Finite Group Databasebeta

← #29575574

Subgroups — #29575574

Order 15616.

632 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839815C211yesmaximal, characteristic
2C2×#16839499C212yesmaximal
3#21444046C211yesmaximal, characteristic
4#21443697C212yesmaximal
5C61×#2855C211yesmaximal, characteristic
6#16839815—24no—
7C2×C4⋊#92418—21no—
8C2×C22⋊#92418C2212yes—
9C2×C4×#92418—21no—
10C2×#14519684—21no—
11C2×#14519684—21no—
12C2×#14519684C2212yes—
13#16839499—24no—
14C2×C22⋊Q8×C61C2211yescharacteristic
15C22×C42×C61C2211yescharacteristic
16C61×#391C411yescharacteristic, complemented
17C61×#391C411yescharacteristic, complemented
18C61×#389C411yescharacteristic, complemented
19C61×#389C411yescharacteristic, complemented
20C61×#387—21no—
21C61×#387—21no—
22C61×#385—21no—
23C61×#381—21no—
24C61×#380C2211yescharacteristic
25C23×Dic61—22no—
26C22×#92418—22no—
27C4⋊#92418—24no—
28C22⋊#92418—22no—
29C22⋊#92418D414yes—
30C4×#92418—24no—
31#14519684—24no—
32#14519684—22no—
33#14519684—22no—
34#14519684—42no—
35C22×Q8×C61C2×C411yescharacteristic
36C23×C4×C61D411yescharacteristic
37C23×C4×C61D411yescharacteristic
38C23×C4×C61C2311yescharacteristic
39C22⋊Q8×C61—22no—
40C22⋊Q8×C61—22no—
41C2×C4⋊C4×C61—21no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61C2×C411yescharacteristic
45C2×C4⋊C4×C61C2×C411yescharacteristic
46C2×C4⋊C4×C61C2×C411yescharacteristic
47C2×C22⋊C4×C61—21no—
48C2×C22⋊C4×C61—21no—
49C2×C42×C61—22no—
50C2×C42×C61—22no—
51C2×C42×C61C2×C411yescharacteristic
52C2×C42×C61C2×C411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C2×C42×C61D411yescharacteristic
55#95×C61—21no—
56#95×C61—21no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62C24×C61C2×D411yescharacteristic
63C2×Q8×C61—22no—
64C2×Q8×C61—41no—
65C2×Q8×C61—41no—
66C22×C4×C61—22no—
67C22×C4×C61—22no—
68C22×C4×C61—22no—
69C22×C4×C61—22no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—41no—
75C22×C4×C61—41no—
76C22×C4×C61—41no—
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61C22⋊C411yescharacteristic
80C22×C4×C61C22⋊C411yescharacteristic
81C22×C4×C61SD1612yes—
82C22×C4×C61Q1612yes—
83C22×C4×C61C22×C411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D412yes—
86C22×C4×C61#4112yes—
87C22×Dic61—24no—
88C22×Dic61—42no—
89C22×Dic61—42no—
90C22×Dic61—42no—
91C22×Dic61—42no—
92C22×Dic61—42no—
93C22×Dic61—42no—
94C4⋊C4×C61—22no—
95C4⋊C4×C61—42no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—42no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C22⋊C4×C61—42no—
102C22⋊C4×C61—42no—
103C42×C61—22no—
104C42×C61—22no—
105C42×C61—21no—
106C42×C61—21no—
107C42×C61—21no—
108C42×C61—21no—
109C2×#92418—24no—
110C2×#92418—42no—
111C2×#92418—42no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61C2×C22⋊C411yescharacteristic
117C23×C61#12112yes—
118C23×C61C2×SD1611yescharacteristic
119C23×C61C2×Q1611yescharacteristic
120C23×C61#13512yes—
121Q8×C61—82no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—24no—
133C2×C4×C61—24no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—42no—
138C2×C4×C61—42no—
139C2×C4×C61—44no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61#10312yes—
153C2×C4×C61#10312yes—
154C2×C4×C61#10412yes—
155C2×C4×C61C4×D412yes—
156C2×C4×C61#12011yescharacteristic
157C2×C4×C61#12311yescharacteristic
158C2×Dic61—44no—
159C2×Dic61—44no—
160C2×Dic61—44no—
161C2×Dic61—82no—
162C2×Dic61—82no—
163C2×Dic61—82no—
164C2×Dic61—82no—
165#92418—44no—
166#9112—611nomaximal, Sylow
167C22×C61—22no—
168C22×C61—22no—
169C22×C61—22no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—22no—
175C22×C61#38611yescharacteristic
176C22×C61#41011yescharacteristic
177C22×C61#41011yescharacteristic
178C22×C61C2×#10311yescharacteristic
179C22×C61#41611yescharacteristic
180C22×C61C2×#10411yescharacteristic
181C22×C61#42111yescharacteristic
182C22×C61#46512yes—
183C22×C61#46712yes—
184C4×C61—22no—
185C4×C61—22no—
186C4×C61—22no—
187C4×C61—21no—
188C4×C61—22no—
189C4×C61—21no—
190C4×C61—41no—
191C4×C61—81no—
192C4×C61—81no—
193C4×C61—81no—
194C4×C61—81no—
195Dic61—84no—
196C2×#431—611no—
197#2855D6111yescharacteristic
198C2×#328—612no—
199#1434—611no—
200#1294—612no—
201C2×C61—22no—
202C2×C61—22no—
203C2×C61#150011yescharacteristic
204C2×C61#150311yescharacteristic
205C2×C61#151811yescharacteristic
206C2×C61#152111yescharacteristic
207C2×C61#187111yescharacteristic
208C2×C61#189211yescharacteristic
209C2×C61#189911yescharacteristic
210C2×C22⋊Q8C2×D6111yescharacteristic
211C22×C42C2×D6111yescharacteristic
212#431—1224no—
213C2×C4⋊C8—1221no—
214C2×C22⋊C8—612no—
215C2×C4×C8—1221no—
216#391Dic6111yescharacteristic, complemented
217#391Dic6111yescharacteristic, complemented
218#389Dic6111yescharacteristic, complemented
219#389Dic6111yescharacteristic, complemented
220#387—21no—
221#387—21no—
222#385—21no—
223#381—21no—
224#380C2×D6111yescharacteristic
225C2×#95—612no—
226C2×#95—1221no—
227C2×#95—1221no—
228#328—1224no—
229C61#911211yescharacteristic, complemented, Sylow
230C22×Q8C2×Dic6111yescharacteristic
231C23×C4—1222no—
232C23×C4C22⋊D6111yescharacteristic
233C23×C4C22⋊D6111yescharacteristic
234C23×C4C22×D6111yescharacteristic
235C22×C8—1222no—
236C22⋊Q8—22no—
237C22⋊Q8—22no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C2×Dic6111yescharacteristic
242C2×C4⋊C4C2×Dic6111yescharacteristic
243C2×C4⋊C4C2×Dic6111yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C42—22no—
247C2×C42—22no—
248C2×C42C2×Dic6111yescharacteristic
249C2×C42C2×Dic6111yescharacteristic
250C2×C42C22⋊D6111yescharacteristic
251C2×C42C22⋊D6111yescharacteristic
252C4⋊C8—1224no—
253C22⋊C8—614no—
254C22⋊C8—1222no—
255C4×C8—1224no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—1224no—
264#95—1222no—
265#95—1222no—
266#95—2442no—
267C24C2×C22⋊D6111yescharacteristic
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—41no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—1224no—
283C22×C4—2442no—
284C22×C4—2442no—
285C22×C4—2442no—
286C22×C4—2442no—
287C22×C4—2442no—
288C22×C4—2442no—
289C22×C4#1175820112yes—
290C22×C4#1175820212yes—
291C22×C4C22⋊Dic6111yescharacteristic
292C22×C4C22⋊Dic6111yescharacteristic
293C22×C4C22⋊Dic6111yescharacteristic
294C22×C4C22⋊Dic6111yescharacteristic
295C22×C4D4×D6112yes—
296C22×C4#1175822412yes—
297C22×C4C22×Dic6111yescharacteristic
298C22×C4C2×C22⋊D6111yescharacteristic
299C2×C8—1224no—
300C2×C8—2442no—
301C2×C8—2442no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C42—22no—
312C42—22no—
313C42—21no—
314C42—21no—
315C42—21no—
316C42—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×C22⋊Dic6111yescharacteristic
322C23#1451974912yes—
323C23C2×#1175820111yescharacteristic
324C23C2×#1175820211yescharacteristic
325C23#1451979712yes—
326Q8—82no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—44no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—4882no—
358C2×C4—4882no—
359C2×C4—4882no—
360C2×C4—4882no—
361C2×C4—2444no—
362C2×C4—2444no—
363C2×C4—2444no—
364C2×C4#1451970112yes—
365C2×C4#1451970112yes—
366C2×C4#1451970412yes—
367C2×C4D4×Dic6112yes—
368C2×C4#1451974511yescharacteristic
369C2×C4#1451975811yescharacteristic
370C8—2444no—
371C22—21no—
372C22—21no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22#1683964211yescharacteristic
380C22#1683973611yescharacteristic
381C22#1683973611yescharacteristic
382C22C2×#1451970111yescharacteristic
383C22#1683975811yescharacteristic
384C22C2×#1451970411yescharacteristic
385C22#1683977911yescharacteristic
386C22#1683999312yes—
387C22#1684000112yes—
388C4—22no—
389C4—22no—
390C4—21no—
391C4—22no—
392C4—21no—
393C4—22no—
394C4—41no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—81no—
399C4—4884no—
400C2—22no—
401C2—22no—
402C2#2144430511yescharacteristic
403C2#2144431811yescharacteristic
404C2#2144438311yescharacteristic
405C2#2144439611yescharacteristic
406C2#2144612211yescharacteristic
407C2#2144624311yescharacteristic
408C2#2144627811yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#2855C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#2855D61
hypocenterC61#9112
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
16. C61×#391C4semidirect
17. C61×#391C4semidirect
18. C61×#389C4semidirect
19. C61×#389C4semidirect
216. #391Dic61semidirect
217. #391Dic61semidirect
218. #389Dic61semidirect
219. #389Dic61semidirect
229. C61#9112semidirect

Maximal subgroups

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

subgroupindex
C2×#168398152
C2×#168394992
#214440462
#214436972
C61×#28552
#911261