Finite Group Databasebeta

← #29650116

Subgroups — #29650116

Order 15616.

598 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#21455891C211yesmaximal, characteristic
2#21454928C211yesmaximal, characteristic
3#21454916C211yesmaximal, characteristic, complemented
4#21444689C211yesmaximal, characteristic, complemented
5#21444675C211yesmaximal, characteristic, complemented
6#21444668C211yesmaximal, characteristic, complemented
7#21444654C211yesmaximal, characteristic, complemented
8#21444637C211yesmaximal, characteristic, complemented
9#21444630C211yesmaximal, characteristic, complemented
10#21444625C211yesmaximal, characteristic, complemented
11#21444618C211yesmaximal, characteristic, complemented
12#21444251C211yesmaximal, characteristic
13#21444221C211yesmaximal, characteristic, complemented
14#21444119C211yesmaximal, characteristic, complemented
15C61×#1573C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17C4×#11758222C2211yescharacteristic
18#16840104C411yescharacteristic
19#16840104C411yescharacteristic
20#16840048C411yescharacteristic
21#16840043C411yescharacteristic
22#16839973C411yescharacteristic
23#16839968C411yescharacteristic
24#16839926C411yescharacteristic
25#16839926C411yescharacteristic
26#16839890—21no—
27#16839890—21no—
28#16839889C2211yescharacteristic
29#16839889C2211yescharacteristic
30#16839886C2211yescharacteristic
31#16839886C2211yescharacteristic
32#16839886C2211yescharacteristic
33#16839886C2211yescharacteristic
34C4×Dic244C2211yescharacteristic
35C4×Dic244C2211yescharacteristic
36C4×#11758190C2211yescharacteristic
37C4×#11758190C2211yescharacteristic
38#16839827C2211yescharacteristic
39#16839827C2211yescharacteristic
40C8×C22⋊D61—21no—
41C8×C22⋊D61—21no—
42#16839820—21no—
43#16839820—21no—
44#16839815C2211yescharacteristic
45#16839815C2211yescharacteristic
46#16839814—21no—
47C4⋊C8×D61—21no—
48#16839492C2211yescharacteristic
49#16839492C2211yescharacteristic
50#16839492C2211yescharacteristic
51#16839492C2211yescharacteristic
52#16839492C2211yescharacteristic
53#16839492C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839489C2211yescharacteristic
56#16839484C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839483C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#432C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#334C2211yescharacteristic
66C61×#334C2211yescharacteristic
67C2×#11758222C2×C411yescharacteristic
68C2×Dic244C2×C411yescharacteristic
69C2×Dic244C2×C411yescharacteristic
70C2×#11758190C2×C411yescharacteristic
71C2×#11758190C2×C411yescharacteristic
72C2×C8×D61—21no—
73C2×C8×D61—21no—
74#14519777C2×C411yescharacteristic
75#14519777C2×C411yescharacteristic
76#14519769—21no—
77#14519756—21no—
78#14519756C2×C411yescharacteristic
79#14519756C2×C411yescharacteristic
80C4×Dic122—21no—
81C4×Dic122C2×C411yescharacteristic
82C4×Dic122C2311yescharacteristic
83C4×Dic122C2311yescharacteristic
84C4×Dic122C2311yescharacteristic
85C4×D244C2×C411yescharacteristic
86C4×D244C2311yescharacteristic
87C4×C22⋊D61—21no—
88C4×C22⋊D61—21no—
89#14519736—21no—
90#14519736C2×C411yescharacteristic
91#14519734—21no—
92C42×D61—21no—
93#14519711C2×C411yescharacteristic
94#14519711C2×C411yescharacteristic
95#14519709C2×C411yescharacteristic
96#14519709C2×C411yescharacteristic
97C4⋊#92418—21no—
98C4⋊#92418D411yescharacteristic
99C4⋊#92418D411yescharacteristic
100#14519706—21no—
101#14519706—21no—
102#14519706—21no—
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519702C2×C411yescharacteristic
107#14519702C2×C411yescharacteristic
108#14519702C2×C411yescharacteristic
109#14519702C2×C411yescharacteristic
110#14519702C2×C411yescharacteristic
111#14519702C2×C411yescharacteristic
112#14519699C2×C411yescharacteristic
113#14519699C2×C411yescharacteristic
114C22⋊#92418—21no—
115C22⋊#92418D411yescharacteristic
116C22⋊#92418D411yescharacteristic
117#14519689—21no—
118#14519689—21no—
119#14519687—21no—
120#14519687—21no—
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C8×Dic61—21no—
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61—21no—
129C22×C8×C61—21no—
130C2×C42×C61C2311yescharacteristic
131C4⋊C8×C61—21no—
132C4⋊C8×C61C2×C411yescharacteristic
133C4⋊C8×C61C2×C411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C22⋊C8×C61—21no—
139C22⋊C8×C61C2×C411yescharacteristic
140C22⋊C8×C61C2×C411yescharacteristic
141#97×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C2×C22⋊D61—21no—
148#11758222—22no—
149#11758222—22no—
150C2×D244C22×C411yescharacteristic
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×Dic122—21no—
155C2×Dic122C22×C411yescharacteristic
156C2×Dic122C22×C411yescharacteristic
157C2×Dic122C22×C411yescharacteristic
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—81no—
163C2×C8×C61C22×C411yescharacteristic
164C2×C8×C61C22×C411yescharacteristic
165C2×C8×C61C22×C411yescharacteristic
166C2×C8×C61C22×C411yescharacteristic
167C42×C61C22×C411yescharacteristic
168C42×C61C2×D411yescharacteristic
169C42×C61#4111yescharacteristic
170C42×C61C2411yescharacteristic
171C22⋊Dic61—21no—
172C22⋊Dic61—21no—
173C22⋊Dic61—21no—
174#11758198—21no—
175#11758198—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61C22×C411yescharacteristic
180C4⋊Dic61C22×C411yescharacteristic
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—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418C2×D411yescharacteristic
197C2×#92418C2×D411yescharacteristic
198C2×#92418C2×D411yescharacteristic
199C2×#92418C2×D411yescharacteristic
200Dic244—22no—
201Dic244—22no—
202#11758190—22no—
203#11758190—22no—
204C8×D61—81no—
205C8×D61—81no—
206C23×C61C4×D411yescharacteristic
207C22×D61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—41no—
213C2×C4×C61C4×D411yescharacteristic
214C2×C4×C61C4×D411yescharacteristic
215C2×C4×C61C4×D411yescharacteristic
216C2×C4×C61C23×C411yescharacteristic
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C22⋊D61—24no—
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227D244—21no—
228D244#13112yes—
229C4×D61—24no—
230C4×D61—41no—
231C4×D61—41no—
232C4×D61—81no—
233Dic122—21no—
234Dic122—21no—
235Dic122—21no—
236Dic122—21no—
237Dic122—21no—
238Dic122—81no—
239Dic122#13112yes—
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—41no—
245C8×C61—41no—
246C8×C61—41no—
247C8×C61—41no—
248#92418—21no—
249#92418—21no—
250#92418—21no—
251#92418—21no—
252#92418—41no—
253#92418—41no—
254#17921—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61C2×C4×D411yescharacteristic
259C2×D61—22no—
260C2×D61—41no—
261C2×D61—41no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61C2×#13111yescharacteristic
267C4×C61C2×#13111yescharacteristic
268C4×C61#57711yescharacteristic
269C4×C61#57811yescharacteristic
270Dic61—22no—
271Dic61—41no—
272Dic61—41no—
273Dic61—41no—
274Dic61—41no—
275Dic61—41no—
276Dic61—41no—
277#3107—611no—
278#2988—611no—
279#2985—611no—
280#1587—611no—
281#1585—611no—
282#1584—611no—
283#1582—611no—
284#1579—611no—
285SD16⋊C8—611no—
286C8×Q16—611no—
287C8×SD16—611no—
288#1573D6111yescharacteristic, complemented
289#1488—611no—
290#1481—611no—
291#1454—611no—
292C2×C61—41no—
293C2×C61#292911yescharacteristic
294C2×C61#294711yescharacteristic
295C2×C61#295711yescharacteristic
296D61—42no—
297#533—611no—
298C4×#41—611no—
299#485—611no—
300#485—611no—
301#475—611no—
302#474—611no—
303#462—611no—
304#461—611no—
305#452—611no—
306#452—611no—
307#446—611no—
308#446—611no—
309#446—1221no—
310#446—1221no—
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—611no—
314C8×Q8—611no—
315C4×Q16—611no—
316C4×Q16—611no—
317C4×SD16—611no—
318C4×SD16—611no—
319C8×D4—611no—
320C8×D4—611no—
321C8×D4—1221no—
322C8×D4—1221no—
323#433—1221no—
324#433—1221no—
325#432C2×D6111yescharacteristic
326#431—611no—
327#431—611no—
328#431—1221no—
329#431C2×D6111yescharacteristic
330C2×C4⋊C8—1221no—
331C2×C4⋊C8C2×D6111yescharacteristic
332#335C2×D6111yescharacteristic
333#335C2×D6111yescharacteristic
334#334C2×D6111yescharacteristic
335#334C2×D6111yescharacteristic
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342D4⋊C8—611no—
343D4⋊C8—611no—
344#322—611no—
345#322—611no—
346#322—611no—
347C82—611no—
348C61#1792111yescharacteristic, complemented, Sylow
349C2×#41—611no—
350C2×Q16—611no—
351C2×Q16—611no—
352C2×SD16—611no—
353C2×SD16—611no—
354C22×C8—21no—
355C22×C8—1221no—
356C22×C8—1221no—
357C4⋊Q8—611no—
358C4⋊Q8—611no—
359#125—1221no—
360C22⋊Q8—611no—
361C22⋊Q8—611no—
362C22⋊Q8—1221no—
363C4×Q8—611no—
364C4×Q8—611no—
365C4×Q8—611no—
366C4×Q8—611no—
367C4×Q8—1221no—
368C4×D4—611no—
369C4×D4—611no—
370C4×D4—1221no—
371C4×D4—1221no—
372#117—611no—
373#117—1221no—
374#117—1221no—
375C2×C42—1221no—
376C2×C42C22×D6111yescharacteristic
377#107—611no—
378#107—611no—
379#106—611no—
380#106—611no—
381C4⋊C8—21no—
382C4⋊C8—611no—
383C4⋊C8—611no—
384C4⋊C8—1221no—
385C4⋊C8—1221no—
386C4⋊C8—1221no—
387C4⋊C8—1221no—
388C4⋊C8—1221no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8C4×D6111yescharacteristic
392C4⋊C8C4×D6111yescharacteristic
393C4⋊C8C22×D6111yescharacteristic
394C4⋊C8C22×D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396C4⋊C8C22×D6111yescharacteristic
397#103—611no—
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#103—611no—
403#102—611no—
404#102—611no—
405C22⋊C8—21no—
406C22⋊C8—611no—
407C22⋊C8—611no—
408C22⋊C8—1221no—
409C22⋊C8—1221no—
410C22⋊C8—1221no—
411C22⋊C8C4×D6111yescharacteristic
412C22⋊C8C4×D6111yescharacteristic
413#97—21no—
414#97—1221no—
415#97—1221no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8—1221no—
423C4×C8—1221no—
424C4×C8C22×D6111yescharacteristic
425C4×C8C22×D6111yescharacteristic
426#41—1222no—
427#41—1222no—
428C2×Q8—611no—
429C2×Q8—611no—
430C2×Q8—611no—
431C2×Q8—1221no—
432C2×D4—611no—
433C2×D4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4C2×C4×D6111yescharacteristic
438C22×C4D4×D6111yescharacteristic
439C22×C4#1175822611yescharacteristic
440Q16—1222no—
441Q16—1222no—
442SD16—1222no—
443SD16—1222no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—81no—
449C2×C8—611no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—4881no—
456C2×C8—4881no—
457C2×C8C2×C4×D6111yescharacteristic
458C2×C8C2×C4×D6111yescharacteristic
459C2×C8C2×C4×D6111yescharacteristic
460C2×C8C2×C4×D6111yescharacteristic
461C4⋊C4—611no—
462C4⋊C4—611no—
463C4⋊C4—611no—
464C4⋊C4—611no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C22⋊C4—1221no—
475C22⋊C4—1221no—
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C42—1221no—
480C42—1221no—
481C42—1221no—
482C42—1221no—
483C42—1221no—
484C42C2×C4×D6111yescharacteristic
485C42D4×D6111yescharacteristic
486C42#1175822611yescharacteristic
487C42C23×D6111yescharacteristic
488C23—1221no—
489C23#1451973911yescharacteristic
490Q8—612no—
491Q8—1221no—
492Q8—1221no—
493Q8—1221no—
494Q8—1221no—
495Q8—1221no—
496Q8—4881no—
497D4—612no—
498D4—1224no—
499D4—1221no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—1224no—
506C2×C4—1221no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—4881no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4#1451973911yescharacteristic
517C2×C4#1451973911yescharacteristic
518C2×C4#1451973911yescharacteristic
519C2×C4C22×C4×D6111yescharacteristic
520C2×C4C2×D4×D6111yescharacteristic
521C2×C4C2×#1175822611yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—1221no—
531C8—1221no—
532C8—1221no—
533C8—1221no—
534C8—2441no—
535C8—2441no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—1222no—
540C22—2441no—
541C22—2441no—
542C22C2×#1451973911yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—1222no—
548C4—2441no—
549C4—2441no—
550C4—2441no—
551C4—2441no—
552C4—2441no—
553C4—2441no—
554C4#131×D6111yescharacteristic
555C4#131×D6111yescharacteristic
556C4#1684057211yescharacteristic
557C4#1684057811yescharacteristic
558C2—41no—
559C2—2442no—
560C2#2145451211yescharacteristic
561C2#2145466011yescharacteristic
562C2#2145473511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1573C2
socleC22×C61C2×C4×D4
prime radicalC2×#11758222C2×C4
cosocleC42×C61C24
hypercenter#1573D61
hypocenterC61#17921
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
3. #21454916C2semidirect
4. #21444689C2semidirect
5. #21444675C2semidirect
6. #21444668C2semidirect
7. #21444654C2semidirect
8. #21444637C2semidirect
9. #21444630C2semidirect
10. #21444625C2semidirect
11. #21444618C2semidirect
13. #21444221C2semidirect
14. #21444119C2semidirect
15. C61×#1573C2semidirect
288. #1573D61semidirect
348. C61#17921semidirect

Maximal subgroups

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

subgroupindex
#214558912
#214549282
#214549162
#214446892
#214446752
#214446682
#214446542
#214446372
#214446302
#214446252
#214446182
#214442512
#214442212
#214441192
C61×#15732
#1792161