Finite Group Databasebeta

← #29646255

Subgroups — #29646255

Order 15616.

1002 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840474C211yesmaximal, characteristic
2#21454478C211yesmaximal, characteristic, complemented
3#21454472C211yesmaximal, characteristic, complemented
4#21444177C211yesmaximal, characteristic, complemented
5#21444177C211yesmaximal, characteristic, complemented
6#21444171C211yesmaximal, characteristic, complemented
7#21444169C211yesmaximal, characteristic, complemented
8#21444169C211yesmaximal, characteristic, complemented
9#21444154C211yesmaximal, characteristic, complemented
10#21444151C211yesmaximal, characteristic, complemented
11#21444150C211yesmaximal, characteristic, complemented
12#21444134C211yesmaximal, characteristic, complemented
13#21444131C211yesmaximal, characteristic, complemented
14#21444130C211yesmaximal, characteristic, complemented
15C61×#1469C211yesmaximal, characteristic, complemented
16#16840474—21no—
17#16840474—21no—
18#16840474—21no—
19#16840474—21no—
20#16840474—21no—
21#16840474—21no—
22#16840474—21no—
23#16840474—21no—
24C2×#14519775C411yescharacteristic
25C2×#14519766C411yescharacteristic
26C2×#14519763C411yescharacteristic
27C2×#14519763C2211yescharacteristic
28C2×#14519750C411yescharacteristic
29C2×#14519750C2211yescharacteristic
30C2×#14519749C411yescharacteristic
31C2×#14519749C411yescharacteristic
32C2×#14519737C411yescharacteristic
33C2×#14519737C2211yescharacteristic
34C2×#14519734C2211yescharacteristic
35C2×#14519734C2211yescharacteristic
36C2×#14519733C411yescharacteristic
37C2×#14519733C2211yescharacteristic
38#16839824—21no—
39#16839822—21no—
40#16839822—21no—
41#16839821—21no—
42#16839819C2211yescharacteristic
43#16839816C2211yescharacteristic
44#16839816C2211yescharacteristic
45#16839815C2211yescharacteristic
46#16839812C2211yescharacteristic
47#16839812C2211yescharacteristic
48#16839787—21no—
49#16839787—21no—
50#16839724C2211yescharacteristic
51#16839724C2211yescharacteristic
52C22⋊C8×D61C2211yescharacteristic
53C22⋊C8×D61C2211yescharacteristic
54#16839719—21no—
55#16839716—21no—
56#16839487C2211yescharacteristic
57#16839487C2211yescharacteristic
58#16839487C2211yescharacteristic
59#16839487C2211yescharacteristic
60#16839486C2211yescharacteristic
61#16839486C2211yescharacteristic
62#16839486C2211yescharacteristic
63#16839486C2211yescharacteristic
64#16839485C2211yescharacteristic
65#16839485C2211yescharacteristic
66#16839485C2211yescharacteristic
67#16839485C2211yescharacteristic
68C2×#124×C61C2211yescharacteristic
69C61×#432C2211yescharacteristic
70C61×#431C2211yescharacteristic
71C61×#323C2211yescharacteristic
72C61×#323C2211yescharacteristic
73C61×#323C2211yescharacteristic
74C61×#323C2211yescharacteristic
75C22×Dic122C2×C411yescharacteristic
76C22×D244C2×C411yescharacteristic
77C22×C22⋊D61C2×C411yescharacteristic
78C22×C22⋊D61C2×C411yescharacteristic
79C22×C22⋊D61C2×C411yescharacteristic
80C22×C22⋊D61C2×C411yescharacteristic
81C23×Dic61C2×C411yescharacteristic
82C23×Dic61C2×C411yescharacteristic
83C22×C4×D61C2×C411yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C2×#11758189—21no—
86C2×#11758189—21no—
87C2×C8×D61—21no—
88C2×C8×D61—21no—
89#14519775—21no—
90#14519775—21no—
91#14519775—21no—
92#14519775—21no—
93#14519766—21no—
94#14519766—21no—
95#14519766—21no—
96#14519766—21no—
97#14519763—21no—
98#14519763—21no—
99#14519763—21no—
100#14519763—21no—
101#14519763—21no—
102#14519763—21no—
103#14519763—21no—
104#14519763—21no—
105#14519750—21no—
106#14519750—21no—
107#14519750—21no—
108#14519750—21no—
109#14519750—21no—
110#14519750—21no—
111#14519750—21no—
112#14519750—21no—
113#14519749—21no—
114#14519749—21no—
115#14519749—21no—
116#14519749—21no—
117#14519749—21no—
118#14519749—21no—
119#14519749—21no—
120#14519749—21no—
121#14519737—21no—
122#14519737—21no—
123#14519737—21no—
124#14519737—21no—
125#14519737—21no—
126#14519737—21no—
127#14519737—21no—
128#14519737—21no—
129#14519734—21no—
130#14519734—21no—
131#14519734—21no—
132#14519734—21no—
133#14519734D411yescharacteristic
134#14519734D411yescharacteristic
135#14519734D411yescharacteristic
136#14519734D411yescharacteristic
137#14519734D411yescharacteristic
138#14519734D411yescharacteristic
139#14519734D411yescharacteristic
140#14519734D411yescharacteristic
141#14519733—21no—
142#14519733—21no—
143#14519733—21no—
144#14519733—21no—
145#14519733—21no—
146#14519733—21no—
147#14519733—21no—
148#14519733—21no—
149C2×#11758196C2×C411yescharacteristic
150C2×#11758196C2×C411yescharacteristic
151C2×#11758196C2×C411yescharacteristic
152C2×#11758196C2×C411yescharacteristic
153C2×#11758196C2×C411yescharacteristic
154C2×#11758196C2311yescharacteristic
155C2×C22⋊Dic61C2×C411yescharacteristic
156C2×C22⋊Dic61C2×C411yescharacteristic
157C2×#11758198C2×C411yescharacteristic
158C2×#11758198C2×C411yescharacteristic
159C2×#11758198C2×C411yescharacteristic
160C2×#11758198C2×C411yescharacteristic
161C2×#11758198C2×C411yescharacteristic
162C2×#11758198C2311yescharacteristic
163C2×C4×Dic61C2×C411yescharacteristic
164C2×C4×Dic61C2×C411yescharacteristic
165C2×C4×Dic61C2×C411yescharacteristic
166C2×C4×Dic61C2311yescharacteristic
167C4⋊#92418—21no—
168C4⋊#92418—21no—
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418C2311yescharacteristic
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2311yescharacteristic
176C22⋊#92418C2311yescharacteristic
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519689—21no—
181#14519688—21no—
182#14519687—21no—
183#14519687—21no—
184C4×#92418—21no—
185C8×Dic61—21no—
186C8×Dic61—21no—
187C22×Q8×C61C2×C411yescharacteristic
188C22×D4×C61C2×C411yescharacteristic
189#124×C61—21no—
190#124×C61—21no—
191#124×C61—21no—
192#124×C61—21no—
193C2×C22⋊C4×C61C2×C411yescharacteristic
194C2×C22⋊C4×C61C2×C411yescharacteristic
195C2×C22⋊C4×C61C2311yescharacteristic
196C2×C22⋊C4×C61C2311yescharacteristic
197C2×C42×C61C2311yescharacteristic
198C4⋊C8×C61—21no—
199C4⋊C8×C61—21no—
200C22⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204#97×C61—21no—
205C4×C8×C61—21no—
206C24×C61C22×C411yescharacteristic
207C24×C61C22×C411yescharacteristic
208C23×D61C22×C411yescharacteristic
209C23×D61C22×C411yescharacteristic
210C2×Q8×C61—21no—
211C2×Q8×C61—21no—
212C2×Q8×C61—81no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—81no—
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C2411yescharacteristic
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—22no—
230C2×C22⋊D61—41no—
231C2×C22⋊D61—42no—
232C2×C22⋊D61—81no—
233C2×C22⋊D61—81no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—22no—
239C22×Dic61—41no—
240C22×Dic61—42no—
241C22×Dic61C22×C411yescharacteristic
242C22×Dic61C22×C411yescharacteristic
243C22×Dic61C22×C411yescharacteristic
244C22×Dic61C22×C411yescharacteristic
245C22×Dic61C22×C411yescharacteristic
246C22×Dic61C22×C411yescharacteristic
247C2×D244—21no—
248C2×D244—21no—
249C2×D244—81no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—22no—
253C2×C4×D61—42no—
254C2×C4×D61—41no—
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×Dic122—21no—
260C2×Dic122—21no—
261C2×Dic122—81no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C22⋊C4×C61—21no—
267C22⋊C4×C61—21no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61—21no—
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C42×C61C2×D411yescharacteristic
275C42×C61C2×D411yescharacteristic
276C42×C61C2×D411yescharacteristic
277C42×C61C2×D411yescharacteristic
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198C22⋊C411yescharacteristic
291#11758198C22⋊C411yescharacteristic
292#11758198C22⋊C411yescharacteristic
293#11758198C22⋊C411yescharacteristic
294#11758198C22⋊C411yescharacteristic
295#11758198C22⋊C411yescharacteristic
296#11758198C22⋊C411yescharacteristic
297#11758198C22⋊C411yescharacteristic
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308#11758196C22⋊C411yescharacteristic
309#11758196C22⋊C411yescharacteristic
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312#11758196C22⋊C411yescharacteristic
313#11758196C22⋊C411yescharacteristic
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C2×#92418—21no—
325C2×#92418—21no—
326C2×#92418—21no—
327C2×#92418—21no—
328#11758189—42no—
329#11758189—42no—
330C8×D61—42no—
331C8×D61—42no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61C23×C411yescharacteristic
343C22×D61—21no—
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—21no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61C2×C22⋊C411yescharacteristic
353C22×D61C2×C22⋊C411yescharacteristic
354Q8×C61—81no—
355Q8×C61—81no—
356D4×C61—81no—
357D4×C61—81no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61C2×C22⋊C411yescharacteristic
367C2×C4×C61C2×C22⋊C411yescharacteristic
368C2×C4×C61C2×C22⋊C411yescharacteristic
369C2×C4×C61C2×C22⋊C411yescharacteristic
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C22×D411yescharacteristic
372C22⋊D61—42no—
373C22⋊D61—42no—
374C22⋊D61—42no—
375C22⋊D61—42no—
376C22⋊D61—81no—
377C22⋊D61—81no—
378C22⋊D61—81no—
379C22⋊D61—81no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—22no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—41no—
388C2×Dic61—42no—
389C2×Dic61—42no—
390C2×Dic61—42no—
391C2×Dic61—42no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61C2×C22⋊C411yescharacteristic
395C2×Dic61C2×C22⋊C411yescharacteristic
396C2×Dic61C2×C22⋊C411yescharacteristic
397C2×Dic61C2×C22⋊C411yescharacteristic
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61#13112yes—
401D244—81no—
402D244—81no—
403C4×D61—22no—
404C4×D61—22no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—42no—
408C4×D61—42no—
409Dic122—81no—
410Dic122—81no—
411C8×C61—41no—
412C8×C61—41no—
413C8×C61—41no—
414C8×C61—41no—
415#92418—41no—
416#92418—41no—
417#92418—41no—
418#92418—41no—
419#17418—611nomaximal, Sylow
420C22×C61—21no—
421C22×C61—21no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61—41no—
428C22×C61—81no—
429C22×C61—81no—
430C22×C61—81no—
431C22×C61—81no—
432C22×C61C22×C22⋊C411yescharacteristic
433C22×C61C2×#13111yescharacteristic
434C22×C61#56811yescharacteristic
435C2×D61—21no—
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—41no—
442C2×D61—41no—
443C2×D61—41no—
444C2×D61—81no—
445C2×D61—81no—
446C2×D61—81no—
447C2×D61—81no—
448C4×C61—21no—
449C4×C61—21no—
450C4×C61—21no—
451C4×C61—21no—
452C4×C61—21no—
453C4×C61—21no—
454C4×C61—41no—
455C4×C61—41no—
456Dic61—22no—
457Dic61—21no—
458Dic61—21no—
459Dic61—21no—
460Dic61—21no—
461Dic61—21no—
462Dic61—41no—
463Dic61—41no—
464Dic61#41012yes—
465C2×#555—611no—
466#2924—611no—
467#2924—611no—
468#1471—611no—
469#1471—611no—
470#1469—611no—
471#1469—611no—
472#1469—611no—
473#1469D6111yescharacteristic, complemented
474#1465—611no—
475#1464—611no—
476#1464—611no—
477#1459—611no—
478#1458—611no—
479#1458—611no—
480C2×C61—21no—
481C2×C61—21no—
482C2×C61—81no—
483C2×C61—81no—
484C2×C61#288011yescharacteristic
485C2×C61C2×#41011yescharacteristic
486C2×C61#288811yescharacteristic
487D61—41no—
488D61—41no—
489D61—81no—
490#555—1221no—
491#555—1221no—
492#555—1221no—
493#555—1221no—
494#555—1221no—
495#555—1221no—
496#555—1221no—
497#555—1221no—
498C2×C4⋊Q8—611no—
499C2×#124—611no—
500C2×#124—611no—
501C2×#124—611no—
502C2×#124C2×D6111yescharacteristic
503C2×#121—611no—
504C2×#121—611no—
505C2×#121—611no—
506C2×#121—611no—
507C2×C4×D4—611no—
508C2×C4×D4—611no—
509C2×#117—611no—
510C2×#117—611no—
511C2×#117—611no—
512C2×#117—611no—
513#433—1221no—
514#433—1221no—
515#433—1221no—
516#433—1221no—
517#432—611no—
518#432—611no—
519#432—611no—
520#432C2×D6111yescharacteristic
521#431—611no—
522#431—611no—
523#431—611no—
524#431C2×D6111yescharacteristic
525#424—1221no—
526#424—1221no—
527#407—611no—
528#407—611no—
529C2×C22⋊C8—611no—
530C2×C22⋊C8—611no—
531#405—1221no—
532#405—1221no—
533#324—611no—
534#324—611no—
535#324—611no—
536#324—611no—
537#323—611no—
538#323—611no—
539#323—611no—
540#323—611no—
541#323—611no—
542#323—611no—
543#323—611no—
544#323—611no—
545#323C2×D6111yescharacteristic
546#323C2×D6111yescharacteristic
547#323C2×D6111yescharacteristic
548#323C2×D6111yescharacteristic
549C61#1741811yescharacteristic, complemented, Sylow
550C22×Q8—611no—
551C22×Q8C4×D6111yescharacteristic
552C22×D4—611no—
553C22×D4—611no—
554C22×D4—611no—
555C22×D4—611no—
556C22×D4—611no—
557C22×D4C4×D6111yescharacteristic
558C23×C4—611no—
559C23×C4—611no—
560C23×C4—611no—
561C23×C4—611no—
562C2×M16—1221no—
563C2×M16—1221no—
564C22×C8—1221no—
565C22×C8—1221no—
566C4⋊Q8—1221no—
567C4⋊Q8—1221no—
568C4⋊Q8—1221no—
569C4⋊Q8—1221no—
570#124—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#124—1221no—
575#124—1221no—
576#124—1221no—
577#124—1221no—
578#124—1221no—
579#124—1221no—
580#124—1221no—
581#124—1221no—
582#124—1221no—
583#124—1221no—
584#124—1221no—
585#124—1221no—
586#121—1221no—
587#121—1221no—
588#121—1221no—
589#121—1221no—
590#121—1221no—
591#121—1221no—
592#121—1221no—
593#121—1221no—
594#121—1221no—
595#121—1221no—
596#121—1221no—
597#121—1221no—
598#121—1221no—
599#121—1221no—
600#121—1221no—
601#121—1221no—
602C4×D4—1221no—
603C4×D4—1221no—
604C4×D4—1221no—
605C4×D4—1221no—
606C4×D4—1221no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610#117—611no—
611#117—611no—
612#117—611no—
613#117—611no—
614#117—611no—
615#117—611no—
616#117—611no—
617#117—611no—
618#117—1221no—
619#117—1221no—
620#117—1221no—
621#117—1221no—
622#117—1221no—
623#117—1221no—
624#117—1221no—
625#117—1221no—
626#117—1221no—
627#117—1221no—
628#117—1221no—
629#117—1221no—
630C2×C4⋊C4—611no—
631C2×C4⋊C4—611no—
632C2×C4⋊C4—611no—
633C2×C4⋊C4—611no—
634C2×C4⋊C4—611no—
635C2×C4⋊C4—611no—
636C2×C22⋊C4—611no—
637C2×C22⋊C4—611no—
638C2×C22⋊C4—611no—
639C2×C22⋊C4—611no—
640C2×C22⋊C4—611no—
641C2×C22⋊C4—611no—
642C2×C22⋊C4—611no—
643C2×C22⋊C4—611no—
644C2×C22⋊C4C4×D6111yescharacteristic
645C2×C22⋊C4C4×D6111yescharacteristic
646C2×C22⋊C4C22×D6111yescharacteristic
647C2×C22⋊C4C22×D6111yescharacteristic
648C2×C42—611no—
649C2×C42—611no—
650C2×C42—611no—
651C2×C42—611no—
652C2×C42C22×D6111yescharacteristic
653C4⋊C8—21no—
654C4⋊C8—21no—
655C4⋊C8—1221no—
656C4⋊C8—1221no—
657C4⋊C8—1221no—
658C4⋊C8—1221no—
659C4⋊C8—1221no—
660C4⋊C8—1221no—
661C22⋊C8—611no—
662C22⋊C8—611no—
663C22⋊C8—611no—
664C22⋊C8—611no—
665C22⋊C8—1221no—
666C22⋊C8—1221no—
667C22⋊C8—1221no—
668C22⋊C8—1221no—
669C22⋊C8C22×D6111yescharacteristic
670C22⋊C8C22×D6111yescharacteristic
671C22⋊C8C22×D6111yescharacteristic
672C22⋊C8C22×D6111yescharacteristic
673#97—21no—
674#97—1221no—
675#97—1221no—
676#97—1221no—
677C4×C8—21no—
678C4×C8—1221no—
679C4×C8—1221no—
680C4×C8—1221no—
681C24—611no—
682C24—611no—
683C24C2×C4×D6111yescharacteristic
684C24C2×C4×D6111yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—81no—
688C2×Q8—1221no—
689C2×Q8—1221no—
690C2×Q8—4881no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—81no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4—1221no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1222no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—4881no—
706C2×D4—4881no—
707C2×D4—4881no—
708C2×D4—2441no—
709C2×D4—2442no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—1222no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1222no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—2441no—
729C22×C4—2442no—
730C22×C4—2441no—
731C22×C4—2442no—
732C22×C4C2×C4×D6111yescharacteristic
733C22×C4C2×C4×D6111yescharacteristic
734C22×C4C2×C4×D6111yescharacteristic
735C22×C4C2×C4×D6111yescharacteristic
736C22×C4C23×D6111yescharacteristic
737M16—2442no—
738M16—2442no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—1221no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—2442no—
748C2×C8—2442no—
749C4⋊C4—611no—
750C4⋊C4—611no—
751C4⋊C4—611no—
752C4⋊C4—611no—
753C4⋊C4—611no—
754C4⋊C4—611no—
755C4⋊C4—611no—
756C4⋊C4—611no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—611no—
774C22⋊C4—611no—
775C22⋊C4—611no—
776C22⋊C4—611no—
777C22⋊C4—611no—
778C22⋊C4—611no—
779C22⋊C4—611no—
780C22⋊C4—611no—
781C22⋊C4—1221no—
782C22⋊C4—1221no—
783C22⋊C4—1221no—
784C22⋊C4—1221no—
785C22⋊C4—1221no—
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C42—611no—
794C42—611no—
795C42—611no—
796C42—611no—
797C42—1221no—
798C42—1221no—
799C42—1221no—
800C42—1221no—
801C42—1221no—
802C42—1221no—
803C42D4×D6111yescharacteristic
804C42D4×D6111yescharacteristic
805C42D4×D6111yescharacteristic
806C42D4×D6111yescharacteristic
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—611no—
818C23—611no—
819C23—1221no—
820C23—1221no—
821C23—1221no—
822C23—1221no—
823C23—1221no—
824C23—2441no—
825C23—2441no—
826C23—2441no—
827C23—2441no—
828C23C22×C4×D6111yescharacteristic
829Q8—81no—
830Q8—81no—
831Q8—4881no—
832Q8—4881no—
833D4—81no—
834D4—81no—
835D4—4881no—
836D4—4881no—
837D4—4881no—
838D4—4881no—
839D4—4881no—
840D4—4881no—
841D4—2442no—
842D4—2442no—
843D4—2442no—
844D4—2442no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—611no—
854C2×C4—611no—
855C2×C4—611no—
856C2×C4—611no—
857C2×C4—611no—
858C2×C4—611no—
859C2×C4—612no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—1222no—
863C2×C4—1221no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—1221no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2442no—
872C2×C4—2442no—
873C2×C4—2442no—
874C2×C4—2441no—
875C2×C4—2442no—
876C2×C4—2442no—
877C2×C4—2442no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4C22⋊C4×D6111yescharacteristic
881C2×C4C22⋊C4×D6111yescharacteristic
882C2×C4C22⋊C4×D6111yescharacteristic
883C2×C4C22⋊C4×D6111yescharacteristic
884C2×C4C2×D4×D6111yescharacteristic
885C2×C4C2×D4×D6111yescharacteristic
886C8—41no—
887C8—41no—
888C8—41no—
889C8—41no—
890C8—2441no—
891C8—2441no—
892C8—2441no—
893C8—2441no—
894C22—21no—
895C22—21no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—1221no—
907C22—1221no—
908C22—1221no—
909C22—1221no—
910C22—1221no—
911C22—1221no—
912C22—4881no—
913C22—4881no—
914C22—4881no—
915C22—4881no—
916C22—2441no—
917C22—2441no—
918C22—2441no—
919C22C2×C22⋊C4×D6111yescharacteristic
920C22#131×D6111yescharacteristic
921C22#1684052711yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—41no—
929C4—41no—
930C4—612no—
931C4—1221no—
932C4—1221no—
933C4—1222no—
934C4—1221no—
935C4—1221no—
936C4—1221no—
937C4—2441no—
938C4—2441no—
939C2—21no—
940C2—21no—
941C2—81no—
942C2—81no—
943C2—4881no—
944C2—2441no—
945C2—2441no—
946C2#2145426711yescharacteristic
947C2#410×D6111yescharacteristic
948C2#2145429511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1469C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840474C2
cosocleC22×C4×C61C24
hypercenter#1469D61
hypocenterC61#17418
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1469

Complements

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

NH ≅ G/Ntype
2. #21454478C2semidirect
3. #21454472C2semidirect
4. #21444177C2semidirect
5. #21444177C2semidirect
6. #21444171C2semidirect
7. #21444169C2semidirect
8. #21444169C2semidirect
9. #21444154C2semidirect
10. #21444151C2semidirect
11. #21444150C2semidirect
12. #21444134C2semidirect
13. #21444131C2semidirect
14. #21444130C2semidirect
15. C61×#1469C2semidirect
473. #1469D61semidirect
549. C61#17418semidirect

Maximal subgroups

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

subgroupindex
C2×#168404742
#214544782
#214544722
#214441772
#214441712
#214441692
#214441542
#214441512
#214441502
#214441342
#214441312
#214441302
C61×#14692
#1741861