Finite Group Databasebeta

← #29647188

Subgroups — #29647188

Order 15616.

1364 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#532×D61C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic, complemented
3#21448158C211yesmaximal, characteristic, complemented
4#21444333C214yesmaximal, complemented
5#21444328C211yesmaximal, characteristic, complemented
6#21444327C211yesmaximal, characteristic, complemented
7#21444326C211yesmaximal, characteristic, complemented
8#21444312C214yesmaximal, complemented
9C61×#1505C211yesmaximal, characteristic, complemented
10C2×#41×D61—21no—
11#16840313C411yescharacteristic, complemented
12#16840312C2211yescharacteristic
13#16840311—21no—
14#16840310C411yescharacteristic, complemented
15#16840309—21no—
16#16840309C412yescomplemented
17#16840308—21no—
18#16840307—21no—
19#16840307C2212yes—
20C4⋊Q8×D61C411yescharacteristic, complemented
21#127×D61C411yescharacteristic, complemented
22#124×D61—21no—
23#121×D61—21no—
24#121×D61C2212yes—
25C4×D4×D61—21no—
26C4×D4×D61C412yescomplemented
27C2×#14519734—21no—
28C2×C42×D61C2211yescharacteristic
29#16839819C2211yescharacteristic, complemented
30#16839817—21no—
31#16839814—21no—
32#16839812C2212yescomplemented
33#16839784—21no—
34#16839724C2212yes—
35#16839714—21no—
36#16839613—21no—
37#16839613C2212yescomplemented
38#16839609—21no—
39#16839609C2212yes—
40#16839608C2211yescharacteristic, complemented
41C42×Dic61—21no—
42#16839497C2214yescomplemented
43#16839496C2214yescomplemented
44#16839495C2214yescomplemented
45C61×#532C2211yescharacteristic
46C61×#432C2211yescharacteristic, complemented
47C61×#376C2211yescharacteristic, complemented
48C61×#327C2214yescomplemented
49C2×#11758226—21no—
50C2×#11758222—21no—
51C2×#11758222—22no—
52C2×#11758224—22no—
53C2×#11758224—21no—
54#41×D61—48no—
55C2×Q8×D61—21no—
56C2×D4×D61—22no—
57C2×D4×D61—21no—
58C2×D4×D61—21no—
59C2×D4×D61C2×C412yes—
60C22×C4×D61—22no—
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C2×#11758189—22no—
65#14519777C2×C411yescharacteristic
66#14519776—21no—
67#14519776C2×C412yes—
68#14519775—21no—
69#14519774C2×C411yescharacteristic
70#14519773—21no—
71#14519773—21no—
72#14519773C2×C412yes—
73#14519766—21no—
74#14519765—21no—
75#14519764—21no—
76#14519763—22no—
77#14519763—22no—
78#14519752—21no—
79#14519752C2×C412yes—
80#14519751—21no—
81#14519751C2312yes—
82#14519750—22no—
83#14519750—22no—
84#14519749—22no—
85#14519749—22no—
86#14519748—21no—
87#14519748C2×C412yes—
88C4×D244—21no—
89C4×D244C2×C412yes—
90D4×Dic61—21no—
91D4×Dic61C2×C412yes—
92#14519739—21no—
93#14519739C2×C412yes—
94C4×C22⋊D61—22no—
95C4×C22⋊D61—22no—
96#14519737—22no—
97#14519737—22no—
98#14519734—28no—
99C2×#11758196—22no—
100C4⋊C4×D61—21no—
101C4⋊C4×D61C2×C412yes—
102C2×#11758198—22no—
103C22⋊C4×D61—22no—
104C22⋊C4×D61—22no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61—22no—
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C42×D61C2×C411yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61C2×C411yescharacteristic
114C42×D61C2×C411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C4⋊#92418—21no—
120#14519706—22no—
121C22⋊#92418C2312yes—
122#14519689—22no—
123#14519688—21no—
124C8×Dic61—22no—
125#14519684—21no—
126#14519684C2312yes—
127C2×#41×C61—21no—
128C4⋊Q8×C61C2×C411yescharacteristic
129#127×C61C2×C411yescharacteristic
130#124×C61—21no—
131#121×C61—21no—
132#121×C61C2312yes—
133C4×D4×C61—21no—
134C4×D4×C61C2×C412yes—
135C2×C42×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—21no—
138C22⋊C8×C61C2312yes—
139#97×C61—21no—
140#95×C61—21no—
141#95×C61C2312yes—
142C23×D61—22no—
143C23×D61C2×D411yescharacteristic
144#41×C61—44no—
145C2×Q8×C61—21no—
146C2×D4×C61—22no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61C22×C412yes—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2411yescharacteristic
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165#11758226—44no—
166Q8×D61—44no—
167#11758224—44no—
168#11758224—48no—
169D4×D61—44no—
170D4×D61—44no—
171D4×D61—48no—
172D4×D61—44no—
173#11758222—48no—
174#11758222—44no—
175C2×D244—22no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244C22×C412yes—
179C2×C4×D61—24no—
180C2×C4×D61—24no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—22no—
184C2×C4×D61—42no—
185C2×C4×D61—48no—
186C2×C4×D61C22⋊C411yescharacteristic
187C2×C4×D61C22⋊C411yescharacteristic
188C2×C4×D61C22⋊C411yescharacteristic
189C2×C4×D61C22⋊C411yescharacteristic
190C2×C4×D61C22⋊C411yescharacteristic
191C2×C4×D61C22⋊C411yescharacteristic
192C2×C4×D61C22⋊C411yescharacteristic
193C2×C4×D61C22⋊C411yescharacteristic
194C2×C4×D61C22×C411yescharacteristic
195C2×C4×D61C22×C411yescharacteristic
196C2×C4×D61C2×D411yescharacteristic
197C2×C4×D61C2×D411yescharacteristic
198C2×Dic122—21no—
199C2×Dic122—22no—
200C2×C8×C61—22no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61C22×C412yes—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—22no—
205C42×C61—24no—
206C42×C61C22×C411yescharacteristic
207C42×C61C22×C411yescharacteristic
208C42×C61C2×D411yescharacteristic
209C42×C61C2×D411yescharacteristic
210C22⋊Dic61—22no—
211C22⋊Dic61—22no—
212#11758198—28no—
213#11758198—22no—
214#11758198—22no—
215#11758198—22no—
216#11758198—22no—
217C4⋊Dic61—21no—
218C4⋊Dic61C22×C412yes—
219#11758196—28no—
220#11758196—22no—
221#11758196—22no—
222C4×Dic61—24no—
223C4×Dic61—44no—
224C4×Dic61—44no—
225C4×Dic61C22⋊C411yescharacteristic
226C4×Dic61C22⋊C411yescharacteristic
227C4×Dic61C22⋊C411yescharacteristic
228C4×Dic61C22⋊C411yescharacteristic
229C4×Dic61C22⋊C411yescharacteristic
230C4×Dic61C22⋊C411yescharacteristic
231C4×Dic61C22⋊C411yescharacteristic
232C4×Dic61C22⋊C411yescharacteristic
233C4×Dic61C22×C411yescharacteristic
234C4×Dic61C22×C411yescharacteristic
235C4×Dic61C2×D411yescharacteristic
236C4×Dic61C2×D411yescharacteristic
237C2×#92418—22no—
238#11758189—44no—
239C23×C61—22no—
240C23×C61C22×D411yescharacteristic
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—41no—
245C22×D61—44no—
246C22×D61—44no—
247C22×D61—44no—
248C22×D61C2×C22⋊C411yescharacteristic
249C22×D61C2×C22⋊C411yescharacteristic
250Q8×C61—42no—
251D4×C61—42no—
252D4×C61—42no—
253D4×C61—44no—
254D4×C61—42no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—24no—
258C2×C4×C61—22no—
259C2×C4×C61—41no—
260C2×C4×C61—44no—
261C2×C4×C61—42no—
262C2×C4×C61—42no—
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61C2×C22⋊C411yescharacteristic
265C2×C4×C61C2×C22⋊C411yescharacteristic
266C2×C4×C61C2×C22⋊C411yescharacteristic
267C2×C4×C61C23×C411yescharacteristic
268C2×C4×C61C22×D411yescharacteristic
269C22⋊D61—44no—
270C22⋊D61—44no—
271C22⋊D61—44no—
272C22⋊D61—44no—
273C22⋊D61—44no—
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—24no—
277C2×Dic61—22no—
278C2×Dic61—42no—
279C2×Dic61—42no—
280C2×Dic61—44no—
281C2×Dic61C2×C22⋊C411yescharacteristic
282C2×Dic61C2×C22⋊C411yescharacteristic
283C2×Dic61C2×C22⋊C411yescharacteristic
284C2×Dic61C2×C22⋊C411yescharacteristic
285C2×Dic61C2×C22⋊C411yescharacteristic
286C2×Dic61C2×C22⋊C411yescharacteristic
287C2×Dic61AGL(1,ℤ/8)14yes—
288D244—42no—
289D244—42no—
290D244—44no—
291D244—42no—
292C4×D61—22no—
293C4×D61—22no—
294C4×D61—22no—
295C4×D61—22no—
296C4×D61—22no—
297C4×D61—22no—
298C4×D61—22no—
299C4×D61—22no—
300C4×D61—22no—
301C4×D61—41no—
302C4×D61—41no—
303C4×D61—44no—
304C4×D61—44no—
305C4×D61—44no—
306C4×D61#10414yes—
307Dic122—42no—
308Dic122—44no—
309C8×C61—42no—
310#92418—42no—
311#17544—611nomaximal, Sylow
312C22×C61—21no—
313C22×C61—21no—
314C22×C61—42no—
315C22×C61—42no—
316C22×C61—42no—
317C22×C61C22×C22⋊C411yescharacteristic
318C22×C61C2×AGL(1,ℤ/8)12yes—
319C2×D61—21no—
320C2×D61—21no—
321C2×D61—21no—
322C2×D61—21no—
323C2×D61—21no—
324C2×D61—44no—
325C2×D61—42no—
326C2×D61—42no—
327C2×D61—42no—
328C2×D61—88no—
329C2×D61C2×#10412yes—
330C4×C61—21no—
331C4×C61—21no—
332C4×C61—21no—
333C4×C61—21no—
334C4×C61—21no—
335C4×C61—44no—
336C4×C61—42no—
337C4×C61C2×#10412yes—
338Dic61—21no—
339Dic61—21no—
340Dic61—44no—
341Dic61—42no—
342Dic61#41012yes—
343Dic61#41812yes—
344Dic61#41812yes—
345Dic61C2×#10412yes—
346C2×#532—611no—
347#2920—611no—
348C4×#117—611no—
349#1507—614no—
350#1505—611no—
351#1505—611no—
352#1505—611no—
353#1505D6111yescharacteristic, complemented
354#1502—614no—
355C2×C61—22no—
356C2×C61—82no—
357C2×C61C2×#41011yescharacteristic
358C2×C61C2×#41811yescharacteristic
359C2×C61C22×#10411yescharacteristic
360D61—22no—
361D61—41no—
362D61—82no—
363C22×#41—1221no—
364#532—611no—
365#532—611no—
366#532—612no—
367#532—612no—
368#532—611no—
369#532—1221no—
370#532—1221no—
371#532—1221no—
372#532—1221no—
373#532C2×D6111yescharacteristic
374C2×C4⋊Q8—611no—
375C2×#127—611no—
376C2×#124—1221no—
377C2×#121—612no—
378C2×#121—1221no—
379C2×C4×D4—612no—
380C2×C4×D4—1221no—
381C2×#117—1221no—
382C22×C42—611no—
383#432—611no—
384#432—1221no—
385#432C2×D6111yescharacteristic, complemented
386#431—612no—
387#431—1221no—
388#423—1221no—
389#407—612no—
390C4×M16—1221no—
391C4×C4⋊C4—612no—
392C4×C4⋊C4—1221no—
393C4×C22⋊C4—612no—
394C4×C22⋊C4—1221no—
395#376—611no—
396#376C2×D6111yescharacteristic, complemented
397C43—1221no—
398#327—614no—
399#327—614no—
400#327—614no—
401#327C2×D6114yescomplemented
402C61#1754411yescharacteristic, complemented, Sylow
403C2×#41—21no—
404C2×#41—1222no—
405C2×#41—1222no—
406C2×#41—1221no—
407C2×#41—1221no—
408C2×#41—1221no—
409C2×#41—2448no—
410C22×Q8—1221no—
411C22×D4—612no—
412C22×D4—1221no—
413C22×D4—1221no—
414C22×D4—1222no—
415C23×C4—611no—
416C23×C4—611no—
417C23×C4—611no—
418C23×C4—1222no—
419C2×M16—1222no—
420C4⋊Q8—612no—
421C4⋊Q8—611no—
422C4⋊Q8—1221no—
423C4⋊Q8—1221no—
424C4⋊Q8C4×D6111yescharacteristic
425#127—612no—
426#127—611no—
427#127—1221no—
428#127—1221no—
429#127C4×D6111yescharacteristic
430#124—21no—
431#124—1222no—
432#124—1222no—
433#124—1221no—
434#124—1221no—
435#124—1221no—
436#121—21no—
437#121—612no—
438#121—612no—
439#121—612no—
440#121—1222no—
441#121—1222no—
442#121—1221no—
443#121—1222no—
444#121—1221no—
445#121—1222no—
446#121—1221no—
447#121C22×D6112yes—
448C4×D4—21no—
449C4×D4—612no—
450C4×D4—612no—
451C4×D4—612no—
452C4×D4—1222no—
453C4×D4—1222no—
454C4×D4—1221no—
455C4×D4—1222no—
456C4×D4—1222no—
457C4×D4—1221no—
458C4×D4—1221no—
459C4×D4C4×D6112yes—
460#117—1228no—
461C2×C4⋊C4—612no—
462C2×C4⋊C4—1221no—
463C2×C4⋊C4—1222no—
464C2×C22⋊C4—1222no—
465C2×C22⋊C4—1222no—
466C2×C22⋊C4—1222no—
467C2×C42—21no—
468C2×C42—611no—
469C2×C42—611no—
470C2×C42—611no—
471C2×C42—611no—
472C2×C42—611no—
473C2×C42—611no—
474C2×C42—611no—
475C2×C42—611no—
476C2×C42—611no—
477C2×C42—611no—
478C2×C42—611no—
479C2×C42—1221no—
480C2×C42—1222no—
481C2×C42—1222no—
482C2×C42C22×D6111yescharacteristic
483C4⋊C8—21no—
484C4⋊C8—1222no—
485C4⋊C8—1221no—
486C22⋊C8—612no—
487C22⋊C8—1222no—
488C22⋊C8C22×D6112yes—
489#97—21no—
490#97—1221no—
491C4×C8—1222no—
492#95—21no—
493#95—612no—
494#95—1221no—
495#95C22×D6112yes—
496C24—611no—
497C24—1222no—
498#41—44no—
499#41—2444no—
500#41—2448no—
501#41—2448no—
502#41—2444no—
503#41—2444no—
504C2×Q8—21no—
505C2×Q8—1222no—
506C2×Q8—1221no—
507C2×Q8—2444no—
508C2×D4—22no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—612no—
512C2×D4—1222no—
513C2×D4—1222no—
514C2×D4—1222no—
515C2×D4—1222no—
516C2×D4—1222no—
517C2×D4—1222no—
518C2×D4—1221no—
519C2×D4—1221no—
520C2×D4—2444no—
521C2×D4—2444no—
522C2×D4—2444no—
523C2×D4—2448no—
524C2×D4C2×C4×D6112yes—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—1224no—
543C22×C4—1224no—
544C22×C4—1222no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—2442no—
550C22×C4—2448no—
551C22×C4D4×D6111yescharacteristic
552C22×C4D4×D6111yescharacteristic
553C22×C4C23×D6111yescharacteristic
554M16—2444no—
555C2×C8—22no—
556C2×C8—1222no—
557C4⋊C4—21no—
558C4⋊C4—612no—
559C4⋊C4—1222no—
560C4⋊C4—1222no—
561C4⋊C4—1228no—
562C4⋊C4—1221no—
563C4⋊C4C2×C4×D6112yes—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—1222no—
567C22⋊C4—1222no—
568C22⋊C4—1228no—
569C22⋊C4—1222no—
570C22⋊C4—1222no—
571C22⋊C4—1222no—
572C22⋊C4—1222no—
573C42—24no—
574C42—611no—
575C42—611no—
576C42—611no—
577C42—611no—
578C42—611no—
579C42—611no—
580C42—611no—
581C42—611no—
582C42—611no—
583C42—611no—
584C42—611no—
585C42—611no—
586C42—1224no—
587C42—2444no—
588C42—2444no—
589C42C2×C4×D6111yescharacteristic
590C42C2×C4×D6111yescharacteristic
591C42D4×D6111yescharacteristic
592C42D4×D6111yescharacteristic
593C23—22no—
594C23—611no—
595C23—611no—
596C23—1222no—
597C23—1222no—
598C23—1222no—
599C23—2441no—
600C23—2444no—
601C23—2444no—
602C23—2444no—
603C23C2×D4×D6111yescharacteristic
604Q8—42no—
605Q8—2442no—
606Q8—2444no—
607D4—42no—
608D4—42no—
609D4—44no—
610D4—42no—
611D4—2442no—
612D4—2442no—
613D4—2444no—
614D4—2444no—
615D4—2444no—
616D4—2444no—
617D4—2444no—
618D4—2444no—
619D4—2442no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—24no—
623C2×C4—22no—
624C2×C4—41no—
625C2×C4—44no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—611no—
629C2×C4—611no—
630C2×C4—611no—
631C2×C4—611no—
632C2×C4—614no—
633C2×C4—614no—
634C2×C4—611no—
635C2×C4—611no—
636C2×C4—1222no—
637C2×C4—1222no—
638C2×C4—1222no—
639C2×C4—1222no—
640C2×C4—1222no—
641C2×C4—1222no—
642C2×C4—1222no—
643C2×C4—1222no—
644C2×C4—1222no—
645C2×C4—1222no—
646C2×C4—1222no—
647C2×C4—1224no—
648C2×C4—1222no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4—2444no—
652C2×C4—2444no—
653C2×C4—2444no—
654C2×C4—2444no—
655C2×C4—2442no—
656C2×C4—2442no—
657C2×C4C22⋊C4×D6111yescharacteristic
658C2×C4C22⋊C4×D6111yescharacteristic
659C2×C4C22⋊C4×D6111yescharacteristic
660C2×C4C22⋊C4×D6111yescharacteristic
661C2×C4C22×C4×D6111yescharacteristic
662C2×C4C2×D4×D6111yescharacteristic
663C8—42no—
664C8—2442no—
665C22—21no—
666C22—21no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—612no—
671C22—1221no—
672C22—1221no—
673C22—1221no—
674C22—1221no—
675C22—1221no—
676C22—4888no—
677C22—2444no—
678C22—2442no—
679C22—2442no—
680C22—2442no—
681C22C2×C22⋊C4×D6111yescharacteristic
682C22AGL(1,ℤ/8)×D6112yes—
683C4—21no—
684C4—21no—
685C4—21no—
686C4—21no—
687C4—21no—
688C4—44no—
689C4—42no—
690C4—612no—
691C4—612no—
692C4—612no—
693C4—612no—
694C4—1221no—
695C4—1221no—
696C4—2444no—
697C4—2442no—
698C4#104×D6112yes—
699C2—22no—
700C2—82no—
701C2—1222no—
702C2—4882no—
703C2—2441no—
704C2#410×D6111yescharacteristic
705C2#418×D6111yescharacteristic
706C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1505C2
socleC22×C61C22×C22⋊C4
prime radical#532×D61C2
cosocleC22×C4×C61C24
hypercenter#1505D61
hypocenterC61#17544
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1505

Complements

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

NH ≅ G/Ntype
2. #21454449C2semidirect
3. #21448158C2semidirect
4. #21444333C2semidirect
5. #21444328C2semidirect
6. #21444327C2semidirect
7. #21444326C2semidirect
8. #21444312C2semidirect
9. C61×#1505C2semidirect
11. #16840313C4semidirect
14. #16840310C4semidirect
16. #16840309C4semidirect
20. C4⋊Q8×D61C4semidirect
21. #127×D61C4semidirect
26. C4×D4×D61C4semidirect
29. #16839819C22semidirect
32. #16839812C22semidirect
37. #16839613C22semidirect
40. #16839608C22semidirect
42. #16839497C22semidirect
43. #16839496C22semidirect
44. #16839495C22semidirect
46. C61×#432C22semidirect
47. C61×#376C22semidirect
48. C61×#327C22semidirect
353. #1505D61semidirect
385. #432C2×D61semidirect
396. #376C2×D61semidirect
401. #327C2×D61semidirect
402. C61#17544semidirect

Maximal subgroups

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

subgroupindex
#532×D612
#214544492
#214481582
#214443332
#214443282
#214443272
#214443262
#214443122
C61×#15052
#1754461