Finite Group Databasebeta

← #29593326

Subgroups — #29593326

Order 15616.

278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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#21457268C211yesmaximal, characteristic
2#21448019C211yesmaximal, characteristic
3#21448017C211yesmaximal, characteristic
4#21447326C211yesmaximal, characteristic
5#21443836C211yesmaximal, characteristic
6#21443760C211yesmaximal, characteristic
7C61×#1350C211yesmaximal, characteristic
8#16840372—21no—
9#16840071—21no—
10#16840068—21no—
11#16840018—21no—
12#16840003C2211yescharacteristic
13#16839971—21no—
14#16839970—21no—
15#16839804—21no—
16C2×#14519711C2211yescharacteristic
17#16839788C2211yescharacteristic
18#16839590—21no—
19#16839587—21no—
20#16839567—21no—
21#16839566—21no—
22C22⋊#11758185C2211yescharacteristic
23#16839530—21no—
24C61×#467C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×#341C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28C2×#11758202—21no—
29C2×#11758194D411yescharacteristic
30#14519775—21no—
31#14519770—41no—
32#14519770—41no—
33#14519768—21no—
34#14519768—41no—
35#14519767—41no—
36#14519756—21no—
37Q8×Dic61—21no—
38#14519742—21no—
39#14519736D411yescharacteristic
40C2×C4⋊Dic61—21no—
41C2×#11758185—21no—
42#14519711—21no—
43#14519711—21no—
44#14519711—41no—
45#14519711D411yescharacteristic
46#14519709—41no—
47#14519708—21no—
48#14519706—21no—
49#14519706—21no—
50#14519702—21no—
51#14519701—21no—
52#14519700—21no—
53C2×Q16×C61D411yescharacteristic
54C2×M16×C61—21no—
55C22×C8×C61C2311yescharacteristic
56C22⋊Q8×C61—21no—
57C2×C16×C61—21no—
58#107×C61D411yescharacteristic
59#103×C61—21no—
60C2×Q8×C61—21no—
61C22×C4×C61C2×D411yescharacteristic
62C22×Dic61—41no—
63C2×Dic122—21no—
64Q16×C61—41no—
65M16×C61—22no—
66M16×C61—41no—
67C2×C8×C61—41no—
68C2×C8×C61—41no—
69C2×C8×C61C2×D411yescharacteristic
70C2×C8×C61C2×D411yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊C4×C61—41no—
73C22⋊C4×C61—41no—
74C22⋊Dic61—21no—
75C22⋊Dic61—41no—
76#11758202—81no—
77C4⋊Dic61—21no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C4⋊Dic61D811yescharacteristic
83C4⋊Dic61D811yescharacteristic
84#11758196—41no—
85#11758196—41no—
86#11758196—41no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—21no—
90C4×Dic61—41no—
91C4×Dic61—41no—
92#11758194—41no—
93C2×#92418—21no—
94Dic244—41no—
95C16×C61—41no—
96#11758185—41no—
97C23×C61AGL(1,ℤ/8)11yescharacteristic
98Q8×C61—41no—
99Q8×C61—41no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61#12011yescharacteristic
105C2×C4×C61C2×D811yescharacteristic
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—81no—
111C2×Dic61—161no—
112Dic122—41no—
113Dic122—41no—
114C8×C61—21no—
115C8×C61—21no—
116C8×C61—42no—
117#92418—41no—
118#12296—611nomaximal, Sylow
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—21no—
122C22×C61#44711yescharacteristic
123C4×C61—21no—
124C4×C61—81no—
125C4×C61—81no—
126C4×C61#45611yescharacteristic
127C4×C61#45811yescharacteristic
128Dic61—41no—
129Dic61—41no—
130Dic61—81no—
131Dic61—81no—
132Dic61—161no—
133#3261—611no—
134#2236—611no—
135#2235—611no—
136#2089—611no—
137#1350—611no—
138#1350D6111yescharacteristic
139#1323—611no—
140C2×C61—41no—
141C2×C61#161011yescharacteristic
142C2×C61#219311yescharacteristic
143C2×C61#219511yescharacteristic
144#541—1221no—
145#479—1221no—
146#479—1221no—
147#470—1221no—
148#467—611no—
149#467C2×D6111yescharacteristic
150#462—1221no—
151#462—1221no—
152#428—1221no—
153C2×#107—611no—
154#424—611no—
155#367—1221no—
156#366—1221no—
157#358—1221no—
158#358—1221no—
159C22⋊C16—611no—
160C22⋊C16C2×D6111yescharacteristic
161#343—1221no—
162#341C2×D6111yescharacteristic
163C61#1229611yescharacteristic, complemented, Sylow
164C2×Q16—611no—
165C2×Q16—1221no—
166C2×Q16D24411yescharacteristic
167C2×M16—21no—
168C2×M16—611no—
169C22×C8C22×D6111yescharacteristic
170C4⋊Q8—1221no—
171#126—2441no—
172#126—2441no—
173#125—1221no—
174#125—2441no—
175#125—2441no—
176C22⋊Q8—21no—
177C22⋊Q8—1221no—
178C4×Q8—1221no—
179C4×Q8—1221no—
180#117—611no—
181C2×C4⋊C4—1221no—
182C2×C16—21no—
183C2×C16—1221no—
184#107—611no—
185#107—1221no—
186#107—1221no—
187#107—2441no—
188#107D24411yescharacteristic
189#106—1221no—
190#106—2441no—
191C4⋊C8—1221no—
192C4⋊C8—1221no—
193#103—21no—
194#103—1221no—
195#103—1221no—
196#103—1221no—
197C2×Q8—21no—
198C2×Q8—1221no—
199C22×C4—2441no—
200C22×C4D4×D6111yescharacteristic
201Q16—41no—
202Q16—4881no—
203Q16—2441no—
204M16—22no—
205M16—41no—
206M16—2441no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—1221no—
210C2×C8C2×D24411yescharacteristic
211C2×C8D4×D6111yescharacteristic
212C4⋊C4—21no—
213C4⋊C4—41no—
214C4⋊C4—611no—
215C4⋊C4—611no—
216C4⋊C4—1221no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C22⋊C4—41no—
227C22⋊C4—1221no—
228C22⋊C4—2441no—
229C42—1221no—
230C42—2441no—
231C42—2441no—
232C16—41no—
233C16—2441no—
234C23#1451980411yescharacteristic
235Q8—41no—
236Q8—41no—
237Q8—2441no—
238Q8—2441no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—9761no—
246C2×C4—4881no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4#1451974711yescharacteristic
250C2×C4D8×D6111yescharacteristic
251C8—21no—
252C8—21no—
253C8—42no—
254C8—2441no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22#1683989711yescharacteristic
259C4—21no—
260C4—81no—
261C4—81no—
262C4—9761no—
263C4—4881no—
264C4—4881no—
265C4—2441no—
266C4—2441no—
267C4#1683994611yescharacteristic
268C4#1683995311yescharacteristic
269C2—41no—
270C2#2144482311yescharacteristic
271C2#2144778411yescharacteristic
272C2#2144780011yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1350C2
socleC22×C61#447
prime radicalC23×C61AGL(1,ℤ/8)
hypercenter#1350D61
hypocenterC61#12296
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1350

Complements

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

NH ≅ G/Ntype
163. C61#12296semidirect

Maximal subgroups

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

subgroupindex
#214572682
#214480192
#214480172
#214473262
#214438362
#214437602
C61×#13502
#1229661