Finite Group Databasebeta

← #29670890

Subgroups — #29670890

Order 15616.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458870C211yesmaximal, characteristic, complemented
2#21458694C211yesmaximal, characteristic, complemented
3#21458479C211yesmaximal, characteristic
4#21445442C211yesmaximal, characteristic, complemented
5#21445344C211yesmaximal, characteristic, complemented
6#21445237C211yesmaximal, characteristic, complemented
7#21445203C211yesmaximal, characteristic, complemented
8#21445160C211yesmaximal, characteristic
9#21445033C211yesmaximal, characteristic, complemented
10#21444975C211yesmaximal, characteristic, complemented
11#21444939C211yesmaximal, characteristic, complemented
12#21444891C211yesmaximal, characteristic
13#21444655C211yesmaximal, characteristic, complemented
14#21444638C211yesmaximal, characteristic, complemented
15C61×#3338C211yesmaximal, characteristic, complemented
16#16840497C2211yescharacteristic
17#16840490C2211yescharacteristic
18#16840161—21no—
19#16840158C2211yescharacteristic
20#16840155—21no—
21#16840136C2211yescharacteristic
22#16840135C2211yescharacteristic
23#16840119—21no—
24#16840112C2211yescharacteristic
25#16840110C2211yescharacteristic
26#16840066—21no—
27#16840062—21no—
28#16840059—21no—
29#16840054C2211yescharacteristic
30#16840054C2211yescharacteristic
31#16840042C2211yescharacteristic
32#16839987—21no—
33#16839977—21no—
34#16839972C2211yescharacteristic
35#16839966—21no—
36#16839962C2211yescharacteristic
37#16839957C2211yescharacteristic
38#16839892C2211yescharacteristic
39Q8×#92418C2211yescharacteristic
40Q8×#92418C2211yescharacteristic
41#16839861—21no—
42C4×#11758200—21no—
43C4×#11758200C2211yescharacteristic
44C4×#11758199—21no—
45#16839513C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839511C2211yescharacteristic
49#16839509C2211yescharacteristic
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#554C2211yescharacteristic
57C61×#554C2211yescharacteristic
58C61×#500C2211yescharacteristic
59C61×#484—21no—
60C61×#484—21no—
61C61×#477C2211yescharacteristic
62C61×#477C2211yescharacteristic
63C61×#467—21no—
64C4×Q16×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic
66C2×#107×C61—21no—
67C2×#11758202—21no—
68C2×#11758190—21no—
69C2×#11758190—21no—
70C2×#11758200D411yescharacteristic
71C2×#11758201—21no—
72C2×#11758201—41no—
73C2×#11758199—21no—
74#14519777C2311yescharacteristic
75#14519775—21no—
76#14519774C2311yescharacteristic
77#14519769—21no—
78#14519767—41no—
79#14519766—21no—
80#14519765—21no—
81#14519762—41no—
82C4×Dic122—21no—
83C4×Dic122C2311yescharacteristic
84#14519742—21no—
85C4×D244—21no—
86#14519739—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519708—21no—
91#14519708—21no—
92#14519708D411yescharacteristic
93C4⋊#92418—21no—
94C4⋊#92418—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519706—21no—
99#14519701—41no—
100#14519700—21no—
101#14519700—21no—
102#14519700—21no—
103#14519700D411yescharacteristic
104#14519698—21no—
105#14519698D411yescharacteristic
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—21no—
110#14519687—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#125×C61—21no—
120#125×C61—21no—
121C22⋊Q8×C61—21no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—41no—
124C22⋊Q8×C61—41no—
125C4×Q8×C61C2311yescharacteristic
126C4×Q8×C61C2311yescharacteristic
127C4×D4×C61—21no—
128C4×D4×C61—21no—
129C4×D4×C61C2311yescharacteristic
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132#107×C61—21no—
133#107×C61—21no—
134#107×C61—21no—
135#107×C61—21no—
136#107×C61D411yescharacteristic
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—
150C22×C4×C61—41no—
151C22×C4×C61—41no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×C4×D61—41no—
156C2×Dic122—21no—
157C2×Dic122C2×D411yescharacteristic
158Q16×C61—22no—
159C2×C8×C61—21no—
160C2×C8×C61—42no—
161C2×C8×C61C2×D411yescharacteristic
162C2×C8×C61C2×D411yescharacteristic
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61—41no—
172C4⋊C4×C61—41no—
173C4⋊C4×C61C2×D411yescharacteristic
174C4⋊C4×C61C2×D411yescharacteristic
175C4⋊C4×C61C2×D411yescharacteristic
176C22⋊C4×C61—21no—
177C22⋊C4×C61—41no—
178C22⋊C4×C61—41no—
179C42×C61—21no—
180C42×C61—21no—
181C42×C61C2411yescharacteristic
182#11758202—81no—
183#11758201—81no—
184#11758201—82no—
185#11758200—22no—
186#11758199—42no—
187#11758198—41no—
188#11758198—41no—
189#11758198—41no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61C2×D411yescharacteristic
193#11758196—21no—
194#11758196—41no—
195#11758196—41no—
196#11758196—41no—
197C4×Dic61—21no—
198C4×Dic61—41no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205#11758190—42no—
206#11758190—81no—
207C23×C61—21no—
208C22×D61—41no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—81no—
214Q8×C61—81no—
215D4×C61—21no—
216D4×C61#13712yes—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—161no—
227C2×C4×C61—161no—
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61H(5,𝔽2)11yescharacteristic
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—41no—
234D244—41no—
235D244—41no—
236D244—41no—
237D244—41no—
238D244—81no—
239C4×D61—161no—
240Dic122—21no—
241Dic122—21no—
242Dic122—41no—
243Dic122—41no—
244C8×C61—21no—
245C8×C61—41no—
246C8×C61#13512yes—
247#92418—21no—
248#92418—21no—
249#92418—41no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#19857—611nomaximal, Sylow
254C22×C61—22no—
255C22×C61—41no—
256C22×C61—41no—
257C22×C61D4211yescharacteristic
258C2×D61—81no—
259C2×D61—81no—
260C2×D61—81no—
261C4×C61—21no—
262C4×C61—41no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61—81no—
268C4×C61—81no—
269C4×C61C2×#13511yescharacteristic
270C4×C61C2×#13711yescharacteristic
271C4×C61#57711yescharacteristic
272C4×C61#57811yescharacteristic
273Dic61—41no—
274Dic61—41no—
275Dic61—81no—
276#3400—611no—
277#3381—611no—
278#3361—611no—
279#3338D6111yescharacteristic, complemented
280#1714—611no—
281#1696—611no—
282#1678—611no—
283#1672—611no—
284#1665—611no—
285#1644—611no—
286#1636—611no—
287#1630—611no—
288#1622—611no—
289#1582—611no—
290#1579—611no—
291C2×C61—42no—
292C2×C61#327011yescharacteristic
293C2×C61#328411yescharacteristic
294C2×C61#328811yescharacteristic
295D61—161no—
296#559—611no—
297#557—611no—
298#554C2×D6111yescharacteristic
299#554C2×D6111yescharacteristic
300#500C2×D6111yescharacteristic
301#499—1221no—
302#498—611no—
303#497—1221no—
304#492—611no—
305#492—611no—
306#488—1221no—
307#487—611no—
308#486—611no—
309#484—21no—
310#484—21no—
311#479—1221no—
312#478—1221no—
313#478—1221no—
314#477—611no—
315#477—611no—
316#477C2×D6111yescharacteristic
317#477C2×D6111yescharacteristic
318#474—611no—
319#467—21no—
320#464—1221no—
321#463—1221no—
322#462—611no—
323#461—1221no—
324#460—611no—
325#459—611no—
326#446—611no—
327C8×Q8—611no—
328C8×Q8—611no—
329#440—1221no—
330C4×Q16C2×D6111yescharacteristic
331C4×SD16—611no—
332C4×SD16—1221no—
333C4×D8—1221no—
334C8×D4C2×D6111yescharacteristic
335C2×#107—21no—
336#334—611no—
337#334—611no—
338#333—611no—
339#333—611no—
340#332—611no—
341#331—611no—
342Q8⋊C8—611no—
343Q8⋊C8—611no—
344Q8⋊C8—611no—
345D4⋊C8—611no—
346#322—611no—
347C61#1985711yescharacteristic, complemented, Sylow
348C2×Q16—1221no—
349C2×Q16C22⋊D6111yescharacteristic
350C2×SD16—611no—
351C2×SD16—1221no—
352C2×SD16—1221no—
353C2×SD16—1221no—
354C2×SD16—2441no—
355C2×D8—1221no—
356C22×C8—21no—
357C4⋊Q8—611no—
358C4⋊Q8—1221no—
359C4⋊Q8C22×D6111yescharacteristic
360C4⋊Q8C22×D6111yescharacteristic
361#127—611no—
362#125—21no—
363#125—21no—
364#125—1221no—
365#125—2441no—
366#124—1221no—
367#124—1221no—
368#123—2441no—
369C22⋊Q8—21no—
370C22⋊Q8—21no—
371C22⋊Q8—41no—
372C22⋊Q8—41no—
373C4×Q8—611no—
374C4×Q8—1221no—
375C4×Q8—1221no—
376C4×Q8C22×D6111yescharacteristic
377C4×Q8C22×D6111yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—1221no—
381C4×D4—1221no—
382C4×D4C22×D6111yescharacteristic
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#107—1221no—
390#107—1221no—
391#107—1221no—
392#107C22⋊D6111yescharacteristic
393#106—611no—
394#106—1221no—
395#106—1221no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8C22×D6111yescharacteristic
403#103—21no—
404#103—21no—
405#103—611no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—2441no—
410#103C22⋊D6111yescharacteristic
411#103C22⋊D6111yescharacteristic
412#102—611no—
413#102—1221no—
414#102—1221no—
415#102—1221no—
416#102—1221no—
417#102—1221no—
418C22⋊C8—21no—
419#97—1221no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—1221no—
423C4×C8—1221no—
424C4×C8C22×D6111yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—611no—
428C2×Q8—1221no—
429C2×Q8C2×C22⋊D6111yescharacteristic
430C2×Q8C2×C22⋊D6111yescharacteristic
431C2×D4—1221no—
432C2×D4—1221no—
433C2×D4—1221no—
434C2×D4D4×D6111yescharacteristic
435C22×C4—21no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—2441no—
439Q16—22no—
440Q16—4881no—
441SD16—1222no—
442SD16—4881no—
443SD16—4882no—
444SD16—4881no—
445SD16—2442no—
446D8—2442no—
447C2×C8—21no—
448C2×C8—42no—
449C2×C8—611no—
450C2×C8—611no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8C2×C22⋊D6111yescharacteristic
456C2×C8C2×C22⋊D6111yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—611no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—2441no—
472C4⋊C4—2441no—
473C4⋊C4—2441no—
474C4⋊C4D4×D6111yescharacteristic
475C4⋊C4C2×C22⋊D6111yescharacteristic
476C4⋊C4C2×C22⋊D6111yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—2441no—
481C22⋊C4—2441no—
482C22⋊C4—2441no—
483C42—21no—
484C42—21no—
485C42—1221no—
486C42—2441no—
487C42C23×D6111yescharacteristic
488C23—21no—
489C23—2441no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—81no—
496Q8—1221no—
497Q8—1221no—
498Q8—2441no—
499Q8—2441no—
500D4—21no—
501D4—4881no—
502D4—2441no—
503D4—2441no—
504D4—2441no—
505D4—2441no—
506D4#1451980912yes—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—161no—
517C2×C4—161no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—9761no—
521C2×C4—2441no—
522C2×C4C2×D4×D6111yescharacteristic
523C2×C4C22×C22⋊D6111yescharacteristic
524C2×C4#1451982211yescharacteristic
525C8—21no—
526C8—41no—
527C8—1221no—
528C8—1221no—
529C8—2441no—
530C8—2441no—
531C8—2441no—
532C8—2441no—
533C8#1451979712yes—
534C22—22no—
535C22—41no—
536C22—41no—
537C22—4881no—
538C22—4881no—
539C22—4881no—
540C22D4×C22⋊D6111yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—81no—
548C4—81no—
549C4—4881no—
550C4—2441no—
551C4—2441no—
552C4C2×#1451979711yescharacteristic
553C4C2×#1451980911yescharacteristic
554C4#1684057011yescharacteristic
555C4#1684057511yescharacteristic
556C2—42no—
557C2—9761no—
558C2#2145738911yescharacteristic
559C2#2145754511yescharacteristic
560C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3338C2
socleC22×C61D42
prime radical#16839957C22
hypercenter#3338D61
hypocenterC61#19857
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3338

Complements

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

NH ≅ G/Ntype
1. #21458870C2semidirect
2. #21458694C2semidirect
4. #21445442C2semidirect
5. #21445344C2semidirect
6. #21445237C2semidirect
7. #21445203C2semidirect
9. #21445033C2semidirect
10. #21444975C2semidirect
11. #21444939C2semidirect
13. #21444655C2semidirect
14. #21444638C2semidirect
15. C61×#3338C2semidirect
279. #3338D61semidirect
347. C61#19857semidirect

Maximal subgroups

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

subgroupindex
#214588702
#214586942
#214584792
#214454422
#214453442
#214452372
#214452032
#214451602
#214450332
#214449752
#214449392
#214448912
#214446552
#214446382
C61×#33382
#1985761