Finite Group Databasebeta

← #29593763

Subgroups — #29593763

Order 15616.

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

normal subgroups only

This group has 278 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#21447866C211yesmaximal, characteristic
3#21445310C211yesmaximal, characteristic
4#21443871C211yesmaximal, characteristic
5#21443802C211yesmaximal, characteristic
6#21443790C211yesmaximal, characteristic
7C61×#2245C211yesmaximal, characteristic
8#16840489—21no—
9C2×#14519723—21no—
10#16840169—21no—
11#16840068—21no—
12#16840066—21no—
13#16840056—21no—
14#16840044—21no—
15#16839892C2211yescharacteristic
16#16839868—21no—
17C4×Dic244C2211yescharacteristic
18C4⋊#11758185C2211yescharacteristic
19#16839566—21no—
20#16839513C2211yescharacteristic
21#16839508—21no—
22C61×#499C2211yescharacteristic
23C61×#494C2211yescharacteristic
24C61×#358—21no—
25C61×#358—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—
38#14519723—42no—
39C2×#11758185—21no—
40#14519711D411yescharacteristic
41#14519710—21no—
42#14519708—21no—
43#14519708—41no—
44C4⋊#92418—21no—
45C4⋊#92418D411yescharacteristic
46#14519706—21no—
47#14519702—21no—
48#14519700—21no—
49#14519700—21no—
50#14519700—41no—
51#14519687—21no—
52C2×Q16×C61—21no—
53C2×Q16×C61—21no—
54C4⋊Q8×C61—21no—
55#125×C61—21no—
56C2×C16×C61—21no—
57#107×C61D411yescharacteristic
58#107×C61D411yescharacteristic
59#106×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×Q8×C61—41no—
62C2×Dic122—21no—
63C2×Dic122—41no—
64C2×Dic122D811yescharacteristic
65Q16×C61—42no—
66Q16×C61—41no—
67Q16×C61—41no—
68C2×C8×C61C2×D411yescharacteristic
69C2×C8×C61C2×D411yescharacteristic
70C4⋊C4×C61—21no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C42×C61C2×D411yescharacteristic
77C4⋊Dic61—21no—
78C4⋊Dic61—41no—
79C4⋊Dic61D811yescharacteristic
80#11758196—21no—
81#11758196—41no—
82#11758196—41no—
83#11758196—41no—
84#11758196—41no—
85#11758196—41no—
86C4×Dic61—21no—
87C4×Dic61—41no—
88C4×Dic61—41no—
89C4×Dic61—41no—
90C2×#92418—21no—
91C2×#92418—41no—
92Dic244—21no—
93Dic244SD1612yes—
94C16×C61—41no—
95#11758185—41no—
96Q8×C61—81no—
97Q8×C61—81no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—81no—
101C2×C4×C61#12011yescharacteristic
102C2×C4×C61C2×D811yescharacteristic
103C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108Dic122—22no—
109Dic122—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—81no—
122C4×C61—81no—
123C4×C61—161no—
124C4×C61#44811yescharacteristic
125C4×C61#45411yescharacteristic
126Dic61—42no—
127Dic61—41no—
128Dic61—41no—
129Dic61—81no—
130#3390—611no—
131#2245D6111yescharacteristic
132#2209—611no—
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—1221no—
142#501—1221no—
143#499C2×D6111yescharacteristic
144#494C2×D6111yescharacteristic
145#479—1221no—
146#479—1221no—
147#477—1221no—
148#475—1221no—
149#446—611no—
150#441—1221no—
151C4×Q16—611no—
152C4⋊C16—611no—
153#358—21no—
154#358—21no—
155#358—1221no—
156#346C2×D6111yescharacteristic
157#334—611no—
158#332—1221no—
159C61#1236311yescharacteristic, complemented, Sylow
160C2×Q16—21no—
161C2×Q16—21no—
162C2×Q16—611no—
163C4⋊Q8—21no—
164C4⋊Q8—1221no—
165C4⋊Q8—2441no—
166#125—21no—
167#125—1221no—
168#125—2441no—
169#125—2441no—
170C4×Q8—611no—
171C4×Q8—1221no—
172C4×Q8—1221no—
173C4×Q8—1221no—
174C4×Q8—2441no—
175Q32—2442no—
176C2×C16—21no—
177C2×C16—1221no—
178#107—611no—
179#107—1221no—
180#107C22⋊D6111yescharacteristic
181#107C22⋊D6111yescharacteristic
182#106—21no—
183#106—1221no—
184#106—2441no—
185C4⋊C8—611no—
186C4⋊C8—1221no—
187C4⋊C8—1221no—
188#103—1221no—
189#103—1221no—
190#103—1221no—
191#103—2441no—
192#97—1221no—
193C4×C8C22×D6111yescharacteristic
194C2×Q8—41no—
195C2×Q8—611no—
196C2×Q8—1221no—
197C2×Q8—2441no—
198Q16—42no—
199Q16—41no—
200Q16—41no—
201Q16—612no—
202Q16—1221no—
203C2×C8—1221no—
204C2×C8—2441no—
205C2×C8D4×D6111yescharacteristic
206C2×C8C2×C22⋊D6111yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—611no—
214C4⋊C4—1221no—
215C4⋊C4—1221no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C42—1221no—
223C42—2441no—
224C42—2441no—
225C42—2441no—
226C42D4×D6111yescharacteristic
227C16—41no—
228C16—2441no—
229Q8—81no—
230Q8—81no—
231Q8—1222no—
232Q8—4882no—
233Q8—2441no—
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—
248C8SD16×D6111yescharacteristic
249C8#1451980611yescharacteristic
250C22#1683989411yescharacteristic
251C4—21no—
252C4—21no—
253C4—81no—
254C4—81no—
255C4—161no—
256C4—4881no—
257C4—2442no—
258C4—2441no—
259C4—2441no—
260C4#1683989911yescharacteristic
261C4#1683993411yescharacteristic
262C2#2144491911yescharacteristic
263C2#2144776811yescharacteristic
264C2#2144779411yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2245C2
socle, prime radicalC22×C61#447
hypercenter#2245D61
hypocenterC61#12363
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2245

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
#214587892
#214478662
#214453102
#214438712
#214438022
#214437902
C61×#22452
#1236361