Finite Group Databasebeta

← #29576011

Subgroups — #29576011

Order 15616.

436 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 103 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#21451695C211yesmaximal, characteristic
2C4×#14519696C211yesmaximal, characteristic
3#21444422C212yesmaximal
4#21443685C212yesmaximal
5C61×#2983C211yesmaximal, characteristic
6C2×#14519769C2211yescharacteristic
7C2×#14519696—21no—
8C4×#11758194C2212yes—
9#16839701C411yescharacteristic
10#16839701C411yescharacteristic
11#16839700—21no—
12#16839692C411yescharacteristic
13#16839692C411yescharacteristic
14#16839681—21no—
15#16839646—21no—
16#16839646—21no—
17#16839630C2211yescharacteristic
18#16839531—21no—
19#16839503—24no—
20C2×C4×Q8×C61C2211yescharacteristic
21C61×#446—24no—
22C61×#432—21no—
23C61×#432C2212yes—
24C61×#431—21no—
25C2×#11758194—22no—
26#14519769—22no—
27#14519769—22no—
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34#14519696—24no—
35#14519688—22no—
36C4×#92418—22no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684C2×C411yescharacteristic
46#14519684C2×C411yescharacteristic
47C22×Q8×C61D411yescharacteristic
48C4×Q8×C61—22no—
49C4×Q8×C61—22no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C2×C42×C61D411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56C4⋊C8×C61—22no—
57C4⋊C8×C61—22no—
58C4⋊C8×C61—22no—
59C22⋊C8×C61—22no—
60#97×C61—22no—
61#97×C61D414yes—
62C4×C8×C61—22no—
63C2×Q8×C61—22no—
64C2×Q8×C61—22no—
65C2×Q8×C61—41no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C2×C8×C61—24no—
78C4⋊C4×C61—22no—
79C4⋊C4×C61—22no—
80C4⋊C4×C61—22no—
81C42×C61—21no—
82C42×C61—21no—
83C42×C61—21no—
84C42×C61—21no—
85C42×C61C2×D412yes—
86C42×C61#4112yes—
87C4⋊Dic61—22no—
88C4⋊Dic61—22no—
89#11758196—42no—
90#11758196—42no—
91#11758196—41no—
92#11758196—42no—
93#11758196—41no—
94#11758194—24no—
95#11758194—42no—
96C2×#92418—42no—
97C23×C61C2×C22⋊C411yescharacteristic
98Q8×C61—44no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61#10412yes—
113C2×C4×C61C4×D412yes—
114C2×C4×C61#12011yescharacteristic
115C2×C4×C61#12112yes—
116C2×C4×C61#12311yescharacteristic
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—42no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C8×C61—44no—
129#92418—44no—
130#9190—611nomaximal, Sylow
131C22×C61—21no—
132C22×C61—21no—
133C22×C61#38611yescharacteristic
134C22×C61C2×#10411yescharacteristic
135C22×C61#42111yescharacteristic
136C4×C61—22no—
137C4×C61—22no—
138C4×C61—21no—
139C4×C61—21no—
140C4×C61—22no—
141C4×C61—41no—
142C4×C61—41no—
143C4×C61—41no—
144Dic61—81no—
145Dic61—81no—
146Dic61—81no—
147Dic61—81no—
148#2983D6111yescharacteristic
149#2634—611no—
150C4×#101—611no—
151#1528—612no—
152#1288—612no—
153C2×C61—21no—
154C2×C61—21no—
155C2×C61#187111yescharacteristic
156C2×C61#191211yescharacteristic
157C2×C61#191511yescharacteristic
158C2×#125—611no—
159C2×C4×Q8C2×D6111yescharacteristic
160#446—24no—
161#432—21no—
162#432C2×D6112yes—
163#431—21no—
164C2×#101—1221no—
165C4×M16—612no—
166#400—611no—
167#400—611no—
168#400—1221no—
169#398—611no—
170#398—611no—
171#395—1221no—
172#387—1221no—
173#387—1221no—
174#383—611no—
175#343—1221no—
176#330—1224no—
177C61#919011yescharacteristic, complemented, Sylow
178C22×Q8D24411yescharacteristic
179C2×M16—1222no—
180#125—1222no—
181#125—1222no—
182C4×Q8—22no—
183C4×Q8—22no—
184C2×C4⋊C4—611no—
185C2×C4⋊C4—611no—
186C2×C4⋊C4—1221no—
187C2×C4⋊C4—1221no—
188C2×C4⋊C4—1221no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4C4×D6111yescharacteristic
191C2×C4⋊C4C4×D6111yescharacteristic
192C2×C4⋊C4D24411yescharacteristic
193C2×C42C22⋊D6111yescharacteristic
194C2×C42C22⋊D6111yescharacteristic
195C2×C42C22×D6111yescharacteristic
196C4⋊C8—22no—
197C4⋊C8—22no—
198C4⋊C8—22no—
199#101—1224no—
200C22⋊C8—22no—
201#97—22no—
202#97—1222no—
203#97C22⋊D6114yes—
204C4×C8—22no—
205C4×C8—1222no—
206#95—611no—
207#95—611no—
208#95—1221no—
209#95—1221no—
210#95—1221no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—41no—
219C22×C4—1221no—
220C22×C4—1221no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4#1175819811yescharacteristic
224C22×C4#1175819811yescharacteristic
225C22×C4#1175819811yescharacteristic
226C22×C4#1175819811yescharacteristic
227C22×C4C2×C4×D6111yescharacteristic
228C22×C4C2×D24411yescharacteristic
229C22×C4C2×C22⋊D6111yescharacteristic
230M16—1224no—
231M16—2442no—
232C2×C8—24no—
233C2×C8—2442no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—1222no—
238C4⋊C4—1222no—
239C4⋊C4—2442no—
240C4⋊C4—2442no—
241C4⋊C4—2441no—
242C4⋊C4—2442no—
243C4⋊C4—2441no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42#1175822212yes—
249C42C2×C22⋊D6112yes—
250C23C2×#1175819811yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4—2442no—
270C2×C4—2441no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4#1451970312yes—
277C2×C4C4×C22⋊D6112yes—
278C2×C4#1451974611yescharacteristic
279C2×C4#1451975112yes—
280C2×C4#1451976011yescharacteristic
281C8—44no—
282C8—2444no—
283C22—21no—
284C22—21no—
285C22#1683964111yescharacteristic
286C22C2×#1451970311yescharacteristic
287C22#1683977811yescharacteristic
288C4—21no—
289C4—21no—
290C4—22no—
291C4—22no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—4881no—
297C4—4881no—
298C4—4881no—
299C4—4881no—
300C2—21no—
301C2—21no—
302C2#2144612111yescharacteristic
303C2#2144635611yescharacteristic
304C2#2144637111yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2983C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2983D61
hypocenterC61#9190
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
177. C61#9190semidirect

Maximal subgroups

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

subgroupindex
#214516952
C4×#145196962
#214444222
#214436852
C61×#29832
#919061