Finite Group Databasebeta

← #29576009

Subgroups — #29576009

Order 15616.

436 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 99 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#21454904C211yesmaximal, characteristic
2#21451695C211yesmaximal, characteristic
3#21444420C212yesmaximal
4#21443684C212yesmaximal
5C4×#101×C61C211yesmaximal, characteristic
6C2×#14519769C2211yescharacteristic
7#16839893—24no—
8#16839819—21no—
9#16839819C2212yes—
10#16839815—21no—
11#16839701C411yescharacteristic
12#16839701C411yescharacteristic
13#16839700—21no—
14#16839692C411yescharacteristic
15#16839692C411yescharacteristic
16#16839681—21no—
17#16839646—21no—
18#16839646—21no—
19#16839630C2211yescharacteristic
20#16839503—24no—
21C2×C4×Q8×C61C2211yescharacteristic
22C2×#101×C61—21no—
23C4×M16×C61C2212yes—
24C61×#343—21no—
25#14519769—22no—
26#14519769—22no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C4⋊#92418—22no—
34C4⋊#92418—22no—
35C4⋊#92418—22no—
36C22⋊#92418—22no—
37#14519688—22no—
38#14519688D414yes—
39C4×#92418—22no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684C2×C411yescharacteristic
49#14519684C2×C411yescharacteristic
50C22×Q8×C61D411yescharacteristic
51C2×M16×C61—22no—
52C4×Q8×C61—22no—
53C4×Q8×C61—22no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C42×C61D411yescharacteristic
58C2×C42×C61D411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60#101×C61—24no—
61#97×C61—22no—
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—
77M16×C61—24no—
78M16×C61—42no—
79C2×C8×C61—42no—
80C4⋊C4×C61—22no—
81C4⋊C4×C61—22no—
82C4⋊C4×C61—22no—
83C42×C61—21no—
84C42×C61—21no—
85C42×C61—21no—
86C42×C61—21no—
87C42×C61C2×D412yes—
88C42×C61#4112yes—
89C4⋊Dic61—22no—
90C4⋊Dic61—22no—
91#11758196—42no—
92#11758196—42no—
93#11758196—41no—
94#11758196—42no—
95#11758196—41no—
96C2×#92418—24no—
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#2983—611no—
149#2634—611no—
150C4×#101D6111yescharacteristic
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—1224no—
161#432—612no—
162#432—1221no—
163#431—1221no—
164C2×#101—21no—
165C4×M16C2×D6112yes—
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—21no—
176#330—1224no—
177C61#919011yescharacteristic, complemented, Sylow
178C22×Q8C22⋊D6111yescharacteristic
179C2×M16—22no—
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⋊C4C22⋊D6111yescharacteristic
193C2×C42D24411yescharacteristic
194C2×C42D24411yescharacteristic
195C2×C42C22×D6111yescharacteristic
196C4⋊C8—1222no—
197C4⋊C8—1222no—
198C4⋊C8—1222no—
199#101—24no—
200C22⋊C8—1222no—
201#97—22no—
202#97—614no—
203#97—1222no—
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—24no—
231M16—42no—
232C2×C8—42no—
233C2×C8—1224no—
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—
248C42D4×D6112yes—
249C42#1175822412yes—
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#1451970512yes—
277C2×C4#1451973712yes—
278C2×C4#1451974711yescharacteristic
279C2×C4#1451974912yes—
280C2×C4#1451976111yescharacteristic
281C8—44no—
282C8—2444no—
283C22—21no—
284C22—21no—
285C22#1683963911yescharacteristic
286C22C2×#1451970511yescharacteristic
287C22#1683978011yescharacteristic
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#2144611911yescharacteristic
303C2#2144635411yescharacteristic
304C2#2144636911yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC4×#101×C61C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenterC4×#101D61
hypocenterC61#9190
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#101

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
#214549042
#214516952
#214444202
#214436842
C4×#101×C612
#919061