Finite Group Databasebeta

← #29583959

Subgroups — #29583959

Order 15616.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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#21456965C211yesmaximal, characteristic
2#21446807C211yesmaximal, characteristic
3#21444556C211yesmaximal, characteristic
4#21444503C211yesmaximal, characteristic
5#21444239C211yesmaximal, characteristic
6#21443710C211yesmaximal, characteristic
7C61×#1574C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×#14519777C2211yescharacteristic
10#16840160—21no—
11#16840113—21no—
12#16840093—22no—
13#16840048—21no—
14#16840048—21no—
15#16839786C2211yescharacteristic
16C4×#11758194C2211yescharacteristic
17#16839530—22no—
18#16839509—21no—
19#16839509—22no—
20#16839507—21no—
21#16839492—22no—
22C61×#431C2211yescharacteristic
23C61×#431C2211yescharacteristic
24C61×#423C2211yescharacteristic
25C61×#335—21no—
26C61×#334—21no—
27C22×Dic122—21no—
28C2×#11758194—21no—
29C2×#11758194—21no—
30#14519777—21no—
31#14519777—21no—
32#14519777—21no—
33#14519777—21no—
34#14519777D411yescharacteristic
35#14519777D411yescharacteristic
36#14519769—21no—
37#14519756—21no—
38#14519756—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41#14519736—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61D412yes—
44#14519709—22no—
45#14519709—22no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48#14519702—22no—
49#14519702—22no—
50#14519688—21no—
51C4×#92418—21no—
52C2×M16×C61—21no—
53C2×C42×C61C2311yescharacteristic
54C4⋊C8×C61—21no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61D412yes—
57C4⋊C8×C61D411yescharacteristic
58C4⋊C8×C61D411yescharacteristic
59C22⋊C8×C61—21no—
60C22⋊C8×C61—21no—
61C4×C8×C61—21no—
62C4×C8×C61—21no—
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61#4111yescharacteristic
65C22×C4×C61#4111yescharacteristic
66C22×Dic61—22no—
67C2×Dic122—21no—
68C2×Dic122—21no—
69C2×Dic122—41no—
70C2×Dic122—41no—
71C2×Dic122—82no—
72M16×C61—42no—
73C2×C8×C61—21no—
74C2×C8×C61—21no—
75C2×C8×C61—22no—
76C2×C8×C61—41no—
77C42×C61C2×D411yescharacteristic
78C42×C61C2×D411yescharacteristic
79C42×C61C2×D411yescharacteristic
80C42×C61#4111yescharacteristic
81C22⋊Dic61—41no—
82C4⋊Dic61—22no—
83C4⋊Dic61—21no—
84C4⋊Dic61—22no—
85C4⋊Dic61—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90#11758196—41no—
91#11758196—41no—
92C4×Dic61—41no—
93#11758194—22no—
94#11758194—41no—
95#11758194—81no—
96C2×#92418—41no—
97C2×#92418—41no—
98C23×C61#12311yescharacteristic
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—22no—
103C2×C4×C61—21no—
104C2×C4×C61#12011yescharacteristic
105C2×C4×C61#12111yescharacteristic
106C2×C4×C61#12111yescharacteristic
107C2×C4×C61#12111yescharacteristic
108C2×C4×C61#12311yescharacteristic
109C2×C4×C61#12411yescharacteristic
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—42no—
113C2×Dic61—82no—
114Dic122—41no—
115Dic122—41no—
116Dic122—41no—
117Dic122—41no—
118Dic122—82no—
119Dic122—82no—
120C8×C61—41no—
121C8×C61—41no—
122C8×C61—42no—
123C8×C61—81no—
124#92418—42no—
125#92418—81no—
126#10494—611nomaximal, Sylow
127C22×C61—21no—
128C22×C61—21no—
129C22×C61—21no—
130C22×C61#39411yescharacteristic
131C4×C61—21no—
132C4×C61—21no—
133C4×C61—21no—
134C4×C61#45411yescharacteristic
135C4×C61#45611yescharacteristic
136C4×C61#47112yes—
137C4×C61#47111yescharacteristic
138C4×C61#47311yescharacteristic
139Dic61—81no—
140Dic61—81no—
141Dic61—82no—
142#3229—611no—
143#1997—611no—
144#1574D6111yescharacteristic
145#1561—611no—
146#1549—611no—
147#1485—611no—
148#1299—611no—
149C2×C61—41no—
150C2×C61#203811yescharacteristic
151C2×C61#204611yescharacteristic
152C2×C61#205211yescharacteristic
153#533—611no—
154C2×C4⋊Q8—611no—
155#498—1221no—
156#487—1221no—
157#483—1222no—
158#475—1221no—
159#475—1221no—
160#431C2×D6111yescharacteristic
161#431C2×D6111yescharacteristic
162#423—611no—
163#423C2×D6111yescharacteristic
164C4×M16—611no—
165#343—1222no—
166#335—21no—
167#334—21no—
168#332—1221no—
169#332—1221no—
170#332—1222no—
171Q8⋊C8—1222no—
172C61#1049411yescharacteristic, complemented, Sylow
173C22×Q8—1221no—
174C2×M16—21no—
175C2×M16—1221no—
176C2×M16—1221no—
177C4⋊Q8—611no—
178C4⋊Q8—611no—
179C4⋊Q8—1221no—
180C4⋊Q8—1221no—
181C4⋊Q8—1221no—
182C4⋊Q8—1221no—
183#125—1221no—
184C22⋊Q8—1221no—
185C22⋊Q8—1221no—
186C4×Q8—1221no—
187C4×Q8—1221no—
188#117—1221no—
189C2×C4⋊C4—612no—
190C2×C4⋊C4—1221no—
191C2×C42C22×D6111yescharacteristic
192#106—1222no—
193#106—1222no—
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—1221no—
197C4⋊C8—1221no—
198C4⋊C8D24412yes—
199C4⋊C8C22⋊D6111yescharacteristic
200C4⋊C8C22⋊D6111yescharacteristic
201#103—1222no—
202#103—1222no—
203C22⋊C8—21no—
204C22⋊C8—21no—
205#97—1221no—
206C4×C8—21no—
207C4×C8—21no—
208C4×C8—1221no—
209C2×Q8—1221no—
210C2×Q8—1221no—
211C2×Q8—4882no—
212C2×Q8—2441no—
213C2×Q8—2441no—
214C22×C4—1222no—
215C22×C4#1175822211yescharacteristic
216C22×C4D4×D6111yescharacteristic
217C22×C4#1175822611yescharacteristic
218M16—42no—
219M16—1222no—
220M16—4881no—
221M16—2441no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—22no—
225C2×C8—41no—
226C2×C8—2441no—
227C2×C8—2441no—
228C4⋊C4—1222no—
229C4⋊C4—1221no—
230C4⋊C4—1222no—
231C4⋊C4—1221no—
232C4⋊C4—1221no—
233C4⋊C4—1221no—
234C4⋊C4—2441no—
235C4⋊C4—2441no—
236C4⋊C4—2441no—
237C4⋊C4—2441no—
238C22⋊C4—2441no—
239C42—2441no—
240C42C2×D24411yescharacteristic
241C42D4×D6111yescharacteristic
242C42#1175822611yescharacteristic
243C42C2×C22⋊D6111yescharacteristic
244C23#1451976211yescharacteristic
245Q8—4882no—
246Q8—4882no—
247Q8—2441no—
248Q8—2441no—
249Q8—2441no—
250Q8—2441no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—4882no—
257C2×C4—2441no—
258C2×C4—2441no—
259C2×C4—2442no—
260C2×C4#1451974511yescharacteristic
261C2×C4#1451975111yescharacteristic
262C2×C4#1451975211yescharacteristic
263C2×C4#1451975211yescharacteristic
264C2×C4#1451976211yescharacteristic
265C2×C4#1451976611yescharacteristic
266C8—41no—
267C8—42no—
268C8—41no—
269C8—81no—
270C8—4881no—
271C8—2442no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22#1683967911yescharacteristic
276C4—21no—
277C4—21no—
278C4—21no—
279C4—4881no—
280C4—4882no—
281C4—4881no—
282C4#1683993311yescharacteristic
283C4#1683994311yescharacteristic
284C4#1684002512yes—
285C4#1684002611yescharacteristic
286C4#1684003811yescharacteristic
287C2—41no—
288C2#2144703811yescharacteristic
289C2#2144708211yescharacteristic
290C2#2144712011yescharacteristic
subgroupG/H
centerC22#16839679
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1574C2
socleC22×C61#394
prime radicalC23×C61#123
hypercenter#1574D61
hypocenterC61#10494
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
172. C61#10494semidirect

Maximal subgroups

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

subgroupindex
#214569652
#214468072
#214445562
#214445032
#214442392
#214437102
C61×#15742
#1049461