Finite Group Databasebeta

← #29834878

Subgroups — #29834878

Order 15616.

568 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455490C211yesmaximal, characteristic
2#21454415C211yesmaximal, characteristic, complemented
3#21448025C211yesmaximal, characteristic, complemented
4#21448024C211yesmaximal, characteristic, complemented
5#21448020C211yesmaximal, characteristic, complemented
6#21448013C211yesmaximal, characteristic, complemented
7#21448011C211yesmaximal, characteristic, complemented
8#21448001C211yesmaximal, characteristic, complemented
9#21447999C211yesmaximal, characteristic, complemented
10#21447604C211yesmaximal, characteristic, complemented
11#366×D61C211yesmaximal, characteristic, complemented
12#21447530C211yesmaximal, characteristic, complemented
13#21447525C211yesmaximal, characteristic, complemented
14#21447431C211yesmaximal, characteristic, complemented
15C61×#2236C211yesmaximal, characteristic, complemented
16C2×#14519800C2211yescharacteristic
17C2×#14519783C2211yescharacteristic
18#16840342—21no—
19#16840243—21no—
20C2×#14519716C2211yescharacteristic
21C2×C16×D61C2211yescharacteristic
22#16840011—21no—
23#16840010—21no—
24#16840000C2211yescharacteristic
25#16839999C2211yescharacteristic
26#16839998C2211yescharacteristic
27#16839803—21no—
28#16839803—21no—
29#16839802—21no—
30#16839800C2211yescharacteristic
31#16839799C2211yescharacteristic
32#16839799C2211yescharacteristic
33#107×D61C2211yescharacteristic
34#107×D61C2211yescharacteristic
35#107×D61C2211yescharacteristic
36#16839762—21no—
37#16839590C2211yescharacteristic
38#16839589C2211yescharacteristic
39#16839588C2211yescharacteristic
40#16839587C2211yescharacteristic
41#16839587C2211yescharacteristic
42#16839587C2211yescharacteristic
43#16839566C2211yescharacteristic
44#16839566C2211yescharacteristic
45#16839564C2211yescharacteristic
46#16839564C2211yescharacteristic
47#16839562C2211yescharacteristic
48#16839562C2211yescharacteristic
49C22⋊#11758185C2211yescharacteristic
50#16839541C2211yescharacteristic
51#16839541C2211yescharacteristic
52C61×#467C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C61×#366C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×#358C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×C22⋊C16C2211yescharacteristic
59C2×#11758226—21no—
60C2×#11758222D411yescharacteristic
61#14519800—22no—
62#14519800—22no—
63C2×#11758201—21no—
64C2×D488C2311yescharacteristic
65#14519783—22no—
66#14519783—22no—
67C2×#11758194D411yescharacteristic
68C2×#11758189D411yescharacteristic
69C2×#11758189D411yescharacteristic
70C2×C8×D61C2311yescharacteristic
71C2×C8×D61C2311yescharacteristic
72#14519755—41no—
73#14519753—21no—
74#14519752—21no—
75#14519752—41no—
76#14519751—21no—
77#14519750—41no—
78#14519750—41no—
79#14519742—41no—
80#14519739—41no—
81C4×C22⋊D61—41no—
82C4×C22⋊D61—41no—
83#14519736—21no—
84#14519735—21no—
85#14519735—21no—
86C4⋊C4×D61—21no—
87C4⋊C4×D61—21no—
88C4⋊C4×D61—21no—
89#14519716—22no—
90C2×#11758185C2311yescharacteristic
91C2×#11758185C2311yescharacteristic
92C16×D61—22no—
93#14519711C2311yescharacteristic
94#14519711C2311yescharacteristic
95#14519711C2311yescharacteristic
96#14519710—21no—
97#14519710—21no—
98#14519710—21no—
99#14519709—21no—
100#14519708—21no—
101#14519708—21no—
102#14519701—21no—
103#14519699—21no—
104#14519697—21no—
105C2×Q16×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22⋊Q8×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111#107×C61—21no—
112#107×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#107×C61C2311yescharacteristic
115#103×C61—21no—
116C2×Q8×C61—21no—
117C22×C4×C61—41no—
118C22×C4×C61C2×D411yescharacteristic
119C2×C22⋊D61—41no—
120C2×C22⋊D61D811yescharacteristic
121C2×C22⋊D61D811yescharacteristic
122#11758226—42no—
123#11758226—42no—
124#11758222—22no—
125#11758222—22no—
126C2×D244—21no—
127C2×D244—41no—
128C2×D244—41no—
129C2×D244D811yescharacteristic
130C2×C4×D61—41no—
131C2×C4×D61—41no—
132C2×C4×D61—41no—
133C2×C4×D61—41no—
134C2×C4×D61C2×D411yescharacteristic
135C2×C4×D61C2×D411yescharacteristic
136C2×Dic122D811yescharacteristic
137Q16×C61—21no—
138Q16×C61—21no—
139C2×C8×C61—21no—
140C2×C8×C61—21no—
141C2×C8×C61C2×D411yescharacteristic
142C2×C8×C61C2411yescharacteristic
143C4⋊C4×C61—21no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—41no—
147C4⋊C4×C61—41no—
148C22⋊C4×C61—41no—
149C22⋊Dic61—41no—
150#11758201—42no—
151#11758198—41no—
152#11758198—41no—
153#11758198—41no—
154#11758198—41no—
155#11758198—41no—
156C4⋊Dic61—21no—
157C4⋊Dic61—21no—
158C4⋊Dic61—21no—
159#11758196—41no—
160#11758196—41no—
161#11758196—41no—
162#11758196—41no—
163C4×Dic61—41no—
164C4×Dic61—41no—
165C4×Dic61—41no—
166#11758194—22no—
167C2×#92418C2×D411yescharacteristic
168C2×#92418C2×D411yescharacteristic
169D488—21no—
170D488—21no—
171#11758189—22no—
172#11758189—22no—
173C8×D61—21no—
174C8×D61—21no—
175C8×D61#4112yes—
176C8×D61#4112yes—
177C16×C61—21no—
178C16×C61—21no—
179#11758185—21no—
180#11758185—21no—
181C23×C61C2×D811yescharacteristic
182C22×D61—41no—
183C22×D61C2×D811yescharacteristic
184C22×D61C2×D811yescharacteristic
185Q8×C61—41no—
186Q8×C61—41no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—161no—
194C2×C4×C61C2×D811yescharacteristic
195C2×C4×C61C22×D411yescharacteristic
196C22⋊D61—22no—
197C22⋊D61—22no—
198C22⋊D61—161no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61C2×D811yescharacteristic
203C2×Dic61C2×D811yescharacteristic
204D244—22no—
205D244—41no—
206D244—41no—
207D244—82no—
208D244—161no—
209C4×D61—21no—
210C4×D61—21no—
211C4×D61—82no—
212C4×D61—161no—
213C4×D61—161no—
214C4×D61—161no—
215C4×D61#12312yes—
216C4×D61#13712yes—
217Dic122—22no—
218C8×C61—21no—
219C8×C61C2×#4111yescharacteristic
220C8×C61C2×#4111yescharacteristic
221#92418—21no—
222#92418#12312yes—
223#33652—611nomaximal, Sylow
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61C22×D811yescharacteristic
228C2×D61—21no—
229C2×D61—21no—
230C2×D61—21no—
231C2×D61—21no—
232C2×D61—21no—
233C2×D61—81no—
234C2×D61—81no—
235C2×D61—81no—
236C2×D61#48012yes—
237C4×C61—21no—
238C4×C61—81no—
239C4×C61—81no—
240C4×C61—81no—
241C4×C61—81no—
242C4×C61C2×#12311yescharacteristic
243C4×C61C2×#13711yescharacteristic
244Dic61—21no—
245Dic61—81no—
246Dic61—81no—
247Dic61—81no—
248Dic61#48012yes—
249#3061—611no—
250#2913—611no—
251#2237—611no—
252#2237—611no—
253#2236—611no—
254#2236D6111yescharacteristic, complemented
255#2234—611no—
256#2234—611no—
257#2232—611no—
258#2232—611no—
259#2159—611no—
260C2×#366—611no—
261#2139—611no—
262#2138—611no—
263#2113—611no—
264C2×C61—41no—
265C2×C61C2×#48011yescharacteristic
266C2×C61#341511yescharacteristic
267C2×C61#341711yescharacteristic
268D61—22no—
269D61—41no—
270D61—161no—
271C2×#135—611no—
272C2×#131—611no—
273#537—1221no—
274#520—1221no—
275C2×M32—611no—
276C22×C16—611no—
277#468—1221no—
278#468—1221no—
279#467—611no—
280#467C2×D6111yescharacteristic
281#466—611no—
282#466—611no—
283#428—1221no—
284#428—1221no—
285#428—1221no—
286#427—611no—
287#427—611no—
288#427—611no—
289C2×#107—611no—
290C2×#107—611no—
291C2×#107—611no—
292C2×#107C2×D6111yescharacteristic
293#417—1221no—
294#367—611no—
295#367—611no—
296#366—611no—
297#366—611no—
298#366—611no—
299#366—611no—
300#366C2×D6111yescharacteristic
301#366C2×D6111yescharacteristic
302#358—611no—
303#358—611no—
304#358C2×D6111yescharacteristic
305#358C2×D6111yescharacteristic
306#357—611no—
307#357—611no—
308#357—611no—
309#357—611no—
310C22⋊C16—611no—
311C22⋊C16—611no—
312C22⋊C16—611no—
313C22⋊C16C2×D6111yescharacteristic
314C61#3365211yescharacteristic, complemented, Sylow
315C2×#41—611no—
316C2×#41—1221no—
317#135—1222no—
318#135—1222no—
319C2×Q16C22×D6111yescharacteristic
320C2×SD16—1221no—
321C2×D8—611no—
322#131—1222no—
323#131—1222no—
324C2×M16—611no—
325C2×M16—611no—
326C2×M16—611no—
327C22×C8—611no—
328C22×C8—611no—
329C22×C8C22×D6111yescharacteristic
330C22⋊Q8—21no—
331C22⋊Q8—1221no—
332C22⋊Q8—2441no—
333#121—1221no—
334#121—1221no—
335#121—2441no—
336#121—2441no—
337#121—2441no—
338C4×Q8—2441no—
339C4×D4—2441no—
340C4×D4—2441no—
341C4×D4—2441no—
342#117—1221no—
343#117—1221no—
344#117—1221no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—1221no—
347C2×C4⋊C4—1221no—
348C2×C4⋊C4—1221no—
349M32—1222no—
350C2×C16—611no—
351C2×C16—611no—
352C2×C16—1222no—
353C2×C16C22×D6111yescharacteristic
354C2×C16C22×D6111yescharacteristic
355#107—21no—
356#107—611no—
357#107—611no—
358#107—611no—
359#107—1221no—
360#107—1221no—
361#107—1221no—
362#107C22×D6111yescharacteristic
363#107C22×D6111yescharacteristic
364#107C22×D6111yescharacteristic
365#106—1221no—
366#106—1221no—
367#106—1221no—
368#103—21no—
369#103—1221no—
370#102—1221no—
371#102—1221no—
372#41—1222no—
373#41—1222no—
374#41—2442no—
375#41—2442no—
376C2×Q8—21no—
377C2×Q8—611no—
378C2×D4—611no—
379C2×D4—611no—
380C2×D4—611no—
381C2×D4—1221no—
382C2×D4—2441no—
383C2×D4—2441no—
384C2×D4—2441no—
385C22×C4—41no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—2441no—
389C22×C4—2441no—
390C22×C4—2441no—
391C22×C4—2441no—
392C22×C4D4×D6111yescharacteristic
393Q16—21no—
394Q16—21no—
395SD16—2442no—
396D8—1221no—
397D8—1221no—
398M16—1222no—
399M16—1222no—
400M16—1222no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—611no—
404C2×C8—612no—
405C2×C8—612no—
406C2×C8—611no—
407C2×C8—1221no—
408C2×C8—1221no—
409C2×C8D4×D6111yescharacteristic
410C2×C8C23×D6111yescharacteristic
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—1221no—
417C4⋊C4—1221no—
418C4⋊C4—1221no—
419C4⋊C4—2441no—
420C4⋊C4—2441no—
421C4⋊C4—2441no—
422C4⋊C4—2441no—
423C22⋊C4—41no—
424C22⋊C4—2441no—
425C22⋊C4—2441no—
426C22⋊C4—2441no—
427C22⋊C4—2441no—
428C22⋊C4—2441no—
429C22⋊C4—2441no—
430C42—2441no—
431C42—2441no—
432C42—2441no—
433C16—21no—
434C16—21no—
435C16—1221no—
436C16—1221no—
437C23—611no—
438C23—611no—
439C23—2441no—
440C23D8×D6111yescharacteristic
441Q8—41no—
442Q8—41no—
443Q8—1222no—
444D4—1222no—
445D4—1222no—
446D4—1222no—
447D4—9761no—
448D4—9761no—
449D4—4882no—
450D4—2441no—
451D4—2441no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—161no—
459C2×C4—611no—
460C2×C4—612no—
461C2×C4—612no—
462C2×C4—611no—
463C2×C4—1221no—
464C2×C4—1221no—
465C2×C4—9761no—
466C2×C4—9761no—
467C2×C4—9761no—
468C2×C4—4882no—
469C2×C4—2441no—
470C2×C4—2441no—
471C2×C4—2441no—
472C2×C4D8×D6111yescharacteristic
473C2×C4C2×D4×D6111yescharacteristic
474C8—21no—
475C8—612no—
476C8—1221no—
477C8#41×D6111yescharacteristic
478C8#41×D6111yescharacteristic
479C22—21no—
480C22—21no—
481C22—21no—
482C22—612no—
483C22—1221no—
484C22—1221no—
485C22—1221no—
486C22—1221no—
487C22—1221no—
488C22—4881no—
489C22—4881no—
490C22—4881no—
491C22C2×D8×D6111yescharacteristic
492C4—21no—
493C4—81no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4—612no—
498C4—1221no—
499C4—4881no—
500C4—4881no—
501C4—4881no—
502C4#123×D6111yescharacteristic
503C4#137×D6111yescharacteristic
504C2—41no—
505C2—1222no—
506C2—9761no—
507C2—2441no—
508C2#480×D6111yescharacteristic
509C2#2145895911yescharacteristic
510C2#2145896811yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2236C2
socleC22×C61C22×D8
prime radical#21455490C2
hypercenter#2236D61
hypocenterC61#33652
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2236

Complements

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

NH ≅ G/Ntype
2. #21454415C2semidirect
3. #21448025C2semidirect
4. #21448024C2semidirect
5. #21448020C2semidirect
6. #21448013C2semidirect
7. #21448011C2semidirect
8. #21448001C2semidirect
9. #21447999C2semidirect
10. #21447604C2semidirect
11. #366×D61C2semidirect
12. #21447530C2semidirect
13. #21447525C2semidirect
14. #21447431C2semidirect
15. C61×#2236C2semidirect
254. #2236D61semidirect
314. C61#33652semidirect

Maximal subgroups

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

subgroupindex
#214554902
#214544152
#214480252
#214480242
#214480202
#214480132
#214480112
#214480012
#214479992
#214476042
#366×D612
#214475302
#214475252
#214474312
C61×#22362
#3365261