Finite Group Databasebeta

← #30599333

Subgroups — #30599333

Order 15616.

450 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461072C211yesmaximal, characteristic
2#21461072C211yesmaximal, characteristic
3#21460670C212yesmaximal, complemented
4#21460670C212yesmaximal, complemented
5#21448299C211yesmaximal, characteristic
6#16840782C2212yes—
7#16840782C2212yes—
8#16840608—21no—
9#16840608—21no—
10#16840606—21no—
11#16840606—21no—
12C2×#14519734C411yescharacteristic
13C2×#14519734C2211yescharacteristic
14C2×C42×D61C411yescharacteristic
15#16839659—21no—
16#16839657—21no—
17#16839636—21no—
18#16839633—21no—
19C4×#11758196C2211yescharacteristic
20C4×#11758196C2211yescharacteristic
21C4×C4⋊Dic61C411yescharacteristic
22C4×C4⋊C4×C61C411yescharacteristic
23#14519844—22no—
24#14519844—22no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27#14519832—22no—
28#14519832—22no—
29C22×C4×D61—21no—
30C22×C4×D61C2×C411yescharacteristic
31#14519734—22no—
32#14519734—22no—
33#14519734—42no—
34C2×C4⋊Dic61—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196D411yescharacteristic
39C2×#11758196D411yescharacteristic
40C2×#11758198—21no—
41C2×#11758198D411yescharacteristic
42C2×#11758198D411yescharacteristic
43C2×C4×Dic61—21no—
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61C2311yescharacteristic
47C42×D61—42no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C2×C4⋊C4×C61—21no—
52C2×C42×C61C2×C411yescharacteristic
53C2×C42×C61C2×C411yescharacteristic
54C2×C42×C61C2×C411yescharacteristic
55#95×C61—21no—
56C23×D61C22⋊C411yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C2×C4×D61—22no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—22no—
71C2×C4×D61—42no—
72C2×C4×D61—42no—
73C2×C4×D61—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76C4⋊C4×C61—42no—
77C42×C61—21no—
78C42×C61—21no—
79C42×C61—41no—
80C42×C61—41no—
81#11758198—22no—
82#11758198—22no—
83#11758198—42no—
84C4⋊Dic61—42no—
85#11758196—22no—
86#11758196—22no—
87#11758196—42no—
88#11758196—42no—
89#11758196—42no—
90C4×Dic61—42no—
91C4×Dic61—41no—
92C4×Dic61—41no—
93C4×Dic61#4112yes—
94C4×Dic61#4112yes—
95C23×C61C2×C22⋊C411yescharacteristic
96C22×D61—21no—
97C22×D61—21no—
98C22×D61—41no—
99C22×D61—41no—
100C22×D61#10012yes—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—22no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61#11711yescharacteristic
114C2×C4×C61#11711yescharacteristic
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—22no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61#10112yes—
126C2×Dic61#12312yes—
127C2×Dic61#12312yes—
128C4×D61—24no—
129C4×D61—24no—
130C4×D61—48no—
131#92420—82no—
132#92420—82no—
133#8742—611nomaximal, Sylow
134C22×C61—21no—
135C22×C61—21no—
136C22×C61#38111yescharacteristic
137C22×C61C2×#10011yescharacteristic
138C22×C61C2×#10111yescharacteristic
139C2×D61—22no—
140C2×D61—42no—
141C2×D61—41no—
142C2×D61—41no—
143C2×D61—42no—
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—42no—
147C4×C61—41no—
148C4×C61—41no—
149C4×C61—81no—
150Dic61—22no—
151Dic61—22no—
152Dic61—22no—
153Dic61—42no—
154Dic61—81no—
155#2296—611no—
156#1464—611no—
157#1464—611no—
158#1285—612no—
159#1285—612no—
160C2×C61—21no—
161C2×C61—21no—
162C2×C61#182111yescharacteristic
163C2×C61#182711yescharacteristic
164C2×C61#182711yescharacteristic
165D61—42no—
166C2×#117—611no—
167C2×#117—611no—
168C22×C42—611no—
169#432—612no—
170#432—612no—
171#389—1221no—
172#389—1221no—
173#385—1221no—
174#385—1221no—
175C4×C4⋊C4—611no—
176C4×C4⋊C4—611no—
177C4×C4⋊C4—611no—
178C4×C4⋊C4#692311yescharacteristic
179#324—1221no—
180#324—1221no—
181#323—1221no—
182#323—1221no—
183C61#874211yescharacteristic, complemented, Sylow
184C23×C4—611no—
185C23×C4—1221no—
186#117—1222no—
187#117—1222no—
188#117—2442no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4—1221no—
196C2×C22⋊C4—611no—
197C2×C22⋊C4—611no—
198C2×C22⋊C4—1221no—
199C2×C42—611no—
200C2×C42—611no—
201C2×C42—611no—
202C2×C42—1221no—
203C2×C42—2442no—
204C2×C42C2×#692311yescharacteristic
205C2×C42C2×#692311yescharacteristic
206C2×C42C2×#692311yescharacteristic
207C4⋊C8—1222no—
208C4⋊C8—1222no—
209C22⋊C8—1222no—
210C22⋊C8—1222no—
211#97—1222no—
212#97—1222no—
213#95—21no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217C24—611no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—1222no—
224C22×C4—1222no—
225C22×C4—1221no—
226C22×C4—1221no—
227C22×C4—1221no—
228C22×C4—1221no—
229C22×C4—2442no—
230C22×C4—2442no—
231C22×C4—2442no—
232C22×C4C22⋊#692311yescharacteristic
233C22×C4C22⋊#692311yescharacteristic
234C22×C4C22×#692311yescharacteristic
235C2×C8—2442no—
236C2×C8—2442no—
237C4⋊C4—42no—
238C4⋊C4—1222no—
239C4⋊C4—1222no—
240C4⋊C4—2442no—
241C4⋊C4—2442no—
242C4⋊C4—2442no—
243C4⋊C4—2442no—
244C22⋊C4—1222no—
245C22⋊C4—1222no—
246C22⋊C4—2442no—
247C42—21no—
248C42—21no—
249C42—41no—
250C42—41no—
251C42—612no—
252C42—612no—
253C42—2441no—
254C42—2441no—
255C42—2442no—
256C23—612no—
257C23—1221no—
258C23—1221no—
259C23—2441no—
260C23—2441no—
261C23C2×C22⋊#692311yescharacteristic
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—612no—
275C2×C4—612no—
276C2×C4—612no—
277C2×C4—1224no—
278C2×C4—1224no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1222no—
282C2×C4—2448no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4#1451985611yescharacteristic
291C2×C4#1451985611yescharacteristic
292C8—4882no—
293C8—4882no—
294C22—21no—
295C22—21no—
296C22—1222no—
297C22—2442no—
298C22—2442no—
299C22—2441no—
300C22—2441no—
301C22#1684070511yescharacteristic
302C22D61⋊#10011yescharacteristic
303C22D61⋊#10111yescharacteristic
304C4—21no—
305C4—21no—
306C4—42no—
307C4—41no—
308C4—41no—
309C4—81no—
310C4—1222no—
311C4—1222no—
312C4—1222no—
313C4—4881no—
314C4—2442no—
315C2—21no—
316C2—21no—
317C2—2442no—
318C2#2146171911yescharacteristic
319C2#2146172811yescharacteristic
320C2#2146172911yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC22×C61#381
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#8742
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460670C2semidirect
4. #21460670C2semidirect
183. C61#8742semidirect

Maximal subgroups

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

subgroupindex
#214610722
#214606702
#214482992
#874261