Finite Group Databasebeta

← #30604236

Subgroups — #30604236

Order 15616.

380 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 68 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#21461070C211yesmaximal, characteristic
2#21461050C211yesmaximal, characteristic
3#21460764C212yesmaximal
4#21460745C212yesmaximal
5#21450106C211yesmaximal, characteristic
6#16840782—21no—
7#16840778—21no—
8#16840607—21no—
9#16840607—21no—
10#16840605C2212yes—
11#16840605C2212yes—
12C2×#14519736C2211yescharacteristic
13#16839701—21no—
14#16839692—21no—
15#16839643—21no—
16#16839643—21no—
17#16839635C411yescharacteristic
18#16839635C2211yescharacteristic
19#16839625C411yescharacteristic
20#16839625C411yescharacteristic
21#16839625C2211yescharacteristic
22C22×C4⋊C4×C61C411yescharacteristic
23#14519844—41no—
24C4⋊#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27#14519832—41no—
28C4×#92420—41no—
29#14519736—41no—
30#14519736—41no—
31C2×C4⋊Dic61D411yescharacteristic
32C2×C4⋊Dic61D411yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C22⋊Dic61C2×C411yescharacteristic
36C2×C22⋊Dic61C2×C411yescharacteristic
37C2×C22⋊Dic61C2×C411yescharacteristic
38C2×C22⋊Dic61C2311yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C23×C4×C61C2×C411yescharacteristic
50C23×C4×C61C2×C411yescharacteristic
51C23×C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61—41no—
55C2×C4⋊C4×C61—41no—
56C24×C61C22×C411yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—22no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—22no—
63C22×C4×C61—41no—
64C22×C4×C61—42no—
65C22×C4×C61—41no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×#92420—42no—
77C2×#92420—42no—
78C4⋊C4×C61—42no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C22⋊Dic61—22no—
82C22⋊Dic61—41no—
83C22⋊Dic61—41no—
84C22⋊Dic61—41no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87#11758196—42no—
88#11758196—42no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—41no—
96C23×C61—41no—
97C23×C61C2×C22⋊C411yescharacteristic
98C23×C61#13112yes—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—42no—
106C2×C4×C61—42no—
107C2×C4×C61—41no—
108C2×C4×C61—42no—
109C2×C4×C61—41no—
110C2×C4×C61—42no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—82no—
115C2×C4×C61#9911yescharacteristic
116C2×C4×C61#9911yescharacteristic
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131#92420—82no—
132#92420—82no—
133#11544—611nomaximal, Sylow
134C22×C61—21no—
135C22×C61—21no—
136C22×C61—22no—
137C22×C61—42no—
138C22×C61—42no—
139C22×C61—41no—
140C22×C61—41no—
141C22×C61#40811yescharacteristic
142C22×C61C2×#9911yescharacteristic
143C22×C61#41311yescharacteristic
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—42no—
147C4×C61—41no—
148C4×C61—81no—
149Dic61—41no—
150Dic61—41no—
151Dic61—41no—
152Dic61—41no—
153Dic61—81no—
154Dic61—81no—
155#2484—611no—
156#1464—611no—
157#1458—611no—
158#1326—612no—
159#1317—612no—
160C2×C61—21no—
161C2×C61—21no—
162C2×C61—42no—
163C2×C61#146811yescharacteristic
164C2×C61#212011yescharacteristic
165C2×C61#212311yescharacteristic
166C2×#117—611no—
167C22×C4⋊C4#692311yescharacteristic
168#432—1221no—
169#431—1221no—
170#400—1221no—
171#398—1221no—
172#387—1221no—
173#387—1221no—
174#385—611no—
175#385—611no—
176#381—611no—
177#381—611no—
178#381—611no—
179#324—1221no—
180#324—1221no—
181#323—612no—
182#323—612no—
183C61#1154411yescharacteristic, complemented, Sylow
184C23×C4C2×#692311yescharacteristic
185C23×C4C2×#692311yescharacteristic
186C23×C4C2×#692311yescharacteristic
187#117—2441no—
188#117—2441no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—41no—
192C2×C4⋊C4—41no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—611no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C22⋊C4—611no—
198C2×C22⋊C4—611no—
199C2×C22⋊C4—611no—
200C2×C22⋊C4—611no—
201C2×C42—611no—
202C2×C42—611no—
203C4⋊C8—2441no—
204C4⋊C8—2441no—
205C22⋊C8—1222no—
206C22⋊C8—1222no—
207#97—2441no—
208C4×C8—2441no—
209#95—1221no—
210#95—1221no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217C24C22×#692311yescharacteristic
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—41no—
225C22×C4—42no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4C22⋊#692311yescharacteristic
236C22×C4C22⋊#692311yescharacteristic
237C2×C8—2442no—
238C2×C8—2442no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—2441no—
243C4⋊C4—2441no—
244C4⋊C4—2442no—
245C4⋊C4—2442no—
246C22⋊C4—1222no—
247C22⋊C4—2441no—
248C22⋊C4—2441no—
249C22⋊C4—2441no—
250C42—1221no—
251C42—1221no—
252C42—1221no—
253C42—1221no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×C22⋊#692311yescharacteristic
259C23#1451986412yes—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—82no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4#1451983511yescharacteristic
291C2×C4#1451983511yescharacteristic
292C8—4882no—
293C8—4882no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22#1684073511yescharacteristic
302C22C2×#1451983511yescharacteristic
303C22#1684074911yescharacteristic
304C4—21no—
305C4—21no—
306C4—42no—
307C4—41no—
308C4—81no—
309C4—4881no—
310C4—4881no—
311C4—2441no—
312C4—2441no—
313C4—2441no—
314C4—2441no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#2146108411yescharacteristic
319C2#2146207011yescharacteristic
320C2#2146208111yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C2×#99
cosocleC2×C22⋊Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#11544
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
183. C61#11544semidirect

Maximal subgroups

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

subgroupindex
#214610702
#214610502
#214607642
#214607452
#214501062
#1154461