Finite Group Databasebeta

← #30594440

Subgroups — #30594440

Order 15616.

422 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 60 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#21461718C211yesmaximal, characteristic
2#21461069C211yesmaximal, characteristic
3#21444054C211yesmaximal, characteristic
4#16840732—21no—
5#16840732—21no—
6#16840642—21no—
7#16840642C412yescomplemented
8#16840608—21no—
9#16840608C412yescomplemented
10C22×#11758196C2211yescharacteristic
11C22×C4×Dic61C411yescharacteristic
12C2×#14519684—21no—
13C2×#14519684—21no—
14C2×#95×C61C411yescharacteristic
15C2×#11758217—22no—
16C2×#11758217—41no—
17C22⋊#92420—22no—
18C22⋊#92420—41no—
19C22⋊#92420—41no—
20C22⋊#92420—41no—
21C23×Dic61—21no—
22C23×Dic61D411yescharacteristic
23C23×Dic61D411yescharacteristic
24C2×#11758196—41no—
25C2×#11758196—41no—
26C2×#11758196C2×C411yescharacteristic
27C2×#11758196C2×C411yescharacteristic
28C2×#11758196D411yescharacteristic
29C2×#11758196Q811yescharacteristic
30C2×C4×Dic61—41no—
31C2×C4×Dic61—42no—
32#14519684—24no—
33#14519684—42no—
34C23×C4×C61—21no—
35C23×C4×C61C2×C411yescharacteristic
36#95×C61—41no—
37C24×C61C22⋊C411yescharacteristic
38C22×C4×C61—21no—
39C22×C4×C61—21no—
40C22×C4×C61—22no—
41C22×C4×C61—41no—
42C22×C4×C61—41no—
43C22×C4×C61—41no—
44C22×C4×C61—41no—
45C22×C4×C61—41no—
46C22×C4×C61—41no—
47C22×C4×C61—41no—
48C22×C4×C61—41no—
49C22×C4×C61C4211yescharacteristic
50C22×C4×C61C4⋊C411yescharacteristic
51C22×Dic61—22no—
52C22×Dic61—22no—
53C22×Dic61—22no—
54C22×Dic61—21no—
55C22×Dic61—21no—
56C22×Dic61—21no—
57C22×Dic61—21no—
58C22×Dic61—22no—
59C22×Dic61—41no—
60C22×Dic61—41no—
61C22×Dic61—41no—
62C22×Dic61—41no—
63C22×Dic61—41no—
64C22×Dic61—41no—
65C22×Dic61—41no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C4⋊C411yescharacteristic
69C22×Dic61C4⋊C411yescharacteristic
70#11758217—42no—
71#11758217—42no—
72#11758217—81no—
73#11758217—81no—
74C2×#92420—42no—
75C2×#92420—42no—
76#11758196—41no—
77#11758196—41no—
78#11758196—41no—
79#11758196—41no—
80C4×Dic61—42no—
81C4×Dic61—42no—
82C23×C61—21no—
83C23×C61—21no—
84C23×C61—21no—
85C23×C61—21no—
86C23×C61—21no—
87C23×C61—21no—
88C23×C61#9511yescharacteristic
89C23×C61#9911yescharacteristic
90C23×C61#9911yescharacteristic
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—42no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—42no—
99C2×C4×C61—42no—
100C2×C4×C61—42no—
101C2×C4×C61—81no—
102C2×C4×C61—81no—
103C2×C4×C61—81no—
104C2×C4×C61—81no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—24no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—42no—
114C2×Dic61—42no—
115C2×Dic61—42no—
116C2×Dic61—42no—
117C2×Dic61—42no—
118C2×Dic61—42no—
119C2×Dic61—42no—
120C2×Dic61—42no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—81no—
126C2×Dic61#10412yes—
127#92420—82no—
128#92420—82no—
129#7215—611nomaximal, Sylow
130C22×C61—21no—
131C22×C61—21no—
132C22×C61—21no—
133C22×C61—21no—
134C22×C61—21no—
135C22×C61—21no—
136C22×C61—21no—
137C22×C61—21no—
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—21no—
144C22×C61H(3,ℤ/4)11yescharacteristic
145C22×C61#33911yescharacteristic
146C22×C61#34211yescharacteristic
147C22×C61AΣL(1,𝔽16)11yescharacteristic
148C22×C61#35211yescharacteristic
149C22×C61#35511yescharacteristic
150C22×C61#35611yescharacteristic
151C4×C61—41no—
152C4×C61—41no—
153C4×C61—82no—
154Dic61—22no—
155Dic61—44no—
156Dic61—41no—
157Dic61—41no—
158Dic61—41no—
159#1821—611no—
160#1463—611no—
161#1436—611no—
162C2×C61—21no—
163C2×C61—21no—
164C2×C61—21no—
165C2×C61—21no—
166C2×C61—21no—
167C2×C61—21no—
168C2×C61#128411yescharacteristic
169C2×C61#139011yescharacteristic
170C2×C61#139411yescharacteristic
171C22×C4⋊C4—611no—
172C22×C42—611no—
173#407—1221no—
174#407—1221no—
175C2×#95—1221no—
176C2×#95—1221no—
177C2×#95#692311yescharacteristic
178#343—612no—
179#343—1221no—
180#324—612no—
181#324—1221no—
182C61#721511yescharacteristic, complemented, Sylow
183C23×C4—21no—
184C23×C4—611no—
185C23×C4—611no—
186C23×C4—1221no—
187C23×C4C2×#692311yescharacteristic
188C2×M16—1222no—
189C2×M16—2441no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—2441no—
195C2×C4⋊C4—2441no—
196C2×C42—2441no—
197C2×C42—2442no—
198C22⋊C8—1222no—
199C22⋊C8—2441no—
200C22⋊C8—2441no—
201C22⋊C8—2441no—
202#95—41no—
203#95—1224no—
204#95—2442no—
205C24C22⋊#692311yescharacteristic
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—1222no—
222C22×C4—1221no—
223C22×C4—1222no—
224C22×C4—1222no—
225C22×C4—1222no—
226C22×C4—1221no—
227C22×C4—1221no—
228C22×C4—1221no—
229C22×C4—2441no—
230C22×C4—2441no—
231C22×C4—2441no—
232C22×C4—2441no—
233C22×C4—2441no—
234C22×C4—2441no—
235C22×C4—2441no—
236C22×C4C4×#692311yescharacteristic
237C22×C4C4⋊#692311yescharacteristic
238M16—4881no—
239M16—4881no—
240M16—2442no—
241M16—2442no—
242C2×C8—2442no—
243C2×C8—2442no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C4⋊C4—2441no—
247C4⋊C4—2441no—
248C42—2442no—
249C42—2442no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23(C2×#6923)⋊C411yescharacteristic
257C23#1451983511yescharacteristic
258C23#1451983611yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—612no—
274C2×C4—1221no—
275C2×C4—1221no—
276C2×C4—1224no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—4881no—
283C2×C4—2442no—
284C2×C4—2442no—
285C2×C4—2442no—
286C2×C4—2442no—
287C2×C4—2442no—
288C2×C4—2442no—
289C2×C4—2442no—
290C2×C4—2442no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C8—4882no—
296C8—4882no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22#1684062911yescharacteristic
312C22#1684063311yescharacteristic
313C22#1684064011yescharacteristic
314C22#1684066311yescharacteristic
315C22#1684066511yescharacteristic
316C22#1684067011yescharacteristic
317C22#1684067211yescharacteristic
318C4—41no—
319C4—41no—
320C4—82no—
321C4—1222no—
322C4—2444no—
323C4—2441no—
324C4—2441no—
325C4—2441no—
326C2—21no—
327C2—21no—
328C2—21no—
329C2—21no—
330C2—21no—
331C2—21no—
332C2#2146066711yescharacteristic
333C2#2146090411yescharacteristic
334C2#2146091711yescharacteristic
subgroupG/H
centerC22#16840640
commutatorC22×C4×C61C42
FrattiniC23×C4C2×#6923
FittingC2×#95×C61C4
socleC22×C61#342
prime radicalC24×C61C22⋊C4
cosocleC22×#11758196C22
hypercenterC2×#95#6923
hypocenterC61#7215
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
7. #16840642C4semidirect
9. #16840608C4semidirect
182. C61#7215semidirect

Maximal subgroups

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

subgroupindex
#214617182
#214610692
#214440542
#721561