Finite Group Databasebeta

← #29729476

Subgroups — #29729476

Order 15616.

792 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840129C211yesmaximal, characteristic, complemented
2C2×#16840061C211yesmaximal, characteristic
3#21450816C211yesmaximal, characteristic
4#21448911C211yesmaximal, characteristic, complemented
5#21447214C211yesmaximal, characteristic, complemented
6#21447195C211yesmaximal, characteristic, complemented
7#21447061C211yesmaximal, characteristic
8#21447057C211yesmaximal, characteristic
9#21446751C211yesmaximal, characteristic
10#21446748C211yesmaximal, characteristic
11#21446740C211yesmaximal, characteristic, complemented
12#21446541C211yesmaximal, characteristic, complemented
13#21446458C211yesmaximal, characteristic, complemented
14#21445643C211yesmaximal, characteristic
15C61×#1927C211yesmaximal, characteristic, complemented
16C2×#14519775C2211yescharacteristic
17C2×#14519768C2211yescharacteristic
18C2×#14519766C2211yescharacteristic
19C2×#14519765C2211yescharacteristic
20C2×#14519739C2211yescharacteristic
21#16840129—24no—
22#16840061—24no—
23C2×#14519710C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519687C2211yescharacteristic
38#16839691—21no—
39#16839691—21no—
40#16839667C2211yescharacteristic
41#16839661C2211yescharacteristic
42#16839660—21no—
43#16839660C2211yescharacteristic
44#16839649—21no—
45#16839645—21no—
46#16839621—21no—
47#16839621—21no—
48C4⋊C4×Dic61C2211yescharacteristic
49C4⋊C4×Dic61C2211yescharacteristic
50C4×#11758196—21no—
51C4×#11758196C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic
55C2×#103×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic
57C61×#391C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C4×D61—21no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519775—22no—
67#14519775—22no—
68#14519768—22no—
69#14519768D414yes—
70#14519766—22no—
71#14519766—41no—
72#14519765—22no—
73#14519765—41no—
74#14519739—22no—
75#14519739—22no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196D411yescharacteristic
85C2×#11758196D411yescharacteristic
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61C2311yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95#14519710—22no—
96C4⋊#92418—41no—
97#14519706—22no—
98#14519706—41no—
99#14519702—22no—
100#14519702—41no—
101#14519701—22no—
102#14519701—41no—
103#14519700—22no—
104#14519700—22no—
105#14519699—22no—
106#14519699—22no—
107#14519697—22no—
108#14519697—22no—
109#14519687—22no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684D411yescharacteristic
117#14519684D411yescharacteristic
118C22×Q8×C61C2311yescharacteristic
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C42×C61—21no—
125C2×C42×C61C2311yescharacteristic
126#106×C61—22no—
127#103×C61—22no—
128#103×C61—22no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61—21no—
132C23×D61—21no—
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2411yescharacteristic
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61C2×D411yescharacteristic
150C22×Dic61C2×D411yescharacteristic
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C2×D244—21no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244#4112yes—
159C2×C4×D61—42no—
160C2×C4×D61—42no—
161C2×C4×D61—42no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165C2×Dic122—21no—
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61C2×D412yes—
179C4⋊C4×C61#4112yes—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61—81no—
183#11758198—42no—
184#11758198—42no—
185#11758198—42no—
186#11758198—42no—
187#11758198—42no—
188C4⋊Dic61—21no—
189C4⋊Dic61—24no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—81no—
193C4⋊Dic61C2×D412yes—
194#11758196—24no—
195#11758196—41no—
196#11758196—41no—
197#11758196—42no—
198#11758196—42no—
199#11758196—42no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—42no—
203C4×Dic61—81no—
204C4×Dic61C2×D412yes—
205C4×Dic61#4112yes—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C23×C61C22×D411yescharacteristic
213C22×D61—22no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—41no—
218C22×D61—41no—
219C22×D61—41no—
220Q8×C61—41no—
221Q8×C61—41no—
222Q8×C61—41no—
223Q8×C61—41no—
224C2×C4×C61—22no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—22no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61H(5,𝔽2)11yescharacteristic
247C2×C4×C612−1+411yescharacteristic
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—22no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61#12112yes—
268C2×Dic61#12112yes—
269D244—22no—
270D244—22no—
271D244—41no—
272D244—41no—
273C4×D61—84no—
274Dic122—41no—
275Dic122—41no—
276Dic122—41no—
277Dic122—41no—
278C8×C61—41no—
279C8×C61—41no—
280#92418—41no—
281#92418—41no—
282#25289—611nomaximal, Sylow
283C22×C61C2×#12111yescharacteristic
284C22×C61#54611yescharacteristic
285C22×C61#54811yescharacteristic
286C22×C61#57511yescharacteristic
287C22×C61#57511yescharacteristic
288C22×C61#57711yescharacteristic
289C22×C61#57811yescharacteristic
290C2×D61—42no—
291C2×D61—42no—
292C2×D61—42no—
293C2×D61—81no—
294C2×D61—81no—
295C2×D61—81no—
296C2×D61—81no—
297C4×C61—42no—
298C4×C61—42no—
299C4×C61—41no—
300C4×C61—41no—
301C4×C61—81no—
302C4×C61—81no—
303C4×C61#52911yescharacteristic
304C4×C61#54211yescharacteristic
305C4×C61#54811yescharacteristic
306C4×C61#55011yescharacteristic
307Dic61—22no—
308Dic61—22no—
309Dic61—42no—
310Dic61—41no—
311Dic61—41no—
312Dic61—81no—
313Dic61—81no—
314C2×#491—611no—
315C2×#478—611no—
316#2547—611no—
317#2370—611no—
318#2068—611no—
319#2066—611no—
320#2042—611no—
321#2042—611no—
322#1983—611no—
323#1983—611no—
324#1981—611no—
325#1940—611no—
326#1928—611no—
327#1927D6111yescharacteristic, complemented
328#1762—611no—
329C2×C61#242611yescharacteristic
330C2×C61#304011yescharacteristic
331C2×C61#304611yescharacteristic
332C2×C61#330711yescharacteristic
333C2×C61#331511yescharacteristic
334C2×C61#337611yescharacteristic
335C2×C61#337711yescharacteristic
336D61—82no—
337C2×C4⋊Q8—611no—
338C2×#125—611no—
339C2×#124—611no—
340C2×#124—611no—
341C2×C4×D4—611no—
342#491—1224no—
343#478—1224no—
344C2×#107—611no—
345C2×#106C2×D6111yescharacteristic
346C2×C4⋊C8—611no—
347C2×C4⋊C8—611no—
348C2×C4⋊C8—611no—
349C2×#103—611no—
350C2×#103—611no—
351C2×#103—611no—
352C2×#103—611no—
353C2×#103—611no—
354C2×#103—611no—
355C2×#103C2×D6111yescharacteristic
356C2×#103C2×D6111yescharacteristic
357C2×#102—611no—
358C2×#102—611no—
359C2×#102—611no—
360C2×#102—611no—
361C2×#97—611no—
362#397—1221no—
363#397—1221no—
364#391—611no—
365#391C2×D6111yescharacteristic
366#389—611no—
367#389—611no—
368#389—1221no—
369#387—1221no—
370#387—1221no—
371#380—1221no—
372#380—1221no—
373C4×C4⋊C4—611no—
374C4×C4⋊C4—611no—
375C4×C4⋊C4—611no—
376C4×C4⋊C4—1221no—
377C4×C4⋊C4C2×D6111yescharacteristic
378#340—611no—
379#340C2×D6111yescharacteristic
380#336—611no—
381#336C2×D6111yescharacteristic
382C61#2528911yescharacteristic, complemented, Sylow
383C22×Q8—611no—
384C22×Q8C22×D6111yescharacteristic
385C22×D4—611no—
386C23×C4—1221no—
387C22×C8—611no—
388C22×C8—611no—
389C22×C8C22×D6111yescharacteristic
390C22×C8C22×D6111yescharacteristic
391C4⋊Q8—1222no—
392C4⋊Q8—1222no—
393#125—614no—
394#125—1222no—
395#124—1222no—
396#124—1222no—
397#124—2441no—
398#124—2441no—
399C4×D4—1222no—
400C4×D4—1222no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4C22×D6111yescharacteristic
412C2×C4⋊C4C22×D6111yescharacteristic
413C2×C4⋊C4C22×D6111yescharacteristic
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4—1221no—
419C2×C42—21no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—1221no—
423C2×C42—1221no—
424C2×C42C22×D6111yescharacteristic
425#107—1222no—
426#106—22no—
427C4⋊C8—1222no—
428C4⋊C8—2441no—
429C4⋊C8—2441no—
430#103—22no—
431#103—22no—
432#103—1222no—
433#103—1222no—
434#103—1222no—
435#103—1222no—
436#103—2441no—
437#103—2441no—
438#102—1222no—
439#102—1222no—
440#102—1222no—
441#102—1222no—
442#97—1222no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—611no—
447#95—611no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452#95—1221no—
453#95—1221no—
454C24—1221no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—1221no—
462C2×Q8—1221no—
463C2×Q8—1221no—
464C2×Q8—1221no—
465C2×Q8—1221no—
466C2×Q8—1221no—
467C2×D4—612no—
468C2×D4—1221no—
469C2×D4—1221no—
470C2×D4—1221no—
471C2×D4—1221no—
472C2×D4—1221no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—2442no—
485C22×C4—2442no—
486C22×C4—2442no—
487C22×C4D4×D6111yescharacteristic
488C22×C4D4×D6111yescharacteristic
489C22×C4C23×D6111yescharacteristic
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—1221no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—612no—
507C4⋊C4—1224no—
508C4⋊C4—1224no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—4881no—
513C4⋊C4—2441no—
514C4⋊C4—2441no—
515C4⋊C4—2442no—
516C4⋊C4—2442no—
517C4⋊C4—2442no—
518C4⋊C4#1175822212yes—
519C4⋊C4D4×D6112yes—
520C22⋊C4—2442no—
521C22⋊C4—2442no—
522C22⋊C4—2442no—
523C22⋊C4—2442no—
524C22⋊C4—2442no—
525C42—21no—
526C42—21no—
527C42—81no—
528C42—612no—
529C42—612no—
530C42—1221no—
531C42—1221no—
532C42—4881no—
533C42—2442no—
534C23—1222no—
535C23—2441no—
536C23—2441no—
537C23—2441no—
538C23—2441no—
539C23—2441no—
540C23—2441no—
541C23C2×D4×D6111yescharacteristic
542Q8—41no—
543Q8—41no—
544Q8—41no—
545Q8—41no—
546Q8—2441no—
547Q8—2441no—
548Q8—2441no—
549Q8—2441no—
550D4—1222no—
551D4—1222no—
552D4—2441no—
553D4—2441no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—612no—
573C2×C4—612no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1222no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—4884no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4C2×D4×D6111yescharacteristic
595C2×C4#41×D6111yescharacteristic
596C2×C4#41×D6111yescharacteristic
597C2×C4C2×#1175822211yescharacteristic
598C2×C4#1451982311yescharacteristic
599C2×C4#1451982411yescharacteristic
600C8—41no—
601C8—41no—
602C8—2441no—
603C8—2441no—
604C22—4881no—
605C22—4881no—
606C22—4881no—
607C22—4881no—
608C22—2442no—
609C22—2442no—
610C22—2442no—
611C22#121×D6111yescharacteristic
612C22#1684040411yescharacteristic
613C22#1684042111yescharacteristic
614C22#1684055911yescharacteristic
615C22#1684056111yescharacteristic
616C22#1684056811yescharacteristic
617C22#1684057811yescharacteristic
618C4—42no—
619C4—41no—
620C4—42no—
621C4—41no—
622C4—81no—
623C4—81no—
624C4—1222no—
625C4—1222no—
626C4—4881no—
627C4—4881no—
628C4—2441no—
629C4—2442no—
630C4—2441no—
631C4#1684029011yescharacteristic
632C4#1684037811yescharacteristic
633C4#1684042011yescharacteristic
634C4#1684043311yescharacteristic
635C2—4882no—
636C2#2144938411yescharacteristic
637C2#2145531011yescharacteristic
638C2#2145536411yescharacteristic
639C2#2145779811yescharacteristic
640C2#2145791311yescharacteristic
641C2#2145864211yescharacteristic
642C2#2145866611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1927C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#1927D61
hypocenterC61#25289
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1927

Complements

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

NH ≅ G/Ntype
1. C2×#16840129C2semidirect
4. #21448911C2semidirect
5. #21447214C2semidirect
6. #21447195C2semidirect
11. #21446740C2semidirect
12. #21446541C2semidirect
13. #21446458C2semidirect
15. C61×#1927C2semidirect
327. #1927D61semidirect
382. C61#25289semidirect

Maximal subgroups

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

subgroupindex
C2×#168401292
C2×#168400612
#214508162
#214489112
#214472142
#214471952
#214470612
#214470572
#214467512
#214467482
#214467402
#214465412
#214464582
#214456432
C61×#19272
#2528961