Finite Group Databasebeta

← #29730445

Subgroups — #29730445

Order 15616.

716 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456219C211yesmaximal, characteristic
2C2×#16840070C211yesmaximal, characteristic, complemented
3#21455287C211yesmaximal, characteristic
4#21447264C211yesmaximal, characteristic, complemented
5#21447259C211yesmaximal, characteristic, complemented
6#21447117C211yesmaximal, characteristic, complemented
7#21447117C211yesmaximal, characteristic, complemented
8#21446812C211yesmaximal, characteristic, complemented
9#21446595C211yesmaximal, characteristic, complemented
10#21446334C211yesmaximal, characteristic, complemented
11#21446334C211yesmaximal, characteristic, complemented
12#21445883C211yesmaximal, characteristic, complemented
13#21445878C211yesmaximal, characteristic, complemented
14C4×#14519695C211yesmaximal, characteristic, complemented
15C61×#2935C211yesmaximal, characteristic
16C2×#14519807C2211yescharacteristic
17C2×#14519807C2211yescharacteristic
18C2×#14519769C2211yescharacteristic
19C2×C4×Dic122C2211yescharacteristic
20#16840130—21no—
21#16840126—21no—
22#16840116—21no—
23#16840116—21no—
24#16840070—21no—
25#16840070—21no—
26#16840070—21no—
27#16840070—21no—
28#16839981—21no—
29#16839981—21no—
30#16839969—21no—
31#16839959—21no—
32C2×#14519713C2211yescharacteristic
33C2×#14519713C2211yescharacteristic
34C2×#14519711C2211yescharacteristic
35C2×#14519709C2211yescharacteristic
36#16839786C2211yescharacteristic
37#16839763C2211yescharacteristic
38#16839763C2211yescharacteristic
39#16839763C2211yescharacteristic
40#16839763C2211yescharacteristic
41#16839763C2211yescharacteristic
42#16839763C2211yescharacteristic
43C2×#14519702C2211yescharacteristic
44C2×#14519702C2211yescharacteristic
45C2×#14519695C2211yescharacteristic
46C2×#14519695C2211yescharacteristic
47C4×#11758194C2211yescharacteristic
48#16839530C2211yescharacteristic
49#16839530C2211yescharacteristic
50#16839530C2211yescharacteristic
51#16839530C2211yescharacteristic
52#16839530C2211yescharacteristic
53#16839530C2211yescharacteristic
54#16839527C2211yescharacteristic
55#16839527C2211yescharacteristic
56C2×#131×C61C2211yescharacteristic
57C2×#131×C61C2211yescharacteristic
58C61×#532C2211yescharacteristic
59C61×#436—21no—
60C61×#435—21no—
61C61×#435—21no—
62C8×D4×C61—21no—
63C2×C4⋊C8×C61C2211yescharacteristic
64C61×#408C2211yescharacteristic
65C61×#408C2211yescharacteristic
66C4×M16×C61C2211yescharacteristic
67C22×Dic122C2311yescharacteristic
68#14519807—22no—
69#14519807—22no—
70#14519807—41no—
71#14519807—41no—
72C2×#11758202—21no—
73C2×#11758202—21no—
74C2×#11758200—21no—
75C2×#11758200—21no—
76C2×#11758194C2311yescharacteristic
77C2×#11758194C2311yescharacteristic
78C2×#11758194C2311yescharacteristic
79C2×#11758194C2311yescharacteristic
80#14519769—21no—
81#14519769—21no—
82#14519769—21no—
83#14519769—21no—
84C4×Dic122—21no—
85C4×Dic122—21no—
86C4×Dic122—21no—
87C4×Dic122—21no—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×C4×Dic61—21no—
95#14519713—41no—
96#14519713—41no—
97#14519711—21no—
98#14519711—21no—
99#14519709—21no—
100#14519709—21no—
101C4⋊#92418—21no—
102C4⋊#92418—21no—
103#14519702—21no—
104#14519702—21no—
105#14519702—21no—
106#14519702—21no—
107#14519701—21no—
108#14519701—21no—
109#14519701—21no—
110#14519701—21no—
111#14519701—21no—
112#14519701—21no—
113#14519698—21no—
114#14519698—21no—
115#14519698—21no—
116#14519698—21no—
117#14519698—21no—
118#14519698—21no—
119#14519695—22no—
120#14519695—22no—
121#14519688—21no—
122C4×#92418—21no—
123C2×#41×C61C2311yescharacteristic
124C2×#41×C61C2311yescharacteristic
125#131×C61—22no—
126#131×C61—22no—
127#131×C61—41no—
128#131×C61—41no—
129C2×M16×C61—21no—
130C2×M16×C61—21no—
131C2×M16×C61C2311yescharacteristic
132C2×M16×C61C2311yescharacteristic
133C22×C8×C61—21no—
134C22×C8×C61—21no—
135C22×C8×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137C4⋊Q8×C61D411yescharacteristic
138#127×C61D411yescharacteristic
139#124×C61D411yescharacteristic
140#124×C61D411yescharacteristic
141#121×C61—21no—
142#121×C61—21no—
143C4×D4×C61—21no—
144C4×D4×C61—21no—
145C2×C42×C61C2311yescharacteristic
146C4⋊C8×C61D411yescharacteristic
147C4⋊C8×C61D411yescharacteristic
148C4⋊C8×C61D411yescharacteristic
149C4⋊C8×C61D411yescharacteristic
150C22⋊C8×C61—21no—
151C22⋊C8×C61—21no—
152C22⋊C8×C61—21no—
153C22⋊C8×C61—21no—
154#97×C61—21no—
155C4×C8×C61—21no—
156#41×C61—21no—
157#41×C61—21no—
158#41×C61—21no—
159#41×C61—21no—
160#41×C61—21no—
161#41×C61—21no—
162#41×C61—21no—
163#41×C61—21no—
164C2×Q8×C61C2×D411yescharacteristic
165C2×Q8×C61C2×D411yescharacteristic
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61C2×D411yescharacteristic
171C2×D4×C61C2×D411yescharacteristic
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61#4111yescharacteristic
175C22×C4×C61#4111yescharacteristic
176C22×C4×C61C2411yescharacteristic
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C2×Dic122—21no—
182C2×Dic122—21no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122#4112yes—
187M16×C61—21no—
188M16×C61—21no—
189M16×C61—21no—
190M16×C61—42no—
191M16×C61—42no—
192M16×C61#4112yes—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—42no—
200C2×C8×C61—42no—
201C2×C8×C61C2×D411yescharacteristic
202C2×C8×C61C2×D411yescharacteristic
203C2×C8×C61C2×D411yescharacteristic
204C2×C8×C61C2×D411yescharacteristic
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C22⋊C4×C61—21no—
208C22⋊C4×C61—21no—
209C22⋊C4×C61—21no—
210C22⋊C4×C61—21no—
211C42×C61C2×D411yescharacteristic
212C42×C61C2×D411yescharacteristic
213C42×C61C2×D411yescharacteristic
214C42×C61C2×D411yescharacteristic
215#11758202—42no—
216#11758202—42no—
217#11758200—42no—
218#11758200—42no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225#11758196—41no—
226#11758196—41no—
227#11758196—41no—
228#11758196—41no—
229#11758196—41no—
230#11758196—41no—
231C4×Dic61—41no—
232C4×Dic61—41no—
233#11758194—21no—
234#11758194—21no—
235#11758194—21no—
236#11758194—21no—
237#11758194—21no—
238#11758194—21no—
239#11758194—21no—
240#11758194—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61C2×#4111yescharacteristic
248Q8×C61—21no—
249Q8×C61—21no—
250Q8×C61—21no—
251Q8×C61—21no—
252D4×C61—21no—
253D4×C61—21no—
254D4×C61—21no—
255D4×C61—21no—
256D4×C61—42no—
257D4×C61—41no—
258D4×C61—41no—
259D4×C61—41no—
260D4×C61—41no—
261D4×C61—81no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61#12111yescharacteristic
271C2×C4×C61#12111yescharacteristic
272C2×C4×C61#12111yescharacteristic
273C2×C4×C61#12111yescharacteristic
274C2×C4×C61C22×D411yescharacteristic
275C2×C4×C61C22×D411yescharacteristic
276C2×C4×C61C2×#4111yescharacteristic
277C2×C4×C61C2×#4111yescharacteristic
278C2×C4×C61H(5,𝔽2)11yescharacteristic
279C2×C4×C612−1+411yescharacteristic
280C2×Dic61—22no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—81no—
287C2×Dic61—81no—
288C2×Dic61—81no—
289Dic122—22no—
290Dic122—22no—
291Dic122—41no—
292Dic122—41no—
293C8×C61—21no—
294C8×C61—21no—
295C8×C61—21no—
296C8×C61—21no—
297C8×C61—22no—
298C8×C61—41no—
299#92418—41no—
300#92418—41no—
301#92418—41no—
302#92418—41no—
303#25363—611nomaximal, Sylow
304C22×C61—21no—
305C22×C61—21no—
306C22×C61—41no—
307C22×C61—41no—
308C22×C61—41no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61—41no—
312C22×C61C2×#12111yescharacteristic
313C22×C61#52911yescharacteristic
314C22×C61#54211yescharacteristic
315C4×C61—21no—
316C4×C61—21no—
317C4×C61—21no—
318C4×C61—21no—
319C4×C61—41no—
320C4×C61—41no—
321C4×C61#54611yescharacteristic
322C4×C61#54611yescharacteristic
323C4×C61#54711yescharacteristic
324C4×C61#54811yescharacteristic
325Dic61—42no—
326Dic61—81no—
327Dic61—81no—
328Dic61—81no—
329#3142—611no—
330C2×#479—611no—
331#3037—611no—
332#2935D6111yescharacteristic
333#2079—611no—
334#2078—611no—
335#2052—611no—
336#2052—611no—
337#1998—611no—
338#1950—611no—
339#1908—611no—
340#1908—611no—
341#1816—611no—
342#1815—611no—
343C4×#101—611no—
344C2×C61—21no—
345C2×C61—21no—
346C2×C61—81no—
347C2×C61—81no—
348C2×C61#242711yescharacteristic
349C2×C61#306711yescharacteristic
350C2×C61#306911yescharacteristic
351C2×#137—611no—
352C2×#137—611no—
353C2×#131C2×D6111yescharacteristic
354C2×#131C2×D6111yescharacteristic
355#532C2×D6111yescharacteristic
356C2×#125—611no—
357C2×C4×Q8—611no—
358#491—1221no—
359#490—1221no—
360#488—1221no—
361#488—1221no—
362#479—1221no—
363#479—1221no—
364#479—1221no—
365#479—1221no—
366#464—1221no—
367#464—1221no—
368#462—1221no—
369#460—1221no—
370#436—21no—
371#435—21no—
372#435—21no—
373C8×D4—21no—
374C2×#108—611no—
375C2×#108—611no—
376C2×#107—611no—
377C2×#106—611no—
378#423—611no—
379C2×C4⋊C8C2×D6111yescharacteristic
380#417—611no—
381#417—611no—
382#417—611no—
383#417—611no—
384#417—611no—
385#417—611no—
386C2×#103—611no—
387C2×#103—611no—
388C2×#101—611no—
389C2×#101—611no—
390#408C2×D6111yescharacteristic
391#408C2×D6111yescharacteristic
392C4×M16—611no—
393C4×M16C2×D6111yescharacteristic
394#343—611no—
395#343—611no—
396#343—611no—
397#343—611no—
398#343—611no—
399#343—611no—
400#341—611no—
401#341—611no—
402C61#2536311yescharacteristic, complemented, Sylow
403C2×#41C22×D6111yescharacteristic
404C2×#41C22×D6111yescharacteristic
405C22×Q8—611no—
406#137—1222no—
407#137—1222no—
408#137—2441no—
409#137—2441no—
410C2×Q16—1221no—
411C2×Q16—1221no—
412C2×SD16—1221no—
413C2×SD16—1221no—
414#131—22no—
415#131—22no—
416#131—41no—
417#131—41no—
418C2×M16—21no—
419C2×M16—21no—
420C2×M16—611no—
421C2×M16—611no—
422C2×M16—611no—
423C2×M16—611no—
424C2×M16C22×D6111yescharacteristic
425C2×M16C22×D6111yescharacteristic
426C22×C8—21no—
427C22×C8—21no—
428C22×C8C22×D6111yescharacteristic
429C22×C8C22×D6111yescharacteristic
430C4⋊Q8D24411yescharacteristic
431#127D24411yescharacteristic
432#125—1221no—
433#125—1221no—
434#125—1221no—
435#125—1221no—
436#124D24411yescharacteristic
437#124D24411yescharacteristic
438#121—21no—
439#121—21no—
440C4×Q8—1221no—
441C4×Q8—1221no—
442C4×Q8—1221no—
443C4×Q8—1221no—
444C4×D4—21no—
445C4×D4—21no—
446C2×C4⋊C4—611no—
447C2×C4⋊C4—611no—
448C2×C4⋊C4—611no—
449C2×C4⋊C4—1221no—
450C2×C4⋊C4—1221no—
451C2×C4⋊C4—1221no—
452C2×C42—1221no—
453C2×C42C22×D6111yescharacteristic
454#108—2441no—
455#108—2441no—
456#107—1221no—
457#107—1221no—
458#106—1221no—
459#106—1221no—
460C4⋊C8—1221no—
461C4⋊C8—1221no—
462C4⋊C8C22⋊D6111yescharacteristic
463C4⋊C8C22⋊D6111yescharacteristic
464C4⋊C8C22⋊D6111yescharacteristic
465C4⋊C8C22⋊D6111yescharacteristic
466#103—1221no—
467#103—1221no—
468#103—1221no—
469#103—1221no—
470#103—1221no—
471#103—1221no—
472#103—1221no—
473#103—1221no—
474#103—1221no—
475#103—1221no—
476#102—1221no—
477#102—1221no—
478#102—1221no—
479#102—1221no—
480#102—1221no—
481#102—1221no—
482#101—1222no—
483#101—1222no—
484C22⋊C8—21no—
485C22⋊C8—21no—
486C22⋊C8—21no—
487C22⋊C8—21no—
488#97—21no—
489#97—1221no—
490C4×C8—21no—
491C4×C8—1221no—
492#41—21no—
493#41—21no—
494#41—21no—
495#41—21no—
496#41—21no—
497#41—21no—
498#41—21no—
499#41—21no—
500C2×Q8—612no—
501C2×Q8—1221no—
502C2×Q8—1221no—
503C2×Q8—1221no—
504C2×Q8—1221no—
505C2×Q8—1221no—
506C2×Q8C2×D24411yescharacteristic
507C2×Q8C2×D24411yescharacteristic
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4C2×D24411yescharacteristic
513C2×D4C2×D24411yescharacteristic
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—1221no—
517C22×C4—1221no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4#1175822211yescharacteristic
521C22×C4#1175822211yescharacteristic
522C22×C4C23×D6111yescharacteristic
523Q16—2442no—
524Q16—2442no—
525SD16—2442no—
526SD16—2442no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—42no—
531M16—42no—
532M16—1221no—
533M16—1221no—
534M16—1221no—
535M16—1221no—
536M16—1221no—
537M16—1221no—
538M16—1221no—
539M16—1221no—
540M16#1175822412yes—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—42no—
548C2×C8—42no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8C2×C22⋊D6111yescharacteristic
554C2×C8C2×C22⋊D6111yescharacteristic
555C2×C8C2×C22⋊D6111yescharacteristic
556C2×C8C2×C22⋊D6111yescharacteristic
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—1221no—
560C4⋊C4—1221no—
561C4⋊C4—1221no—
562C4⋊C4—1221no—
563C4⋊C4—1221no—
564C4⋊C4—1221no—
565C4⋊C4—2441no—
566C4⋊C4—2441no—
567C4⋊C4—2441no—
568C4⋊C4—2441no—
569C4⋊C4—2441no—
570C4⋊C4—2441no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C42—2441no—
576C42—2441no—
577C42C2×D24411yescharacteristic
578C42C2×D24411yescharacteristic
579C42C2×C22⋊D6111yescharacteristic
580C42C2×C22⋊D6111yescharacteristic
581C23—21no—
582C23—21no—
583C23C2×#1175822211yescharacteristic
584Q8—21no—
585Q8—21no—
586Q8—21no—
587Q8—21no—
588Q8—1222no—
589Q8—1222no—
590Q8—2441no—
591Q8—2441no—
592D4—21no—
593D4—21no—
594D4—21no—
595D4—21no—
596D4—42no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—81no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—1222no—
611C2×C4—4881no—
612C2×C4—4881no—
613C2×C4—4881no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4#1451975111yescharacteristic
620C2×C4#1451975111yescharacteristic
621C2×C4#1451975111yescharacteristic
622C2×C4#1451975111yescharacteristic
623C2×C4C22×C22⋊D6111yescharacteristic
624C2×C4C22×D24411yescharacteristic
625C2×C4#41×D6111yescharacteristic
626C2×C4C2×#1175822411yescharacteristic
627C2×C4#1451982211yescharacteristic
628C2×C4#1451982411yescharacteristic
629C8—21no—
630C8—21no—
631C8—21no—
632C8—21no—
633C8—22no—
634C8—41no—
635C8—2441no—
636C8—2441no—
637C8—2441no—
638C8—2441no—
639C22—21no—
640C22—21no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22C2×#1451975111yescharacteristic
648C22#1684029411yescharacteristic
649C22#1684037711yescharacteristic
650C4—21no—
651C4—21no—
652C4—21no—
653C4—21no—
654C4—41no—
655C4—41no—
656C4—4881no—
657C4—4881no—
658C4—4881no—
659C4—2442no—
660C4#1684040611yescharacteristic
661C4#1684040711yescharacteristic
662C4#1684041611yescharacteristic
663C4#1684041911yescharacteristic
664C2—21no—
665C2—21no—
666C2—81no—
667C2—81no—
668C2#2144939011yescharacteristic
669C2#2145553911yescharacteristic
670C2#2145555611yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2935C2
socleC22×C61C2×#121
prime radicalC61×#532C22
hypercenter#2935D61
hypocenterC61#25363
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
2. C2×#16840070C2semidirect
4. #21447264C2semidirect
5. #21447259C2semidirect
6. #21447117C2semidirect
7. #21447117C2semidirect
8. #21446812C2semidirect
9. #21446595C2semidirect
10. #21446334C2semidirect
11. #21446334C2semidirect
12. #21445883C2semidirect
13. #21445878C2semidirect
14. C4×#14519695C2semidirect
402. C61#25363semidirect

Maximal subgroups

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

subgroupindex
#214562192
C2×#168400702
#214552872
#214472642
#214472592
#214471172
#214468122
#214465952
#214463342
#214458832
#214458782
C4×#145196952
C61×#29352
#2536361