Finite Group Databasebeta

← #29579351

Subgroups — #29579351

Order 15616.

406 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
1#21456329C211yesmaximal, characteristic
2C4⋊C4×#92418C211yesmaximal, characteristic
3#21444565C211yesmaximal, characteristic
4#21444317C211yesmaximal, characteristic
5#21444223C211yesmaximal, characteristic
6#21444222C211yesmaximal, characteristic
7C61×#1503C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840165C411yescharacteristic, complemented
10#16840165C411yescharacteristic, complemented
11#16840161—21no—
12#16840161—21no—
13#16840158C411yescharacteristic, complemented
14#16840158C411yescharacteristic, complemented
15#16839815C2211yescharacteristic
16#16839798—21no—
17#16839798—21no—
18C2×C4⋊#92418C2211yescharacteristic
19C2×C4×#92418—21no—
20C2×C4×#92418C2211yescharacteristic
21#16839517—21no—
22#16839514—21no—
23#16839512—21no—
24#16839498—22no—
25#16839494—22no—
26Q8⋊#92418—22no—
27C61×#533C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C4×C4⋊C4×C61C2211yescharacteristic
30C61×#328—22no—
31C22×#92418—21no—
32C22×#92418D411yescharacteristic
33C22×#92418D411yescharacteristic
34#14519777C2×C411yescharacteristic
35#14519777C2×C411yescharacteristic
36#14519769—21no—
37#14519756—21no—
38#14519756—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41#14519736—21no—
42#14519710—21no—
43#14519710—21no—
44#14519710—21no—
45#14519710—21no—
46#14519708—21no—
47#14519708—21no—
48#14519708—21no—
49#14519708—21no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52C4⋊#92418D412yes—
53C22⋊#92418—21no—
54C4×#92418—21no—
55C4×#92418—42no—
56C4×#92418C2×C411yescharacteristic
57C4×#92418C2×C411yescharacteristic
58C4×#92418D411yescharacteristic
59C4×#92418D411yescharacteristic
60C4⋊Q8×C61C2×C411yescharacteristic
61C4⋊Q8×C61C2×C411yescharacteristic
62#125×C61—21no—
63C22⋊Q8×C61—21no—
64C22⋊Q8×C61—21no—
65C4×Q8×C61—21no—
66C4×Q8×C61—21no—
67#117×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C42×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73C4×C8×C61—21no—
74#95×C61D412yes—
75C2×Q8×C61—21no—
76C2×Q8×C61—21no—
77C22×C4×C61—22no—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C2×Dic122—21no—
82C2×Dic122—21no—
83C2×C8×C61—41no—
84C4⋊C4×C61—24no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C42×C61—41no—
93C42×C61—41no—
94C42×C61—41no—
95C42×C61C22×C411yescharacteristic
96C42×C61C2×D411yescharacteristic
97C42×C61C2×D411yescharacteristic
98C42×C61#4111yescharacteristic
99C22⋊Dic61—41no—
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104#11758196—41no—
105#11758196—41no—
106C4×Dic61—41no—
107C2×#92418—21no—
108C2×#92418—21no—
109C2×#92418—22no—
110C2×#92418—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C2×#92418C22⋊C411yescharacteristic
114C2×#92418C22⋊C411yescharacteristic
115C2×#92418C22⋊C411yescharacteristic
116C2×#92418C22⋊C411yescharacteristic
117C2×#92418SD1612yes—
118C2×#92418Q1612yes—
119C23×C61#12111yescharacteristic
120Q8×C61—42no—
121Q8×C61—81no—
122C2×C4×C61—22no—
123C2×C4×C61—24no—
124C2×C4×C61—41no—
125C2×C4×C61—42no—
126C2×C4×C61—42no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61C2×C22⋊C411yescharacteristic
130C2×C4×C61C4×D411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61#12111yescharacteristic
133C2×C4×C61#12411yescharacteristic
134C2×C4×C61#12711yescharacteristic
135C2×C4×C61C2×SD1611yescharacteristic
136C2×C4×C61C2×Q1611yescharacteristic
137C2×C4×C61#13711yescharacteristic
138C2×C4×C61#13711yescharacteristic
139C2×Dic61—41no—
140C2×Dic61—41no—
141Dic122—42no—
142Dic122—81no—
143C8×C61—81no—
144#92418—21no—
145#92418—21no—
146#92418—42no—
147#92418—81no—
148#92418#10312yes—
149#92418#10312yes—
150#9749—611nomaximal, Sylow
151C22×C61—21no—
152C22×C61—21no—
153C22×C61#39011yescharacteristic
154C22×C61#46111yescharacteristic
155C22×C61#46211yescharacteristic
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—44no—
160C4×C61—81no—
161C4×C61—81no—
162C4×C61C2×#10311yescharacteristic
163C4×C61#41911yescharacteristic
164C4×C61#44312yes—
165C4×C61#46111yescharacteristic
166C4×C61#46211yescharacteristic
167Dic61—81no—
168Dic61—81no—
169#3160—611no—
170C8×C4⋊C4—611no—
171#1564—611no—
172#1503—611no—
173#1503D6111yescharacteristic
174#1481—611no—
175#1481—611no—
176C2×C61—21no—
177C2×C61—21no—
178C2×C61#197411yescharacteristic
179C2×C61#197611yescharacteristic
180C2×C61#198111yescharacteristic
181#533—611no—
182#533C2×D6111yescharacteristic
183#500—611no—
184#500—611no—
185#499—1221no—
186#499—1221no—
187#498—611no—
188#498—611no—
189#431—611no—
190#431C2×D6111yescharacteristic
191#427—1221no—
192#427—1221no—
193C2×C4⋊C8—611no—
194C2×C4×C8—611no—
195C2×C4×C8—1221no—
196C4×C4⋊C4C2×D6111yescharacteristic
197#336—1221no—
198#335—1221no—
199#334—1221no—
200#328—22no—
201#328—1222no—
202Q8⋊C8—1222no—
203Q8⋊C8—1222no—
204C61#974911yescharacteristic, complemented, Sylow
205C22×C8—611no—
206C22×C8—611no—
207C22×C8—1221no—
208C4⋊Q8—611no—
209C4⋊Q8—611no—
210C4⋊Q8C4×D6111yescharacteristic
211C4⋊Q8C4×D6111yescharacteristic
212#125—21no—
213#125—1221no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C22⋊Q8—1221no—
217C22⋊Q8—1221no—
218C4×Q8—21no—
219C4×Q8—21no—
220C4×Q8—1221no—
221C4×Q8—1221no—
222#117—21no—
223#117—1221no—
224C2×C4⋊C4—21no—
225C2×C42—21no—
226C2×C42C22×D6111yescharacteristic
227#107—1221no—
228#107—1221no—
229#107—1221no—
230#107—1221no—
231#106—1221no—
232#106—1221no—
233#106—1221no—
234#106—1221no—
235C4⋊C8—21no—
236C4⋊C8—612no—
237C4⋊C8—1221no—
238C4⋊C8—1221no—
239C22⋊C8—21no—
240C22⋊C8—1221no—
241C4×C8—21no—
242C4×C8—611no—
243C4×C8—611no—
244C4×C8—611no—
245C4×C8—611no—
246C4×C8—1221no—
247C4×C8—2442no—
248#95C22⋊D6112yes—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—1221no—
252C2×Q8—1221no—
253C22×C4—22no—
254C22×C4D4×D6111yescharacteristic
255C22×C4#1175822411yescharacteristic
256C22×C4C2×C22⋊D6111yescharacteristic
257C2×C8—41no—
258C2×C8—611no—
259C2×C8—611no—
260C2×C8—612no—
261C2×C8—612no—
262C2×C8—611no—
263C2×C8—611no—
264C2×C8—1221no—
265C2×C8—1221no—
266C2×C8—1222no—
267C2×C8—2441no—
268C2×C8—2441no—
269C2×C8—2441no—
270C4⋊C4—24no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C22⋊C4—41no—
284C22⋊C4—2441no—
285C42—41no—
286C42—41no—
287C42—41no—
288C42—2441no—
289C42C2×C4×D6111yescharacteristic
290C42#1175822211yescharacteristic
291C42D4×D6111yescharacteristic
292C42D4×D6111yescharacteristic
293C23#1451974911yescharacteristic
294Q8—42no—
295Q8—81no—
296Q8—4881no—
297Q8—2442no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4C22⋊C4×D6111yescharacteristic
308C2×C4#1451973711yescharacteristic
309C2×C4C4×C22⋊D6111yescharacteristic
310C2×C4#1451975011yescharacteristic
311C2×C4#1451976311yescharacteristic
312C2×C4#1451977311yescharacteristic
313C2×C4SD16×D6111yescharacteristic
314C2×C4Q16×D6111yescharacteristic
315C2×C4#1451980611yescharacteristic
316C2×C4#1451980911yescharacteristic
317C8—81no—
318C8—612no—
319C8—612no—
320C8—1221no—
321C8—1221no—
322C8—4881no—
323C8—2442no—
324C22—21no—
325C22—21no—
326C22#1683966211yescharacteristic
327C22#1683996511yescharacteristic
328C22#1683997011yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—44no—
333C4—81no—
334C4—81no—
335C4—4881no—
336C4—4881no—
337C4#103×D6111yescharacteristic
338C4#1683976911yescharacteristic
339C4#1683987612yes—
340C4#1683996611yescharacteristic
341C4#1683997111yescharacteristic
342C2—21no—
343C2—21no—
344C2#2144670411yescharacteristic
345C2#2144671411yescharacteristic
346C2#2144674011yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1503C2
socleC22×C61#390
prime radicalC23×C61#121
cosocleC2×C42×C61C23
hypercenter#1503D61
hypocenterC61#9749
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
9. #16840165C4semidirect
10. #16840165C4semidirect
13. #16840158C4semidirect
14. #16840158C4semidirect
204. C61#9749semidirect

Maximal subgroups

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

subgroupindex
#214563292
C4⋊C4×#924182
#214445652
#214443172
#214442232
#214442222
C61×#15032
#974961