Finite Group Databasebeta

← #29835584

Subgroups — #29835584

Order 15616.

554 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456395C211yesmaximal, characteristic, complemented
2#21456392C211yesmaximal, characteristic, complemented
3#21448104C211yesmaximal, characteristic, complemented
4#21448084C211yesmaximal, characteristic, complemented
5#21448059C211yesmaximal, characteristic, complemented
6#21448057C211yesmaximal, characteristic, complemented
7#21447935C211yesmaximal, characteristic, complemented
8#21447929C211yesmaximal, characteristic, complemented
9#21447923C211yesmaximal, characteristic, complemented
10#21447921C211yesmaximal, characteristic, complemented
11C4×#14519720C211yesmaximal, characteristic, complemented
12C4×D976C211yesmaximal, characteristic, complemented
13C4×#14519718C211yesmaximal, characteristic, complemented
14C4×#14519716C211yesmaximal, characteristic, complemented
15C4×SD32×C61C211yesmaximal, characteristic, complemented
16#16840309—21no—
17#16840299—21no—
18C2×#14519720C2211yescharacteristic
19C2×D976C2211yescharacteristic
20C2×#14519718C2211yescharacteristic
21C2×#14519716C2211yescharacteristic
22C2×#14519716C2211yescharacteristic
23#16840166C2211yescharacteristic
24#16840163C2211yescharacteristic
25#16840147C2211yescharacteristic
26#16840137C2211yescharacteristic
27#16840118—21no—
28#16840107—21no—
29#16840000C2211yescharacteristic
30#16839999C2211yescharacteristic
31#16839999C2211yescharacteristic
32#16839997—21no—
33#16839995C2211yescharacteristic
34#16839994—21no—
35C4×#11758201—21no—
36C4×D488C2211yescharacteristic
37C4×D488C2211yescharacteristic
38C4×#11758199—21no—
39C4×C8×D61C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839587C2211yescharacteristic
43#16839566C2211yescharacteristic
44#16839564C2211yescharacteristic
45#16839564C2211yescharacteristic
46#16839563C2211yescharacteristic
47#16839562C2211yescharacteristic
48#16839562C2211yescharacteristic
49#16839537C2211yescharacteristic
50#16839537C2211yescharacteristic
51C4×#11758185C2211yescharacteristic
52C2×SD32×C61C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic
54C4×D8×C61C2211yescharacteristic
55C61×#367C2211yescharacteristic
56C61×#358C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C4×C16×C61C2211yescharacteristic
59C2×#11758222—41no—
60C2×#11758201—21no—
61C2×D488C2311yescharacteristic
62C2×D488C2311yescharacteristic
63C2×#11758199—21no—
64C2×C8×D61D411yescharacteristic
65C2×C8×D61C2311yescharacteristic
66#14519776—21no—
67#14519773—21no—
68#14519772—41no—
69#14519768—21no—
70#14519766—21no—
71#14519763—41no—
72#14519762—41no—
73#14519753—21no—
74#14519752—21no—
75#14519752—21no—
76#14519750—41no—
77#14519748—21no—
78C4×D244—21no—
79C4×D244—21no—
80C4×D244—41no—
81C4×C22⋊D61—41no—
82#14519734—41no—
83C42×D61D411yescharacteristic
84#14519720—22no—
85D976—22no—
86#14519718—22no—
87#14519716—22no—
88#14519716—22no—
89C2×#11758185C2311yescharacteristic
90C2×#11758185C2311yescharacteristic
91#14519711C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519710—21no—
94#14519708—21no—
95#14519701—21no—
96#14519699—21no—
97#14519699—21no—
98#14519698—21no—
99#14519697—21no—
100#14519697—21no—
101C4×#92418D411yescharacteristic
102C8×Dic61D411yescharacteristic
103C8×Dic61C2311yescharacteristic
104C2×Q16×C61C2311yescharacteristic
105C2×D8×C61C2311yescharacteristic
106C4×Q8×C61—21no—
107C4×D4×C61—21no—
108SD32×C61—22no—
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#103×C61—21no—
114#102×C61—21no—
115C4×C8×C61C2311yescharacteristic
116C2×Q8×C61—21no—
117C2×D4×C61—21no—
118C22×C4×C61—41no—
119C2×C22⋊D61—41no—
120C2×C22⋊D61—41no—
121C2×C22⋊D61—41no—
122#11758222—84no—
123C2×D244—21no—
124C2×D244—21no—
125C2×D244—41no—
126C2×D244—41no—
127C2×C4×D61—41no—
128C2×C4×D61—41no—
129C2×C4×D61D811yescharacteristic
130C2×C4×D61D811yescharacteristic
131C2×C4×D61C2×D411yescharacteristic
132C2×Dic122—41no—
133Q16×C61—21no—
134Q16×C61—21no—
135D8×C61—21no—
136D8×C61—21no—
137C2×C8×C61C2×D411yescharacteristic
138C2×C8×C61C2411yescharacteristic
139C4⋊C4×C61—21no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—41no—
142C22⋊C4×C61—41no—
143C42×C61—41no—
144C42×C61C2×D411yescharacteristic
145C22⋊Dic61—41no—
146#11758201—42no—
147#11758199—42no—
148#11758198—41no—
149#11758198—41no—
150#11758198—41no—
151#11758198—41no—
152#11758198—41no—
153#11758198—41no—
154#11758198—41no—
155C4⋊Dic61—21no—
156C4⋊Dic61—21no—
157C4⋊Dic61—41no—
158#11758196—41no—
159#11758196—41no—
160#11758196—41no—
161C4×Dic61D811yescharacteristic
162C4×Dic61D811yescharacteristic
163C4×Dic61C2×D411yescharacteristic
164C2×#92418C2×D411yescharacteristic
165C2×#92418C2×D411yescharacteristic
166D488—21no—
167D488—21no—
168D488—21no—
169D488—21no—
170C8×D61—21no—
171C8×D61—21no—
172C8×D61—22no—
173C16×C61—21no—
174C16×C61#4112yescomplemented
175#11758185—21no—
176#11758185#4112yescomplemented
177C23×C61—41no—
178C22×D61—41no—
179C22×D61—41no—
180C22×D61C2×D811yescharacteristic
181Q8×C61—41no—
182Q8×C61—41no—
183D4×C61—41no—
184D4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—82no—
189C2×C4×C61C2×D811yescharacteristic
190C2×C4×C61C2×D811yescharacteristic
191C2×C4×C61C22×D411yescharacteristic
192C22⋊D61—82no—
193C22⋊D61—82no—
194C22⋊D61—82no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61C2×D811yescharacteristic
198C2×Dic61C2×D811yescharacteristic
199C2×Dic61C2×D811yescharacteristic
200D244—41no—
201D244—41no—
202D244—41no—
203D244—41no—
204D244—82no—
205D244—82no—
206C4×D61—21no—
207C4×D61—21no—
208C4×D61—22no—
209C4×D61—41no—
210C4×D61—82no—
211C4×D61—82no—
212Dic122—82no—
213C8×C61—21no—
214C8×C61C2×#4111yescharacteristic
215C8×C61C2×#4111yescharacteristic
216#92418—21no—
217#92418#13512yes—
218#33737—611nomaximal, Sylow
219C22×C61—81no—
220C22×C61—81no—
221C22×C61—81no—
222C22×C61C22×D811yescharacteristic
223C2×D61—21no—
224C2×D61—21no—
225C2×D61—21no—
226C2×D61—81no—
227C2×D61—81no—
228C2×D61—81no—
229C2×D61—81no—
230C2×D61—81no—
231C2×D61—81no—
232C4×C61—21no—
233C4×C61—81no—
234C4×C61—81no—
235C4×C61—81no—
236C4×C61#50912yes—
237C4×C61#53211yescharacteristic
238C4×C61C2×#13511yescharacteristic
239Dic61—21no—
240Dic61—21no—
241Dic61—21no—
242Dic61—81no—
243Dic61—81no—
244#3169—611no—
245#3168—611no—
246#2255—611no—
247#2250—611no—
248#2244—611no—
249#2243—611no—
250#2220—611no—
251#2220—611no—
252#2218—611no—
253#2218—611no—
254C4×SD32—611no—
255C4×SD32D6111yescharacteristic, complemented
256C4×D16—611no—
257C4×D16—611no—
258C4×M32—611no—
259C2×C61—161no—
260C2×C61#316911yescharacteristic
261C2×C61C2×#50911yescharacteristic
262C2×C61#341411yescharacteristic
263D61—41no—
264D61—161no—
265D61—161no—
266#532—1221no—
267#529—1221no—
268C2×SD32—611no—
269C2×SD32C2×D6111yescharacteristic
270C2×D16—611no—
271C2×D16—611no—
272C2×M32—611no—
273C2×M32—611no—
274#500—611no—
275#499—611no—
276#495—611no—
277#493—611no—
278#488—1221no—
279#486—1221no—
280#467—611no—
281#466—611no—
282#466—611no—
283#466—611no—
284#466—1221no—
285#465—1221no—
286C4×Q16C2×D6111yescharacteristic
287C4×SD16—1221no—
288C4×D8—611no—
289C4×D8—611no—
290C4×D8—1221no—
291C4×D8C2×D6111yescharacteristic
292C2×C4×C8—611no—
293#367—611no—
294#367C2×D6111yescharacteristic
295#366—611no—
296#366—611no—
297#358—611no—
298#358C2×D6111yescharacteristic
299#357—611no—
300#357—611no—
301#357—611no—
302#357—611no—
303#357—611no—
304#357C2×D6111yescharacteristic
305#346—611no—
306#346—611no—
307C4×C16—611no—
308C4×C16C2×D6111yescharacteristic
309C61#3373711yescharacteristic, complemented, Sylow
310C2×#41—2441no—
311C2×Q16C22×D6111yescharacteristic
312C2×SD16—1221no—
313C2×D8—611no—
314C2×D8—611no—
315C2×D8—1221no—
316C2×D8C22×D6111yescharacteristic
317C22×C8—611no—
318C22×C8—611no—
319C4⋊Q8—1221no—
320#127—1221no—
321#126—2441no—
322#125—1221no—
323#124—1221no—
324#124—2441no—
325#123—2441no—
326C22⋊Q8—1221no—
327#121—1221no—
328#121—1221no—
329#121—1221no—
330#121—2441no—
331C4×Q8—21no—
332C4×D4—21no—
333C4×D4—1221no—
334C4×D4—1221no—
335C4×D4—2441no—
336C4×D4—2441no—
337#117—2441no—
338C2×C42—611no—
339SD32—22no—
340SD32—1222no—
341D16—1222no—
342D16—1222no—
343M32—1222no—
344M32—1222no—
345C2×C16—611no—
346C2×C16—611no—
347C2×C16C22×D6111yescharacteristic
348C2×C16C22×D6111yescharacteristic
349#107—611no—
350#107—611no—
351#107—1221no—
352#107C22×D6111yescharacteristic
353#107C22×D6111yescharacteristic
354#106—1221no—
355#103—21no—
356#103—1221no—
357#102—21no—
358#102—1221no—
359#102—1221no—
360#102—1221no—
361#102—1221no—
362#102—1221no—
363C4×C8—611no—
364C4×C8—611no—
365C4×C8—611no—
366C4×C8C22×D6111yescharacteristic
367#41—4884no—
368C2×Q8—21no—
369C2×Q8—2441no—
370C2×D4—21no—
371C2×D4—1221no—
372C2×D4—1221no—
373C2×D4—2441no—
374C2×D4—2441no—
375C2×D4—2441no—
376C2×D4—2441no—
377C2×D4—2441no—
378C22×C4—41no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—2441no—
383C22×C4—2441no—
384Q16—21no—
385Q16—21no—
386SD16—2442no—
387D8—21no—
388D8—21no—
389D8—1221no—
390D8—1221no—
391D8—1221no—
392D8—1221no—
393D8—2442no—
394C2×C8—611no—
395C2×C8—611no—
396C2×C8—1222no—
397C2×C8—1221no—
398C2×C8—1221no—
399C2×C8D4×D6111yescharacteristic
400C2×C8C23×D6111yescharacteristic
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—41no—
404C4⋊C4—1221no—
405C4⋊C4—1221no—
406C4⋊C4—2441no—
407C4⋊C4—2441no—
408C4⋊C4—2441no—
409C4⋊C4—2441no—
410C22⋊C4—41no—
411C22⋊C4—2441no—
412C22⋊C4—2441no—
413C22⋊C4—2441no—
414C22⋊C4—2441no—
415C22⋊C4—2441no—
416C22⋊C4—2441no—
417C22⋊C4—2441no—
418C22⋊C4—2441no—
419C42—41no—
420C42—611no—
421C42—611no—
422C42—611no—
423C42D4×D6111yescharacteristic
424C16—21no—
425C16—612no—
426C16—1221no—
427C16#1175822212yescomplemented
428C23—41no—
429C23—611no—
430C23—2441no—
431C23—2441no—
432Q8—41no—
433Q8—41no—
434Q8—4882no—
435D4—41no—
436D4—41no—
437D4—4882no—
438D4—4882no—
439D4—4882no—
440D4—4882no—
441D4—4882no—
442D4—2441no—
443D4—2441no—
444D4—2441no—
445D4—2441no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—82no—
450C2×C4—611no—
451C2×C4—611no—
452C2×C4—611no—
453C2×C4—1222no—
454C2×C4—1221no—
455C2×C4—1221no—
456C2×C4—4882no—
457C2×C4—4882no—
458C2×C4—2441no—
459C2×C4—2441no—
460C2×C4—2441no—
461C2×C4D8×D6111yescharacteristic
462C2×C4D8×D6111yescharacteristic
463C2×C4C2×D4×D6111yescharacteristic
464C8—21no—
465C8—612no—
466C8—1221no—
467C8#41×D6111yescharacteristic
468C8C2×#1175822211yescharacteristic
469C22—81no—
470C22—81no—
471C22—81no—
472C22—1221no—
473C22—1221no—
474C22—1221no—
475C22—4881no—
476C22—4881no—
477C22—4881no—
478C22—4881no—
479C22—4881no—
480C22—4881no—
481C22C2×D8×D6111yescharacteristic
482C4—21no—
483C4—81no—
484C4—81no—
485C4—81no—
486C4—1221no—
487C4—1221no—
488C4—1221no—
489C4—4881no—
490C4—4881no—
491C4#1684019912yes—
492C4#1684030911yescharacteristic
493C4#135×D6111yescharacteristic
494C2—161no—
495C2—9761no—
496C2—9761no—
497C2—2441no—
498C2#2145639511yescharacteristic
499C2C2×#1684019911yescharacteristic
500C2#2145895211yescharacteristic
subgroupG/H
centerC2×C4D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC4×SD32×C61C2
socleC22×C61C22×D8
hypercenterC4×SD32D61
hypocenterC61#33737
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
1. #21456395C2semidirect
2. #21456392C2semidirect
3. #21448104C2semidirect
4. #21448084C2semidirect
5. #21448059C2semidirect
6. #21448057C2semidirect
7. #21447935C2semidirect
8. #21447929C2semidirect
9. #21447923C2semidirect
10. #21447921C2semidirect
11. C4×#14519720C2semidirect
12. C4×D976C2semidirect
13. C4×#14519718C2semidirect
14. C4×#14519716C2semidirect
15. C4×SD32×C61C2semidirect
174. C16×C61#41semidirect
176. #11758185#41semidirect
255. C4×SD32D61semidirect
309. C61#33737semidirect
427. C16#11758222semidirect

Maximal subgroups

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

subgroupindex
#214563952
#214563922
#214481042
#214480842
#214480592
#214480572
#214479352
#214479292
#214479232
#214479212
C4×#145197202
C4×D9762
C4×#145197182
C4×#145197162
C4×SD32×C612
#3373761