Finite Group Databasebeta

← #11904906

Subgroups — #11904906

Order 1152.

2987 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64162C211yesmaximal, characteristic, complemented
2C2×C3×#953C211yesmaximal, characteristic, complemented
3C22×C3×#217C211yesmaximal, characteristic, complemented
4#10595521C211yesmaximal, characteristic, complemented
5#10595519C211yesmaximal, characteristic, complemented
6#10595510C211yesmaximal, characteristic, complemented
7#10595509C214yesmaximal, complemented
8#10595507C214yesmaximal, complemented
9#10595506C211yesmaximal, characteristic, complemented
10#10595500C214yesmaximal, complemented
11#10595498C214yesmaximal, complemented
12#10595493C214yesmaximal, complemented
13#10595476C214yesmaximal, complemented
14#85913—31nomaximal
15#85697—31nomaximal
16C25×C32C2211yescharacteristic
17C22×#638C2211yescharacteristic
18C22×#638C2212yescomplemented
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2212yescomplemented
21C23×C3×Dic3C2212yescomplemented
22C2×#3804C2214yescomplemented
23#64162C2214yes—
24#64162C2212yescomplemented
25#64162C2212yescomplemented
26C2×#3757C2211yescharacteristic
27C2×#3757C2212yescomplemented
28C3×#953C2214yes—
29C3×#953C2212yescomplemented
30C3×#953C2212yescomplemented
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2214yescomplemented
35C2×C3×#217C2214yescomplemented
36C2×C3×#217C2212yescomplemented
37C2×C3×#217C2212yescomplemented
38#63982C2214yescomplemented
39#63981C2212yescomplemented
40#63978C2214yescomplemented
41#63978C2214yescomplemented
42#63977C2212yescomplemented
43#63975C2214yescomplemented
44#63974C2212yescomplemented
45#67⋊Dic3C2214yescomplemented
46Dic3×#67C2214yescomplemented
47Dic3×#67C2214yescomplemented
48#63971C2214yescomplemented
49#63969C2214yescomplemented
50D3×#217C2212yescomplemented
51#63966C2212yescomplemented
52#63966C2214yescomplemented
53#63964C2214yescomplemented
54#63964C2214yescomplemented
55#63964C2214yescomplemented
56#63962C2212yescomplemented
57#63961C2214yescomplemented
58#63959C2214yescomplemented
59#63958C2214yescomplemented
60#63957C2212yescomplemented
61#63956C2214yescomplemented
62#63956C2214yescomplemented
63#63955C2212yescomplemented
64#63955C2214yescomplemented
65#63953C2214yescomplemented
66#63952C2214yescomplemented
67#63952C2214yescomplemented
68#63952C2214yescomplemented
69C2×C3×#120—31no—
70C22×C3×C22⋊C4—31no—
71C2×#953—31no—
72C2×#953—31no—
73C2×#953—61no—
74C2×#953D311yescharacteristic, complemented
75C22×#217D311yescharacteristic, complemented
76#5806—34no—
77#5804—31no—
78#5798—31no—
79#5791—34no—
80#5593—34no—
81#5591—34no—
82#5587—34no—
83#5586—34no—
84#5495—34no—
85#5495—34no—
86#5495—34no—
87#5494—34no—
88#5493—31no—
89#5490—34no—
90#5490—34no—
91#5486—31no—
92#5486—31no—
93#5486—31no—
94#5483—31no—
95#5483—31no—
96C24×C32—24no—
97C24×C32—44no—
98C24×C32C2311yescharacteristic
99C24×C32C2312yes—
100C24×C32C2312yes—
101C24×C32C2311yescharacteristic
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C2×#638—24no—
106C2×#638—44no—
107C2×#638C2314yes—
108C2×#638C2312yes—
109C2×#638C2312yes—
110C2×#638C2314yes—
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2312yes—
113C2×C3×#67—24no—
114C2×C3×#67—44no—
115C2×C3×#67C2314yes—
116C2×C3×#67C2312yes—
117C2×C3×#67C2312yes—
118C2×C3×#67C2314yes—
119C22×C3×Dic3—44no—
120C22×C3×Dic3C2314yes—
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2312yes—
123C22×C3×Dic3C2312yes—
124C22×C3×Dic3C2312yes—
125C22×C3×Dic3C2314yes—
126C2×#627C2314yescomplemented
127C2×#626C2314yescomplemented
128C2×#624C2314yescomplemented
129#3804—48no—
130C2×D3×Dic3C2314yescomplemented
131#3757C2312yes—
132#3757C2312yes—
133#3757C2314yes—
134#3757C2314yes—
135C3×#217C2312yes—
136C3×#217C2312yes—
137C3×#217C2312yes—
138C3×#217C2312yes—
139C3×#217C2312yes—
140C3×#217C2312yes—
141C3×#217C2314yes—
142C3×#217C2314yes—
143C3×#217C2314yes—
144C3×#217C2314yes—
145#3724C2314yescomplemented
146#3724C2314yescomplemented
147Dic3⋊Dic3C2314yescomplemented
148Dic3⋊Dic3C2314yescomplemented
149Dic3⋊Dic3C2314yescomplemented
150Dic3⋊Dic3C2314yescomplemented
151#3722C2314yescomplemented
152#3722C2314yescomplemented
153(C2×D3)⋊Dic3C2314yescomplemented
154(C2×D3)⋊Dic3C2314yescomplemented
155Dic32C2314yescomplemented
156Dic32C2314yescomplemented
157#3490—91noSylow
158C25×C3—21no—
159C25×C3C2×D311yescharacteristic
160C25×C3C2×D311yescharacteristic
161C22×C3×D4—31no—
162C22×C3×D4—32no—
163C23×C3×C4—32no—
164C22×#67—31no—
165C22×#67—31no—
166C22×#67—32no—
167C22×#67—32no—
168C22×#67—61no—
169C22×#67—62no—
170C22×#67C2×D311yescharacteristic
171C22×#67C2×D312yescomplemented
172C23×Dic3C2×D312yescomplemented
173C2×#237—34no—
174C2×#235—34no—
175C3×#120—34no—
176C3×#120—32no—
177C3×#120—32no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—34no—
182C2×C3×C22⋊C4—34no—
183C2×C3×C22⋊C4—32no—
184C2×C3×C22⋊C4—32no—
185#953—34no—
186#953—32no—
187#953—34no—
188#953—32no—
189#953—32no—
190#953—32no—
191#953—32no—
192#953—64no—
193#953—62no—
194#953—62no—
195#953C2×D314yes—
196#953C2×D312yescomplemented
197#953C2×D312yescomplemented
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—32no—
201C2×#217—32no—
202C2×#217—32no—
203C2×#217—61no—
204C2×#217—62no—
205C2×#217C2×D311yescharacteristic
206C2×#217C2×D311yescharacteristic
207C2×#217C2×D311yescharacteristic
208C2×#217C2×D312yescomplemented
209C2×#217C2×D314yescomplemented
210C2×#217C2×D314yescomplemented
211C2×#217C2×D312yescomplemented
212#939—34no—
213#939—34no—
214#939—34no—
215#938—34no—
216#937—32no—
217#936—34no—
218#935—34no—
219#935—32no—
220#935—34no—
221D4×Dic3—34no—
222D4×Dic3—34no—
223D4×Dic3—34no—
224#930—34no—
225#930—34no—
226#929—34no—
227#929—34no—
228#929—32no—
229C4×#67—34no—
230C4×#67—34no—
231C4×#67—34no—
232C4×#67—34no—
233C4×#67—34no—
234#926—34no—
235#926—32no—
236#924—34no—
237#924—34no—
238#924—34no—
239#886—32no—
240#886—32no—
241#886—34no—
242#885—34no—
243#885—34no—
244#885—34no—
245#884—34no—
246#884—34no—
247#883—34no—
248#883—34no—
249#883—34no—
250#882—32no—
251#882—32no—
252#67⋊C4—34no—
253#67⋊C4—34no—
254#67⋊C4—34no—
255#67⋊C4—34no—
256D3×C22⋊C4—32no—
257D3×C22⋊C4—32no—
258D3×C22⋊C4—32no—
259#879—34no—
260#879—34no—
261#879—34no—
262#879—34no—
263#878—34no—
264#878—34no—
265#878—34no—
266#878—34no—
267#878—34no—
268#877—32no—
269#877—34no—
270#877—32no—
271#877—32no—
272C23×C32—24no—
273C23×C32—22no—
274C23×C32—24no—
275C23×C32—24no—
276C23×C32—24no—
277C23×C32—22no—
278C23×C32—24no—
279C23×C32—42no—
280C23×C32—42no—
281C23×C32—42no—
282C23×C32—42no—
283C23×C32—416no—
284C23×C32#4114yescomplemented
285C23×C32C2412yes—
286C23×C32C2411yescharacteristic
287C23×C32C2411yescharacteristic
288C23×C32C2411yescharacteristic
289C23×C32C2412yes—
290C22×C3⋊D3—22no—
291C22×C3⋊D3—42no—
292C22×C3⋊D3C2412yes—
293C22×C3×D3—22no—
294C22×C3×D3—42no—
295C22×C3×D3C2412yes—
296#638—24no—
297#638—24no—
298#638—28no—
299#638—44no—
300C2×C3⋊Dic3—22no—
301C2×C3⋊Dic3—42no—
302C2×C3⋊Dic3C2412yes—
303C2×C3⋊Dic3C2414yes—
304C3×#67—24no—
305C3×#67—24no—
306C3×#67—28no—
307C3×#67—44no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—28no—
310C2×C3×Dic3—42no—
311C2×C3×Dic3—44no—
312C2×C3×Dic3—42no—
313C2×C3×Dic3—42no—
314C2×C3×Dic3C2414yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2414yes—
317C2×C3×Dic3C2414yes—
318#627—44no—
319#626—44no—
320#624—44no—
321D3×Dic3—44no—
322#551—94no—
323#551—94no—
324#546—94no—
325#546—94no—
326#543—91no—
327#538—94no—
328#534—91no—
329#525—94no—
330C2×#120—31no—
331C2×#120—91no—
332#518—91no—
333#518—91no—
334C22×C22⋊C4—31no—
335C24×C3—24no—
336C24×C3—24no—
337C24×C3—22no—
338C24×C3—21no—
339C24×C3—21no—
340C24×C3—22no—
341C24×C3—21no—
342C24×C3—31no—
343C24×C3—44no—
344C24×C3—44no—
345C24×C3—44no—
346C24×C3—48no—
347C24×C3C22×D311yescharacteristic
348C24×C3C22×D311yescharacteristic
349C24×C3C22×D312yes—
350C24×C3C22×D312yes—
351C24×C3C22×D312yes—
352C24×C3C22×D312yes—
353C24×C3C22×D311yescharacteristic
354C24×C3C22×D311yescharacteristic
355C24×C3C22×D311yescharacteristic
356C24×C3C22×D311yescharacteristic
357C23×D3—31no—
358C23×D3—31no—
359C23×D3—61no—
360C23×D3C22×D311yescharacteristic
361C2×C3×D4—32no—
362C2×C3×D4—32no—
363C2×C3×D4—34no—
364C2×C3×D4—34no—
365C2×C3×D4—64no—
366C2×C3×D4—124no—
367C22×C3×C4—31no—
368C22×C3×C4—34no—
369C22×C3×C4—32no—
370C22×C3×C4—32no—
371C22×C3×C4—34no—
372C22×C3×C4—32no—
373C22×C3×C4—124no—
374C2×#67—24no—
375C2×#67—32no—
376C2×#67—32no—
377C2×#67—34no—
378C2×#67—32no—
379C2×#67—32no—
380C2×#67—34no—
381C2×#67—34no—
382C2×#67—34no—
383C2×#67—34no—
384C2×#67—44no—
385C2×#67—62no—
386C2×#67—62no—
387C2×#67—64no—
388C2×#67—64no—
389C2×#67—64no—
390C2×#67—64no—
391C2×#67—124no—
392C2×#67—124no—
393C2×#67—124no—
394C2×#67—128no—
395C2×#67C22×D312yes—
396C2×#67C22×D312yes—
397C2×#67C22×D314yes—
398C2×#67C22×D314yes—
399C22×Dic3—31no—
400C22×Dic3—31no—
401C22×Dic3—32no—
402C22×Dic3—32no—
403C22×Dic3—34no—
404C22×Dic3—44no—
405C22×Dic3—61no—
406C22×Dic3—62no—
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D314yes—
409C22×Dic3C22×D312yes—
410C22×Dic3C22×D312yes—
411C22×Dic3C22×D314yes—
412C22×Dic3C22×D312yes—
413#237—128no—
414#235—128no—
415C2×D12—34no—
416C2×C4×D3—34no—
417C2×C4×D3—34no—
418C2×C4×D3—34no—
419C2×Dic6—34no—
420C2×Dic6—34no—
421C3×C22⋊C4—32no—
422C3×C22⋊C4—34no—
423C3×C22⋊C4—32no—
424C3×C22⋊C4—32no—
425C3×C22⋊C4—32no—
426C3×C22⋊C4—32no—
427C3×C22⋊C4—32no—
428C3×C22⋊C4—34no—
429C3×C22⋊C4—34no—
430C3×C22⋊C4—34no—
431#217—32no—
432#217—34no—
433#217—32no—
434#217—34no—
435#217—34no—
436#217—32no—
437#217—32no—
438#217—34no—
439#217—34no—
440#217—34no—
441#217—62no—
442#217—64no—
443#217—62no—
444#217—64no—
445#217C22×D312yes—
446#217C22×D312yes—
447#217C22×D312yes—
448#217C22×D314yes—
449#217C22×D314yes—
450#217C22×D314yes—
451#217C22×D312yes—
452#217C22×D312yes—
453#217C22×D314yes—
454#217C22×D312yes—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—34no—
457(C2×D3)⋊C4—34no—
458(C2×D3)⋊C4—34no—
459(C2×D3)⋊C4—34no—
460(C2×D3)⋊C4—34no—
461C4⋊Dic3—34no—
462C4⋊Dic3—34no—
463C4⋊Dic3—34no—
464C4⋊Dic3—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473C4×Dic3—34no—
474C4×Dic3—34no—
475C4×Dic3—34no—
476C4×Dic3—34no—
477C22×C32—22no—
478C22×C32—22no—
479C22×C32—28no—
480C22×C32—22no—
481C22×C32—22no—
482C22×C32—22no—
483C22×C32—22no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—44no—
487C22×C32—48no—
488C22×C32—48no—
489C22×C32—44no—
490C22×C32C2×#4112yes—
491C22×C32C2×#4112yes—
492C22×C32C2×#4112yes—
493C22×C32H(5,𝔽2)14yes—
494C22×C32C2511yescharacteristic
495C2×C3⋊D3—22no—
496C2×C3⋊D3—24no—
497C2×C3⋊D3—82no—
498C2×C3×D3—22no—
499C2×C3×D3—24no—
500C2×C3×D3—82no—
501C3⋊Dic3—22no—
502C3⋊Dic3—24no—
503C3×Dic3—22no—
504C3×Dic3—24no—
505C3×Dic3—24no—
506C3×Dic3—24no—
507C25D3211yescharacteristic
508C2×#41—94no—
509C22×D4—31no—
510C22×D4—32no—
511C22×D4—91no—
512C22×D4—92no—
513C23×C4—32no—
514#126—94no—
515#126—94no—
516#124—94no—
517#124—94no—
518#123—94no—
519#123—94no—
520#123—92no—
521#123—92no—
522#123—94no—
523#123—94no—
524C22⋊Q8—94no—
525C22⋊Q8—94no—
526C22⋊Q8—94no—
527C22⋊Q8—94no—
528#121—94no—
529#121—94no—
530#121—94no—
531#121—94no—
532#120—32no—
533#120—32no—
534#120—34no—
535#120—92no—
536#120—92no—
537#120—92no—
538#120—92no—
539#120—94no—
540C4×D4—94no—
541C4×D4—94no—
542C4×D4—94no—
543C4×D4—94no—
544C4×D4—94no—
545C4×D4—94no—
546#117—92no—
547#117—92no—
548#117—94no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—32no—
552C2×C22⋊C4—34no—
553C2×C22⋊C4—34no—
554C2×C22⋊C4—31no—
555C2×C22⋊C4—32no—
556C2×C22⋊C4—92no—
557C2×C22⋊C4—92no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—92no—
560C23×C3—22no—
561C23×C3—22no—
562C23×C3—24no—
563C23×C3—24no—
564C23×C3—28no—
565C23×C3—24no—
566C23×C3—24no—
567C23×C3—22no—
568C23×C3—24no—
569C23×C3—24no—
570C23×C3—22no—
571C23×C3—24no—
572C23×C3—24no—
573C23×C3—24no—
574C23×C3—24no—
575C23×C3—21no—
576C23×C3—22no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—22no—
580C23×C3—24no—
581C23×C3—32no—
582C23×C3—42no—
583C23×C3—44no—
584C23×C3—44no—
585C23×C3—44no—
586C23×C3—42no—
587C23×C3—44no—
588C23×C3—42no—
589C23×C3—42no—
590C23×C3—42no—
591C23×C3—42no—
592C23×C3—42no—
593C23×C3—42no—
594C23×C3—42no—
595C23×C3—42no—
596C23×C3—44no—
597C23×C3—44no—
598C23×C3—44no—
599C23×C3—44no—
600C23×C3—416no—
601C23×C3—416no—
602C23×C3—432no—
603C23×C3—62no—
604C23×C3—122no—
605C23×C3#23514yescomplemented
606C23×C3#23714yescomplemented
607C23×C3C23×D312yes—
608C23×C3C23×D312yes—
609C23×C3C23×D311yescharacteristic
610C23×C3C23×D311yescharacteristic
611C23×C3C23×D311yescharacteristic
612C23×C3C23×D311yescharacteristic
613C23×C3C23×D311yescharacteristic
614C23×C3C23×D311yescharacteristic
615C23×C3C23×D312yes—
616C23×C3C23×D312yes—
617C22×D3—22no—
618C22×D3—32no—
619C22×D3—32no—
620C22×D3—42no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—62no—
624C22×D3—122no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—124no—
628C22×D3C23×D312yes—
629C3×D4—64no—
630C3×D4—64no—
631C3×D4—68no—
632C3×D4—124no—
633C2×C3×C4—32no—
634C2×C3×C4—34no—
635C2×C3×C4—34no—
636C2×C3×C4—34no—
637C2×C3×C4—62no—
638C2×C3×C4—68no—
639C2×C3×C4—122no—
640C2×C3×C4—124no—
641C2×C3×C4—122no—
642C2×C3×C4—122no—
643#67—24no—
644#67—24no—
645#67—28no—
646#67—44no—
647#67—64no—
648#67—64no—
649#67—64no—
650#67—64no—
651#67—68no—
652#67—68no—
653#67—124no—
654#67—124no—
655#67—128no—
656#67—124no—
657#67—124no—
658#67—124no—
659#67—128no—
660C2×Dic3—22no—
661C2×Dic3—28no—
662C2×Dic3—32no—
663C2×Dic3—32no—
664C2×Dic3—34no—
665C2×Dic3—34no—
666C2×Dic3—42no—
667C2×Dic3—44no—
668C2×Dic3—42no—
669C2×Dic3—42no—
670C2×Dic3—62no—
671C2×Dic3—64no—
672C2×Dic3—62no—
673C2×Dic3—62no—
674C2×Dic3—122no—
675C2×Dic3—124no—
676C2×Dic3—122no—
677C2×Dic3—122no—
678C2×Dic3—124no—
679C2×Dic3C23×D312yes—
680C2×Dic3C23×D314yes—
681C2×Dic3C23×D314yes—
682C2×Dic3C23×D314yes—
683D12—124no—
684C4×D3—124no—
685C4×D3—124no—
686C4×D3—124no—
687Dic6—124no—
688Dic6—124no—
689C2×C32—22no—
690C2×C32—22no—
691C2×C32—22no—
692C2×C32—24no—
693C2×C32—42no—
694C2×C32C22×#4111yescharacteristic
695C2×C32C2×H(5,𝔽2)12yes—
696C3⋊D3—42no—
697C3×D3—42no—
698C24—24no—
699C24—31no—
700C24—44no—
701C24—91no—
702C24C2×D3211yescharacteristic
703C24C2×D3212yes—
704C24C2×D3212yes—
705C24C2×D3211yescharacteristic
706C24C2×D3211yescharacteristic
707#41—368no—
708C2×Q8—94no—
709C2×D4—32no—
710C2×D4—32no—
711C2×D4—34no—
712C2×D4—34no—
713C2×D4—64no—
714C2×D4—94no—
715C2×D4—92no—
716C2×D4—92no—
717C2×D4—94no—
718C2×D4—94no—
719C2×D4—124no—
720C2×D4—184no—
721C2×D4—364no—
722C22×C4—31no—
723C22×C4—34no—
724C22×C4—32no—
725C22×C4—34no—
726C22×C4—32no—
727C22×C4—32no—
728C22×C4—94no—
729C22×C4—94no—
730C22×C4—91no—
731C22×C4—92no—
732C22×C4—124no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C22⋊C4—32no—
740C22⋊C4—32no—
741C22⋊C4—32no—
742C22⋊C4—32no—
743C22⋊C4—34no—
744C22⋊C4—34no—
745C22⋊C4—32no—
746C22⋊C4—34no—
747C22⋊C4—32no—
748C22⋊C4—34no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C22⋊C4—94no—
752C22⋊C4—94no—
753C22⋊C4—92no—
754C22⋊C4—94no—
755C22⋊C4—92no—
756C22⋊C4—94no—
757C42—94no—
758C42—94no—
759C22×C3—24no—
760C22×C3—28no—
761C22×C3—28no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—24no—
773C22×C3—22no—
774C22×C3—22no—
775C22×C3—22no—
776C22×C3—22no—
777C22×C3—22no—
778C22×C3—22no—
779C22×C3—22no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—24no—
783C22×C3—21no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—42no—
787C22×C3—42no—
788C22×C3—42no—
789C22×C3—42no—
790C22×C3—48no—
791C22×C3—44no—
792C22×C3—44no—
793C22×C3—48no—
794C22×C3—48no—
795C22×C3—48no—
796C22×C3—48no—
797C22×C3—48no—
798C22×C3—416no—
799C22×C3—44no—
800C22×C3—44no—
801C22×C3—416no—
802C22×C3—48no—
803C22×C3—62no—
804C22×C3—64no—
805C22×C3—242no—
806C22×C3C2×#23512yes—
807C22×C3C2×#23512yes—
808C22×C3C2×#23512yes—
809C22×C3C2×#23712yes—
810C22×C3C2×#23712yes—
811C22×C3C2×#23712yes—
812C22×C3#100414yes—
813C22×C3#100414yes—
814C22×C3C24×D311yescharacteristic
815C22×C3C24×D311yescharacteristic
816C2×D3—22no—
817C2×D3—24no—
818C2×D3—62no—
819C2×D3—62no—
820C2×D3—64no—
821C2×D3—64no—
822C2×D3—82no—
823C2×D3—122no—
824C2×D3—124no—
825C2×D3—242no—
826C2×D3—242no—
827C2×D3—244no—
828C3×C4—62no—
829C3×C4—64no—
830C3×C4—64no—
831C3×C4—64no—
832Dic3—22no—
833Dic3—24no—
834Dic3—24no—
835Dic3—24no—
836Dic3—62no—
837Dic3—62no—
838Dic3—64no—
839Dic3—64no—
840Dic3—122no—
841Dic3—124no—
842C32#349011yescharacteristic, complemented, Sylow
843C23—22no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—22no—
848C23—24no—
849C23—24no—
850C23—32no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—416no—
856C23—62no—
857C23—92no—
858C23—122no—
859C23—182no—
860C23—362no—
861C23#380414yescomplemented
862C23C22×D3212yes—
863C23C22×D3211yescharacteristic
864C23C22×D3211yescharacteristic
865C23C22×D3211yescharacteristic
866C23C22×D3212yes—
867Q8—364no—
868D4—64no—
869D4—64no—
870D4—68no—
871D4—124no—
872D4—184no—
873D4—184no—
874D4—188no—
875D4—364no—
876D4—364no—
877C2×C4—32no—
878C2×C4—34no—
879C2×C4—34no—
880C2×C4—34no—
881C2×C4—62no—
882C2×C4—68no—
883C2×C4—92no—
884C2×C4—94no—
885C2×C4—122no—
886C2×C4—124no—
887C2×C4—122no—
888C2×C4—122no—
889C2×C4—182no—
890C2×C4—364no—
891C2×C4—364no—
892C2×C4—362no—
893C2×C3—24no—
894C2×C3—22no—
895C2×C3—22no—
896C2×C3—22no—
897C2×C3—24no—
898C2×C3—22no—
899C2×C3—22no—
900C2×C3—24no—
901C2×C3—22no—
902C2×C3—21no—
903C2×C3—22no—
904C2×C3—42no—
905C2×C3—44no—
906C2×C3—42no—
907C2×C3—44no—
908C2×C3—42no—
909C2×C3—42no—
910C2×C3—122no—
911C2×C3C22×#23511yescharacteristic
912C2×C3C22×#23711yescharacteristic
913C2×C3C2×#100412yes—
914C2×C3C2×#100412yes—
915D3—42no—
916D3—122no—
917D3—122no—
918D3—242no—
919C22—28no—
920C22—22no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—44no—
929C22—48no—
930C22—48no—
931C22—44no—
932C22—62no—
933C22—64no—
934C22—182no—
935C22—184no—
936C22—242no—
937C22—722no—
938C22C2×#380412yes—
939C22C2×#380412yes—
940C22C2×#380412yes—
941C22#6433014yes—
942C22C23×D3211yescharacteristic
943C4—62no—
944C4—64no—
945C4—64no—
946C4—64no—
947C4—182no—
948C4—184no—
949C3—21no—
950C3#8569711yescharacteristic, complemented
951C3#8591311yescharacteristic, complemented
952C2—22no—
953C2—24no—
954C2—22no—
955C2—22no—
956C2—42no—
957C2—122no—
958C2—362no—
959C2C22×#380411yescharacteristic
960C2C2×#6433012yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC25×C32C22
hypercenterC25D32
hypocenterC32#3490
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C2×#64162C2semidirect
2. C2×C3×#953C2semidirect
3. C22×C3×#217C2semidirect
4. #10595521C2semidirect
5. #10595519C2semidirect
6. #10595510C2semidirect
7. #10595509C2semidirect
8. #10595507C2semidirect
9. #10595506C2semidirect
10. #10595500C2semidirect
11. #10595498C2semidirect
12. #10595493C2semidirect
13. #10595476C2semidirect
18. C22×#638C22semidirect
20. C22×C3×#67C22semidirect
21. C23×C3×Dic3C22semidirect
22. C2×#3804C22semidirect
24. #64162C22semidirect
25. #64162C22semidirect
27. C2×#3757C22semidirect
29. C3×#953C22semidirect
30. C3×#953C22semidirect
34. C2×C3×#217C22semidirect
35. C2×C3×#217C22semidirect
36. C2×C3×#217C22semidirect
37. C2×C3×#217C22semidirect
38. #63982C22semidirect
39. #63981C22semidirect
40. #63978C22semidirect
41. #63978C22semidirect
42. #63977C22semidirect
43. #63975C22semidirect
44. #63974C22semidirect
45. #67⋊Dic3C22semidirect
46. Dic3×#67C22semidirect
47. Dic3×#67C22semidirect
48. #63971C22semidirect
49. #63969C22semidirect
50. D3×#217C22semidirect
51. #63966C22semidirect
52. #63966C22semidirect
53. #63964C22semidirect
54. #63964C22semidirect
55. #63964C22semidirect
56. #63962C22semidirect
57. #63961C22semidirect
58. #63959C22semidirect
59. #63958C22semidirect
60. #63957C22semidirect
61. #63956C22semidirect
62. #63956C22semidirect
63. #63955C22semidirect
64. #63955C22semidirect
65. #63953C22semidirect
66. #63952C22semidirect
67. #63952C22semidirect
68. #63952C22semidirect
74. C2×#953D3semidirect
75. C22×#217D3semidirect
126. C2×#627C23semidirect
127. C2×#626C23semidirect
128. C2×#624C23semidirect
130. C2×D3×Dic3C23semidirect
145. #3724C23semidirect
146. #3724C23semidirect
147. Dic3⋊Dic3C23semidirect
148. Dic3⋊Dic3C23semidirect
149. Dic3⋊Dic3C23semidirect
150. Dic3⋊Dic3C23semidirect
151. #3722C23semidirect
152. #3722C23semidirect
153. (C2×D3)⋊Dic3C23semidirect
154. (C2×D3)⋊Dic3C23semidirect
155. Dic32C23semidirect
156. Dic32C23semidirect
171. C22×#67C2×D3semidirect
172. C23×Dic3C2×D3semidirect
196. #953C2×D3semidirect
197. #953C2×D3semidirect
208. C2×#217C2×D3semidirect
209. C2×#217C2×D3semidirect
210. C2×#217C2×D3semidirect
211. C2×#217C2×D3semidirect
284. C23×C32#41semidirect
605. C23×C3#235semidirect
606. C23×C3#237semidirect
842. C32#3490semidirect
861. C23#3804semidirect
950. C3#85697semidirect
951. C3#85913semidirect

Maximal subgroups

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

subgroupindex
C2×#641622
C2×C3×#9532
C22×C3×#2172
#105955212
#105955192
#105955102
#105955092
#105955072
#105955062
#105955002
#105954982
#105954932
#105954762
#859133
#856973