Finite Group Databasebeta

← #29649708

Subgroups — #29649708

Order 15616.

626 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#21454901C211yesmaximal, characteristic
2#21454898C211yesmaximal, characteristic
3C4×Q16×D61C211yesmaximal, characteristic
4#21444692C211yesmaximal, characteristic, complemented
5#21444691C211yesmaximal, characteristic, complemented
6#21444689C211yesmaximal, characteristic, complemented
7#21444672C211yesmaximal, characteristic, complemented
8#21444669C211yesmaximal, characteristic, complemented
9#21444667C211yesmaximal, characteristic, complemented
10#21444666C211yesmaximal, characteristic, complemented
11#21444564C211yesmaximal, characteristic
12#21444212C211yesmaximal, characteristic
13#21444212C211yesmaximal, characteristic
14#21444110C211yesmaximal, characteristic
15C61×#1587C211yesmaximal, characteristic, complemented
16C2×Q16×D61C411yescharacteristic
17C4×Q8×D61C2211yescharacteristic
18C4×Q8×D61C2211yescharacteristic
19#16839893C2211yescharacteristic
20#16839892C2211yescharacteristic
21#16839891—21no—
22#16839890—21no—
23#16839889C2211yescharacteristic
24Q8×#92418C2211yescharacteristic
25C8×Dic122—21no—
26C8×Dic122C2211yescharacteristic
27#16839886—21no—
28#16839886C2211yescharacteristic
29C4×Dic244C2211yescharacteristic
30Q16×Dic61C411yescharacteristic
31#16839856C411yescharacteristic
32C4×#11758202C2211yescharacteristic
33C4×#11758202C2211yescharacteristic
34#16839854C411yescharacteristic
35#16839854C411yescharacteristic
36#16839818—21no—
37#16839817—21no—
38#16839814—21no—
39#16839814C2211yescharacteristic
40#16839814C2211yescharacteristic
41#16839813—21no—
42#16839813C2211yescharacteristic
43#16839813C2211yescharacteristic
44#107×D61C411yescharacteristic
45#103×D61C411yescharacteristic
46#103×D61C411yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839513C2211yescharacteristic
51#16839494C2211yescharacteristic
52#16839494C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54Q8⋊#92418C2211yescharacteristic
55#16839492C2211yescharacteristic
56#16839492C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839484C2211yescharacteristic
59#16839483C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C8×Q8×C61C2211yescharacteristic
62C4×Q16×C61C2211yescharacteristic
63C61×#334C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×Q8⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×Q8×D61C2×C411yescharacteristic
68C2×Q8×D61C2×C411yescharacteristic
69C2×Dic244C2×C411yescharacteristic
70C2×#11758202C2×C411yescharacteristic
71C2×#11758202C2×C411yescharacteristic
72Q16×D61—24no—
73C2×C8×D61C2×C411yescharacteristic
74C2×C8×D61C2×C411yescharacteristic
75Q8×Dic61C2×C411yescharacteristic
76Q8×Dic61C2×C411yescharacteristic
77C4×Dic122—21no—
78C4×Dic122—21no—
79C4×Dic122C2311yescharacteristic
80C4×Dic122C2311yescharacteristic
81#14519742—21no—
82#14519742—21no—
83#14519742C2×C411yescharacteristic
84#14519742C2×C411yescharacteristic
85C4⋊C4×D61—21no—
86C4⋊C4×D61—21no—
87C4⋊C4×D61C2×C411yescharacteristic
88C4⋊C4×D61C2×C411yescharacteristic
89C42×D61—21no—
90C42×D61—21no—
91C42×D61C2311yescharacteristic
92#14519711C2×C411yescharacteristic
93#14519710C2×C411yescharacteristic
94#14519710C2×C411yescharacteristic
95C4⋊#92418—21no—
96C4⋊#92418—21no—
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519706—21no—
100#14519706—21no—
101#14519706—21no—
102#14519706—21no—
103#14519706—21no—
104#14519706D411yescharacteristic
105#14519706D411yescharacteristic
106#14519702C2×C411yescharacteristic
107#14519702C2×C411yescharacteristic
108#14519701C2×C411yescharacteristic
109#14519701C2×C411yescharacteristic
110#14519700C2×C411yescharacteristic
111#14519700C2×C411yescharacteristic
112#14519689—21no—
113#14519689—21no—
114#14519689—21no—
115#14519689D411yescharacteristic
116#14519689D411yescharacteristic
117#14519688—21no—
118#14519687—21no—
119#14519687—21no—
120C4×#92418—21no—
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C8×Dic61—21no—
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61C2×C411yescharacteristic
129C8×Dic61C2×C411yescharacteristic
130C2×Q16×C61C2×C411yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132C4×Q8×C61C2311yescharacteristic
133#107×C61C2×C411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61C2×C411yescharacteristic
139#103×C61C2×C411yescharacteristic
140#97×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×Q8×C61C22×C411yescharacteristic
147Q8×D61—22no—
148Q8×D61—22no—
149Q8×D61—22no—
150Q8×D61M1614yes—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61C22×C411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61#4111yescharacteristic
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122C22×C411yescharacteristic
161C2×Dic122C22×C411yescharacteristic
162Q16×C61—22no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61C22×C411yescharacteristic
167C2×C8×C61C22×C411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61C22×C411yescharacteristic
173C4⋊C4×C61C22×C411yescharacteristic
174C42×C61—21no—
175C42×C61—21no—
176C42×C61C2411yescharacteristic
177#11758202—22no—
178#11758202—22no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61C22×C411yescharacteristic
182C4⋊Dic61C22×C411yescharacteristic
183#11758196—21no—
184#11758196—21no—
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61C22×C411yescharacteristic
196C4×Dic61C2×D411yescharacteristic
197C4×Dic61#4111yescharacteristic
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205Dic244—22no—
206C8×D61—22no—
207C8×D61—22no—
208C22×D61C4×D411yescharacteristic
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61C2×M1612yes—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61C23×C411yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61C4×D411yescharacteristic
225C2×Dic61C4×D411yescharacteristic
226C2×Dic61C4×D411yescharacteristic
227C4×D61—24no—
228C4×D61—21no—
229C4×D61—21no—
230C4×D61—41no—
231C4×D61—42no—
232C4×D61—81no—
233C4×D61—81no—
234C4×D61C2×M1612yes—
235C4×D61#13112yes—
236Dic122—21no—
237Dic122—24no—
238Dic122—21no—
239Dic122—21no—
240Dic122—42no—
241Dic122C2×M1612yes—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—41no—
247C8×C61—41no—
248C8×C61—41no—
249#92418—21no—
250#92418—21no—
251#92418—21no—
252#92418—21no—
253#92418—41no—
254#92418—41no—
255#92418—41no—
256#17880—611nomaximal, Sylow
257C22×C61C2×C4×D411yescharacteristic
258C2×D61—21no—
259C2×D61—21no—
260C2×D61#43512yes—
261C4×C61—22no—
262C4×C61—21no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61C22×M1611yescharacteristic
267C4×C61C2×#13111yescharacteristic
268C4×C61#57811yescharacteristic
269C4×C61#57811yescharacteristic
270Dic61—22no—
271Dic61—21no—
272Dic61—21no—
273Dic61—41no—
274Dic61—41no—
275Dic61—41no—
276Dic61#43512yes—
277#2983—611no—
278#2982—611no—
279C2×C4×Q16—611no—
280#1587—611no—
281#1587—611no—
282#1587—611no—
283#1587D6111yescharacteristic, complemented
284#1584—611no—
285#1584—611no—
286#1584—611no—
287#1584—611no—
288#1564—611no—
289#1479—611no—
290#1479—611no—
291#1452—611no—
292C2×C61C2×#43511yescharacteristic
293C2×C61#295011yescharacteristic
294C2×C61#295711yescharacteristic
295D61—22no—
296C22×Q16—611no—
297C2×C4×Q8—611no—
298C2×C4×Q8—611no—
299#446—611no—
300#446—611no—
301#446—611no—
302#446—1221no—
303#446—1221no—
304#446C2×D6111yescharacteristic
305C8×Q8—611no—
306C8×Q8—611no—
307C8×Q8—611no—
308C8×Q8—1221no—
309C8×Q8—1221no—
310C8×Q8C2×D6111yescharacteristic
311C4×Q16—611no—
312C4×Q16—611no—
313C4×Q16—611no—
314C4×Q16—611no—
315C4×Q16—611no—
316C4×Q16—611no—
317C4×Q16—611no—
318C4×Q16C2×D6111yescharacteristic
319#432—1221no—
320#432—1221no—
321#431—611no—
322#431—611no—
323#431—611no—
324#431—611no—
325#431—1221no—
326#431—1221no—
327C2×#107—611no—
328C2×#103—611no—
329C2×#103—611no—
330C2×C4×C8—611no—
331#335—611no—
332#335—611no—
333#334—611no—
334#334C2×D6111yescharacteristic
335Q8⋊C8—611no—
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8C2×D6111yescharacteristic
342Q8⋊C8C2×D6111yescharacteristic
343#322—611no—
344#322—611no—
345#322—611no—
346#322C2×D6111yescharacteristic
347C61#1788011yescharacteristic, complemented, Sylow
348C22×Q8—611no—
349C22×Q8—611no—
350C2×Q16—611no—
351C2×Q16—611no—
352C2×Q16—611no—
353C2×Q16—1224no—
354C2×Q16C4×D6111yescharacteristic
355C22×C8—611no—
356C22×C8—611no—
357C4×Q8—611no—
358C4×Q8—611no—
359C4×Q8—611no—
360C4×Q8—611no—
361C4×Q8—611no—
362C4×Q8—611no—
363C4×Q8—1221no—
364C4×Q8—1221no—
365C4×Q8—1221no—
366C4×Q8—1221no—
367C4×Q8C22×D6111yescharacteristic
368C4×Q8C22×D6111yescharacteristic
369C2×C4⋊C4—611no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—1221no—
372C2×C4⋊C4—1221no—
373C2×C42—611no—
374C2×C42—1221no—
375C2×C42—1221no—
376#107—611no—
377#107—611no—
378#107—611no—
379#107C4×D6111yescharacteristic
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8—611no—
383C4⋊C8—611no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—1221no—
387C4⋊C8—1221no—
388C4⋊C8—1221no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8C22×D6111yescharacteristic
394C4⋊C8C22×D6111yescharacteristic
395#103—611no—
396#103—611no—
397#103—611no—
398#103—611no—
399#103—611no—
400#103—611no—
401#103C4×D6111yescharacteristic
402#103C4×D6111yescharacteristic
403C22⋊C8—611no—
404C22⋊C8—611no—
405C22⋊C8—1221no—
406C22⋊C8—1221no—
407C22⋊C8—1221no—
408#97—21no—
409#97—1221no—
410#97—1221no—
411#97—1221no—
412C4×C8—21no—
413C4×C8—611no—
414C4×C8—611no—
415C4×C8—611no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8—1221no—
419C4×C8—1221no—
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8—1221no—
423C4×C8C22×D6111yescharacteristic
424C4×C8C22×D6111yescharacteristic
425C4×C8C22×D6111yescharacteristic
426C2×Q8—614no—
427C2×Q8—611no—
428C2×Q8—611no—
429C2×Q8—1221no—
430C2×Q8—1221no—
431C2×Q8—1222no—
432C2×Q8—1222no—
433C2×Q8—1222no—
434C2×Q8C2×C4×D6111yescharacteristic
435C2×Q8C2×C4×D6111yescharacteristic
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1221no—
443Q16—22no—
444Q16—1222no—
445Q16—1222no—
446Q16—1222no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—1222no—
455C2×C8—1222no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8C2×C4×D6111yescharacteristic
460C2×C8C2×C4×D6111yescharacteristic
461C2×C8D4×D6111yescharacteristic
462C2×C8D4×D6111yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—611no—
466C4⋊C4—611no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4C2×C4×D6111yescharacteristic
476C4⋊C4C2×C4×D6111yescharacteristic
477C42—21no—
478C42—21no—
479C42—611no—
480C42—611no—
481C42—611no—
482C42—1221no—
483C42—1221no—
484C42—1221no—
485C42—1221no—
486C42—1221no—
487C42—1221no—
488C42C23×D6111yescharacteristic
489C23—611no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—612no—
494Q8—1224no—
495Q8—1221no—
496Q8—1221no—
497Q8—1221no—
498Q8—2442no—
499Q8M16×D6112yes—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—611no—
505C2×C4—612no—
506C2×C4—612no—
507C2×C4—611no—
508C2×C4—611no—
509C2×C4—1224no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—4881no—
517C2×C4—4881no—
518C2×C4—2441no—
519C2×C4—2442no—
520C2×C4C22×C4×D6111yescharacteristic
521C2×C4C2×D4×D6111yescharacteristic
522C2×C4#41×D6111yescharacteristic
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—1221no—
531C8—1221no—
532C8—1221no—
533C8—1221no—
534C8—2441no—
535C8—2441no—
536C8—2441no—
537C22—612no—
538C22—1221no—
539C22—1221no—
540C22C4×D4×D6111yescharacteristic
541C4—21no—
542C4—22no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—612no—
547C4—1221no—
548C4—1221no—
549C4—1222no—
550C4—2441no—
551C4—2441no—
552C4—2441no—
553C4C2×M16×D6111yescharacteristic
554C4#131×D6111yescharacteristic
555C4#1684057811yescharacteristic
556C4#1684057811yescharacteristic
557C2—1222no—
558C2#435×D6111yescharacteristic
559C2#2145468411yescharacteristic
560C2#2145473111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1587C2
socleC22×C61C2×C4×D4
prime radicalC22×D61C4×D4
cosocleC42×C61C24
hypercenter#1587D61
hypocenterC61#17880
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
4. #21444692C2semidirect
5. #21444691C2semidirect
6. #21444689C2semidirect
7. #21444672C2semidirect
8. #21444669C2semidirect
9. #21444667C2semidirect
10. #21444666C2semidirect
15. C61×#1587C2semidirect
283. #1587D61semidirect
347. C61#17880semidirect

Maximal subgroups

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

subgroupindex
#214549012
#214548982
C4×Q16×D612
#214446922
#214446912
#214446892
#214446722
#214446692
#214446672
#214446662
#214445642
#214442122
#214441102
C61×#15872
#1788061