Finite Group Databasebeta

← #29651276

Subgroups — #29651276

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455895C211yesmaximal, characteristic
2#21454906C211yesmaximal, characteristic, complemented
3#21444726C211yesmaximal, characteristic, complemented
4#21444721C211yesmaximal, characteristic, complemented
5#21444669C211yesmaximal, characteristic, complemented
6#21444667C211yesmaximal, characteristic, complemented
7#21444660C211yesmaximal, characteristic, complemented
8#21444655C211yesmaximal, characteristic, complemented
9#21444636C211yesmaximal, characteristic, complemented
10#21444631C211yesmaximal, characteristic, complemented
11#21444602C211yesmaximal, characteristic, complemented
12#21444279C211yesmaximal, characteristic
13C2×#16839492C211yesmaximal, characteristic, complemented
14#21444112C211yesmaximal, characteristic, complemented
15C61×#2994C211yesmaximal, characteristic
16C2×C4×Dic122C2211yescharacteristic
17#16840090C411yescharacteristic
18#16840073C411yescharacteristic
19#16840066C411yescharacteristic
20#16840066C411yescharacteristic
21#16839981C411yescharacteristic
22#16839981C411yescharacteristic
23#16839917C411yescharacteristic
24#16839900C411yescharacteristic
25#16839892C2211yescharacteristic
26#16839892C2211yescharacteristic
27#16839891—21no—
28#16839891—21no—
29C8×Dic122C2211yescharacteristic
30C8×Dic122C2211yescharacteristic
31C4×#11758202C2211yescharacteristic
32C4×#11758202C2211yescharacteristic
33C4×#11758200C2211yescharacteristic
34C4×#11758200C2211yescharacteristic
35#16839819C2211yescharacteristic
36#16839816—21no—
37#16839815C2211yescharacteristic
38#16839812—21no—
39C2×C4×#92418C2211yescharacteristic
40#16839514C2211yescharacteristic
41#16839514C2211yescharacteristic
42#16839512C2211yescharacteristic
43#16839512C2211yescharacteristic
44Q8⋊#92418C2211yescharacteristic
45Q8⋊#92418C2211yescharacteristic
46#16839492C2211yescharacteristic
47#16839492C2211yescharacteristic
48#16839492C2211yescharacteristic
49#16839492C2211yescharacteristic
50D4⋊#92418C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52#16839484C2211yescharacteristic
53#16839484C2211yescharacteristic
54#16839483C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#529C2211yescharacteristic
57C61×#446C2211yescharacteristic
58C8×Q8×C61C2211yescharacteristic
59C61×#436C2211yescharacteristic
60C61×#435—21no—
61C8×D4×C61—21no—
62C8×D4×C61C2211yescharacteristic
63C61×#433—21no—
64C61×#431C2211yescharacteristic
65C61×#424—21no—
66C2×C4⋊C8×C61C2211yescharacteristic
67C22×Dic122C2×C411yescharacteristic
68C2×#11758202C2×C411yescharacteristic
69C2×#11758202C2×C411yescharacteristic
70C2×#11758200C2×C411yescharacteristic
71C2×#11758200C2×C411yescharacteristic
72C22×#92418—21no—
73C4×Dic122—21no—
74C4×Dic122—21no—
75C4×Dic122C2×C411yescharacteristic
76C4×Dic122C2×C411yescharacteristic
77C4×Dic122C2311yescharacteristic
78C4×Dic122C2311yescharacteristic
79C2×C4⋊Dic61C2×C411yescharacteristic
80C2×#11758196—21no—
81C2×C4×Dic61—21no—
82#14519710C2×C411yescharacteristic
83#14519710C2×C411yescharacteristic
84#14519708C2×C411yescharacteristic
85#14519708C2×C411yescharacteristic
86C4⋊#92418C2×C411yescharacteristic
87C4⋊#92418C2×C411yescharacteristic
88C4⋊#92418C2311yescharacteristic
89C4⋊#92418C2311yescharacteristic
90#14519706—21no—
91#14519706—21no—
92#14519706—21no—
93#14519706—21no—
94#14519701C2×C411yescharacteristic
95#14519701C2×C411yescharacteristic
96#14519700C2×C411yescharacteristic
97#14519700C2×C411yescharacteristic
98#14519700C2×C411yescharacteristic
99#14519700C2×C411yescharacteristic
100#14519698C2×C411yescharacteristic
101#14519698C2×C411yescharacteristic
102C22⋊#92418—21no—
103C22⋊#92418C2×C411yescharacteristic
104C22⋊#92418C2×C411yescharacteristic
105#14519688—21no—
106#14519687—21no—
107#14519687—21no—
108C4×#92418—21no—
109C4×#92418C2311yescharacteristic
110C4×#92418C2311yescharacteristic
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C8×Dic61—21no—
114C8×Dic61—21no—
115C2×M16×C61—21no—
116C22×C8×C61—21no—
117C22×C8×C61—21no—
118#126×C61—21no—
119#125×C61C2×C411yescharacteristic
120#124×C61C2×C411yescharacteristic
121#123×C61—21no—
122C22⋊Q8×C61C2×C411yescharacteristic
123#121×C61C2×C411yescharacteristic
124C4×Q8×C61C2311yescharacteristic
125C4×D4×C61—21no—
126C4×D4×C61C2311yescharacteristic
127#117×C61—21no—
128C2×C42×C61C2311yescharacteristic
129C4⋊C8×C61—21no—
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61D411yescharacteristic
133C4⋊C8×C61D411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61D411yescharacteristic
139C22⋊C8×C61D411yescharacteristic
140#97×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C22×Dic61—21no—
152C22×Dic61—21no—
153C2×Dic122—22no—
154C2×Dic122—21no—
155C2×Dic122—41no—
156C2×Dic122C22×C411yescharacteristic
157C2×Dic122C22×C411yescharacteristic
158M16×C61—81no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—81no—
162C2×C8×C61—81no—
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61C22×C411yescharacteristic
172C4⋊C4×C61C22×C411yescharacteristic
173C22⋊C4×C61—21no—
174C22⋊C4×C61—21no—
175C22⋊C4×C61—21no—
176C22⋊C4×C61—21no—
177C22⋊C4×C61—21no—
178C42×C61—21no—
179C42×C61C22×C411yescharacteristic
180C42×C61C2×D411yescharacteristic
181C42×C61#4111yescharacteristic
182C42×C61C2411yescharacteristic
183#11758202—22no—
184#11758202—41no—
185#11758200—22no—
186#11758200—41no—
187C4⋊Dic61—21no—
188C4⋊Dic61C22×C411yescharacteristic
189C4⋊Dic61C22×C411yescharacteristic
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193#11758196—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—42no—
203C2×#92418C22×C411yescharacteristic
204C2×#92418C22×C411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207C23×C61—21no—
208C23×C61C4×D411yescharacteristic
209Q8×C61—21no—
210Q8×C61—21no—
211D4×C61—21no—
212D4×C61—21no—
213D4×C61—42no—
214C2×C4×C61—22no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
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×C61C4×D411yescharacteristic
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C23×C411yescharacteristic
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C2×#4111yescharacteristic
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—42no—
235C2×Dic61—42no—
236Dic122—21no—
237Dic122—21no—
238Dic122—21no—
239Dic122—42no—
240Dic122#13112yes—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—41no—
246C8×C61—41no—
247#92418—21no—
248#92418—21no—
249#92418—21no—
250#92418—21no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#92418—41no—
255#18023—611nomaximal, Sylow
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61#44412yes—
262C22×C61C2×C4×D411yescharacteristic
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61C2×#13111yescharacteristic
271C4×C61#56811yescharacteristic
272C4×C61#57711yescharacteristic
273C4×C61#57811yescharacteristic
274Dic61—22no—
275Dic61—41no—
276Dic61—41no—
277Dic61—41no—
278#3108—611no—
279#2994D6111yescharacteristic
280#2984—611no—
281#1593—611no—
282#1592—611no—
283#1584—611no—
284#1584—611no—
285#1583—611no—
286#1582—611no—
287#1579—611no—
288SD16⋊C8—611no—
289#1573—611no—
290#1494—611no—
291C2×Q8⋊C8—611no—
292#1452—611no—
293C2×C61—22no—
294C2×C61—81no—
295C2×C61#293311yescharacteristic
296C2×C61#294711yescharacteristic
297C2×C61C2×#44411yescharacteristic
298#529C2×D6111yescharacteristic
299C2×C4×Q8—611no—
300#483—611no—
301#480—611no—
302#479—611no—
303#479—611no—
304#464—611no—
305#464—611no—
306#451—611no—
307#448—611no—
308#446—611no—
309#446—611no—
310#446—1221no—
311#446—1221no—
312#446C2×D6111yescharacteristic
313C8×Q8—611no—
314C8×Q8—611no—
315C8×Q8C2×D6111yescharacteristic
316C4×Q16—611no—
317C4×Q16—611no—
318C4×SD16—611no—
319C4×SD16—611no—
320#436C2×D6111yescharacteristic
321#435—21no—
322C8×D4—21no—
323C8×D4C2×D6111yescharacteristic
324#433—21no—
325#432—611no—
326#432—1221no—
327#431—611no—
328#431—1221no—
329#431C2×D6111yescharacteristic
330#424—21no—
331C2×C4⋊C8C2×D6111yescharacteristic
332C2×C4×C8—611no—
333#335—611no—
334#335—611no—
335#334—611no—
336#334—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342Q8⋊C8—611no—
343D4⋊C8—611no—
344D4⋊C8—611no—
345#322—611no—
346#322—611no—
347#322—611no—
348#322—611no—
349C61#1802311yescharacteristic, complemented, Sylow
350C22×Q8—611no—
351C2×Q16—611no—
352C2×Q16—611no—
353C2×SD16—611no—
354C2×SD16—611no—
355C2×M16—21no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—1221no—
359#126—21no—
360#125C4×D6111yescharacteristic
361#124C4×D6111yescharacteristic
362#123—21no—
363C22⋊Q8C4×D6111yescharacteristic
364#121C4×D6111yescharacteristic
365C4×Q8—611no—
366C4×Q8—611no—
367C4×Q8—611no—
368C4×Q8—611no—
369C4×Q8—1221no—
370C4×Q8—1221no—
371C4×Q8C22×D6111yescharacteristic
372C4×D4—21no—
373C4×D4C22×D6111yescharacteristic
374#117—21no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—1221no—
377C2×C42—1221no—
378C2×C42C22×D6111yescharacteristic
379#107—611no—
380#107—611no—
381#106—611no—
382#106—611no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8C22⋊D6111yescharacteristic
395C4⋊C8C22⋊D6111yescharacteristic
396C4⋊C8C22×D6111yescharacteristic
397C4⋊C8C22×D6111yescharacteristic
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#103—611no—
403#103—611no—
404#102—611no—
405#102—611no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—611no—
409C22⋊C8—611no—
410C22⋊C8—1221no—
411C22⋊C8C22⋊D6111yescharacteristic
412C22⋊C8C22⋊D6111yescharacteristic
413#97—21no—
414#97—1221no—
415#97—1221no—
416#97—1221no—
417C4×C8—21no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—1221no—
423C4×C8—1221no—
424C4×C8—1221no—
425C4×C8C22×D6111yescharacteristic
426C4×C8C22×D6111yescharacteristic
427C2×Q8—611no—
428C2×Q8—611no—
429C2×Q8—1222no—
430C2×Q8—1221no—
431C2×Q8—2441no—
432C2×Q8C2×C4×D6111yescharacteristic
433C2×D4—21no—
434C2×D4C2×C4×D6111yescharacteristic
435C22×C4—21no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4C2×C4×D6111yescharacteristic
439C22×C4#1175822211yescharacteristic
440C22×C4C2×C22⋊D6111yescharacteristic
441Q16—1222no—
442Q16—2441no—
443SD16—1222no—
444SD16—2441no—
445M16—81no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—81no—
449C2×C8—81no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—2442no—
459C2×C8C2×C22⋊D6111yescharacteristic
460C2×C8C2×C22⋊D6111yescharacteristic
461C2×C8C2×C22⋊D6111yescharacteristic
462C2×C8C2×C22⋊D6111yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—611no—
468C4⋊C4—611no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4C2×C4×D6111yescharacteristic
475C4⋊C4C2×C4×D6111yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C42—21no—
482C42—1221no—
483C42—1221no—
484C42—1221no—
485C42—1221no—
486C42C2×C4×D6111yescharacteristic
487C42#1175822211yescharacteristic
488C42C2×C22⋊D6111yescharacteristic
489C42C23×D6111yescharacteristic
490C23—21no—
491C23C4×C22⋊D6111yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—612no—
495Q8—1221no—
496Q8—1221no—
497Q8—1221no—
498Q8—2442no—
499D4—21no—
500D4—21no—
501D4—42no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—2442no—
517C2×C4—2442no—
518C2×C4C4×C22⋊D6111yescharacteristic
519C2×C4C4×C22⋊D6111yescharacteristic
520C2×C4C4×C22⋊D6111yescharacteristic
521C2×C4C22×C4×D6111yescharacteristic
522C2×C4C22×C22⋊D6111yescharacteristic
523C2×C4C2×#1175822211yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—1221no—
531C8—1221no—
532C8—1221no—
533C8—1221no—
534C8—2441no—
535C8—2441no—
536C8—2441no—
537C8—2441no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22#1683988212yes—
544C22C2×C4×C22⋊D6111yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—1222no—
553C4—2441no—
554C4—2441no—
555C4—2441no—
556C4#131×D6111yescharacteristic
557C4#1684052711yescharacteristic
558C4#1684057311yescharacteristic
559C4#1684057711yescharacteristic
560C2—22no—
561C2—81no—
562C2#2145454111yescharacteristic
563C2#2145465811yescharacteristic
564C2C2×#1683988211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2994C2
socleC22×C61C2×C4×D4
prime radical#121×C61C2×C4
cosocleC42×C61C24
hypercenter#2994D61
hypocenterC61#18023
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #21454906C2semidirect
3. #21444726C2semidirect
4. #21444721C2semidirect
5. #21444669C2semidirect
6. #21444667C2semidirect
7. #21444660C2semidirect
8. #21444655C2semidirect
9. #21444636C2semidirect
10. #21444631C2semidirect
11. #21444602C2semidirect
13. C2×#16839492C2semidirect
14. #21444112C2semidirect
349. C61#18023semidirect

Maximal subgroups

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

subgroupindex
#214558952
#214549062
#214447262
#214447212
#214446692
#214446672
#214446602
#214446552
#214446362
#214446312
#214446022
#214442792
C2×#168394922
#214441122
C61×#29942
#1802361