Finite Group Databasebeta

← #30602127

Subgroups — #30602127

Order 15616.

476 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊#92420C211yesmaximal, characteristic
2C4×C4⋊#92420C211yesmaximal, characteristic
3#21460655C212yesmaximal
4#21460655C212yesmaximal
5#125×Dic61C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C4⋊#92420C2212yes—
8C2×C4×#92420—21no—
9C2×C4×#92420C2212yes—
10#16840628—21no—
11#16840628—21no—
12#16839661C411yescharacteristic
13#16839661C411yescharacteristic
14#16839648—21no—
15#16839648—21no—
16#16839628C411yescharacteristic
17C4⋊C4×Dic61—21no—
18C4⋊C4×Dic61—21no—
19C4⋊C4×Dic61C2211yescharacteristic
20C4⋊C4×Dic61C2211yescharacteristic
21C42×Dic61C2211yescharacteristic
22C2×#125×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—24no—
26C4⋊#92420—22no—
27C4⋊#92420Q814yes—
28C4×#92420—24no—
29C4×#92420—42no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C4×Dic61—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—
48#125×C61—22no—
49#125×C61C814yescomplemented
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C42×C61C2×C411yescharacteristic
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C2×#92420—24no—
67C2×#92420—24no—
68C2×#92420—42no—
69C2×#92420—42no—
70C2×#92420—42no—
71C2×#92420—42no—
72C4⋊C4×C61—24no—
73C4⋊C4×C61—24no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61C2×C812yes—
77C4⋊C4×C61C2×C812yes—
78C42×C61C2×C812yes—
79C42×C61M1612yes—
80C4⋊Dic61—22no—
81C4⋊Dic61—22no—
82C4⋊Dic61—42no—
83C4⋊Dic61—42no—
84C4×Dic61—22no—
85C4×Dic61—22no—
86C4×Dic61—22no—
87C4×Dic61—21no—
88C4×Dic61—21no—
89C4×Dic61—41no—
90C4×Dic61—42no—
91C4×Dic61—41no—
92C4×Dic61—41no—
93C4×Dic61C2×Q812yes—
94C4×Dic61#4112yes—
95C23×C61C2×C22⋊C411yescharacteristic
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61C22⋊C812yes—
107C2×C4×C61C22⋊C812yes—
108C2×C4×C61C4×Q812yes—
109C2×C4×C61C22×C811yescharacteristic
110C2×C4×C61C2×M1611yescharacteristic
111C2×C4×C61#13112yes—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61#10412yes—
126C2×Dic61C22⋊Q812yes—
127C2×Dic61#12411yescharacteristic
128C2×Dic61C4⋊Q811yescharacteristic
129C2×Dic61#13512yes—
130C2×Dic61AGL(1,ℤ/8)11yescharacteristic
131C2×Dic61#13711yescharacteristic
132#92420—44no—
133#92420—44no—
134#9866—611nomaximal, Sylow
135C22×C61#39111yescharacteristic
136C22×C61C2×C22⋊C811yescharacteristic
137C22×C61#40811yescharacteristic
138C22×C61#41611yescharacteristic
139C22×C61#41711yescharacteristic
140C22×C61C2×#10411yescharacteristic
141C22×C61#42111yescharacteristic
142C4×C61—22no—
143C4×C61—22no—
144C4×C61—42no—
145C4×C61—42no—
146C4×C61C8×Q812yes—
147C4×C61#44612yes—
148Dic61—21no—
149Dic61—21no—
150Dic61—22no—
151Dic61—41no—
152Dic61—81no—
153Dic61—81no—
154Dic61#47812yes—
155Dic61#47912yes—
156C4×#125—611no—
157C4×C4⋊C8—611no—
158C4×C4⋊C8—611no—
159#1279—612no—
160#1279—612no—
161C2×C61#147611yescharacteristic
162C2×C61#147711yescharacteristic
163C2×C61#148211yescharacteristic
164C2×C61#148311yescharacteristic
165C2×C61#198411yescharacteristic
166C2×C61#198611yescharacteristic
167C2×C61#198911yescharacteristic
168C2×#125#692311yescharacteristic
169C2×C4⋊C8—612no—
170C2×C4⋊C8—1221no—
171C2×C4×C8—612no—
172C2×C4×C8—1221no—
173#389—611no—
174#389—611no—
175#387—1221no—
176#387—1221no—
177#382—611no—
178C4×C4⋊C4—611no—
179C4×C4⋊C4—611no—
180C4×C4⋊C4—1221no—
181C4×C4⋊C4—1221no—
182C43—611no—
183#336—1221no—
184#336—1221no—
185C61#986611yescharacteristic, complemented, Sylow
186C22×C8—1222no—
187C22×C8—1222no—
188#125—22no—
189#125#9242014yescomplemented
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4C2×#692311yescharacteristic
197C2×C4⋊C4C2×#692311yescharacteristic
198C2×C42—611no—
199C2×C42—611no—
200C2×C42—611no—
201C2×C42—611no—
202C2×C42—611no—
203C2×C42—611no—
204C2×C42—1221no—
205C2×C42—1221no—
206C2×C42C2×#692311yescharacteristic
207C4⋊C8—614no—
208C4⋊C8—1222no—
209C4⋊C8—1224no—
210C4×C8—1224no—
211C4×C8—2442no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217#95—1221no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—1221no—
225C22×C4—1221no—
226C22×C4C22⋊#692311yescharacteristic
227C22×C4C22⋊#692311yescharacteristic
228C22×C4C22×#692311yescharacteristic
229C2×C8—1224no—
230C2×C8—1224no—
231C2×C8—2442no—
232C2×C8—2442no—
233C2×C8—2442no—
234C2×C8—2442no—
235C4⋊C4—24no—
236C4⋊C4—24no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—1222no—
240C4⋊C4—1222no—
241C4⋊C4—2442no—
242C4⋊C4—2442no—
243C4⋊C4C2×#9242012yes—
244C4⋊C4C2×#9242012yes—
245C42—612no—
246C42—612no—
247C42—1221no—
248C42—1222no—
249C42—1222no—
250C42—1221no—
251C42—1222no—
252C42—2441no—
253C42—2442no—
254C42—2441no—
255C42—2441no—
256C42C2×#9242012yes—
257C42#1175821712yes—
258C23C2×C22⋊#692311yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—612no—
270C2×C4—612no—
271C2×C4—611no—
272C2×C4—611no—
273C2×C4—611no—
274C2×C4—611no—
275C2×C4—612no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4C22⋊#9242012yes—
290C2×C4C22⋊#9242012yes—
291C2×C4Q8×#692312yes—
292C2×C4C22×#9242011yescharacteristic
293C2×C4C2×#1175821711yescharacteristic
294C2×C4#1451986512yes—
295C8—2444no—
296C8—2444no—
297C22(C2×#6923)⋊Q811yescharacteristic
298C22C2×C22⋊#9242011yescharacteristic
299C22#1684073711yescharacteristic
300C22#1684075211yescharacteristic
301C22#1684075311yescharacteristic
302C22D61⋊#10411yescharacteristic
303C22#1684075911yescharacteristic
304C4—22no—
305C4—22no—
306C4—42no—
307C4—42no—
308C4—612no—
309C4—612no—
310C4—1222no—
311C4—1221no—
312C4—1221no—
313C4—4881no—
314C4—4881no—
315C4—2441no—
316C4Q8×#9242012yes—
317C4#1684081312yes—
318C2#2146111011yescharacteristic
319C2#2146111411yescharacteristic
320C2#2146113311yescharacteristic
321C2#2146113711yescharacteristic
322C2#2146198811yescharacteristic
323C2#2146199611yescharacteristic
324C2#2146199911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×#125×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#125#6923
hypocenterC61#9866
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
49. #125×C61C8semidirect
185. C61#9866semidirect
189. #125#92420semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#924202
#214606552
#125×Dic612
#986661