Finite Group Databasebeta

← #30600291

Subgroups — #30600291

Order 15616.

522 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 96 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#21462715C211yesmaximal, characteristic, complemented
2#21461120C212yesmaximal
3#21461062C211yesmaximal, characteristic, complemented
4#21460643C212yesmaximal, complemented
5#21448533C211yesmaximal, characteristic
6#16840813—24no—
7#16840782—22no—
8#16840778C2212yes—
9#16840778C2212yes—
10#16840610—24no—
11#16840607—22no—
12C2×#14519766C411yescharacteristic
13C2×Q8×Dic61C2211yescharacteristic
14C2×#14519739C2211yescharacteristic
15#16839664C411yescharacteristic
16#16839651—22no—
17#16839636—22no—
18#16839631C411yescharacteristic
19#16839608C2211yescharacteristic
20C61×#391C411yescharacteristic
21#14519844—24no—
22C4⋊#92420—22no—
23C4⋊#92420—22no—
24C22⋊#92420—22no—
25C22⋊#92420—22no—
26#14519832—24no—
27C4×#92420—22no—
28C4×#92420D414yes—
29C22×D244C2×C411yescharacteristic
30C22×C4×D61—21no—
31#14519766—22no—
32#14519766—22no—
33Q8×Dic61—22no—
34Q8×Dic61—22no—
35#14519739—22no—
36#14519739—22no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C4⋊Dic61D412yes—
39C2×#11758196—22no—
40C2×#11758198—22no—
41C2×#11758198—21no—
42C2×#11758198—22no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D412yes—
45C2×C4×Dic61C2311yescharacteristic
46#14519684—21no—
47#14519684—21no—
48C22×Q8×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C42×C61C2×C411yescharacteristic
51#95×C61—22no—
52C23×D61—21no—
53C2×Q8×C61—22no—
54C2×Q8×C61—21no—
55C2×Q8×C61—21no—
56C2×Q8×C61—22no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C22⋊C412yes—
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61C22⋊C412yes—
63C22×Dic61C2×D411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C2×D244—22no—
66C2×D244—22no—
67C2×D244—21no—
68C2×D244M1612yes—
69C2×C4×D61—42no—
70C2×C4×D61—82no—
71C2×#92420—24no—
72C2×#92420—42no—
73C4⋊C4×C61—22no—
74C42×C61—22no—
75#11758198—28no—
76#11758198—41no—
77#11758198—41no—
78#11758198—82no—
79C4⋊Dic61—22no—
80C4⋊Dic61—24no—
81#11758196—82no—
82C4×Dic61—21no—
83C4×Dic61—22no—
84C4×Dic61—22no—
85C4×Dic61M1612yes—
86C4×Dic61C2×D412yes—
87C4×Dic61#4112yes—
88C23×C61C2×C22⋊C411yescharacteristic
89C22×D61—22no—
90C22×D61—42no—
91C22×D61—42no—
92C22×D61—41no—
93C22×D61—41no—
94Q8×C61—42no—
95Q8×C61—42no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—42no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61C4×D412yes—
105C2×C4×C61C2×M1611yescharacteristic
106C2×C4×C61C2×M1611yescharacteristic
107C2×C4×C61#13112yes—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—42no—
115C2×Dic61#12011yescharacteristic
116C2×Dic61#12112yes—
117C2×Dic61#12311yescharacteristic
118D244—24no—
119D244—42no—
120C4×D61—84no—
121#92420—44no—
122#92420—82no—
123#9106—611nomaximal, Sylow
124C22×C61—21no—
125C22×C61—21no—
126C22×C61#38611yescharacteristic
127C22×C61#40711yescharacteristic
128C22×C61#40811yescharacteristic
129C2×D61—44no—
130C2×D61—42no—
131C2×D61—82no—
132C2×D61—81no—
133C2×D61—81no—
134C4×C61—42no—
135C4×C61—81no—
136C4×C61—81no—
137C4×C61#43512yes—
138C4×C61#43612yes—
139Dic61—22no—
140Dic61—21no—
141Dic61—21no—
142Dic61—42no—
143Dic61—42no—
144#2983—611no—
145#2326—611no—
146#1478—612no—
147#1461—611no—
148#1274—612no—
149C2×C61—21no—
150C2×C61—21no—
151C2×C61#187011yescharacteristic
152C2×C61#191011yescharacteristic
153C2×C61#191211yescharacteristic
154D61—82no—
155C2×#124—611no—
156C2×C4×Q8—611no—
157C2×C4×D4—611no—
158#446—1224no—
159#432—1222no—
160#431—612no—
161#431—612no—
162#391#692311yescharacteristic
163#390—611no—
164#388—1222no—
165#385—1222no—
166#384—611no—
167#376—611no—
168D4⋊C8—1224no—
169#324—1222no—
170C61#910611yescharacteristic, complemented, Sylow
171C22×Q8C2×#692311yescharacteristic
172C22×D4—611no—
173C23×C4—1221no—
174#124—1222no—
175#124—1222no—
176C4×Q8—1222no—
177C4×Q8—1222no—
178C4×D4—1222no—
179C4×D4—1222no—
180C2×C4⋊C4—612no—
181C2×C4⋊C4—611no—
182C2×C4⋊C4—1222no—
183C2×C4⋊C4C2×#692311yescharacteristic
184C2×C22⋊C4—1222no—
185C2×C22⋊C4—1222no—
186C2×C22⋊C4—1221no—
187C2×C42—611no—
188C2×C42—611no—
189C2×C42—612no—
190C2×C42C2×#692311yescharacteristic
191C4⋊C8—1222no—
192C4⋊C8—1222no—
193C4⋊C8—1224no—
194C22⋊C8—1222no—
195C22⋊C8—1222no—
196#97—1224no—
197C4×C8—614no—
198C4×C8—1222no—
199#95—22no—
200#95—1221no—
201#95—1221no—
202C24—1221no—
203C2×Q8—22no—
204C2×Q8—21no—
205C2×Q8—21no—
206C2×Q8—22no—
207C2×D4—612no—
208C2×D4—1222no—
209C2×D4—1221no—
210C2×D4—1222no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—612no—
216C22×C4—1221no—
217C22×C4—4882no—
218C22×C4—2442no—
219C22×C4C22⋊#692312yes—
220C22×C4C22×#692311yescharacteristic
221C2×C8—1224no—
222C2×C8—2442no—
223C4⋊C4—22no—
224C4⋊C4—1224no—
225C4⋊C4—1222no—
226C4⋊C4—4882no—
227C22⋊C4—1228no—
228C22⋊C4—4882no—
229C22⋊C4—2441no—
230C22⋊C4—2441no—
231C42—22no—
232C42—612no—
233C42—612no—
234C42—612no—
235C42—1222no—
236C42—1222no—
237C42—1221no—
238C23—1222no—
239C23—2442no—
240C23—2442no—
241C23—2441no—
242C23—2441no—
243C23C2×C22⋊#692311yescharacteristic
244Q8—42no—
245Q8—42no—
246D4—1224no—
247D4—2442no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—611no—
257C2×C4—612no—
258C2×C4—611no—
259C2×C4—1222no—
260C2×C4—1222no—
261C2×C4—4884no—
262C2×C4—2441no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4—2442no—
267C2×C4D4×#692312yes—
268C2×C4D61⋊M1611yescharacteristic
269C2×C4D61⋊M1611yescharacteristic
270C2×C4#1451986412yes—
271C8—4882no—
272C8—2444no—
273C22—21no—
274C22—21no—
275C22—4882no—
276C22—4881no—
277C22—4881no—
278C22—2444no—
279C22—2442no—
280C22#1684071011yescharacteristic
281C22#1684073411yescharacteristic
282C22#1684073511yescharacteristic
283C4—42no—
284C4—81no—
285C4—81no—
286C4—1222no—
287C4—1221no—
288C4—1221no—
289C4—2442no—
290C4—2442no—
291C4#1684079412yes—
292C4#1684079512yes—
293C2—21no—
294C2—21no—
295C2—4882no—
296C2#2146179811yescharacteristic
297C2#2146186311yescharacteristic
298C2#2146186611yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#9106
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
1. #21462715C2semidirect
3. #21461062C2semidirect
4. #21460643C2semidirect
170. C61#9106semidirect

Maximal subgroups

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

subgroupindex
#214627152
#214611202
#214610622
#214606432
#214485332
#910661