Finite Group Databasebeta

← #29671025

Subgroups — #29671025

Order 15616.

570 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458803C211yesmaximal, characteristic
2#21458464C211yesmaximal, characteristic
3#21458436C211yesmaximal, characteristic, complemented
4#21445497C211yesmaximal, characteristic, complemented
5#21445329C211yesmaximal, characteristic, complemented
6#21445275C211yesmaximal, characteristic, complemented
7#21445194C211yesmaximal, characteristic, complemented
8#21445187C211yesmaximal, characteristic, complemented
9#21445075C211yesmaximal, characteristic, complemented
10#21445074C211yesmaximal, characteristic, complemented
11#21445025C211yesmaximal, characteristic, complemented
12#21444991C211yesmaximal, characteristic, complemented
13#21444648C211yesmaximal, characteristic
14#21444638C211yesmaximal, characteristic, complemented
15C61×#3342C211yesmaximal, characteristic, complemented
16#16840485C2211yescharacteristic
17#16840472C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840160C2211yescharacteristic
20#16840144—21no—
21#16840141C2211yescharacteristic
22#16840116—21no—
23#16840114C2211yescharacteristic
24#16840112C2211yescharacteristic
25#16840101—21no—
26#16840091—21no—
27#16840069—21no—
28#16840057C2211yescharacteristic
29#16840052C2211yescharacteristic
30#16840047C2211yescharacteristic
31#16840017—21no—
32#16839984—21no—
33#16839981—21no—
34#16839974—21no—
35#16839967C2211yescharacteristic
36#16839964C2211yescharacteristic
37#16839964C2211yescharacteristic
38Q8×#92418C2211yescharacteristic
39Q8×#92418C2211yescharacteristic
40C4×#11758202—21no—
41C4×#11758201—21no—
42C4×#11758199C2211yescharacteristic
43#16839841C2211yescharacteristic
44#16839803—21no—
45#16839514C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#556C2211yescharacteristic
57C61×#556C2211yescharacteristic
58C61×#500C2211yescharacteristic
59C61×#485—21no—
60C61×#485—21no—
61C61×#475C2211yescharacteristic
62C61×#475C2211yescharacteristic
63C61×#467—21no—
64C4×Q16×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic
66C61×#427—21no—
67C2×#11758202—21no—
68C2×#11758202—21no—
69C2×#11758200—21no—
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758199D411yescharacteristic
73C2×#11758189—21no—
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519772—41no—
77#14519769—21no—
78#14519765—21no—
79#14519755—41no—
80#14519753—21no—
81#14519753—21no—
82C4×Dic122—21no—
83C4×D244—21no—
84C4×D244C2311yescharacteristic
85#14519735—21no—
86C4⋊C4×D61—21no—
87#14519710—21no—
88#14519710—41no—
89#14519710D411yescharacteristic
90#14519709—21no—
91#14519709—21no—
92#14519708—21no—
93#14519708—21no—
94C4⋊#92418—21no—
95C4⋊#92418—21no—
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519701—21no—
103#14519701—21no—
104#14519701—21no—
105#14519700—21no—
106#14519700—41no—
107#14519698—21no—
108#14519698D411yescharacteristic
109#14519697D411yescharacteristic
110#14519689—21no—
111C4×#92418—21no—
112C4×#92418—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×Q16×C61D411yescharacteristic
116C22×C8×C61—21no—
117C4⋊Q8×C61C2311yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119#126×C61—41no—
120#126×C61—41no—
121#124×C61—21no—
122#124×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C4×Q8×C61—21no—
126C4×Q8×C61—21no—
127C4×Q8×C61C2311yescharacteristic
128C4×Q8×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130#117×C61—21no—
131#117×C61—21no—
132#107×C61—21no—
133#107×C61—21no—
134#107×C61D411yescharacteristic
135#106×C61—21no—
136#106×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#103×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147C2×Q8×C61C2×D411yescharacteristic
148C2×D4×C61C2×D411yescharacteristic
149C22×C4×C61—21no—
150C2×D244C2×D411yescharacteristic
151C2×C4×D61—21no—
152C2×C4×D61—41no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155Q16×C61—22no—
156C2×C8×C61—21no—
157C2×C8×C61—42no—
158C2×C8×C61C2×D411yescharacteristic
159C2×C8×C61C2×D411yescharacteristic
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—41no—
167C4⋊C4×C61—41no—
168C4⋊C4×C61C2×D411yescharacteristic
169C4⋊C4×C61C2×D411yescharacteristic
170C4⋊C4×C61C2×D411yescharacteristic
171C22⋊C4×C61—21no—
172C22⋊C4×C61—41no—
173C22⋊C4×C61—41no—
174C22⋊C4×C61—41no—
175C22⋊C4×C61—41no—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—41no—
179C42×C61—41no—
180C42×C61C2411yescharacteristic
181#11758202—42no—
182#11758202—81no—
183#11758201—42no—
184#11758201—81no—
185#11758200—81no—
186#11758199—41no—
187#11758198—21no—
188#11758198—41no—
189#11758198—41no—
190#11758198—41no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61C2×D411yescharacteristic
196#11758196—41no—
197#11758196—41no—
198#11758196—41no—
199C4×Dic61—41no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206#11758189—42no—
207C23×C61—21no—
208C22×D61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—41no—
217D4×C61—21no—
218D4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61H(5,𝔽2)11yescharacteristic
231C2×Dic61—21no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234D244—21no—
235D244—21no—
236C4×D61—41no—
237C4×D61—41no—
238C4×D61—161no—
239Dic122—41no—
240Dic122—41no—
241Dic122—81no—
242C8×C61—21no—
243C8×C61—41no—
244C8×C61#13512yes—
245#92418—21no—
246#92418—21no—
247#92418—41no—
248#92418—41no—
249#92418—41no—
250#92418—41no—
251#19866—611nomaximal, Sylow
252C22×C61—41no—
253C22×C61—41no—
254C22×C61—41no—
255C22×C61D4211yescharacteristic
256C2×D61—41no—
257C2×D61—41no—
258C2×D61—41no—
259C4×C61—21no—
260C4×C61—41no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—81no—
266C4×C61—81no—
267C4×C61C2×#13511yescharacteristic
268C4×C61#57511yescharacteristic
269C4×C61#57711yescharacteristic
270C4×C61#57811yescharacteristic
271Dic61—41no—
272Dic61—81no—
273Dic61—81no—
274#3393—611no—
275#3360—611no—
276#3356—611no—
277#3342D6111yescharacteristic, complemented
278#1723—611no—
279#1693—611no—
280#1684—611no—
281#1671—611no—
282#1670—611no—
283#1650—611no—
284#1650—611no—
285#1643—611no—
286#1638—611no—
287#1581—611no—
288#1579—611no—
289C2×C61—81no—
290C2×C61#327111yescharacteristic
291C2×C61#328311yescharacteristic
292C2×C61#328911yescharacteristic
293D61—81no—
294#556—611no—
295#556C2×D6111yescharacteristic
296#556C2×D6111yescharacteristic
297#554—611no—
298#500—611no—
299#500C2×D6111yescharacteristic
300#498—611no—
301#495—1221no—
302#494—611no—
303#488—1221no—
304#487—611no—
305#487—611no—
306#485—21no—
307#485—21no—
308#485—1221no—
309#483—1221no—
310#479—1221no—
311#477—611no—
312#476—611no—
313#475—611no—
314#475C2×D6111yescharacteristic
315#475C2×D6111yescharacteristic
316#470—1221no—
317#467—21no—
318#464—1221no—
319#464—1221no—
320#463—1221no—
321#461—611no—
322#461—611no—
323#461—611no—
324C8×Q8—611no—
325C8×Q8—611no—
326C4×Q16—1221no—
327C4×Q16C2×D6111yescharacteristic
328C4×SD16—1221no—
329C4×D8—611no—
330#436—611no—
331C8×D4C2×D6111yescharacteristic
332#428—1221no—
333#427—21no—
334#335—611no—
335#334—611no—
336#333—611no—
337#332—611no—
338#332—611no—
339#332—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342D4⋊C8—611no—
343D4⋊C8—611no—
344#322—611no—
345C61#1986611yescharacteristic, complemented, Sylow
346C2×Q16—1221no—
347C2×Q16—1221no—
348C2×Q16C22⋊D6111yescharacteristic
349C2×SD16—1221no—
350C2×SD16—1221no—
351C2×SD16—1221no—
352C2×D8—611no—
353C2×M16—1221no—
354C22×C8—21no—
355C4⋊Q8—611no—
356C4⋊Q8—611no—
357C4⋊Q8C22×D6111yescharacteristic
358C4⋊Q8C22×D6111yescharacteristic
359#126—41no—
360#126—41no—
361#126—2441no—
362#125—1221no—
363#124—21no—
364#124—21no—
365#124—1221no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—1221no—
369C22⋊Q8—1221no—
370C22⋊Q8—2441no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—1221no—
374C4×Q8C22×D6111yescharacteristic
375C4×Q8C22×D6111yescharacteristic
376C4×D4—611no—
377C4×D4—1221no—
378C4×D4C22×D6111yescharacteristic
379#117—21no—
380#117—21no—
381#117—1221no—
382C2×C4⋊C4—1221no—
383#107—21no—
384#107—21no—
385#107—611no—
386#107—1221no—
387#107—2441no—
388#107C22⋊D6111yescharacteristic
389#106—21no—
390#106—21no—
391#106—1221no—
392#106—1221no—
393#106—1221no—
394#106—1221no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8C22×D6111yescharacteristic
401#103—21no—
402#103—21no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—2441no—
411#103C22⋊D6111yescharacteristic
412#103C22⋊D6111yescharacteristic
413#102—611no—
414#102—611no—
415#102—1221no—
416C22⋊C8—21no—
417C22⋊C8—1221no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8C22×D6111yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×Q8C2×C22⋊D6111yescharacteristic
428C2×Q8C2×C22⋊D6111yescharacteristic
429C2×D4—611no—
430C2×D4D4×D6111yescharacteristic
431C22×C4—21no—
432C22×C4—1221no—
433C22×C4—2441no—
434Q16—22no—
435Q16—4881no—
436Q16—2442no—
437SD16—4881no—
438SD16—4881no—
439SD16—2442no—
440D8—2441no—
441M16—2442no—
442C2×C8—21no—
443C2×C8—42no—
444C2×C8—611no—
445C2×C8—611no—
446C2×C8—1221no—
447C2×C8—1221no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8C2×C22⋊D6111yescharacteristic
451C2×C8C2×C22⋊D6111yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—611no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—2441no—
466C4⋊C4—2441no—
467C4⋊C4—2441no—
468C4⋊C4D4×D6111yescharacteristic
469C4⋊C4C2×C22⋊D6111yescharacteristic
470C4⋊C4C2×C22⋊D6111yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—1221no—
477C22⋊C4—2441no—
478C22⋊C4—2441no—
479C22⋊C4—2441no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42—41no—
484C42—2441no—
485C42C23×D6111yescharacteristic
486C23—21no—
487C23—1221no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—4881no—
497Q8—2441no—
498Q8—2441no—
499D4—21no—
500D4—21no—
501D4—1221no—
502D4—1221no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—1221no—
513C2×C4—9761no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4C2×D4×D6111yescharacteristic
519C2×C4C22×C22⋊D6111yescharacteristic
520C2×C4#1451982211yescharacteristic
521C8—21no—
522C8—41no—
523C8—1221no—
524C8—1221no—
525C8—2441no—
526C8—2441no—
527C8—2441no—
528C8—2441no—
529C8#1451979712yes—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—2441no—
534C22—2441no—
535C22—2441no—
536C22D4×C22⋊D6111yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—81no—
544C4—81no—
545C4—4881no—
546C4—4881no—
547C4—2441no—
548C4C2×#1451979711yescharacteristic
549C4#1684055911yescharacteristic
550C4#1684056911yescharacteristic
551C4#1684057711yescharacteristic
552C2—81no—
553C2—4881no—
554C2#2145740411yescharacteristic
555C2#2145753711yescharacteristic
556C2#2145759011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3342C2
socleC22×C61D42
prime radicalC2×#11758199D4
hypercenter#3342D61
hypocenterC61#19866
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3342

Complements

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

NH ≅ G/Ntype
3. #21458436C2semidirect
4. #21445497C2semidirect
5. #21445329C2semidirect
6. #21445275C2semidirect
7. #21445194C2semidirect
8. #21445187C2semidirect
9. #21445075C2semidirect
10. #21445074C2semidirect
11. #21445025C2semidirect
12. #21444991C2semidirect
14. #21444638C2semidirect
15. C61×#3342C2semidirect
277. #3342D61semidirect
345. C61#19866semidirect

Maximal subgroups

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

subgroupindex
#214588032
#214584642
#214584362
#214454972
#214453292
#214452752
#214451942
#214451872
#214450752
#214450742
#214450252
#214449912
#214446482
#214446382
C61×#33422
#1986661