Finite Group Databasebeta

← #30595391

Subgroups — #30595391

Order 15616.

444 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461734C211yesmaximal, characteristic
2C4×C4⋊#92420C211yesmaximal, characteristic
3#21460640C212yesmaximal
4#21460638C212yesmaximal
5#21448293C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C4⋊#92420—21no—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×C4×Dic122C411yescharacteristic
13#16839667C411yescharacteristic
14#16839667C2211yescharacteristic
15#16839658C411yescharacteristic
16#16839658C2211yescharacteristic
17#16839644—21no—
18#16839644—21no—
19C4×#11758196—21no—
20#16839608—21no—
21C42×Dic61C2211yescharacteristic
22C4×C4⋊C4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—24no—
26C4⋊#92420—42no—
27C4×#92420—42no—
28C22×Dic122C2×C411yescharacteristic
29C4×Dic122—22no—
30C4×Dic122C814yescomplemented
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61C2×C411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61C2311yescharacteristic
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C42×C61—21no—
51C2×C42×C61C2×C411yescharacteristic
52#95×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22×C411yescharacteristic
58C22×Dic61—21no—
59C22×Dic61—21no—
60C22×Dic61C22⋊C411yescharacteristic
61C22×Dic61C22⋊C411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C2×Dic122—21no—
65C2×Dic122—41no—
66C2×Dic122—41no—
67C2×Dic122C2×C812yes—
68C2×#92420—24no—
69C2×#92420—42no—
70C2×#92420—42no—
71C2×#92420—42no—
72C2×#92420—42no—
73C2×#92420—42no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C42×C61—42no—
77C42×C61C2×C812yes—
78C42×C61M1612yes—
79C4⋊Dic61—21no—
80C4⋊Dic61C2×C812yes—
81#11758196—24no—
82#11758196—42no—
83#11758196—41no—
84#11758196—41no—
85C4×Dic61—24no—
86C4×Dic61—22no—
87C4×Dic61—21no—
88C4×Dic61—21no—
89C4×Dic61—41no—
90C4×Dic61—41no—
91C4×Dic61—41no—
92C4×Dic61SD1612yes—
93C4×Dic61Q1612yes—
94C23×C61C2×C22⋊C411yescharacteristic
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61C22⋊C812yes—
106C2×C4×C61C22⋊C812yes—
107C2×C4×C61#10312yes—
108C2×C4×C61#10412yes—
109C2×C4×C61C22×C811yescharacteristic
110C2×C4×C61C2×M1611yescharacteristic
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—22no—
118C2×Dic61—22no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61#10312yes—
127C2×Dic61C2×SD1611yescharacteristic
128C2×Dic61C2×Q1611yescharacteristic
129C2×Dic61AGL(1,ℤ/8)11yescharacteristic
130C2×Dic61#13711yescharacteristic
131Dic122—42no—
132Dic122—42no—
133#92420—44no—
134#92420—82no—
135#7577—611nomaximal, Sylow
136C22×C61C2×C22⋊C811yescharacteristic
137C22×C61#41011yescharacteristic
138C22×C61#41311yescharacteristic
139C22×C61C2×#10311yescharacteristic
140C22×C61#41711yescharacteristic
141C22×C61C2×#10411yescharacteristic
142C22×C61#42111yescharacteristic
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—22no—
146C4×C61—81no—
147C4×C61—81no—
148C4×C61Q8⋊C814yes—
149Dic61—22no—
150Dic61—21no—
151Dic61—21no—
152Dic61—21no—
153Dic61—21no—
154Dic61—42no—
155Dic61—42no—
156Dic61—41no—
157#2295—611no—
158#1831—611no—
159C4×C4⋊C8—611no—
160#1272—612no—
161#1271—612no—
162C2×C61#145811yescharacteristic
163C2×C61C2×Q8⋊C811yescharacteristic
164C2×C61#147711yescharacteristic
165C2×C61#150911yescharacteristic
166C2×C61#151811yescharacteristic
167C2×C61#152911yescharacteristic
168C2×C61#155011yescharacteristic
169C2×C4×Q8—611no—
170C2×C4⋊C8—1221no—
171C2×C4⋊C8—1221no—
172C2×C4×C8—1221no—
173#391—611no—
174#391—611no—
175#389—611no—
176#389—611no—
177#387—1221no—
178#387—1221no—
179C4×C4⋊C4—1221no—
180C4×C4⋊C4#692311yescharacteristic
181#376—1221no—
182C43—611no—
183#336—612no—
184#336—612no—
185#336—1221no—
186C61#757711yescharacteristic, complemented, Sylow
187C22×Q8—611no—
188C22×C8—1222no—
189C22×C8—1222no—
190C4×Q8—614no—
191C4×Q8—1222no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4C2×#692311yescharacteristic
197C2×C4⋊C4C2×#692311yescharacteristic
198C2×C42—21no—
199C2×C42—611no—
200C2×C42—611no—
201C2×C42—611no—
202C2×C42—611no—
203C2×C42—611no—
204C2×C42—611no—
205C2×C42—1221no—
206C2×C42C2×#692311yescharacteristic
207C4⋊C8—1224no—
208C4⋊C8—2442no—
209C4×C8—2442no—
210#95—21no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217C2×Q8—612no—
218C2×Q8—1221no—
219C2×Q8—2441no—
220C2×Q8—2441no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—1221no—
228C22×C4—1221no—
229C22×C4C22⋊#692311yescharacteristic
230C22×C4C22⋊#692311yescharacteristic
231C22×C4C22×#692311yescharacteristic
232C2×C8—1224no—
233C2×C8—2442no—
234C2×C8—2442no—
235C2×C8—2442no—
236C2×C8—2442no—
237C2×C8—2442no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—612no—
241C4⋊C4—1224no—
242C4⋊C4—1221no—
243C4⋊C4—2441no—
244C4⋊C4—2441no—
245C4⋊C4—2442no—
246C42—42no—
247C42—612no—
248C42—612no—
249C42—1221no—
250C42—1221no—
251C42—1224no—
252C42—1222no—
253C42—2441no—
254C42—2441no—
255C42—2441no—
256C42D61⋊C812yes—
257C42#1175821312yes—
258C23C2×C22⋊#692311yescharacteristic
259Q8—2442no—
260Q8—2442no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—612no—
272C2×C4—611no—
273C2×C4—611no—
274C2×C4—611no—
275C2×C4—611no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—1222no—
283C2×C4—1222no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4#1451983412yes—
292C2×C4#1451983412yes—
293C2×C4#1451984012yes—
294C2×C4#1451984112yes—
295C2×C4C2×D61⋊C811yescharacteristic
296C2×C4C2×#1175821311yescharacteristic
297C8—4882no—
298C8—2444no—
299C22C2×#1451983411yescharacteristic
300C22#1684074111yescharacteristic
301C22#1684074811yescharacteristic
302C22C2×#1451984011yescharacteristic
303C22#1684075311yescharacteristic
304C22C2×#1451984111yescharacteristic
305C22#1684075911yescharacteristic
306C4—21no—
307C4—21no—
308C4—22no—
309C4—81no—
310C4—81no—
311C4—1221no—
312C4—1221no—
313C4—1222no—
314C4—1221no—
315C4—1221no—
316C4—2441no—
317C4—2442no—
318C4—2442no—
319C4#1684061214yes—
320C2#2146105211yescharacteristic
321C2C2×#1684061211yescharacteristic
322C2#2146111611yescharacteristic
323C2#2146122111yescharacteristic
324C2#2146125211yescharacteristic
325C2#2146128411yescharacteristic
326C2#2146133611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#7577
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
30. C4×Dic122C8semidirect
186. C61#7577semidirect

Maximal subgroups

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

subgroupindex
#214617342
C4×C4⋊#924202
#214606402
#214606382
#214482932
#757761