Finite Group Databasebeta

← #29677273

Subgroups — #29677273

Order 15616.

578 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458633C211yesmaximal, characteristic, complemented
2#21458631C211yesmaximal, characteristic, complemented
3#21458629C211yesmaximal, characteristic, complemented
4#21445423C211yesmaximal, characteristic
5#21445361C211yesmaximal, characteristic, complemented
6#21445359C211yesmaximal, characteristic, complemented
7#21445357C211yesmaximal, characteristic, complemented
8#21445356C211yesmaximal, characteristic, complemented
9#21444959C211yesmaximal, characteristic, complemented
10#21444958C211yesmaximal, characteristic, complemented
11#21444878C211yesmaximal, characteristic
12#21444877C211yesmaximal, characteristic
13#21444716C211yesmaximal, characteristic, complemented
14#21444714C211yesmaximal, characteristic, complemented
15C61×#3375C211yesmaximal, characteristic, complemented
16#16840497C2211yescharacteristic
17Q8×Dic122C2211yescharacteristic
18#16840141C2211yescharacteristic
19#16840138C2211yescharacteristic
20#16840124—21no—
21#16840123—21no—
22#16840121—21no—
23#16840110C2211yescharacteristic
24#16840109C2211yescharacteristic
25#16840108C2211yescharacteristic
26#16840057C2211yescharacteristic
27#16840057C2211yescharacteristic
28#16840054C2211yescharacteristic
29#16840042—21no—
30#16840041—21no—
31#16840039—21no—
32#16839986—21no—
33#16839984—21no—
34#16839981—21no—
35#16839962C2211yescharacteristic
36#16839962C2211yescharacteristic
37#16839959C2211yescharacteristic
38#16839893C2211yescharacteristic
39#16839893C2211yescharacteristic
40#16839892C2211yescharacteristic
41#16839865—21no—
42#16839862—21no—
43#16839860—21no—
44C4×#11758202C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839506C2211yescharacteristic
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839492C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#559C2211yescharacteristic
57Q82×C61C2211yescharacteristic
58C61×#489—21no—
59C61×#486C2211yescharacteristic
60C61×#477C2211yescharacteristic
61C61×#474—21no—
62C61×#464—21no—
63C61×#460C2211yescharacteristic
64C61×#446C2211yescharacteristic
65C61×#440—21no—
66C4×Q16×C61C2211yescharacteristic
67C2×#11758202—41no—
68C2×#11758202D411yescharacteristic
69C2×#11758200—21no—
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758199—41no—
73#14519777—21no—
74#14519777C2311yescharacteristic
75#14519776—21no—
76#14519776—41no—
77#14519774C2311yescharacteristic
78#14519766—21no—
79#14519765—21no—
80#14519762—41no—
81Q8×Dic61—21no—
82C4×Dic122—21no—
83C4×Dic122C2311yescharacteristic
84C4×D244—21no—
85#14519739—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710D411yescharacteristic
90C4⋊#92418—21no—
91C4⋊#92418—21no—
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519706—21no—
96#14519701—21no—
97#14519701—21no—
98#14519701D411yescharacteristic
99#14519700—21no—
100#14519700D411yescharacteristic
101#14519699—21no—
102#14519699—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—21no—
110#14519688—21no—
111#14519688—21no—
112#14519687—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×Q16×C61D411yescharacteristic
116C2×SD16×C61—21no—
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61—41no—
120C4⋊Q8×C61C2311yescharacteristic
121#127×C61C2311yescharacteristic
122#124×C61—21no—
123#124×C61—21no—
124#123×C61—41no—
125C4×Q8×C61—21no—
126C4×Q8×C61—21no—
127C4×Q8×C61C2311yescharacteristic
128C4×Q8×C61C2311yescharacteristic
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61—21no—
132#107×C61—21no—
133#107×C61D411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61D411yescharacteristic
138#103×C61D411yescharacteristic
139#102×C61—21no—
140#102×C61—21no—
141#102×C61—21no—
142#97×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—41no—
146C2×Q8×C61C2×D411yescharacteristic
147C2×Q8×C61C2×D411yescharacteristic
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C22×C4×C61—41no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244—21no—
156C2×C4×D61—41no—
157C2×Dic122—21no—
158C2×Dic122—41no—
159C2×Dic122C2×D411yescharacteristic
160Q16×C61—41no—
161SD16×C61—42no—
162C2×C8×C61—21no—
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61—41no—
172C4⋊C4×C61C2×D411yescharacteristic
173C4⋊C4×C61C2×D411yescharacteristic
174C4⋊C4×C61C2×D411yescharacteristic
175C22⋊C4×C61—41no—
176C22⋊C4×C61—41no—
177C22⋊C4×C61—41no—
178C42×C61—21no—
179C42×C61—21no—
180C42×C61—21no—
181C42×C61—41no—
182C42×C61C2411yescharacteristic
183#11758202—41no—
184#11758202—82no—
185#11758201—42no—
186#11758201—42no—
187#11758200—42no—
188#11758199—82no—
189#11758198—41no—
190#11758198—41no—
191#11758198—41no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—41no—
195C4⋊Dic61C2×D411yescharacteristic
196#11758196—21no—
197#11758196—41no—
198C4×Dic61—21no—
199C4×Dic61—41no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C23×C61—41no—
207C22×D61—41no—
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—21no—
214Q8×C61—81no—
215Q8×C61—161no—
216D4×C61—41no—
217D4×C61—41no—
218D4×C61—41no—
219D4×C61—41no—
220D4×C61—81no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—41no—
228C2×C4×C61—161no—
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61H(5,𝔽2)11yescharacteristic
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—41no—
235D244—41no—
236D244—41no—
237D244—41no—
238D244—41no—
239D244—81no—
240C4×D61—161no—
241Dic122—21no—
242Dic122—21no—
243Dic122—81no—
244Dic122—161no—
245C8×C61—21no—
246C8×C61—21no—
247C8×C61—41no—
248#92418—22no—
249#92418—21no—
250#92418—21no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#20319—611nomaximal, Sylow
255C22×C61—81no—
256C22×C61—81no—
257C22×C61—81no—
258C22×C61D4211yescharacteristic
259C2×D61—81no—
260C2×D61—81no—
261C2×D61—81no—
262C4×C61—21no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61—81no—
270C4×C61#57511yescharacteristic
271C4×C61#57511yescharacteristic
272C4×C61#57811yescharacteristic
273C4×C61#57811yescharacteristic
274Dic61—41no—
275Dic61—41no—
276Dic61—81no—
277#3375—611no—
278#3375—611no—
279#3375—611no—
280#3375D6111yescharacteristic, complemented
281#1709—611no—
282#1698—611no—
283#1698—611no—
284#1698—611no—
285#1698—611no—
286#1633—611no—
287#1633—611no—
288#1620—611no—
289#1620—611no—
290#1591—611no—
291#1591—611no—
292C2×C61—161no—
293C2×C61#327711yescharacteristic
294C2×C61#327711yescharacteristic
295C2×C61#329211yescharacteristic
296D61—161no—
297#559—611no—
298#559C2×D6111yescharacteristic
299Q82—611no—
300Q82C2×D6111yescharacteristic
301#494—611no—
302#493—611no—
303#489—21no—
304#489—1221no—
305#489—1221no—
306#489—1221no—
307#486—611no—
308#486—611no—
309#486—611no—
310#486C2×D6111yescharacteristic
311#477—611no—
312#477—611no—
313#477—611no—
314#477C2×D6111yescharacteristic
315#474—21no—
316#474—1221no—
317#474—1221no—
318#474—1221no—
319#464—21no—
320#464—1221no—
321#464—1221no—
322#464—1221no—
323#460—611no—
324#460—611no—
325#460—611no—
326#460C2×D6111yescharacteristic
327#446—611no—
328#446—611no—
329#446—611no—
330#446C2×D6111yescharacteristic
331#440—21no—
332#440—1221no—
333#440—1221no—
334#440—1221no—
335C4×Q16—611no—
336C4×Q16C2×D6111yescharacteristic
337#335—611no—
338#335—611no—
339#333—611no—
340#333—611no—
341#331—611no—
342#331—611no—
343Q8⋊C8—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347C82—611no—
348C61#2031911yescharacteristic, complemented, Sylow
349C2×Q16—611no—
350C2×Q16—2441no—
351C2×Q16C22⋊D6111yescharacteristic
352C2×SD16—21no—
353C2×SD16—1221no—
354C2×SD16—1221no—
355C2×SD16—1221no—
356C2×D8—2441no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—41no—
360C4⋊Q8—611no—
361C4⋊Q8—1221no—
362C4⋊Q8—1221no—
363C4⋊Q8—2441no—
364C4⋊Q8C22×D6111yescharacteristic
365#127—611no—
366#127C22×D6111yescharacteristic
367#124—21no—
368#124—21no—
369#124—1221no—
370#124—1221no—
371#123—41no—
372#123—2441no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8—611no—
376C4×Q8—1221no—
377C4×Q8—1221no—
378C4×Q8C22×D6111yescharacteristic
379C4×Q8C22×D6111yescharacteristic
380C4×Q8C22×D6111yescharacteristic
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—1221no—
384C4×D4—1221no—
385#107—21no—
386#107—611no—
387#107—1221no—
388#107—1221no—
389#107—1221no—
390#107C22⋊D6111yescharacteristic
391C4⋊C8—21no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8C22×D6111yescharacteristic
399#103—21no—
400#103—611no—
401#103—611no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103C22⋊D6111yescharacteristic
406#103C22⋊D6111yescharacteristic
407#102—21no—
408#102—21no—
409#102—21no—
410#102—1221no—
411#102—1221no—
412#102—1221no—
413#102—1221no—
414#102—1221no—
415#102—1221no—
416#102—1221no—
417#102—1221no—
418#102—1221no—
419#97—21no—
420#97—1221no—
421#97—1221no—
422#97—1221no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8C22×D6111yescharacteristic
426C2×Q8—21no—
427C2×Q8—41no—
428C2×Q8—611no—
429C2×Q8—1221no—
430C2×Q8—2441no—
431C2×Q8D4×D6111yescharacteristic
432C2×Q8C2×C22⋊D6111yescharacteristic
433C2×Q8C2×C22⋊D6111yescharacteristic
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—1221no—
438C2×D4—1221no—
439C2×D4—1221no—
440C22×C4—41no—
441C22×C4—2441no—
442Q16—41no—
443Q16—4882no—
444Q16—2441no—
445SD16—42no—
446SD16—2442no—
447SD16—2442no—
448SD16—2442no—
449D8—4882no—
450C2×C8—21no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8C2×C22⋊D6111yescharacteristic
458C2×C8C2×C22⋊D6111yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—611no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—2441no—
471C4⋊C4—2441no—
472C4⋊C4D4×D6111yescharacteristic
473C4⋊C4C2×C22⋊D6111yescharacteristic
474C4⋊C4C2×C22⋊D6111yescharacteristic
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—2441no—
479C22⋊C4—2441no—
480C22⋊C4—2441no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—41no—
485C42—1221no—
486C42—2441no—
487C42C23×D6111yescharacteristic
488C23—41no—
489C23—2441no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—81no—
497Q8—161no—
498Q8—1221no—
499Q8—1221no—
500Q8—9761no—
501Q8—4881no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—81no—
507D4—4881no—
508D4—2441no—
509D4—2441no—
510D4—2441no—
511D4—2441no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—161no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—9761no—
523C2×C4—2441no—
524C2×C4C2×D4×D6111yescharacteristic
525C2×C4C22×C22⋊D6111yescharacteristic
526C2×C4#1451982211yescharacteristic
527C8—21no—
528C8—21no—
529C8—41no—
530C8—1222no—
531C8—1221no—
532C8—1221no—
533C8—2441no—
534C8—2441no—
535C8—2441no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—4881no—
540C22—4881no—
541C22—4881no—
542C22D4×C22⋊D6111yescharacteristic
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—81no—
551C4—4881no—
552C4—2441no—
553C4—2441no—
554C4#1684056011yescharacteristic
555C4#1684056111yescharacteristic
556C4#1684057711yescharacteristic
557C4#1684057811yescharacteristic
558C2—161no—
559C2—9761no—
560C2#2145747011yescharacteristic
561C2#2145747211yescharacteristic
562C2#2145761611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3375C2
socleC22×C61D42
prime radical#16840138C22
hypercenter#3375D61
hypocenterC61#20319
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3375

Complements

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

NH ≅ G/Ntype
1. #21458633C2semidirect
2. #21458631C2semidirect
3. #21458629C2semidirect
5. #21445361C2semidirect
6. #21445359C2semidirect
7. #21445357C2semidirect
8. #21445356C2semidirect
9. #21444959C2semidirect
10. #21444958C2semidirect
13. #21444716C2semidirect
14. #21444714C2semidirect
15. C61×#3375C2semidirect
280. #3375D61semidirect
348. C61#20319semidirect

Maximal subgroups

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

subgroupindex
#214586332
#214586312
#214586292
#214454232
#214453612
#214453592
#214453572
#214453562
#214449592
#214449582
#214448782
#214448772
#214447162
#214447142
C61×#33752
#2031961