Finite Group Databasebeta

← #30597580

Subgroups — #30597580

Order 15616.

530 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊#92420C211yesmaximal, characteristic
2C4×#14519832C211yesmaximal, characteristic
3C2×Q8⋊#92420C212yesmaximal
4#21460655C212yesmaximal
5#21448294C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×#14519832—21no—
8C2×#14519832—21no—
9C2×C4×#92420—21no—
10C2×C4×#92420C2212yes—
11#16840628—21no—
12Q8⋊#92420C418yescomplemented
13C2×Q8×Dic61C2211yescharacteristic
14#16839669C411yescharacteristic
15#16839660C411yescharacteristic
16#16839658C411yescharacteristic
17#16839647—21no—
18#16839645—21no—
19C4⋊C4×Dic61C2211yescharacteristic
20#16839613—21no—
21#16839607—21no—
22C42×Dic61C2211yescharacteristic
23C61×#391C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26C4⋊#92420—22no—
27C4⋊#92420C2×C414yes—
28#14519832—24no—
29#14519832—24no—
30C4×#92420—22no—
31C4×#92420—42no—
32C4×#92420C2×C414yes—
33Q8×Dic61—22no—
34Q8×Dic61C2×C414yes—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61C2311yescharacteristic
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C22×Q8×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C42×C61C2×C411yescharacteristic
56#95×C61—21no—
57#95×C61—21no—
58C2×Q8×C61—21no—
59C2×Q8×C61—22no—
60C2×Q8×C61—22no—
61C2×Q8×C61C4212yes—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C2×#92420—24no—
74C2×#92420—24no—
75C2×#92420—24no—
76C2×#92420—24no—
77C2×#92420—42no—
78C2×#92420—42no—
79C4⋊C4×C61—22no—
80C42×C61—22no—
81C4⋊Dic61—21no—
82C4⋊Dic61—24no—
83C4⋊Dic61—22no—
84C4⋊Dic61C4212yes—
85#11758196—42no—
86#11758196—42no—
87C4×Dic61—22no—
88C4×Dic61—22no—
89C4×Dic61—22no—
90C4×Dic61—24no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C4×Dic61—22no—
94C4×Dic61—41no—
95C4×Dic61—41no—
96C4×Dic61C22×C412yes—
97C4×Dic61#4112yes—
98C23×C61C2×C22⋊C411yescharacteristic
99Q8×C61—24no—
100Q8×C61—42no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—22no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61#10412yes—
113C2×C4×C61C2×C4211yescharacteristic
114C2×C4×C61#11711yescharacteristic
115C2×C4×C61#13112yes—
116C2×C4×C61#13112yes—
117C2×Dic61—21no—
118C2×Dic61—21no—
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#10412yes—
131C2×Dic61C4×D412yes—
132C2×Dic61C4×D412yes—
133C2×Dic61AGL(1,ℤ/8)11yescharacteristic
134C2×Dic61#13712yes—
135C2×Dic61#13711yescharacteristic
136#92420—28no—
137#92420—44no—
138#8180—611nomaximal, Sylow
139C22×C61C4×C22⋊C411yescharacteristic
140C22×C61#40811yescharacteristic
141C22×C61#40811yescharacteristic
142C22×C61#41711yescharacteristic
143C22×C61#41911yescharacteristic
144C22×C61C2×#10411yescharacteristic
145C22×C61C2×#10411yescharacteristic
146C4×C61—22no—
147C4×C61—41no—
148C4×C61—42no—
149C4×C61—81no—
150C4×C61#40512yes—
151C4×C61#43312yes—
152Dic61—22no—
153Dic61—22no—
154Dic61—41no—
155Dic61—42no—
156Dic61—81no—
157Dic61#44012yes—
158Dic61#44112yes—
159#2295—611no—
160C4×C4⋊C8—611no—
161C4×#97—611no—
162C2×Q8⋊C8—612no—
163#1279—612no—
164C2×C61#148311yescharacteristic
165C2×C61#148311yescharacteristic
166C2×C61#148511yescharacteristic
167C2×C61#148511yescharacteristic
168C2×C61#175011yescharacteristic
169C2×C61C4×#10411yescharacteristic
170C2×C61#176311yescharacteristic
171C2×C4×Q8—611no—
172C2×C4⋊C8—612no—
173C2×#97—1221no—
174C2×#97—1221no—
175C2×C4×C8—612no—
176C2×C4×C8—1221no—
177#391—611no—
178#391#692311yescharacteristic
179#389—611no—
180#389—611no—
181#387—1221no—
182#387—1221no—
183C4×C4⋊C4—611no—
184C4×C4⋊C4—1221no—
185#376—1221no—
186C43—611no—
187#336—1221no—
188Q8⋊C8—618no—
189C61#818011yescharacteristic, complemented, Sylow
190C22×Q8C2×#692311yescharacteristic
191C22×C8—1222no—
192C22×C8—1222no—
193C4×Q8—614no—
194C4×Q8—1222no—
195C2×C4⋊C4—611no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4—1221no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4C2×#692311yescharacteristic
201C2×C42—611no—
202C2×C42—611no—
203C2×C42—611no—
204C2×C42—611no—
205C2×C42—611no—
206C2×C42—611no—
207C2×C42—1221no—
208C2×C42—1221no—
209C2×C42C2×#692311yescharacteristic
210C4⋊C8—614no—
211C4⋊C8—1222no—
212#97—1224no—
213#97—1224no—
214C4×C8—614no—
215C4×C8—1222no—
216C4×C8—2442no—
217#95—21no—
218#95—21no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223#95—1221no—
224C2×Q8—21no—
225C2×Q8—22no—
226C2×Q8—22no—
227C2×Q8C4×#692312yes—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4C22⋊#692311yescharacteristic
237C22×C4C22⋊#692311yescharacteristic
238C22×C4C22×#692311yescharacteristic
239C2×C8—1224no—
240C2×C8—1224no—
241C2×C8—1224no—
242C2×C8—1224no—
243C2×C8—2442no—
244C2×C8—2442no—
245C4⋊C4—22no—
246C4⋊C4—612no—
247C4⋊C4—1224no—
248C4⋊C4—1221no—
249C4⋊C4—1222no—
250C4⋊C4—2442no—
251C4⋊C4—2442no—
252C42—22no—
253C42—612no—
254C42—612no—
255C42—1221no—
256C42—1222no—
257C42—1221no—
258C42—1222no—
259C42—1224no—
260C42—1222no—
261C42—1222no—
262C42—2441no—
263C42—2441no—
264C23C2×C22⋊#692311yescharacteristic
265Q8—24no—
266Q8—42no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—611no—
279C2×C4—611no—
280C2×C4—612no—
281C2×C4—612no—
282C2×C4—612no—
283C2×C4—612no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1222no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4#1451984212yes—
298C2×C4C2×C4×#692311yescharacteristic
299C2×C4#1451985611yescharacteristic
300C2×C4#1451986412yes—
301C2×C4#1451986412yes—
302C8—1228no—
303C8—2444no—
304C22C4×C22⋊#692311yescharacteristic
305C22#1684073511yescharacteristic
306C22#1684073611yescharacteristic
307C22#1684075311yescharacteristic
308C22#1684075511yescharacteristic
309C22D61⋊#10411yescharacteristic
310C22C2×#1451984211yescharacteristic
311C4—22no—
312C4—42no—
313C4—41no—
314C4—81no—
315C4—612no—
316C4—612no—
317C4—1222no—
318C4—1222no—
319C4—4881no—
320C4—2442no—
321C4—2441no—
322C4#1684072612yes—
323C4#1684078612yes—
324C2#2146113511yescharacteristic
325C2#2146113611yescharacteristic
326C2#2146114111yescharacteristic
327C2#2146114211yescharacteristic
328C2#2146154911yescharacteristic
329C2C4×#1451984211yescharacteristic
330C2#2146159111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#8180
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
12. Q8⋊#92420C4semidirect
189. C61#8180semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#924202
C4×#145198322
C2×Q8⋊#924202
#214606552
#214482942
#818061