Finite Group Databasebeta

← #29594962

Subgroups — #29594962

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839743C211yesmaximal, characteristic
2C2×#16839734C211yesmaximal, characteristic
3#21448406C211yesmaximal, characteristic
4#21443938C211yesmaximal, characteristic, complemented
5#21443937C211yesmaximal, characteristic, complemented
6#21443936C211yesmaximal, characteristic, complemented
7C61×#1390C211yesmaximal, characteristic, complemented
8C22×#11758224C2211yescharacteristic
9C2×M16×D61—21no—
10C2×#14519733—21no—
11C2×#14519733C411yescharacteristic, complemented
12C22×#11758196C411yescharacteristic, complemented
13#16839743—22no—
14#16839743C414yescomplemented
15C2×#14519695—21no—
16C2×#14519694C2211yescharacteristic
17#16839734—22no—
18#16839734C414yescomplemented
19C2×#14519692C2211yescharacteristic
20C2×#14519691—21no—
21#16839666—21no—
22#16839662—21no—
23#16839642C2211yescharacteristic
24#16839641C411yescharacteristic, complemented
25#16839639C411yescharacteristic, complemented
26#16839621—21no—
27#16839620—21no—
28C2×#100×C61C2211yescharacteristic
29C2×#99×C61C2211yescharacteristic
30C61×#386C2211yescharacteristic
31C2×#11758224—41no—
32C2×#11758224—42no—
33C2×#11758224—41no—
34C2×#11758224C2×C412yes—
35C2×#11758224C2×C412yes—
36C2×#11758224D412yes—
37C2×#11758224Q812yes—
38C22×Dic122D411yescharacteristic
39C22×C22⋊D61C2×C411yescharacteristic
40C22×C22⋊D61D411yescharacteristic
41C23×Dic61C2×C411yescharacteristic
42C23×Dic61C2×C411yescharacteristic
43C23×Dic61D411yescharacteristic
44C22×C4×D61D411yescharacteristic
45C2×#11758194—21no—
46C2×#11758189—41no—
47M16×D61—24no—
48M16×D61—42no—
49C2×C8×D61—41no—
50#14519733—24no—
51#14519733—42no—
52#14519733—42no—
53C2×#11758196—21no—
54C2×#11758196—21no—
55C2×#11758196—21no—
56C2×#11758196—41no—
57C2×#11758196—41no—
58C2×#11758196—41no—
59C2×C22⋊Dic61—21no—
60C2×C22⋊Dic61—21no—
61C2×C22⋊Dic61C2×C411yescharacteristic
62C2×#11758198—21no—
63C2×#11758198—21no—
64C2×C4×Dic61—21no—
65C2×C4×Dic61—41no—
66#14519695—24no—
67#14519694—21no—
68#14519694C2×C412yes—
69#14519692—21no—
70#14519692C2×C412yes—
71#14519691—24no—
72#14519684—21no—
73#14519684—21no—
74#14519684—21no—
75C22×D4×C61C2311yescharacteristic
76C23×C4×C61C2×C411yescharacteristic
77C2×M16×C61—21no—
78C2×C22⋊C4×C61—21no—
79C2×C22⋊C4×C61—21no—
80C2×C22⋊C4×C61C2×C411yescharacteristic
81#100×C61—21no—
82#100×C61C2×C412yes—
83#99×C61—21no—
84#99×C61C2×C412yes—
85#95×C61—21no—
86C24×C61C22×C411yescharacteristic
87C24×C61C2×D411yescharacteristic
88C23×D61C22⋊C411yescharacteristic
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61C22×C411yescharacteristic
92C2×D4×C61C22×C411yescharacteristic
93C2×D4×C61C2×D411yescharacteristic
94C2×D4×C61C2×Q811yescharacteristic
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61—81no—
100C22×C4×C61C2×D411yescharacteristic
101C2×C22⋊D61—41no—
102C2×C22⋊D61—41no—
103C2×C22⋊D61—41no—
104C2×C22⋊D61—41no—
105C2×C22⋊D61C4212yes—
106C2×C22⋊D61C22⋊C412yes—
107C2×C22⋊D61C4⋊C412yes—
108C2×C22⋊D61C4⋊C412yes—
109C22×Dic61—21no—
110C22×Dic61—21no—
111C22×Dic61—22no—
112C22×Dic61—21no—
113C22×Dic61—21no—
114C22×Dic61—22no—
115C22×Dic61—21no—
116C22×Dic61—21no—
117C22×Dic61—41no—
118C22×Dic61—41no—
119C22×Dic61—81no—
120C22×Dic61C4212yes—
121C22×Dic61C22⋊C411yescharacteristic
122C22×Dic61C22⋊C411yescharacteristic
123C22×Dic61C22⋊C412yes—
124C22×Dic61C22⋊C411yescharacteristic
125C22×Dic61C4⋊C412yes—
126C22×Dic61C4⋊C412yes—
127#11758224—42no—
128#11758224—42no—
129#11758224—42no—
130#11758224—42no—
131#11758224—42no—
132#11758224—42no—
133#11758224—42no—
134#11758224—42no—
135C2×C4×D61—21no—
136C2×C4×D61—22no—
137C2×C4×D61—21no—
138C2×C4×D61C22⋊C412yes—
139C2×C4×D61C4⋊C412yes—
140C2×Dic122—41no—
141C2×Dic122—41no—
142C2×Dic122C22⋊C412yes—
143C2×Dic122C4⋊C412yes—
144M16×C61—22no—
145M16×C61—41no—
146C2×C8×C61—41no—
147C22⋊C4×C61—22no—
148C22⋊C4×C61—41no—
149C22⋊C4×C61—41no—
150C22⋊C4×C61—81no—
151C22⋊Dic61—22no—
152C22⋊Dic61—41no—
153C22⋊Dic61—41no—
154C22⋊Dic61—81no—
155#11758198—81no—
156#11758198—81no—
157#11758196—42no—
158#11758196—44no—
159#11758196—41no—
160#11758196—41no—
161#11758196—42no—
162C4×Dic61—42no—
163C4×Dic61—44no—
164#11758194—22no—
165#11758194—41no—
166C2×#92418—41no—
167#11758189—44no—
168C8×D61—44no—
169C23×C61—21no—
170C23×C61—21no—
171C23×C61—21no—
172C23×C61—21no—
173C23×C61—41no—
174C23×C61—41no—
175C23×C61—41no—
176C23×C61—41no—
177C23×C61C2×C4211yescharacteristic
178C23×C61C2×C22⋊C411yescharacteristic
179C23×C61C2×C22⋊C411yescharacteristic
180C23×C61C2×C4⋊C411yescharacteristic
181C23×C61C2×C4⋊C411yescharacteristic
182C22×D61—21no—
183C22×D61—21no—
184C22×D61—41no—
185C22×D61—41no—
186C22×D61#9512yes—
187D4×C61—41no—
188D4×C61—41no—
189D4×C61—41no—
190D4×C61—41no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61—42no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—81no—
201C2×C4×C61—81no—
202C2×C4×C61—82no—
203C2×C4×C61C2×C22⋊C411yescharacteristic
204C2×C4×C61C2×C4⋊C411yescharacteristic
205C22⋊D61—42no—
206C22⋊D61—42no—
207C22⋊D61—42no—
208C22⋊D61—42no—
209C2×Dic61—21no—
210C2×Dic61—21no—
211C2×Dic61—21no—
212C2×Dic61—21no—
213C2×Dic61—22no—
214C2×Dic61—22no—
215C2×Dic61—22no—
216C2×Dic61—22no—
217C2×Dic61—22no—
218C2×Dic61—22no—
219C2×Dic61—22no—
220C2×Dic61—22no—
221C2×Dic61—42no—
222C2×Dic61—41no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61—41no—
227C2×Dic61—41no—
228C2×Dic61—81no—
229C2×Dic61—81no—
230C2×Dic61—82no—
231C2×Dic61#9512yes—
232C2×Dic61#9512yes—
233C2×Dic61#9512yes—
234C2×Dic61#9912yes—
235C2×Dic61#9911yescharacteristic
236C2×Dic61#9911yescharacteristic
237C4×D61—22no—
238C4×D61—22no—
239C4×D61—22no—
240C4×D61—22no—
241Dic122—42no—
242Dic122—42no—
243C8×C61—42no—
244#92418—42no—
245#12575—611nomaximal, Sylow
246C22×C61—21no—
247C22×C61—21no—
248C22×C61—21no—
249C22×C61—21no—
250C22×C61—21no—
251C22×C61—21no—
252C22×C61—41no—
253C22×C61—41no—
254C22×C61—41no—
255C22×C61—41no—
256C22×C61—42no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—81no—
262C22×C61C2×#9511yescharacteristic
263C22×C61C2×#9911yescharacteristic
264C22×C61C2×#9911yescharacteristic
265C2×D61—22no—
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—42no—
269C2×D61—81no—
270C4×C61—21no—
271C4×C61—21no—
272C4×C61—81no—
273C4×C61—82no—
274C4×C61—81no—
275Dic61—22no—
276Dic61—22no—
277Dic61—81no—
278Dic61—82no—
279Dic61—81no—
280Dic61#34212yes—
281Dic61#34212yes—
282C2×#413—611no—
283C2×#410—611no—
284#2311—611no—
285#1390—611no—
286#1390—611no—
287#1390—611no—
288#1390D6111yescharacteristic, complemented
289C2×C61—21no—
290C2×C61—21no—
291C2×C61—41no—
292C2×C61—41no—
293C2×C61—41no—
294C2×C61—41no—
295C2×C61C2×#34211yescharacteristic
296C2×C61#212211yescharacteristic
297C2×C61#212311yescharacteristic
298D61—42no—
299C22×#41—611no—
300C22×M16—1221no—
301C2×#117—611no—
302C2×#117—1221no—
303C22×C4⋊C4—611no—
304#413—614no—
305#413—1222no—
306C2×#101—1221no—
307C2×#100—611no—
308C2×#100C2×D6111yescharacteristic
309#410—614no—
310#410—1222no—
311C2×#99—611no—
312C2×#99—1221no—
313C2×#99C2×D6111yescharacteristic
314#391—1221no—
315#390—1221no—
316#386—611no—
317#386—611no—
318#386—611no—
319#386C2×D6111yescharacteristic
320#380—1221no—
321#380—1221no—
322C61#1257511yescharacteristic, complemented, Sylow
323C2×#41—612no—
324C2×#41—612no—
325C2×#41—612no—
326C2×#41—612no—
327C2×#41—2441no—
328C2×#41—2441no—
329C2×#41—2442no—
330C22×Q8—611no—
331C22×D4—611no—
332C22×D4—611no—
333C22×D4C22×D6111yescharacteristic
334C23×C4—611no—
335C23×C4—611no—
336C23×C4—611no—
337C23×C4—611no—
338C23×C4C4×D6111yescharacteristic
339C2×M16—21no—
340C2×M16—1224no—
341C2×M16—1221no—
342C2×M16—2441no—
343C2×M16—2442no—
344C22×C8—2441no—
345#117—1224no—
346#117—2442no—
347#117—2442no—
348C2×C4⋊C4—1221no—
349C2×C4⋊C4—1221no—
350C2×C4⋊C4—1221no—
351C2×C4⋊C4—2441no—
352C2×C4⋊C4—2441no—
353C2×C4⋊C4—2441no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—611no—
357C2×C22⋊C4—1221no—
358C2×C22⋊C4—1221no—
359C2×C22⋊C4—1221no—
360C2×C22⋊C4—1221no—
361C2×C22⋊C4C4×D6111yescharacteristic
362C2×C42—1221no—
363C2×C42—2441no—
364#101—1224no—
365#100—21no—
366#100—612no—
367#100—1221no—
368#100C4×D6112yes—
369#99—21no—
370#99—612no—
371#99—1224no—
372#99—1221no—
373#99C4×D6112yes—
374#95—21no—
375#95—1221no—
376#95—1221no—
377#95—1221no—
378C24—611no—
379C24C2×C4×D6111yescharacteristic
380C24D4×D6111yescharacteristic
381#41—2442no—
382#41—2442no—
383#41—2442no—
384#41—2442no—
385#41—2442no—
386#41—2442no—
387#41—2442no—
388#41—2442no—
389C2×Q8—612no—
390C2×Q8—612no—
391C2×Q8—2441no—
392C2×Q8—2441no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—612no—
396C2×D4—612no—
397C2×D4—612no—
398C2×D4—612no—
399C2×D4—2441no—
400C2×D4—2441no—
401C2×D4—2441no—
402C2×D4—2441no—
403C2×D4C2×C4×D6111yescharacteristic
404C2×D4C2×C4×D6111yescharacteristic
405C2×D4D4×D6111yescharacteristic
406C2×D4Q8×D6111yescharacteristic
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—81no—
412C22×C4—611no—
413C22×C4—612no—
414C22×C4—612no—
415C22×C4—611no—
416C22×C4—611no—
417C22×C4—612no—
418C22×C4—612no—
419C22×C4—612no—
420C22×C4—612no—
421C22×C4—1221no—
422C22×C4—1222no—
423C22×C4—1221no—
424C22×C4—1221no—
425C22×C4—1221no—
426C22×C4—1221no—
427C22×C4—1221no—
428C22×C4—1222no—
429C22×C4—1222no—
430C22×C4—1221no—
431C22×C4—1221no—
432C22×C4—4881no—
433C22×C4—2441no—
434C22×C4—2441no—
435C22×C4D4×D6111yescharacteristic
436M16—22no—
437M16—41no—
438M16—1222no—
439M16—2444no—
440M16—2441no—
441C2×C8—41no—
442C2×C8—2444no—
443C2×C8—2441no—
444C4⋊C4—2441no—
445C4⋊C4—2441no—
446C4⋊C4—2442no—
447C4⋊C4—2442no—
448C4⋊C4—2444no—
449C22⋊C4—22no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—81no—
453C22⋊C4—1222no—
454C22⋊C4—4881no—
455C22⋊C4—4881no—
456C22⋊C4—4881no—
457C22⋊C4—2441no—
458C22⋊C4—2441no—
459C42—2442no—
460C42—2444no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—612no—
470C23—1221no—
471C23—1221no—
472C23—2441no—
473C23—2441no—
474C23C42×D6111yescharacteristic
475C23C22⋊C4×D6111yescharacteristic
476C23C22⋊C4×D6111yescharacteristic
477C23C4⋊C4×D6111yescharacteristic
478C23C4⋊C4×D6111yescharacteristic
479Q8—2442no—
480Q8—2442no—
481D4—41no—
482D4—41no—
483D4—41no—
484D4—41no—
485D4—2442no—
486D4—2442no—
487D4—2442no—
488D4—2442no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—81no—
499C2×C4—81no—
500C2×C4—82no—
501C2×C4—612no—
502C2×C4—611no—
503C2×C4—611no—
504C2×C4—612no—
505C2×C4—612no—
506C2×C4—612no—
507C2×C4—1222no—
508C2×C4—1222no—
509C2×C4—1222no—
510C2×C4—1222no—
511C2×C4—1222no—
512C2×C4—1222no—
513C2×C4—1222no—
514C2×C4—1222no—
515C2×C4—1222no—
516C2×C4—1222no—
517C2×C4—1222no—
518C2×C4—1222no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—4881no—
524C2×C4—4881no—
525C2×C4—4882no—
526C2×C4—2442no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4C22⋊C4×D6111yescharacteristic
534C2×C4C4⋊C4×D6111yescharacteristic
535C8—42no—
536C8—2442no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—42no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—81no—
553C22—1222no—
554C22—4881no—
555C22—2442no—
556C22—2441no—
557C22—2441no—
558C22#95×D6111yescharacteristic
559C22#99×D6111yescharacteristic
560C22#99×D6111yescharacteristic
561C4—21no—
562C4—21no—
563C4—81no—
564C4—82no—
565C4—81no—
566C4—612no—
567C4—612no—
568C4—1222no—
569C4—1222no—
570C4—4881no—
571C4—4882no—
572C4—4881no—
573C2—21no—
574C2—21no—
575C2—41no—
576C2—41no—
577C2—41no—
578C2—41no—
579C2—2442no—
580C2#342×D6111yescharacteristic
581C2#2144746711yescharacteristic
582C2#2144747111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC23×C61C2×C42
FrattiniC22×D4C22×D61
FittingC61×#1390C2
socleC22×C61C2×#99
prime radicalC22×#11758224C22
cosocleC22×D4×C61C23
hypercenter#1390D61
hypocenterC61#12575
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1390

Complements

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

NH ≅ G/Ntype
4. #21443938C2semidirect
5. #21443937C2semidirect
6. #21443936C2semidirect
7. C61×#1390C2semidirect
11. C2×#14519733C4semidirect
12. C22×#11758196C4semidirect
14. #16839743C4semidirect
18. #16839734C4semidirect
24. #16839641C4semidirect
25. #16839639C4semidirect
288. #1390D61semidirect
322. C61#12575semidirect

Maximal subgroups

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

subgroupindex
C2×#168397432
C2×#168397342
#214484062
#214439382
#214439372
#214439362
C61×#13902
#1257561