Finite Group Databasebeta

← #29575782

Subgroups — #29575782

Order 15616.

902 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454107C211yesmaximal, characteristic
2C2×#16839624C211yesmaximal, characteristic
3#21445728C211yesmaximal, characteristic
4C2×#16839500C211yesmaximal, characteristic, complemented
5C2×#16839498C211yesmaximal, characteristic, complemented
6#21443697C211yesmaximal, characteristic, complemented
7C61×#1294C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C2×#14519757C412yescomplemented
10C2×#14519756C2211yescharacteristic
11C22×#11758198—21no—
12C2×C22⋊#92418C2211yescharacteristic
13C2×#14519689—22no—
14#16839637—21no—
15#16839636—22no—
16#16839624—22no—
17#16839624—22no—
18#16839619C412yescomplemented
19#16839617—21no—
20C2×#14519684—21no—
21C2×#14519684C2211yescharacteristic
22#16839500—22no—
23#16839498—22no—
24C2×C22⋊C8×C61C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C2×#95×C61C2211yescharacteristic
27C24×D61D411yescharacteristic
28C22×Dic122C2×C411yescharacteristic
29C23×Dic61—21no—
30C23×Dic61D411yescharacteristic
31C22×C4×D61—21no—
32C22×C4×D61—21no—
33C22×C4×D61—21no—
34C22×C4×D61—21no—
35C22×C4×D61—44no—
36C22×C4×D61C2×C412yes—
37C22×C4×D61D412yes—
38C22×#92418—21no—
39#14519757—44no—
40#14519756—21no—
41#14519756—21no—
42#14519756—21no—
43#14519756—21no—
44C2×C4⋊Dic61—22no—
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×#11758196—21no—
47C2×C22⋊Dic61—21no—
48C2×#11758198—24no—
49C2×#11758198—22no—
50C2×#11758198—22no—
51C2×#11758198—44no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54#14519689—44no—
55#14519684—24no—
56#14519684—21no—
57#14519684—22no—
58#14519684D412yes—
59C23×C4×C61—21no—
60C23×C4×C61C2311yescharacteristic
61C22×C8×C61—21no—
62C2×C4⋊C4×C61C2×C412yes—
63C2×C22⋊C4×C61—21no—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66#95×C61—21no—
67#95×C61—21no—
68#95×C61D412yes—
69C24×C61C2×D411yescharacteristic
70C23×D61—21no—
71C23×D61—21no—
72C23×D61—24no—
73C23×D61—21no—
74C23×D61—21no—
75C23×D61—21no—
76C23×D61—21no—
77C23×D61—42no—
78C23×D61C22⋊C412yes—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61—42no—
82C22×C4×C61—42no—
83C22×C4×C61—42no—
84C22×C4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61C22×C411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61#4111yescharacteristic
91C22×C4×C61#4111yescharacteristic
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61—22no—
97C22×Dic61—42no—
98C22×Dic61—42no—
99C22×Dic61—42no—
100C22×Dic61—41no—
101C22×Dic61—41no—
102C22×Dic61C22⋊C412yes—
103C2×C4×D61—24no—
104C2×C4×D61—24no—
105C2×C4×D61—22no—
106C2×C4×D61—22no—
107C2×C4×D61—22no—
108C2×C4×D61—22no—
109C2×C4×D61—42no—
110C2×C4×D61—42no—
111C2×C4×D61—44no—
112C2×C4×D61—44no—
113C2×C4×D61—44no—
114C2×C4×D61—44no—
115C2×Dic122—21no—
116C2×Dic122—21no—
117C2×Dic122—42no—
118C2×C8×C61—42no—
119C2×C8×C61—41no—
120C4⋊C4×C61—42no—
121C22⋊C4×C61—41no—
122C22⋊C4×C61—41no—
123C22⋊Dic61—41no—
124C22⋊Dic61—41no—
125#11758198—44no—
126#11758198—48no—
127#11758198—44no—
128C4⋊Dic61—21no—
129C4⋊Dic61—21no—
130C4⋊Dic61—44no—
131#11758196—41no—
132#11758196—41no—
133C2×#92418—42no—
134C2×#92418—41no—
135C23×C61—22no—
136C23×C61—22no—
137C23×C61C2×C22⋊C411yescharacteristic
138C23×C61#12011yescharacteristic
139C23×C61#12311yescharacteristic
140C23×C61#13511yescharacteristic
141C23×C61#13511yescharacteristic
142C23×C61#13711yescharacteristic
143C23×C61#13711yescharacteristic
144C22×D61—24no—
145C22×D61—24no—
146C22×D61—22no—
147C22×D61—22no—
148C22×D61—22no—
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—44no—
153C22×D61—44no—
154C22×D61—44no—
155C22×D61—44no—
156C22×D61—42no—
157C22×D61—42no—
158C22×D61—41no—
159C22×D61—41no—
160C22×D61—41no—
161C22×D61—41no—
162C22×D61#9914yes—
163C2×C4×C61—22no—
164C2×C4×C61—22no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61—42no—
172C2×C4×C61—42no—
173C2×C4×C61—42no—
174C2×C4×C61—42no—
175C2×C4×C61—82no—
176C2×C4×C61—82no—
177C2×C4×C61C4×D411yescharacteristic
178C2×C4×C61C4×D411yescharacteristic
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#12111yescharacteristic
181C2×Dic61—22no—
182C2×Dic61—22no—
183C2×Dic61—22no—
184C2×Dic61—42no—
185C2×Dic61—42no—
186C2×Dic61—42no—
187C2×Dic61—42no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193C2×Dic61—82no—
194C2×Dic61—82no—
195C4×D61—44no—
196C4×D61—44no—
197C4×D61—44no—
198C4×D61—44no—
199Dic122—81no—
200Dic122—81no—
201C8×C61—81no—
202#92418—81no—
203#9154—611nomaximal, Sylow
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—22no—
209C22×C61—22no—
210C22×C61—22no—
211C22×C61—22no—
212C22×C61#38611yescharacteristic
213C22×C61C2×#9912yes—
214C22×C61#41611yescharacteristic
215C22×C61#41911yescharacteristic
216C22×C61#42112yes—
217C22×C61#45211yescharacteristic
218C22×C61#45211yescharacteristic
219C22×C61#48511yescharacteristic
220C22×C61#48511yescharacteristic
221C2×D61—24no—
222C2×D61—24no—
223C2×D61—24no—
224C2×D61—44no—
225C2×D61—44no—
226C2×D61—44no—
227C2×D61—44no—
228C2×D61—42no—
229C2×D61—42no—
230C2×D61—42no—
231C2×D61—42no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—82no—
237C4×C61—82no—
238Dic61—42no—
239Dic61—82no—
240Dic61—81no—
241Dic61—81no—
242#2848—611no—
243C2×#381—611no—
244#1779—611no—
245C2×#328—611no—
246C2×#328—611no—
247#1294—611no—
248#1294D6111yescharacteristic, complemented
249C2×C61—21no—
250C2×C61—21no—
251C2×C61—21no—
252C2×C61—21no—
253C2×C61#151112yes—
254C2×C61#151612yes—
255C2×C61#187311yescharacteristic
256C2×C61#189711yescharacteristic
257C2×C61#189811yescharacteristic
258D61—44no—
259C24×C4—611no—
260C2×C22⋊Q8—611no—
261C2×C22⋊Q8—612no—
262C22×C22⋊C4—1221no—
263C2×C22⋊C8—611no—
264C2×C22⋊C8—1222no—
265C2×C22⋊C8C2×D6111yescharacteristic
266#385—1222no—
267#385—1221no—
268#381—1222no—
269#381—1222no—
270#380—612no—
271#380C2×D6111yescharacteristic
272#379—1221no—
273C2×#95—611no—
274C2×#95—1221no—
275C2×#95C2×D6111yescharacteristic
276#328—1222no—
277#328—1222no—
278C61#915411yescharacteristic, complemented, Sylow
279C25—611no—
280C22×Q8—611no—
281C23×C4—21no—
282C23×C4—611no—
283C23×C4—612no—
284C23×C4—612no—
285C23×C4—1221no—
286C23×C4—1221no—
287C23×C4—1221no—
288C23×C4—1221no—
289C23×C4—1221no—
290C23×C4—2444no—
291C23×C4C22×D6111yescharacteristic
292C22×C8—21no—
293C22×C8—1221no—
294C22⋊Q8—1221no—
295C22⋊Q8—1221no—
296C22⋊Q8—1221no—
297C22⋊Q8—1221no—
298C22⋊Q8—2444no—
299C2×C4⋊C4—611no—
300C2×C4⋊C4—1222no—
301C2×C4⋊C4—1221no—
302C2×C4⋊C4C4×D6112yes—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—1222no—
305C2×C22⋊C4—1222no—
306C2×C22⋊C4—1224no—
307C2×C22⋊C4—1221no—
308C2×C22⋊C4—2444no—
309C22⋊C8—21no—
310C22⋊C8—21no—
311C22⋊C8—1221no—
312C22⋊C8—1221no—
313C22⋊C8—2444no—
314#95—21no—
315#95—21no—
316#95—612no—
317#95—1222no—
318#95—1224no—
319#95—1221no—
320#95D24412yes—
321C24—612no—
322C24—1224no—
323C24—1221no—
324C24—1221no—
325C24—1221no—
326C24—1221no—
327C24—1221no—
328C24—1221no—
329C24—2442no—
330C24D4×D6111yescharacteristic
331C2×Q8—1221no—
332C2×Q8—1221no—
333C2×Q8—2442no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—612no—
342C22×C4—1224no—
343C22×C4—1224no—
344C22×C4—1221no—
345C22×C4—1221no—
346C22×C4—1222no—
347C22×C4—1222no—
348C22×C4—1222no—
349C22×C4—1222no—
350C22×C4—1221no—
351C22×C4—1221no—
352C22×C4—1222no—
353C22×C4—2442no—
354C22×C4—2442no—
355C22×C4—2444no—
356C22×C4—2444no—
357C22×C4—2444no—
358C22×C4—2444no—
359C22×C4—2442no—
360C22×C4—2442no—
361C22×C4—2442no—
362C22×C4—2441no—
363C22×C4—2441no—
364C22×C4C2×C4×D6111yescharacteristic
365C22×C4C2×D24411yescharacteristic
366C22×C4#1175822211yescharacteristic
367C22×C4D4×D6111yescharacteristic
368C22×C4D4×D6111yescharacteristic
369C22×C4#1175822611yescharacteristic
370C2×C8—42no—
371C2×C8—41no—
372C2×C8—2442no—
373C2×C8—2441no—
374C4⋊C4—42no—
375C4⋊C4—1221no—
376C4⋊C4—1221no—
377C4⋊C4—2444no—
378C4⋊C4—2441no—
379C4⋊C4—2441no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—2444no—
383C22⋊C4—2448no—
384C22⋊C4—2444no—
385C22⋊C4—2441no—
386C22⋊C4—2441no—
387C23—22no—
388C23—22no—
389C23—614no—
390C23—1224no—
391C23—1224no—
392C23—1222no—
393C23—1222no—
394C23—1222no—
395C23—1222no—
396C23—1222no—
397C23—1222no—
398C23—2444no—
399C23—2444no—
400C23—2444no—
401C23—2444no—
402C23—2442no—
403C23—2442no—
404C23—2441no—
405C23—2441no—
406C23—2441no—
407C23—2441no—
408C23C22⋊C4×D6111yescharacteristic
409C23#1451974711yescharacteristic
410C23#1451976211yescharacteristic
411C23#1451979611yescharacteristic
412C23#1451979811yescharacteristic
413C23#1451980611yescharacteristic
414C23#1451980911yescharacteristic
415Q8—4881no—
416Q8—4881no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—1222no—
432C2×C4—1222no—
433C2×C4—1222no—
434C2×C4—4882no—
435C2×C4—4882no—
436C2×C4—2444no—
437C2×C4—2444no—
438C2×C4—2444no—
439C2×C4—2444no—
440C2×C4—2442no—
441C2×C4—2442no—
442C2×C4—2442no—
443C2×C4—2442no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2442no—
447C2×C4—2442no—
448C2×C4—2442no—
449C2×C4#1451973911yescharacteristic
450C2×C4C4×D24411yescharacteristic
451C2×C4#1451975011yescharacteristic
452C2×C4#1451975211yescharacteristic
453C8—81no—
454C8—4881no—
455C22—22no—
456C22—22no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—22no—
462C22—22no—
463C22—1224no—
464C22—1224no—
465C22—1224no—
466C22—2444no—
467C22—2444no—
468C22—2444no—
469C22—2444no—
470C22—2442no—
471C22—2442no—
472C22—2442no—
473C22—2442no—
474C22#1683964011yescharacteristic
475C22#99×D6112yes—
476C22#1683975511yescharacteristic
477C22#1683976911yescharacteristic
478C22#1683977712yes—
479C22#1683992511yescharacteristic
480C22#1683992711yescharacteristic
481C22#1684010511yescharacteristic
482C22#1684010611yescharacteristic
483C4—21no—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—82no—
488C4—82no—
489C4—4882no—
490C4—4881no—
491C4—4881no—
492C4—2442no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—2444no—
498C2#2144435012yes—
499C2#2144437212yes—
500C2#2144613011yescharacteristic
501C2#2144626611yescharacteristic
502C2#2144627111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61D4
cosocleC23×C4×C61C23
hypercenter#1294D61
hypocenterC61#9154
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
4. C2×#16839500C2semidirect
5. C2×#16839498C2semidirect
6. #21443697C2semidirect
7. C61×#1294C2semidirect
9. C2×#14519757C4semidirect
18. #16839619C4semidirect
248. #1294D61semidirect
278. C61#9154semidirect

Maximal subgroups

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

subgroupindex
#214541072
C2×#168396242
#214457282
C2×#168395002
C2×#168394982
#214436972
C61×#12942
#915461