×Dic24411yescharacteristic
239C8#1451981011yescharacteristic
240C22#1683989711yescharacteristic
241C4—21no—
242C4—21no—
243C4—42no—
244C4—81no—
245C4—9761no—
246C4—4881no—
247C4—4881no—
248C4—2441no—
249C4—2441no—
250C4#1683992011yescharacteristic
251C4#1683994611yescharacteristic
252C2#2144507111yescharacteristic
253C2#2144777111yescharacteristic
254C2#2144778611yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1334C2
socle, prime radicalC22×C61#447
hypercenter#1334D61
hypocenterC61#12413
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1334

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
#214587842
#214481052
#214479612
#214453482
#214438722
#214438022
C61×#13342
#1241361