Finite Group Databasebeta

← #29575296

Subgroups — #29575296

Order 15616.

618 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840109C211yesmaximal, characteristic
2#21448877C211yesmaximal, characteristic, complemented
3#21446746C211yesmaximal, characteristic
4#21446745C211yesmaximal, characteristic
5C2×#16839507C211yesmaximal, characteristic, complemented
6#21443659C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C2×#14519774C2211yescharacteristic
10C2×#14519742—21no—
11#16840109—22no—
12#16840109C414yescomplemented
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519699—22no—
15C2×#14519699—21no—
16C2×#14519699—21no—
17C2×#14519697—21no—
18C2×#14519697—21no—
19#16839667—21no—
20#16839660—21no—
21#16839647—22no—
22C4×C4⋊Dic61—21no—
23C4×C4⋊Dic61C2211yescharacteristic
24#16839507—22no—
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4×C8×C61C2211yescharacteristic
27C4×C4⋊C4×C61C2211yescharacteristic
28C22×Dic122—21no—
29C22×D244—21no—
30C22×D244—21no—
31C22×D244—21no—
32C22×#92418—21no—
33#14519777—21no—
34#14519777—21no—
35#14519777C2×C412yes—
36#14519777D412yes—
37#14519774—21no—
38#14519774—21no—
39#14519774—21no—
40#14519774C2×C412yes—
41#14519742—42no—
42#14519742—42no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61D411yescharacteristic
45C2×C4⋊Dic61D412yes—
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758196—22no—
48C2×C4×Dic61—22no—
49C2×C4×Dic61—21no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52#14519699—28no—
53#14519699—42no—
54#14519699—42no—
55#14519697—42no—
56#14519697—42no—
57#14519684—22no—
58#14519684—22no—
59#14519684—21no—
60C22×C8×C61—21no—
61C22×C8×C61—21no—
62C2×C4⋊C4×C61D411yescharacteristic
63C2×C4⋊C4×C61D411yescharacteristic
64C2×C42×C61—21no—
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4×C8×C61—21no—
69C4×C8×C61C2×C412yes—
70#95×C61—21no—
71C23×D61—41no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×Dic61—22no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C2×D244—22no—
81C2×D244—22no—
82C2×D244—22no—
83C2×D244—42no—
84C2×D244—42no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244—41no—
95C2×D244—41no—
96C2×Dic122—22no—
97C2×Dic122—22no—
98C2×Dic122—41no—
99C2×Dic122—41no—
100C2×Dic122—41no—
101C2×Dic122—41no—
102C2×C8×C61—22no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61D812yes—
112C42×C61—41no—
113C42×C61—41no—
114C42×C61C22×C411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61#4111yescharacteristic
117C42×C61#4111yescharacteristic
118C4⋊Dic61—22no—
119C4⋊Dic61—22no—
120C4⋊Dic61—22no—
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61—21no—
124C4⋊Dic61C22⋊C414yes—
125C4⋊Dic61SD1612yes—
126#11758196—44no—
127C4×Dic61—44no—
128C4×Dic61—41no—
129C4×Dic61—41no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418—41no—
133C23×C61#12011yescharacteristic
134C22×D61—42no—
135C22×D61—81no—
136C22×D61—81no—
137C22×D61—81no—
138C22×D61—81no—
139C22×D61—81no—
140C22×D61—81no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—22no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61C2×C22⋊C411yescharacteristic
150C2×C4×C61C4×D411yescharacteristic
151C2×C4×C61C4×D411yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61#12311yescharacteristic
155C2×C4×C61C2×D811yescharacteristic
156C2×C4×C61C2×SD1611yescharacteristic
157C2×C4×C61#13511yescharacteristic
158C2×C4×C61#13511yescharacteristic
159C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C61#13711yescharacteristic
163C2×Dic61—24no—
164C2×Dic61—22no—
165C2×Dic61—41no—
166C2×Dic61—42no—
167C2×Dic61—42no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172D244—44no—
173D244—42no—
174D244—42no—
175D244—42no—
176D244—42no—
177D244—82no—
178D244—81no—
179D244—81no—
180D244—81no—
181D244—81no—
182Dic122—42no—
183Dic122—42no—
184Dic122—42no—
185Dic122—42no—
186C8×C61—42no—
187C8×C61—81no—
188#92418—81no—
189#9062—611nomaximal, Sylow
190C22×C61#38611yescharacteristic
191C22×C61#44711yescharacteristic
192C22×C61#44811yescharacteristic
193C22×C61#44911yescharacteristic
194C22×C61#44911yescharacteristic
195C22×C61#45411yescharacteristic
196C22×C61#45411yescharacteristic
197C2×D61—82no—
198C2×D61—82no—
199C2×D61—82no—
200C2×D61—161no—
201C2×D61—161no—
202C2×D61—161no—
203C2×D61—161no—
204C4×C61—21no—
205C4×C61—21no—
206C4×C61—42no—
207C4×C61—81no—
208C4×C61C4×D811yescharacteristic
209C4×C61C4×SD1611yescharacteristic
210C4×C61#44011yescharacteristic
211C4×C61#44211yescharacteristic
212C4×C61#45911yescharacteristic
213C4×C61#46011yescharacteristic
214C4×C61#46311yescharacteristic
215C4×C61#46411yescharacteristic
216Dic61—44no—
217Dic61—42no—
218Dic61—81no—
219C2×#486—611no—
220#2365—611no—
221#1982—611no—
222#1982—611no—
223C2×#332—611no—
224#1279—611no—
225#1279D6111yescharacteristic, complemented
226C2×C61#162511yescharacteristic
227C2×C61#162611yescharacteristic
228C2×C61#162711yescharacteristic
229C2×C61#162811yescharacteristic
230C2×C61#187911yescharacteristic
231C2×C61#188011yescharacteristic
232C2×C61#188811yescharacteristic
233D61—162no—
234C2×C4⋊Q8—611no—
235C2×#127—611no—
236C2×C4×Q8—1221no—
237#486—614no—
238#486—1222no—
239C2×C4⋊C8—611no—
240C2×C4⋊C8C2×D6111yescharacteristic
241C2×#102—1222no—
242C2×#102—1221no—
243C2×#102—1221no—
244C2×#102—1221no—
245C2×#102—1221no—
246C2×C4×C8C2×D6111yescharacteristic
247#391—1221no—
248#389—1221no—
249#387—1222no—
250C4×C4⋊C4—611no—
251C4×C4⋊C4—1221no—
252C4×C4⋊C4C2×D6111yescharacteristic
253#332—1222no—
254C61#906211yescharacteristic, complemented, Sylow
255C22×Q8—1221no—
256C22×D4—1221no—
257C22×D4—1221no—
258C22×D4—1221no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—1221no—
262C4⋊Q8—612no—
263C4⋊Q8—612no—
264C4⋊Q8—1221no—
265C4⋊Q8—1221no—
266#127—612no—
267#127—1221no—
268#127—1221no—
269#127—1221no—
270C4×Q8—2442no—
271C4×Q8—2442no—
272C2×C4⋊C4—612no—
273C2×C4⋊C4—611no—
274C2×C4⋊C4—611no—
275C2×C4⋊C4—1221no—
276C2×C4⋊C4—1222no—
277C2×C4⋊C4D24411yescharacteristic
278C2×C4⋊C4D24411yescharacteristic
279C2×C42—21no—
280C2×C42—1222no—
281C2×C42—1221no—
282C2×C42C22×D6111yescharacteristic
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—1221no—
286C4⋊C8—1221no—
287#102—1228no—
288#102—2442no—
289#102—2442no—
290#102—2442no—
291#102—2442no—
292C4×C8—21no—
293C4×C8C4×D6112yes—
294#95—21no—
295#95—1222no—
296#95—1222no—
297#95—1221no—
298C24—2441no—
299C2×Q8—1222no—
300C2×Q8—1222no—
301C2×Q8—2441no—
302C2×Q8—2441no—
303C2×Q8—2441no—
304C2×Q8—2441no—
305C2×D4—1222no—
306C2×D4—1222no—
307C2×D4—1222no—
308C2×D4—2442no—
309C2×D4—2442no—
310C2×D4—2441no—
311C2×D4—2441no—
312C2×D4—2441no—
313C2×D4—2441no—
314C2×D4—2441no—
315C2×D4—2441no—
316C2×D4—2441no—
317C2×D4—2441no—
318C2×D4—2441no—
319C2×D4—2441no—
320C2×D4—2441no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—1221no—
324C22×C4—1222no—
325C22×C4—1221no—
326C22×C4C2×D24411yescharacteristic
327C22×C4D4×D6111yescharacteristic
328C22×C4D4×D6111yescharacteristic
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—2441no—
336C2×C8—2441no—
337C2×C8—2441no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—614no—
342C4⋊C4—612no—
343C4⋊C4—1221no—
344C4⋊C4—1222no—
345C4⋊C4—1222no—
346C4⋊C4—1222no—
347C4⋊C4—1221no—
348C4⋊C4—1221no—
349C4⋊C4—2444no—
350C4⋊C4D48812yes—
351C42—41no—
352C42—41no—
353C42—2444no—
354C42—2441no—
355C42—2441no—
356C42C2×C4×D6111yescharacteristic
357C42#1175822211yescharacteristic
358C42D4×D6111yescharacteristic
359C42#1175822611yescharacteristic
360C23—4881no—
361C23—4881no—
362C23—4881no—
363C23—4881no—
364C23—4881no—
365C23—4881no—
366C23—2442no—
367C23#1451974711yescharacteristic
368Q8—2442no—
369Q8—2442no—
370Q8—2442no—
371Q8—2442no—
372D4—4882no—
373D4—4881no—
374D4—4881no—
375D4—4881no—
376D4—4881no—
377D4—2444no—
378D4—2442no—
379D4—2442no—
380D4—2442no—
381D4—2442no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—1224no—
391C2×C4—1222no—
392C2×C4—2441no—
393C2×C4—2441no—
394C2×C4—2441no—
395C2×C4—2441no—
396C2×C4—2441no—
397C2×C4—2442no—
398C2×C4—2442no—
399C2×C4C22⋊C4×D6111yescharacteristic
400C2×C4#1451973911yescharacteristic
401C2×C4C4×D24411yescharacteristic
402C2×C4#1451975011yescharacteristic
403C2×C4#1451975211yescharacteristic
404C2×C4#1451976211yescharacteristic
405C2×C4C2×D48811yescharacteristic
406C2×C4SD16×D6111yescharacteristic
407C2×C4#1451979811yescharacteristic
408C2×C4#1451979911yescharacteristic
409C2×C4#1451980111yescharacteristic
410C2×C4#1451980511yescharacteristic
411C2×C4#1451980511yescharacteristic
412C2×C4#1451980911yescharacteristic
413C8—42no—
414C8—81no—
415C8—4881no—
416C22—9761no—
417C22—9761no—
418C22—9761no—
419C22—9761no—
420C22—4882no—
421C22—4882no—
422C22—4882no—
423C22#1683964011yescharacteristic
424C22#1683989811yescharacteristic
425C22#1683990211yescharacteristic
426C22#1683990811yescharacteristic
427C22#1683990911yescharacteristic
428C22#1683993611yescharacteristic
429C22#1683993611yescharacteristic
430C4—21no—
431C4—21no—
432C4—42no—
433C4—81no—
434C4—4881no—
435C4—2444no—
436C4—2442no—
437C4C4×D48811yescharacteristic
438C4#1683984911yescharacteristic
439C4#1683986111yescharacteristic
440C4#1683987511yescharacteristic
441C4#1683995811yescharacteristic
442C4#1683996111yescharacteristic
443C4#1683997811yescharacteristic
444C4#1683998711yescharacteristic
445C2—9762no—
446C2#2144491011yescharacteristic
447C2#2144491711yescharacteristic
448C2#2144492411yescharacteristic
449C2#2144493111yescharacteristic
450C2#2144616611yescharacteristic
451C2#2144617511yescharacteristic
452C2#2144622111yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC23×C61#120
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenter#1279D61
hypocenterC61#9062
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #21448877C2semidirect
5. C2×#16839507C2semidirect
6. #21443659C2semidirect
7. C61×#1279C2semidirect
12. #16840109C4semidirect
225. #1279D61semidirect
254. C61#9062semidirect

Maximal subgroups

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

subgroupindex
C2×#168401092
#214488772
#214467462
#214467452
C2×#168395072
#214436592
C61×#12792
#906261