Finite Group Databasebeta

← #29593765

Subgroups — #29593765

Order 15616.

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

normal subgroups only

This group has 278 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#21448064C211yesmaximal, characteristic
3#21445310C211yesmaximal, characteristic
4#21443870C211yesmaximal, characteristic
5#21443800C211yesmaximal, characteristic
6#21443789C211yesmaximal, characteristic
7C61×#2209C211yesmaximal, characteristic
8#16840488—21no—
9#16840170—21no—
10#16840164C2211yescharacteristic
11#16840071—21no—
12#16840069—21no—
13#16840055—21no—
14#16840044—21no—
15#16839892C2211yescharacteristic
16#16839869—21no—
17#16839566—21no—
18#16839566—21no—
19#16839538C2211yescharacteristic
20#16839513C2211yescharacteristic
21#16839508—21no—
22C2×Q32×C61—21no—
23C61×#494C2211yescharacteristic
24C4×Q16×C61C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#358—21no—
27#14519776—21no—
28#14519776—41no—
29#14519769—21no—
30#14519769—41no—
31#14519768—21no—
32#14519768—41no—
33Q8×Dic61—21no—
34Q8×Dic61—21no—
35C4×Dic122—41no—
36C4×Dic122D411yescharacteristic
37C2×#11758185—21no—
38#14519711D411yescharacteristic
39#14519711D411yescharacteristic
40#14519710—21no—
41#14519709—21no—
42#14519708—21no—
43#14519708—41no—
44C4⋊#92418—21no—
45C4⋊#92418D411yescharacteristic
46#14519706—21no—
47#14519701—21no—
48#14519701—21no—
49#14519700—41no—
50#14519687—21no—
51C2×Q16×C61—21no—
52C2×Q16×C61—21no—
53C2×Q16×C61D411yescharacteristic
54C4⋊Q8×C61—21no—
55C4×Q8×C61—21no—
56Q32×C61—42no—
57C2×C16×C61—21no—
58#107×C61D411yescharacteristic
59#103×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×Q8×C61—21no—
62C2×Q8×C61—41no—
63C2×Dic122—41no—
64C2×Dic122D811yescharacteristic
65Q16×C61—21no—
66Q16×C61—42no—
67Q16×C61—41no—
68Q16×C61—41no—
69Q16×C61SD1612yes—
70C2×C8×C61C2×D411yescharacteristic
71C2×C8×C61C2×D411yescharacteristic
72C4⋊C4×C61—21no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C42×C61—41no—
77C42×C61C2×D411yescharacteristic
78C4⋊Dic61—21no—
79C4⋊Dic61—21no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83C4⋊Dic61D811yescharacteristic
84#11758196—21no—
85#11758196—41no—
86#11758196—41no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—21no—
90C4×Dic61—41no—
91C4×Dic61—41no—
92C2×#92418—21no—
93C2×#92418—41no—
94C16×C61—41no—
95#11758185—41no—
96Q8×C61—22no—
97Q8×C61—41no—
98Q8×C61—81no—
99Q8×C61—81no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—81no—
103C2×C4×C61#12011yescharacteristic
104C2×C4×C61C2×D811yescharacteristic
105C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110Dic122—41no—
111Dic122—82no—
112C8×C61—21no—
113C8×C61C2×SD1611yescharacteristic
114C8×C61#13711yescharacteristic
115#92418—41no—
116#92418—81no—
117#12363—611nomaximal, Sylow
118C22×C61#44711yescharacteristic
119C4×C61—21no—
120C4×C61—21no—
121C4×C61—42no—
122C4×C61—81no—
123C4×C61—161no—
124C4×C61#44811yescharacteristic
125C4×C61#45411yescharacteristic
126Dic61—41no—
127Dic61—41no—
128Dic61—81no—
129Dic61—81no—
130#3390—611no—
131#2245—611no—
132#2209D6111yescharacteristic
133#1690—611no—
134#1363—611no—
135#1338—611no—
136#1334—611no—
137C2×C61#162711yescharacteristic
138C2×C61#219111yescharacteristic
139C2×C61#219511yescharacteristic
140#557—1221no—
141C2×Q32—21no—
142#501—1221no—
143#499—611no—
144#494C2×D6111yescharacteristic
145#479—1221no—
146#479—1221no—
147#477—1221no—
148#475—1221no—
149#446—611no—
150#441—1221no—
151C4×Q16C2×D6111yescharacteristic
152C4⋊C16C2×D6111yescharacteristic
153#358—21no—
154#358—1221no—
155#358—1221no—
156#346—611no—
157#334—611no—
158#332—1221no—
159C61#1236311yescharacteristic, complemented, Sylow
160C2×Q16—21no—
161C2×Q16—21no—
162C2×Q16C22⋊D6111yescharacteristic
163C4⋊Q8—21no—
164C4⋊Q8—1221no—
165C4⋊Q8—2441no—
166#125—1221no—
167#125—1221no—
168#125—2441no—
169#125—2441no—
170C4×Q8—21no—
171C4×Q8—611no—
172C4×Q8—1221no—
173C4×Q8—1221no—
174C4×Q8—2441no—
175Q32—42no—
176C2×C16—21no—
177C2×C16—1221no—
178#107—611no—
179#107—611no—
180#107—1221no—
181#107C22⋊D6111yescharacteristic
182#106—1221no—
183#106—1221no—
184#106—2441no—
185C4⋊C8—611no—
186C4⋊C8—1221no—
187C4⋊C8—1221no—
188#103—21no—
189#103—1221no—
190#103—1221no—
191#103—2441no—
192#97—1221no—
193C4×C8C22×D6111yescharacteristic
194C2×Q8—21no—
195C2×Q8—41no—
196C2×Q8—611no—
197C2×Q8—2441no—
198Q16—21no—
199Q16—42no—
200Q16—41no—
201Q16—41no—
202Q16#1175820012yes—
203C2×C8—1221no—
204C2×C8—2441no—
205C2×C8D4×D6111yescharacteristic
206C2×C8C2×C22⋊D6111yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—611no—
212C4⋊C4—1221no—
213C4⋊C4—1221no—
214C4⋊C4—1221no—
215C4⋊C4—2441no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C42—41no—
223C42—1221no—
224C42—2441no—
225C42—2441no—
226C42D4×D6111yescharacteristic
227C16—41no—
228C16—2441no—
229Q8—22no—
230Q8—41no—
231Q8—81no—
232Q8—81no—
233Q8—4882no—
234Q8—2441no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—81no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—2441no—
241C2×C4—2441no—
242C2×C4#1451974511yescharacteristic
243C2×C4D8×D6111yescharacteristic
244C2×C4#1451980111yescharacteristic
245C8—21no—
246C8—4881no—
247C8—2441no—
248C8C2×#1175820011yescharacteristic
249C8#1451980711yescharacteristic
250C22#1683989411yescharacteristic
251C4—21no—
252C4—21no—
253C4—42no—
254C4—81no—
255C4—161no—
256C4—4881no—
257C4—4881no—
258C4—2441no—
259C4—2441no—
260C4#1683990011yescharacteristic
261C4#1683993311yescharacteristic
262C2#2144492111yescharacteristic
263C2#2144776811yescharacteristic
264C2#2144779611yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2209C2
socle, prime radicalC22×C61#447
hypercenter#2209D61
hypocenterC61#12363
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2209

Complements

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

NH ≅ G/Ntype
159. C61#12363semidirect

Maximal subgroups

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

subgroupindex
#214587842
#214480642
#214453102
#214438702
#214438002
#214437892
C61×#22092
#1236361