Finite Group Databasebeta

← #29697358

Subgroups — #29697358

Order 15616.

894 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454473C211yesmaximal, characteristic, complemented
2C2×#16839758C211yesmaximal, characteristic
3#21446533C212yesmaximal, complemented
4#21446464C212yesmaximal, complemented
5#21446094C212yesmaximal, complemented
6#21445916C211yesmaximal, characteristic, complemented
7#21445855C211yesmaximal, characteristic, complemented
8#21445763C211yesmaximal, characteristic
9#21445661C212yesmaximal, complemented
10#21445598C211yesmaximal, characteristic, complemented
11C61×#2880C211yesmaximal, characteristic
12C23×#92418C2211yescharacteristic
13C2×#14519736C2211yescharacteristic
14#16839820—22no—
15#16839816—21no—
16#16839812—21no—
17C2×#14519712C2212yescomplemented
18#16839788C2212yescomplemented
19C2×#14519704C2212yes—
20C2×#14519704C2212yes—
21#16839758C411yescharacteristic, complemented
22#16839758C411yescharacteristic, complemented
23#16839758C411yescharacteristic, complemented
24#16839758C411yescharacteristic, complemented
25#16839758C2211yescharacteristic
26#16839758C2211yescharacteristic
27#16839758C2211yescharacteristic
28#16839758C2211yescharacteristic
29C2×#14519701C411yescharacteristic, complemented
30C2×#14519701C411yescharacteristic, complemented
31C2×#14519698C411yescharacteristic, complemented
32C2×#14519698C411yescharacteristic, complemented
33#16839726C2211yescharacteristic
34#16839717C2212yescomplemented
35C2×#14519687C2212yescomplemented
36C4×C22⋊Dic61C2211yescharacteristic
37#16839526C2212yescomplemented
38#16839523C2212yescomplemented
39#16839523C2212yescomplemented
40#16839516C2212yescomplemented
41C22×#41×C61C2211yescharacteristic
42C2×#131×C61C2212yes—
43C61×#408—22no—
44C61×#408C2212yes—
45C61×#407—21no—
46C61×#407C2211yescharacteristic
47C2×C22⋊C8×C61—21no—
48C2×C22⋊C8×C61C2211yescharacteristic
49C2×#11758194C2312yes—
50C22×#92418—42no—
51C22×#92418C2×C411yescharacteristic
52C22×#92418C2×C411yescharacteristic
53C22×#92418C2×C411yescharacteristic
54C22×#92418C2×C411yescharacteristic
55C22×#92418C2311yescharacteristic
56C22×#92418C2311yescharacteristic
57#14519736—21no—
58#14519736—21no—
59#14519736C2×C411yescharacteristic
60#14519736C2×C411yescharacteristic
61#14519736C2311yescharacteristic
62#14519736C2311yescharacteristic
63C2×C4⋊Dic61C2×C411yescharacteristic
64C2×C4⋊Dic61C2×C411yescharacteristic
65C2×C22⋊Dic61—21no—
66C2×C22⋊Dic61—21no—
67C2×C4×Dic61—21no—
68C2×C4×Dic61C2312yes—
69#14519712—42no—
70#14519706—22no—
71#14519706—22no—
72#14519704—24no—
73#14519704—42no—
74#14519701C2×C411yescharacteristic
75#14519701C2×C411yescharacteristic
76#14519701C2×C411yescharacteristic
77#14519701C2×C411yescharacteristic
78#14519701C2×C411yescharacteristic
79#14519701C2×C411yescharacteristic
80#14519701C2×C411yescharacteristic
81#14519701C2×C411yescharacteristic
82#14519698C2×C411yescharacteristic
83#14519698C2×C411yescharacteristic
84#14519698C2×C411yescharacteristic
85#14519698C2×C411yescharacteristic
86#14519698C2×C411yescharacteristic
87#14519698C2×C411yescharacteristic
88#14519698C2×C411yescharacteristic
89#14519698C2×C411yescharacteristic
90C22⋊#92418—21no—
91C22⋊#92418—21no—
92#14519687—22no—
93#14519687—42no—
94C8×Dic61—22no—
95#14519684—21no—
96C2×#41×C61—21no—
97C2×#41×C61—21no—
98C2×#41×C61—24no—
99C2×#41×C61—42no—
100C2×#41×C61C2×C411yescharacteristic
101C2×#41×C61C2×C411yescharacteristic
102C2×#41×C61C2311yescharacteristic
103C2×#41×C61C2311yescharacteristic
104C22×Q8×C61C2×C411yescharacteristic
105C22×D4×C61—21no—
106C22×D4×C61C2×C411yescharacteristic
107C23×C4×C61—21no—
108C23×C4×C61C2311yescharacteristic
109#131×C61—24no—
110#131×C61—42no—
111C2×M16×C61—22no—
112C2×M16×C61C2312yes—
113C22×C8×C61—22no—
114C22×C8×C61C2312yes—
115C22⋊C8×C61—21no—
116C22⋊C8×C61—21no—
117C22⋊C8×C61—22no—
118C22⋊C8×C61—22no—
119C22⋊C8×C61D411yescharacteristic
120C22⋊C8×C61D411yescharacteristic
121C22⋊C8×C61D412yes—
122C24×C61—21no—
123C24×C61#4111yescharacteristic
124#41×C61—22no—
125#41×C61—22no—
126#41×C61—22no—
127#41×C61—22no—
128#41×C61—22no—
129#41×C61—44no—
130#41×C61—41no—
131#41×C61—41no—
132#41×C61—44no—
133#41×C61#4114yes—
134C2×Q8×C61—21no—
135C2×Q8×C61—22no—
136C2×Q8×C61—41no—
137C2×Q8×C61C22×C411yescharacteristic
138C2×Q8×C61C22×C411yescharacteristic
139C2×D4×C61—21no—
140C2×D4×C61—22no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—41no—
146C2×D4×C61—44no—
147C2×D4×C61C22×C411yescharacteristic
148C2×D4×C61C22×C411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—44no—
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61#4111yescharacteristic
162C22×C4×C61C2411yescharacteristic
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—22no—
166M16×C61—22no—
167M16×C61—22no—
168M16×C61—44no—
169C2×C8×C61—22no—
170C2×C8×C61—22no—
171C2×C8×C61—22no—
172C2×C8×C61—44no—
173C2×C8×C61C2×D412yes—
174C2×C8×C61C2×D412yes—
175C22⋊Dic61—21no—
176C22⋊Dic61—21no—
177C22⋊Dic61—21no—
178C22⋊Dic61—21no—
179C22⋊Dic61—42no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61C22×C411yescharacteristic
183C4⋊Dic61C22×C411yescharacteristic
184C4⋊Dic61C22×C411yescharacteristic
185C4⋊Dic61C22×C411yescharacteristic
186C4×Dic61—21no—
187C4×Dic61—21no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61—22no—
191C4×Dic61—22no—
192#11758194—22no—
193#11758194—22no—
194C2×#92418—22no—
195C2×#92418—22no—
196C2×#92418—22no—
197C2×#92418—41no—
198C2×#92418—41no—
199C2×#92418—41no—
200C2×#92418—41no—
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C22×C411yescharacteristic
205C23×C61—21no—
206C23×C61—22no—
207C23×C61—22no—
208C23×C61—21no—
209C23×C61—41no—
210C23×C61—42no—
211C23×C61—42no—
212C23×C61—81no—
213C23×C61C4×D411yescharacteristic
214C23×C61C4×D411yescharacteristic
215C23×C61C2×#4111yescharacteristic
216Q8×C61—21no—
217Q8×C61—21no—
218Q8×C61—21no—
219Q8×C61—42no—
220Q8×C61#11712yes—
221D4×C61—24no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—42no—
226D4×C61—42no—
227D4×C61—42no—
228D4×C61—42no—
229D4×C61#11712yes—
230C2×C4×C61—21no—
231C2×C4×C61—22no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—24no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—21no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61C4×D411yescharacteristic
245C2×C4×C61C4×D411yescharacteristic
246C2×C4×C61C23×C411yescharacteristic
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C2×#4112yes—
249C2×C4×C61H(5,𝔽2)12yes—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61—42no—
257C2×Dic61—42no—
258C2×Dic61—81no—
259C8×C61—22no—
260C8×C61—22no—
261C8×C61—42no—
262#92418—21no—
263#92418—21no—
264#92418—21no—
265#92418—21no—
266#92418—42no—
267#22586—611nomaximal, Sylow
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—22no—
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—44no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—84no—
283C22×C61#44412yes—
284C22×C61C2×C4×D411yescharacteristic
285C22×C61#55112yes—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—22no—
289C4×C61—41no—
290C4×C61C2×#11711yescharacteristic
291C4×C61#51811yescharacteristic
292C4×C61#54612yes—
293Dic61—41no—
294Dic61—41no—
295Dic61—41no—
296Dic61—41no—
297Dic61—82no—
298#2924—611no—
299C2×#416—611no—
300#2880D6111yescharacteristic
301#1938—612no—
302#1929—612no—
303#1866—612no—
304#1826—611no—
305#1810—611no—
306#1789—611no—
307#1765—612no—
308#1752—611no—
309C2×C61—22no—
310C2×C61—22no—
311C2×C61—41no—
312C2×C61—42no—
313C2×C61—81no—
314C2×C61#234211yescharacteristic
315C2×C61C2×#44411yescharacteristic
316C2×C61#295711yescharacteristic
317C22×#41C2×D6111yescharacteristic
318C2×#131C2×D6112yes—
319C23×C8—611no—
320C2×#117—611no—
321#433—1222no—
322#432—1221no—
323#431—1221no—
324C2×#108—612no—
325#424—612no—
326C2×#104—612no—
327C2×#104—612no—
328#416—611no—
329#416—611no—
330#416—611no—
331#416—611no—
332#416—611no—
333#416—611no—
334#416—611no—
335#416—611no—
336C2×#103—611no—
337C2×#103—611no—
338C2×#102—611no—
339C2×#102—611no—
340#408—22no—
341#408C2×D6112yes—
342#407—21no—
343#407—611no—
344#407C2×D6111yescharacteristic
345C2×C22⋊C8—21no—
346C2×C22⋊C8C2×D6111yescharacteristic
347#405—612no—
348C2×#97—612no—
349C4×C22⋊C4—611no—
350#341—612no—
351#339—612no—
352#339—612no—
353#336—612no—
354C61#2258611yescharacteristic, complemented, Sylow
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—24no—
358C2×#41—42no—
359C2×#41C4×D6111yescharacteristic
360C2×#41C4×D6111yescharacteristic
361C2×#41C22×D6111yescharacteristic
362C2×#41C22×D6111yescharacteristic
363C22×Q8C4×D6111yescharacteristic
364C22×D4—21no—
365C22×D4C4×D6111yescharacteristic
366C23×C4—21no—
367C23×C4C22×D6111yescharacteristic
368#131—24no—
369#131—42no—
370C2×M16—22no—
371C2×M16—612no—
372C2×M16C22×D6112yes—
373C22×C8—22no—
374C22×C8—611no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8—611no—
379C22×C8—611no—
380C22×C8—2442no—
381C22×C8C22×D6112yes—
382#117—611no—
383#117—611no—
384#117—611no—
385#117—611no—
386#117—1221no—
387#117—1221no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—611no—
390C2×C22⋊C4—1221no—
391C2×C22⋊C4—1221no—
392C2×C42—612no—
393C2×C42—1221no—
394#108—2442no—
395C4⋊C8—1222no—
396C4⋊C8—1222no—
397#104—1224no—
398#104—2442no—
399#103—611no—
400#103—611no—
401#103—611no—
402#103—611no—
403#103—611no—
404#103—611no—
405#103—611no—
406#103—611no—
407#102—611no—
408#102—611no—
409#102—611no—
410#102—611no—
411#102—611no—
412#102—611no—
413#102—611no—
414#102—611no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—22no—
418C22⋊C8—22no—
419C22⋊C8—1221no—
420C22⋊C8—1221no—
421C22⋊C8C22⋊D6111yescharacteristic
422C22⋊C8C22⋊D6111yescharacteristic
423C22⋊C8C22⋊D6112yes—
424#97—1222no—
425#97—2442no—
426C4×C8—1222no—
427#95—1221no—
428C24—21no—
429C24#1175822211yescharacteristic
430#41—22no—
431#41—22no—
432#41—22no—
433#41—22no—
434#41—22no—
435#41—44no—
436#41—41no—
437#41—41no—
438#41—44no—
439#41#1175822414yes—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—41no—
443C2×Q8C2×C4×D6111yescharacteristic
444C2×Q8C2×C4×D6111yescharacteristic
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—44no—
453C2×D4C2×C4×D6111yescharacteristic
454C2×D4C2×C4×D6111yescharacteristic
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—44no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1222no—
466C22×C4C2×C4×D6111yescharacteristic
467C22×C4C2×C4×D6111yescharacteristic
468C22×C4#1175822211yescharacteristic
469C22×C4C2×C22⋊D6111yescharacteristic
470C22×C4C2×C22⋊D6111yescharacteristic
471C22×C4C23×D6111yescharacteristic
472M16—22no—
473M16—22no—
474M16—44no—
475M16—1222no—
476M16—1222no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—44no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—611no—
485C2×C8—1222no—
486C2×C8—1222no—
487C2×C8—1222no—
488C2×C8—2441no—
489C2×C8—2441no—
490C2×C8—2441no—
491C2×C8—2441no—
492C2×C8C2×C22⋊D6112yes—
493C2×C8C2×C22⋊D6112yes—
494C4⋊C4—611no—
495C4⋊C4—611no—
496C4⋊C4—611no—
497C4⋊C4—611no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C22⋊C4—1221no—
501C22⋊C4—1221no—
502C22⋊C4—1221no—
503C22⋊C4—1221no—
504C22⋊C4—2442no—
505C42—1221no—
506C42—1221no—
507C42—1221no—
508C42—1221no—
509C42—1222no—
510C42—1222no—
511C23—21no—
512C23—22no—
513C23—22no—
514C23—21no—
515C23—41no—
516C23—42no—
517C23—42no—
518C23—81no—
519C23C4×C22⋊D6111yescharacteristic
520C23C4×C22⋊D6111yescharacteristic
521C23C2×#1175822211yescharacteristic
522Q8—21no—
523Q8—21no—
524Q8—21no—
525Q8—42no—
526Q8#1451973312yes—
527D4—24no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—42no—
533D4—42no—
534D4—42no—
535D4#1451973312yes—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—4881no—
555C2×C4—2442no—
556C2×C4—2442no—
557C2×C4—2442no—
558C2×C4—2442no—
559C2×C4C4×C22⋊D6111yescharacteristic
560C2×C4C4×C22⋊D6111yescharacteristic
561C2×C4C22×C4×D6111yescharacteristic
562C2×C4C22×C22⋊D6111yescharacteristic
563C2×C4C2×#1175822412yes—
564C2×C4#1451982212yes—
565C8—22no—
566C8—22no—
567C8—42no—
568C8—1221no—
569C8—1221no—
570C8—1221no—
571C8—1221no—
572C8—2442no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—22no—
581C22—44no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—84no—
588C22#1683988212yes—
589C22C2×C4×C22⋊D6111yescharacteristic
590C22#1684043812yes—
591C4—21no—
592C4—21no—
593C4—22no—
594C4—41no—
595C4—4882no—
596C4—2441no—
597C4—2441no—
598C4—2441no—
599C4—2441no—
600C4C2×#1451973311yescharacteristic
601C4#1684023511yescharacteristic
602C4#1684040612yes—
603C2—22no—
604C2—22no—
605C2—41no—
606C2—42no—
607C2—81no—
608C2#2144866411yescharacteristic
609C2C2×#1683988211yescharacteristic
610C2#2145473411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2880C2
socleC22×C61C2×C4×D4
prime radicalC22×#41×C61C22
cosocleC22×C4×C61C24
hypercenter#2880D61
hypocenterC61#22586
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
1. #21454473C2semidirect
3. #21446533C2semidirect
4. #21446464C2semidirect
5. #21446094C2semidirect
6. #21445916C2semidirect
7. #21445855C2semidirect
9. #21445661C2semidirect
10. #21445598C2semidirect
17. C2×#14519712C22semidirect
18. #16839788C22semidirect
21. #16839758C4semidirect
22. #16839758C4semidirect
23. #16839758C4semidirect
24. #16839758C4semidirect
29. C2×#14519701C4semidirect
30. C2×#14519701C4semidirect
31. C2×#14519698C4semidirect
32. C2×#14519698C4semidirect
34. #16839717C22semidirect
35. C2×#14519687C22semidirect
37. #16839526C22semidirect
38. #16839523C22semidirect
39. #16839523C22semidirect
40. #16839516C22semidirect
354. C61#22586semidirect

Maximal subgroups

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

subgroupindex
#214544732
C2×#168397582
#214465332
#214464642
#214460942
#214459162
#214458552
#214457632
#214456612
#214455982
C61×#28802
#2258661