Finite Group Databasebeta

← #30597824

Subgroups — #30597824

Order 15616.

528 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461604C211yesmaximal, characteristic
2C4×#14519844C211yesmaximal, characteristic
3C2×#16840621C212yesmaximal
4#21460697C212yesmaximal
5C4×#14519776C211yesmaximal, characteristic
6C2×#14519844C2212yes—
7C2×#14519844C2212yes—
8C2×#14519832—21no—
9C2×C4×#92420—21no—
10#16840628—21no—
11#16840628—21no—
12#16840621C418yescomplemented
13C2×#14519776C2211yescharacteristic
14C2×C4×Dic122—21no—
15#16839666—21no—
16#16839661C411yescharacteristic
17#16839659—21no—
18#16839658C411yescharacteristic
19#16839631C2211yescharacteristic
20C4×#11758196—21no—
21C4×C4⋊Dic61C411yescharacteristic
22C42×Dic61C2211yescharacteristic
23C4×C4⋊C4×C61C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26#14519844—22no—
27#14519844—22no—
28#14519844C2×C414yes—
29#14519844C2×C414yes—
30#14519832—42no—
31C4×#92420—42no—
32C22×Dic122—21no—
33#14519776—22no—
34#14519776C2×C414yes—
35C4×Dic122—44no—
36C2×C4⋊Dic61—21no—
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×Dic61C2×C411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61C2311yescharacteristic
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C42×C61—21no—
56C2×C42×C61C2×C411yescharacteristic
57#95×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C2×Dic122—24no—
70C2×Dic122—41no—
71C2×Dic122—42no—
72C2×Dic122—41no—
73C2×#92420—24no—
74C2×#92420—24no—
75C2×#92420—42no—
76C2×#92420—42no—
77C2×#92420—42no—
78C2×#92420—42no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61C4212yes—
82C42×C61—22no—
83C42×C61—42no—
84C4⋊Dic61—21no—
85C4⋊Dic61—42no—
86C4⋊Dic61—41no—
87C4⋊Dic61C4212yes—
88#11758196—24no—
89#11758196—42no—
90#11758196—42no—
91#11758196—42no—
92C4×Dic61—22no—
93C4×Dic61—21no—
94C4×Dic61—22no—
95C4×Dic61—21no—
96C4×Dic61—41no—
97C4×Dic61—42no—
98C4×Dic61SD1612yes—
99C4×Dic61Q1612yes—
100C4×Dic61C22×C412yes—
101C4×Dic61#4112yes—
102C23×C61C2×C22⋊C411yescharacteristic
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—22no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61#10112yes—
116C2×C4×C61#10312yes—
117C2×C4×C61C2×C4211yescharacteristic
118C2×C4×C61#11711yescharacteristic
119C2×Dic61—21no—
120C2×Dic61—21no—
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#10312yes—
131C2×Dic61C4×D412yes—
132C2×Dic61C4×D412yes—
133C2×Dic61C2×SD1611yescharacteristic
134C2×Dic61C2×Q1611yescharacteristic
135C2×Dic61#13512yes—
136C2×Dic61AGL(1,ℤ/8)12yes—
137C2×Dic61AGL(1,ℤ/8)11yescharacteristic
138C2×Dic61#13711yescharacteristic
139Dic122—44no—
140Dic122—44no—
141#92420—44no—
142#92420—44no—
143#8237—611nomaximal, Sylow
144C22×C61C4×C22⋊C411yescharacteristic
145C22×C61C2×#10111yescharacteristic
146C22×C61#41311yescharacteristic
147C22×C61C2×#10311yescharacteristic
148C22×C61#41611yescharacteristic
149C22×C61#41711yescharacteristic
150C22×C61#41811yescharacteristic
151C4×C61—22no—
152C4×C61—22no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—42no—
156C4×C61—81no—
157Dic61—22no—
158Dic61—41no—
159Dic61—42no—
160Dic61—81no—
161Dic61C4×SD1612yes—
162Dic61C4×Q1612yes—
163Dic61#44012yes—
164Dic61#44212yes—
165C4×C4⋊Q8—611no—
166#1767—611no—
167C4×C4⋊C8—611no—
168C2×#332—612no—
169#1296—612no—
170C2×C61#154911yescharacteristic
171C2×C61#155011yescharacteristic
172C2×C61#155211yescharacteristic
173C2×C61#155311yescharacteristic
174C2×C61C4×#10111yescharacteristic
175C2×C61C4×#10311yescharacteristic
176C2×C61#176211yescharacteristic
177C2×C4⋊Q8—611no—
178C2×C4×Q8—1221no—
179C2×C4⋊C8—612no—
180C2×C4⋊C8—612no—
181C2×#97—1221no—
182C2×C4×C8—1221no—
183#391—1221no—
184#389—611no—
185#389—611no—
186#389—1221no—
187#384—611no—
188C4×C4⋊C4—611no—
189C4×C4⋊C4—1221no—
190C4×C4⋊C4#692311yescharacteristic
191C43—611no—
192#336—1221no—
193#336—1221no—
194#332—618no—
195C61#823711yescharacteristic, complemented, Sylow
196C22×Q8—1221no—
197C22×C8—1222no—
198C22×C8—1222no—
199C4⋊Q8—614no—
200C4⋊Q8—1222no—
201C4×Q8—2444no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4C2×#692311yescharacteristic
210C2×C4⋊C4C2×#692311yescharacteristic
211C2×C42—21no—
212C2×C42—611no—
213C2×C42—611no—
214C2×C42—611no—
215C2×C42—611no—
216C2×C42—611no—
217C2×C42—611no—
218C2×C42—1221no—
219C2×C42C2×#692311yescharacteristic
220C4⋊C8—614no—
221C4⋊C8—614no—
222C4⋊C8—1222no—
223C4⋊C8—1222no—
224#97—2442no—
225C4×C8—2442no—
226#95—21no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230C2×Q8—1224no—
231C2×Q8—2442no—
232C2×Q8—2441no—
233C2×Q8—2441no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—1221no—
241C22×C4—1221no—
242C22×C4C22⋊#692311yescharacteristic
243C22×C4C22⋊#692311yescharacteristic
244C22×C4C22×#692311yescharacteristic
245C2×C8—1224no—
246C2×C8—1224no—
247C2×C8—2442no—
248C2×C8—2442no—
249C2×C8—2442no—
250C2×C8—2442no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—612no—
254C4⋊C4—1224no—
255C4⋊C4—1221no—
256C4⋊C4—2441no—
257C4⋊C4—2442no—
258C4⋊C4—2442no—
259C4⋊C4—2442no—
260C4⋊C4—2442no—
261C4⋊C4C4×#692312yes—
262C42—22no—
263C42—42no—
264C42—612no—
265C42—612no—
266C42—612no—
267C42—612no—
268C42—1221no—
269C42—1222no—
270C42—1221no—
271C42—1222no—
272C42—2441no—
273C42—2442no—
274C23C2×C22⋊#692311yescharacteristic
275Q8—2444no—
276Q8—2444no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—611no—
290C2×C4—611no—
291C2×C4—612no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—612no—
295C2×C4—612no—
296C2×C4—612no—
297C2×C4—612no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1222no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4#1451983812yes—
310C2×C4#1451984012yes—
311C2×C4C2×C4×#692311yescharacteristic
312C2×C4#1451985611yescharacteristic
313C8—2444no—
314C8—2444no—
315C22C4×C22⋊#692311yescharacteristic
316C22C2×#1451983811yescharacteristic
317C22#1684074811yescharacteristic
318C22C2×#1451984011yescharacteristic
319C22#1684075211yescharacteristic
320C22#1684075311yescharacteristic
321C22#1684075411yescharacteristic
322C4—21no—
323C4—21no—
324C4—22no—
325C4—22no—
326C4—42no—
327C4—81no—
328C4—612no—
329C4—612no—
330C4—612no—
331C4—612no—
332C4—1222no—
333C4—4881no—
334C4—2442no—
335C4—2441no—
336C2#2146133411yescharacteristic
337C2#2146133611yescharacteristic
338C2#2146134011yescharacteristic
339C2#2146134211yescharacteristic
340C2C4×#1451983811yescharacteristic
341C2C4×#1451984011yescharacteristic
342C2#2146158911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#8237
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
12. #16840621C4semidirect
195. C61#8237semidirect

Maximal subgroups

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

subgroupindex
#214616042
C4×#145198442
C2×#168406212
#214606972
C4×#145197762
#823761