Finite Group Databasebeta

← #29729843

Subgroups — #29729843

Order 15616.

690 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456205C211yesmaximal, characteristic
2#21455626C211yesmaximal, characteristic, complemented
3C2×#16839981C211yesmaximal, characteristic
4#21454766C211yesmaximal, characteristic, complemented
5#21447182C211yesmaximal, characteristic, complemented
6#21447175C211yesmaximal, characteristic
7#21447085C211yesmaximal, characteristic, complemented
8#21447080C211yesmaximal, characteristic
9#21446731C211yesmaximal, characteristic, complemented
10#21446719C211yesmaximal, characteristic
11#21446592C211yesmaximal, characteristic, complemented
12#21446483C211yesmaximal, characteristic
13#21446476C211yesmaximal, characteristic, complemented
14C4×#14519695C211yesmaximal, characteristic, complemented
15C61×#1967C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18#16840319C2211yescharacteristic
19C2×C4×Dic122C2211yescharacteristic
20#16840121—21no—
21#16840121—21no—
22#16840116—21no—
23#16840116—21no—
24#16840070—21no—
25#16840070—21no—
26#16840058—21no—
27#16840048—21no—
28#16839981—21no—
29#16839981—21no—
30#16839981—21no—
31#16839981—21no—
32#16839892—21no—
33#16839890—21no—
34#16839890—21no—
35C8×Dic122—21no—
36C2×#14519712C2211yescharacteristic
37C2×#14519712C2211yescharacteristic
38#16839804C2211yescharacteristic
39#16839804C2211yescharacteristic
40#16839790C2211yescharacteristic
41#16839790C2211yescharacteristic
42C2×C4⋊#92418C2211yescharacteristic
43#16839772C2211yescharacteristic
44#16839772C2211yescharacteristic
45#16839771C2211yescharacteristic
46#16839771C2211yescharacteristic
47#16839767C2211yescharacteristic
48#16839767C2211yescharacteristic
49C2×#14519701C2211yescharacteristic
50C2×#14519698C2211yescharacteristic
51C2×#14519695C2211yescharacteristic
52C2×#14519695C2211yescharacteristic
53#16839720C2211yescharacteristic
54#16839720C2211yescharacteristic
55C4×#11758194C2211yescharacteristic
56#16839530C2211yescharacteristic
57#16839530C2211yescharacteristic
58#16839526C2211yescharacteristic
59#16839526C2211yescharacteristic
60C2×#124×C61C2211yescharacteristic
61C61×#423C2211yescharacteristic
62C2×#101×C61C2211yescharacteristic
63C2×#101×C61C2211yescharacteristic
64C2×#100×C61C2211yescharacteristic
65C2×#100×C61C2211yescharacteristic
66C4×M16×C61C2211yescharacteristic
67C22×Dic122C2311yescharacteristic
68C2×#11758202—22no—
69C2×#11758202—21no—
70C2×#11758202—21no—
71C2×#11758202—41no—
72C2×#11758200—22no—
73C2×#11758200—21no—
74C2×#11758200—21no—
75C2×#11758200—41no—
76C2×#11758194C2311yescharacteristic
77C2×#11758194C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80#14519777D411yescharacteristic
81#14519777D411yescharacteristic
82#14519769D411yescharacteristic
83#14519769D411yescharacteristic
84#14519756—21no—
85#14519756—21no—
86C4×Dic122—21no—
87C4×Dic122—21no—
88C4×Dic122—21no—
89C4×Dic122—21no—
90C4×Dic122—21no—
91C4×Dic122—21no—
92#14519736C2311yescharacteristic
93#14519736C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×C4×Dic61—21no—
97#14519712—41no—
98#14519712—41no—
99#14519711—21no—
100#14519711—21no—
101#14519709—21no—
102#14519709—21no—
103C4⋊#92418D411yescharacteristic
104C4⋊#92418D411yescharacteristic
105C4⋊#92418D411yescharacteristic
106C4⋊#92418D411yescharacteristic
107#14519706—21no—
108#14519706—21no—
109#14519706—21no—
110#14519706—21no—
111#14519702—21no—
112#14519702—21no—
113#14519702—21no—
114#14519702—21no—
115#14519701—21no—
116#14519701—21no—
117#14519701—21no—
118#14519701—21no—
119#14519701—21no—
120#14519701—21no—
121#14519698—21no—
122#14519698—21no—
123#14519698—21no—
124#14519698—21no—
125#14519698—21no—
126#14519698—21no—
127#14519695—22no—
128#14519695—22no—
129#14519688—21no—
130#14519687—21no—
131#14519687—21no—
132C4×#92418—21no—
133C8×Dic61—21no—
134C8×Dic61—21no—
135C22×Q8×C61C2311yescharacteristic
136C22×D4×C61C2311yescharacteristic
137C2×M16×C61C2311yescharacteristic
138C2×M16×C61C2311yescharacteristic
139C2×M16×C61C2311yescharacteristic
140C2×M16×C61C2311yescharacteristic
141#124×C61—21no—
142#124×C61—21no—
143#124×C61—21no—
144#124×C61—21no—
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147C2×C42×C61C2311yescharacteristic
148C4⋊C8×C61—21no—
149C4⋊C8×C61—21no—
150#101×C61—22no—
151#101×C61—41no—
152#100×C61—22no—
153#100×C61—41no—
154#97×C61—21no—
155C4×C8×C61—21no—
156C24×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61#4111yescharacteristic
171C22×C4×C61#4111yescharacteristic
172C22×C4×C61C2411yescharacteristic
173C22×Dic61—21no—
174C22×Dic61—21no—
175C2×Dic122—21no—
176C2×Dic122—21no—
177C2×Dic122—21no—
178C2×Dic122—21no—
179C2×Dic122—21no—
180C2×Dic122—21no—
181C2×Dic122—21no—
182C2×Dic122#4112yes—
183M16×C61—21no—
184M16×C61—21no—
185M16×C61—21no—
186M16×C61—21no—
187M16×C61—21no—
188M16×C61—21no—
189M16×C61—21no—
190M16×C61#4112yes—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C22⋊C4×C61—41no—
196C22⋊C4×C61—41no—
197C22⋊C4×C61—41no—
198C22⋊C4×C61—41no—
199C42×C61C2×D411yescharacteristic
200C42×C61C2×D411yescharacteristic
201C42×C61C2×D411yescharacteristic
202C42×C61C2×D411yescharacteristic
203C22⋊Dic61—21no—
204C22⋊Dic61—21no—
205#11758202—42no—
206#11758202—42no—
207#11758200—42no—
208#11758200—42no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61C2×D411yescharacteristic
214C4⋊Dic61C2×D411yescharacteristic
215C4⋊Dic61C2×D411yescharacteristic
216C4⋊Dic61C2×D411yescharacteristic
217#11758196—21no—
218#11758196—21no—
219#11758196—21no—
220#11758196—21no—
221#11758196—41no—
222#11758196—41no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—41no—
226C4×Dic61—41no—
227#11758194—21no—
228#11758194—21no—
229#11758194—21no—
230#11758194—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418C2×D411yescharacteristic
238C2×#92418C2×D411yescharacteristic
239C2×#92418C2×D411yescharacteristic
240C2×#92418C2×D411yescharacteristic
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—81no—
245C23×C61—81no—
246C23×C61C2×#4111yescharacteristic
247Q8×C61—41no—
248Q8×C61—41no—
249Q8×C61—41no—
250Q8×C61—41no—
251D4×C61—41no—
252D4×C61—41no—
253D4×C61—41no—
254D4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61#12111yescharacteristic
261C2×C4×C61#12111yescharacteristic
262C2×C4×C61#12111yescharacteristic
263C2×C4×C61#12111yescharacteristic
264C2×C4×C61C22×D411yescharacteristic
265C2×C4×C61C22×D411yescharacteristic
266C2×C4×C61C2×#4111yescharacteristic
267C2×C4×C61C2×#4111yescharacteristic
268C2×C4×C61H(5,𝔽2)11yescharacteristic
269C2×C4×C612−1+411yescharacteristic
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—22no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—81no—
279Dic122—22no—
280Dic122—22no—
281Dic122—42no—
282Dic122—41no—
283Dic122—41no—
284Dic122—81no—
285C8×C61—22no—
286C8×C61—41no—
287C8×C61—41no—
288C8×C61—41no—
289#92418—21no—
290#92418—21no—
291#92418—21no—
292#92418—21no—
293#92418—41no—
294#92418—41no—
295#25317—611nomaximal, Sylow
296C22×C61—21no—
297C22×C61—21no—
298C22×C61—81no—
299C22×C61—81no—
300C22×C61—81no—
301C22×C61—161no—
302C22×C61—161no—
303C22×C61C2×#12111yescharacteristic
304C22×C61#52911yescharacteristic
305C22×C61#54211yescharacteristic
306C4×C61—21no—
307C4×C61—21no—
308C4×C61—21no—
309C4×C61—21no—
310C4×C61—81no—
311C4×C61#54611yescharacteristic
312C4×C61#54811yescharacteristic
313C4×C61#54811yescharacteristic
314C4×C61#55011yescharacteristic
315Dic61—42no—
316Dic61—41no—
317Dic61—41no—
318Dic61—41no—
319Dic61—41no—
320Dic61—81no—
321#3140—611no—
322#3078—611no—
323C2×#464—611no—
324#2962—611no—
325#2064—611no—
326#2063—611no—
327#2047—611no—
328#2046—611no—
329#1979—611no—
330#1977—611no—
331#1967D6111yescharacteristic
332#1950—611no—
333#1931—611no—
334#1930—611no—
335C4×#101—611no—
336C2×C61—21no—
337C2×C61—21no—
338C2×C61—161no—
339C2×C61#242611yescharacteristic
340C2×C61#306711yescharacteristic
341C2×C61#306911yescharacteristic
342C22×Q16—611no—
343C22×SD16—611no—
344#533—611no—
345C2×#124C2×D6111yescharacteristic
346C2×C4×Q8—611no—
347#489—1221no—
348#489—1221no—
349#488—1221no—
350#488—1221no—
351#479—1221no—
352#479—1221no—
353#477—1221no—
354#475—1221no—
355#464—1221no—
356#464—1221no—
357#464—1221no—
358#464—1221no—
359#446—1221no—
360#446—1221no—
361#446—1221no—
362C8×Q8—1221no—
363C2×#108—611no—
364C2×#108—611no—
365#428—611no—
366#428—611no—
367#424—611no—
368#424—611no—
369#423C2×D6111yescharacteristic
370C2×C4⋊C8—611no—
371#419—611no—
372#419—611no—
373#419—611no—
374#419—611no—
375#418—611no—
376#418—611no—
377C2×#103—611no—
378C2×#102—611no—
379C2×#101—611no—
380C2×#101—611no—
381C2×#101C2×D6111yescharacteristic
382C2×#101C2×D6111yescharacteristic
383C2×#100C2×D6111yescharacteristic
384C2×#100C2×D6111yescharacteristic
385#405—611no—
386#405—611no—
387C4×M16—611no—
388C4×M16C2×D6111yescharacteristic
389#343—611no—
390#343—611no—
391#341—611no—
392#341—611no—
393C61#2531711yescharacteristic, complemented, Sylow
394C22×Q8—611no—
395C22×Q8C22×D6111yescharacteristic
396C22×D4C22×D6111yescharacteristic
397C2×Q16—1221no—
398C2×Q16—1221no—
399C2×Q16—1222no—
400C2×Q16—2441no—
401C2×SD16—1221no—
402C2×SD16—1221no—
403C2×SD16—1222no—
404C2×SD16—2441no—
405C2×M16—611no—
406C2×M16—611no—
407C2×M16C22×D6111yescharacteristic
408C2×M16C22×D6111yescharacteristic
409C2×M16C22×D6111yescharacteristic
410C2×M16C22×D6111yescharacteristic
411C22×C8—611no—
412C22×C8—611no—
413C4⋊Q8—611no—
414C4⋊Q8—611no—
415#125—611no—
416#125—611no—
417#124—21no—
418#124—21no—
419#124—21no—
420#124—21no—
421C22⋊Q8—1221no—
422C22⋊Q8—1221no—
423C4×Q8—1221no—
424C4×Q8—1221no—
425C4×Q8—1221no—
426C4×Q8—1221no—
427C4×Q8—1221no—
428C4×Q8—1221no—
429#117—611no—
430#117—611no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—1221no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C42—1221no—
436C2×C42C22×D6111yescharacteristic
437#108—2441no—
438#108—2441no—
439#107—1221no—
440#107—1221no—
441#106—1221no—
442#106—1221no—
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—611no—
446C4⋊C8—611no—
447C4⋊C8—611no—
448C4⋊C8—611no—
449C4⋊C8—1221no—
450C4⋊C8—1221no—
451C4⋊C8—1221no—
452C4⋊C8—1221no—
453#103—1221no—
454#103—1221no—
455#103—1221no—
456#103—1221no—
457#103—1221no—
458#103—1221no—
459#103—1221no—
460#103—1221no—
461#103—1221no—
462#103—1221no—
463#102—1221no—
464#102—1221no—
465#102—1221no—
466#102—1221no—
467#102—1221no—
468#102—1221no—
469#101—22no—
470#101—41no—
471#101—1222no—
472#101—1222no—
473#100—22no—
474#100—41no—
475#97—21no—
476#97—1221no—
477#97—1221no—
478#97—1221no—
479C4×C8—21no—
480C4×C8—1221no—
481C4×C8—1221no—
482C4×C8—1221no—
483C24—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—612no—
491C2×Q8—1221no—
492C2×Q8—1221no—
493C2×Q8—1221no—
494C2×Q8—1221no—
495C2×Q8—1221no—
496C2×Q8—1221no—
497C2×Q8—1221no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C22×C4—21no—
505C22×C4—1221no—
506C22×C4—1221no—
507C22×C4#1175822211yescharacteristic
508C22×C4#1175822211yescharacteristic
509C22×C4C23×D6111yescharacteristic
510Q16—2442no—
511Q16—2442no—
512SD16—2442no—
513SD16—2442no—
514M16—21no—
515M16—21no—
516M16—21no—
517M16—21no—
518M16—21no—
519M16—21no—
520M16—21no—
521M16—1221no—
522M16—1221no—
523M16—1221no—
524M16—1221no—
525M16#1175822412yes—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—611no—
531C2×C8—611no—
532C2×C8—611no—
533C2×C8—611no—
534C2×C8—1221no—
535C2×C8—1221no—
536C2×C8—1221no—
537C2×C8—1221no—
538C2×C8—1221no—
539C2×C8—1221no—
540C4⋊C4—611no—
541C4⋊C4—611no—
542C4⋊C4—611no—
543C4⋊C4—611no—
544C4⋊C4—1221no—
545C4⋊C4—1221no—
546C4⋊C4—1221no—
547C4⋊C4—1221no—
548C4⋊C4—1221no—
549C4⋊C4—1221no—
550C4⋊C4—1221no—
551C4⋊C4—1221no—
552C4⋊C4—2441no—
553C4⋊C4—2441no—
554C22⋊C4—41no—
555C22⋊C4—41no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—1221no—
559C22⋊C4—1221no—
560C42—1221no—
561C42—1221no—
562C42—2441no—
563C42—2441no—
564C42D4×D6111yescharacteristic
565C42D4×D6111yescharacteristic
566C42D4×D6111yescharacteristic
567C42D4×D6111yescharacteristic
568C23—41no—
569C23—41no—
570C23—41no—
571C23—81no—
572C23—81no—
573C23C2×#1175822211yescharacteristic
574Q8—41no—
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—1222no—
579Q8—1222no—
580Q8—4881no—
581Q8—2442no—
582Q8—2441no—
583Q8—2441no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—1222no—
598C2×C4—4881no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4#1451975011yescharacteristic
603C2×C4#1451975011yescharacteristic
604C2×C4#1451975011yescharacteristic
605C2×C4#1451975011yescharacteristic
606C2×C4C2×D4×D6111yescharacteristic
607C2×C4C2×D4×D6111yescharacteristic
608C2×C4#41×D6111yescharacteristic
609C2×C4C2×#1175822411yescharacteristic
610C2×C4#1451982211yescharacteristic
611C2×C4#1451982411yescharacteristic
612C8—22no—
613C8—41no—
614C8—41no—
615C8—41no—
616C8—1221no—
617C8—1221no—
618C8—1221no—
619C8—1221no—
620C8—2441no—
621C8—2441no—
622C22—21no—
623C22—21no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—161no—
628C22—161no—
629C22C2×#1451975011yescharacteristic
630C22#1684029411yescharacteristic
631C22#1684037711yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—81no—
637C4—4881no—
638C4—2442no—
639C4—2441no—
640C4—2441no—
641C4—2441no—
642C4—2441no—
643C4#1684040911yescharacteristic
644C4#1684041811yescharacteristic
645C4#1684042011yescharacteristic
646C4#1684043211yescharacteristic
647C2—21no—
648C2—21no—
649C2—161no—
650C2#2144938611yescharacteristic
651C2#2145553811yescharacteristic
652C2#2145555911yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1967C2
socleC22×C61C2×#121
prime radicalC22×D4×C61C23
hypercenter#1967D61
hypocenterC61#25317
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1967

Complements

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

NH ≅ G/Ntype
2. #21455626C2semidirect
4. #21454766C2semidirect
5. #21447182C2semidirect
7. #21447085C2semidirect
9. #21446731C2semidirect
11. #21446592C2semidirect
13. #21446476C2semidirect
14. C4×#14519695C2semidirect
393. C61#25317semidirect

Maximal subgroups

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

subgroupindex
#214562052
#214556262
C2×#168399812
#214547662
#214471822
#214471752
#214470852
#214470802
#214467312
#214467192
#214465922
#214464832
#214464762
C4×#145196952
C61×#19672
#2531761