Finite Group Databasebeta

← #30597804

Subgroups — #30597804

Order 15616.

540 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519844C211yesmaximal, characteristic
2C4×#14519844C211yesmaximal, characteristic
3C2×#16840621C212yesmaximal
4#21460697C212yesmaximal
5#21448390C211yesmaximal, characteristic
6C2×#14519844C2212yes—
7C2×#14519844C2212yes—
8C2×C4×#92420—21no—
9C2×C4×#92420—21no—
10#16840628—21no—
11#16840628—21no—
12#16840621C418yescomplemented
13C2×#14519776C2211yescharacteristic
14C2×#14519742—21no—
15#16839666—21no—
16#16839660C411yescharacteristic
17#16839657—21no—
18#16839631C2211yescharacteristic
19C4⋊C4×Dic61C411yescharacteristic
20C4⋊C4×Dic61C411yescharacteristic
21#16839613—21no—
22C42×Dic61C2211yescharacteristic
23C61×#389C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26#14519844—22no—
27#14519844—22no—
28#14519844C2×C414yes—
29#14519844C2×C414yes—
30C4×#92420—42no—
31C4×#92420—42no—
32C22×Dic122—21no—
33#14519776—22no—
34#14519776C2×C414yes—
35#14519742—42no—
36#14519742—42no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61C2311yescharacteristic
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C42×C61C2×C411yescharacteristic
58#95×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C2×Dic122—24no—
71C2×Dic122—41no—
72C2×Dic122—41no—
73C2×Dic122—42no—
74C2×#92420—24no—
75C2×#92420—24no—
76C2×#92420—42no—
77C2×#92420—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—42no—
83C4⋊C4×C61C4212yes—
84C42×C61—41no—
85C4⋊Dic61—21no—
86C4⋊Dic61—41no—
87C4⋊Dic61C4212yes—
88#11758196—24no—
89#11758196—42no—
90#11758196—41no—
91#11758196—41no—
92#11758196—42no—
93C4×Dic61—22no—
94C4×Dic61—22no—
95C4×Dic61—22no—
96C4×Dic61—42no—
97C4×Dic61—42no—
98C4×Dic61D812yes—
99C4×Dic61SD1612yes—
100C4×Dic61SD1612yes—
101C4×Dic61Q1612yes—
102C4×Dic61C22×C412yes—
103C4×Dic61#4112yes—
104C23×C61C2×C22⋊C411yescharacteristic
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—22no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61#10212yes—
118C2×C4×C61#10312yes—
119C2×C4×C61C2×C4211yescharacteristic
120C2×C4×C61#11711yescharacteristic
121C2×Dic61—22no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61#10112yes—
131C2×Dic61#10212yes—
132C2×Dic61#10312yes—
133C2×Dic61C4×D412yes—
134C2×Dic61C4×D412yes—
135C2×Dic61C2×D811yescharacteristic
136C2×Dic61C2×SD1611yescharacteristic
137C2×Dic61C2×SD1611yescharacteristic
138C2×Dic61C2×Q1611yescharacteristic
139C2×Dic61#13512yes—
140C2×Dic61#13512yes—
141Dic122—44no—
142Dic122—44no—
143#92420—44no—
144#92420—44no—
145C4×#332—611nomaximal, Sylow
146C22×C61C4×C22⋊C411yescharacteristic
147C22×C61C2×#10111yescharacteristic
148C22×C61#41311yescharacteristic
149C22×C61C2×#10211yescharacteristic
150C22×C61C2×#10311yescharacteristic
151C22×C61#41611yescharacteristic
152C22×C61#41611yescharacteristic
153C4×C61—22no—
154C4×C61—22no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—42no—
158C4×C61—81no—
159Dic61—41no—
160Dic61—42no—
161Dic61—81no—
162Dic61#33214yescomplemented
163Dic61C4×D812yes—
164Dic61C4×SD1612yes—
165Dic61C4×SD1612yes—
166Dic61C4×Q1612yes—
167C4×C4⋊Q8—611no—
168C4×C4⋊C8—611no—
169C4×C4⋊C8—611no—
170C2×#332—612no—
171#1296—612no—
172C2×C61C2×#33211yescharacteristic
173C2×C61#154011yescharacteristic
174C2×C61#154211yescharacteristic
175C2×C61#154411yescharacteristic
176C2×C61C4×#10111yescharacteristic
177C2×C61C4×#10211yescharacteristic
178C2×C61C4×#10311yescharacteristic
179C2×C4⋊Q8—611no—
180C2×C4×Q8—1221no—
181C2×C4⋊C8—612no—
182C2×C4⋊C8—612no—
183C2×C4×C8—1221no—
184C2×C4×C8—1221no—
185#391—1221no—
186#389—611no—
187#389—1221no—
188#389#692311yescharacteristic
189#384—611no—
190C4×C4⋊C4—611no—
191C4×C4⋊C4—611no—
192C4×C4⋊C4—1221no—
193C43—611no—
194#336—1221no—
195#336—1221no—
196#332—618no—
197C61C4×#33211yescharacteristic, complemented, Sylow
198C22×Q8—1221no—
199C22×C8—1222no—
200C22×C8—1222no—
201C4⋊Q8—614no—
202C4⋊Q8—1222no—
203C4×Q8—2442no—
204C4×Q8—2442no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4C2×#692311yescharacteristic
213C2×C4⋊C4C2×#692311yescharacteristic
214C2×C42—611no—
215C2×C42—611no—
216C2×C42—611no—
217C2×C42—611no—
218C2×C42—611no—
219C2×C42—611no—
220C2×C42—1221no—
221C2×C42—1221no—
222C2×C42C2×#692311yescharacteristic
223C4⋊C8—614no—
224C4⋊C8—614no—
225C4⋊C8—1222no—
226C4⋊C8—1222no—
227C4×C8—2442no—
228C4×C8—2442no—
229#95—21no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233C2×Q8—1224no—
234C2×Q8—2441no—
235C2×Q8—2441no—
236C2×Q8—2442no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4C22⋊#692311yescharacteristic
246C22×C4C22⋊#692311yescharacteristic
247C22×C4C22×#692311yescharacteristic
248C2×C8—1224no—
249C2×C8—1224no—
250C2×C8—2442no—
251C2×C8—2442no—
252C2×C8—2442no—
253C2×C8—2442no—
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—612no—
258C4⋊C4—1224no—
259C4⋊C4—1221no—
260C4⋊C4—2441no—
261C4⋊C4—2442no—
262C4⋊C4—2441no—
263C4⋊C4—2441no—
264C4⋊C4—2442no—
265C4⋊C4C4×#692312yes—
266C42—41no—
267C42—612no—
268C42—612no—
269C42—612no—
270C42—612no—
271C42—612no—
272C42—612no—
273C42—1222no—
274C42—1222no—
275C42—1222no—
276C42—2442no—
277C42—2442no—
278C23C2×C22⋊#692311yescharacteristic
279Q8—2444no—
280Q8—2444no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—612no—
294C2×C4—612no—
295C2×C4—611no—
296C2×C4—611no—
297C2×C4—612no—
298C2×C4—611no—
299C2×C4—611no—
300C2×C4—612no—
301C2×C4—612no—
302C2×C4—612no—
303C2×C4—612no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1222no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4#1451983912yes—
314C2×C4#1451984012yes—
315C2×C4C2×C4×#692311yescharacteristic
316C2×C4#1451985611yescharacteristic
317C8—2444no—
318C8—2444no—
319C22C4×C22⋊#692311yescharacteristic
320C22D61⋊#10111yescharacteristic
321C22#1684074911yescharacteristic
322C22C2×#1451983911yescharacteristic
323C22C2×#1451984011yescharacteristic
324C22#1684075211yescharacteristic
325C22#1684075211yescharacteristic
326C4—21no—
327C4—21no—
328C4—22no—
329C4—22no—
330C4—42no—
331C4—81no—
332C4—614no—
333C4—612no—
334C4—612no—
335C4—612no—
336C4—612no—
337C4—4881no—
338C4—2441no—
339C4—2442no—
340C2D61⋊#33211yescharacteristic
341C2#2146131711yescharacteristic
342C2#2146132111yescharacteristic
343C2#2146132511yescharacteristic
344C2#2146157211yescharacteristic
345C2C4×#1451983911yescharacteristic
346C2C4×#1451984011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61C4×#332
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
12. #16840621C4semidirect
162. Dic61#332semidirect
197. C61C4×#332semidirect

Maximal subgroups

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

subgroupindex
C4×#145198442
C2×#168406212
#214606972
#214483902
C4×#33261