Finite Group Databasebeta

← #11904658

Subgroups — #11904658

Order 1152.

3481 conjugacy classes of subgroups.

The subgroup lattice has 1079 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64313C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3#10596077C211yesmaximal, characteristic, complemented
4C3×D3×#121C212yesmaximal, complemented
5#10595291C214yesmaximal, complemented
6#10595240C211yesmaximal, characteristic, complemented
7#10595231C212yesmaximal, complemented
8D4×#625C212yesmaximal, complemented
9#10595142C212yesmaximal, complemented
10#10595081C211yesmaximal, characteristic, complemented
11#10594892C212yesmaximal, complemented
12#10594634C211yesmaximal, characteristic, complemented
13#10594522C212yesmaximal, complemented
14#10594509C211yesmaximal, characteristic, complemented
15#10594278C214yesmaximal, complemented
16#10594190C212yesmaximal, complemented
17#10594183C212yesmaximal, complemented
18#85949—32nomaximal
19C2×#3830C2211yescharacteristic, complemented
20C22×C4×C3⋊D3C2211yescharacteristic, complemented
21C2×C3×D3×D4C2212yescomplemented
22C2×C3×D3×D4C2214yescomplemented
23C22×C3×C4×D3C2212yescomplemented
24C2×#3811C2212yescomplemented
25C2×D3×#67C2214yescomplemented
26C22×#627C2211yescharacteristic, complemented
27C22×#626C2212yescomplemented
28C22×#625C2211yescharacteristic, complemented
29C22×#625C2212yescomplemented
30C2×#3805C2212yescomplemented
31#64313—28no—
32C2×#3802C2211yescharacteristic, complemented
33C2×#3798—28no—
34C2×#3798C2211yescharacteristic
35C2×#3798C2211yescharacteristic, complemented
36C2×#3798C2211yescharacteristic, complemented
37C2×#3798C2211yescharacteristic, complemented
38C2×#3798C2212yescomplemented
39C2×#3798C2212yescomplemented
40C2×#3795C2212yescomplemented
41C32×#121C2211yescharacteristic, complemented
42#64147C2211yescharacteristic, complemented
43#64146C2212yescomplemented
44D4×C3⋊Dic3C2212yescomplemented
45#64133C2211yescharacteristic, complemented
46#64106C2211yescharacteristic, complemented
47#64101C2211yescharacteristic, complemented
48#64092C2212yescomplemented
49#64090C2212yescomplemented
50C3×#939C2214yescomplemented
51C3×#938C2212yescomplemented
52C3×#930C2212yescomplemented
53C3×#895C2212yescomplemented
54C3×D3×C4⋊C4C2212yescomplemented
55C3×#884C2214yescomplemented
56C3×D3×C22⋊C4C2214yescomplemented
57#63982C2212yescomplemented
58#63980C2212yescomplemented
59#63980C2212yescomplemented
60#63979C2214yescomplemented
61#63977C2214yescomplemented
62#63976C2214yescomplemented
63#63976C2214yescomplemented
64Dic3×#67C2214yescomplemented
65#63959C2214yescomplemented
66#63958C2214yescomplemented
67#63922C2214yescomplemented
68#63921C2212yescomplemented
69#63916C2212yescomplemented
70#63915C2212yescomplemented
71#63914C2212yescomplemented
72#63912C2212yescomplemented
73#63908C2212yescomplemented
74#63908C2214yescomplemented
75#63906C2214yescomplemented
76#63905C2214yescomplemented
77#63904C2214yescomplemented
78C4×#625C2212yescomplemented
79#63900C2211yescharacteristic, complemented
80#63893C2214yescomplemented
81#63886C2214yescomplemented
82#63879C2214yescomplemented
83#63857C2212yescomplemented
84#63841C2212yescomplemented
85#63838C2212yescomplemented
86C2×#1004—32no—
87C22×#235—32no—
88C2×C3×#121—32no—
89#5805—32no—
90D4×#67—34no—
91D4×#67—34no—
92#5791—32no—
93#5612—34no—
94#5609—34no—
95#5608—32no—
96#5608—32no—
97#5607—32no—
98#5607—32no—
99#5606—32no—
100#5606—32no—
101#5606—61no—
102D3×#121—32no—
103D3×#121D312yescomplemented
104#5599—34no—
105#5598—34no—
106#5510—32no—
107#5504—32no—
108#5490—34no—
109#5490—34no—
110C23×C3⋊D3C2311yescharacteristic
111C23×C3×D3C2312yes—
112C23×C3×D3C2314yes—
113C22×D32C2312yes—
114C2×C32×D4C2311yescharacteristic
115C2×C32×D4C2312yes—
116C22×C32×C4C2311yescharacteristic
117C2×#638C2312yes—
118C2×#638C2312yes—
119C22×C3⋊Dic3C2312yes—
120C22×C3⋊Dic3C2311yescharacteristic
121#3830—24no—
122C2×C4×C3⋊D3—24no—
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×C4×C3⋊D3C2311yescharacteristic
126C2×C4×C3⋊D3C2311yescharacteristic
127C2×#634C2311yescharacteristic
128C2×C3×#67C2314yes—
129C2×C3×#67C2314yes—
130C2×C3×#67C2314yes—
131C22×C3×Dic3C2312yes—
132C3×D3×D4—28no—
133C3×D3×D4—48no—
134C2×C3×D12C2312yes—
135C2×C3×D12C2314yes—
136C2×C3×C4×D3—28no—
137C2×C3×C4×D3C2312yes—
138C2×C3×C4×D3C2312yes—
139C2×C3×C4×D3C2312yes—
140C2×C3×C4×D3C2314yes—
141C2×C3×C4×D3C2312yes—
142#3811—44no—
143D3×#67—216no—
144C2×#627—24no—
145C2×#627C2312yes—
146C2×#627C2311yescharacteristic
147C2×#627C2311yescharacteristic
148C2×#626—28no—
149C2×#626C2312yes—
150C2×#626C2312yes—
151C2×#626C2312yes—
152C2×#626C2314yes—
153C2×#626C2312yes—
154C2×#625—24no—
155C2×#625—28no—
156C2×#625C2314yes—
157C2×#625C2312yes—
158C2×#625C2311yescharacteristic
159C2×#625C2312yes—
160C2×#625C2314yes—
161C2×#625C2311yescharacteristic
162C2×#624C2312yes—
163#3805—28no—
164C2×D3×Dic3C2314yes—
165#3802—24no—
166#3798—24no—
167#3798—28no—
168#3798—24no—
169#3798—28no—
170#3798—24no—
171#3798D418yescomplemented
172#3795—28no—
173C32×C4⋊C4C2311yescharacteristic
174C32×C22⋊C4C2312yes—
175#3757C2312yes—
176#3757C2312yes—
177#3752C2312yes—
178#3752C2312yes—
179C4⋊(C3⋊Dic3)C2312yes—
180C4⋊(C3⋊Dic3)C2311yescharacteristic
181#3750C2312yes—
182C4×C3⋊Dic3C2312yes—
183C3×#217C2314yes—
184C3×(C2×D3)⋊C4C2314yes—
185C3×(C2×D3)⋊C4C2314yes—
186C3×C4⋊Dic3C2312yes—
187C3×Dic3⋊C4C2314yes—
188#3724C2312yes—
189Dic3⋊Dic3C2314yes—
190(C2×D3)⋊Dic3C2314yes—
191(C2×D3)⋊Dic3C2314yes—
192(C2×D3)⋊Dic3C2314yes—
193(C2×D3)⋊Dic3C2314yes—
194Dic32C2314yes—
195#3488—91noSylow
196C22×C3×D4—32no—
197C22×C3×D4—34no—
198C23×C3×C4—32no—
199C22×#67—32no—
200C22×#67—34no—
201C22×#67—34no—
202C22×#67—32no—
203#1004—616no—
204C2×#237—32no—
205C2×#237—34no—
206C2×#237—32no—
207C2×#237—61no—
208C2×D3×D4—34no—
209C2×D3×D4—34no—
210C2×D3×D4—32no—
211C2×D3×D4C2×D312yescomplemented
212C2×D3×D4C2×D314yescomplemented
213C2×#235—32no—
214C2×#235—32no—
215C2×#235—32no—
216C2×#235—32no—
217C2×#235—32no—
218C2×#235—32no—
219C2×#235—32no—
220C2×#235—32no—
221C2×#235—32no—
222C2×#235—616no—
223C22×D12—32no—
224C22×C4×D3—32no—
225C22×C4×D3—61no—
226C22×C4×D3C2×D312yescomplemented
227C22×Dic6—32no—
228C3×#121—21no—
229C3×#121—32no—
230C3×#121—34no—
231C3×#121—32no—
232C3×#121—32no—
233C3×#121—34no—
234C3×#121C2×D312yescomplemented
235C2×C3×C4⋊C4—32no—
236C2×C3×C22⋊C4—34no—
237#953—34no—
238#953—34no—
239#953—34no—
240#940—34no—
241#940—34no—
242#940—34no—
243#939—34no—
244#939—34no—
245#939—34no—
246#939C2×D314yescomplemented
247#938—32no—
248#938—34no—
249#938—32no—
250#938—34no—
251#938—32no—
252#938—61no—
253#938C2×D312yescomplemented
254#937—34no—
255#937—34no—
256#937—34no—
257#937—34no—
258#937—62no—
259#936—34no—
260D4×Dic3—34no—
261D4×Dic3—34no—
262D4×Dic3—62no—
263#930—34no—
264#930—32no—
265#930—34no—
266#930C2×D312yescomplemented
267#929—34no—
268C4×#67—34no—
269C4×#67—34no—
270C4×#67—34no—
271C4×#67—34no—
272#926—32no—
273#924—32no—
274#924—32no—
275#924—61no—
276#897—32no—
277#897—32no—
278#897—34no—
279#897—61no—
280#895—34no—
281#895—32no—
282#895C2×D312yescomplemented
283#893—34no—
284#892—32no—
285#892—32no—
286#892—61no—
287D3×C4⋊C4—32no—
288D3×C4⋊C4C2×D312yescomplemented
289#887—34no—
290#885—34no—
291#885—34no—
292#884—34no—
293#884—34no—
294#884—34no—
295#884C2×D314yescomplemented
296#883—34no—
297#883—34no—
298#883—62no—
299#882—34no—
300#882—34no—
301#67⋊C4—34no—
302#67⋊C4—34no—
303#67⋊C4—62no—
304D3×C22⋊C4—34no—
305D3×C22⋊C4C2×D314yescomplemented
306#878—34no—
307#878—34no—
308C23×C32C2412yes—
309C23×C32C2411yescharacteristic
310C22×C3⋊D3—22no—
311C22×C3⋊D3—22no—
312C22×C3⋊D3—41no—
313C22×C3⋊D3C2411yescharacteristic
314C22×C3⋊D3C2411yescharacteristic
315C22×C3×D3—24no—
316C22×C3×D3—24no—
317C22×C3×D3—28no—
318C22×C3×D3—42no—
319C22×C3×D3—44no—
320C22×C3×D3—44no—
321C22×C3×D3C2414yes—
322C22×C3×D3C2412yes—
323C22×C3×D3C2412yes—
324C2×D32—24no—
325C2×D32—42no—
326C2×D32—42no—
327C32×D4—24no—
328C32×D4—22no—
329C2×C32×C4—22no—
330C2×C32×C4C2412yes—
331C2×C32×C4C2411yescharacteristic
332C2×C32×C4C2411yescharacteristic
333#638—24no—
334#638—42no—
335C2×C3⋊Dic3—24no—
336C2×C3⋊Dic3—22no—
337C2×C3⋊Dic3C2412yes—
338C2×C3⋊Dic3C2411yescharacteristic
339C2×C3⋊Dic3C2412yes—
340C2×C3⋊Dic3C2411yescharacteristic
341C4×C3⋊D3—22no—
342C4×C3⋊D3—22no—
343C4×C3⋊D3—22no—
344C4×C3⋊D3C2×D414yescomplemented
345#634—22no—
346C3×#67—28no—
347C3×#67—28no—
348C3×#67—44no—
349C2×C3×Dic3—24no—
350C2×C3×Dic3C2414yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C3×D12—24no—
354C3×D12—44no—
355C3×C4×D3—24no—
356C3×C4×D3—24no—
357C3×C4×D3—24no—
358C3×C4×D3—44no—
359C3×C4×D3C2×D418yescomplemented
360#627—22no—
361#627—24no—
362#627C2×D414yescomplemented
363#626—24no—
364#626—24no—
365#626—24no—
366#626—44no—
367#626C2×D418yescomplemented
368#625—28no—
369#625—24no—
370#625—22no—
371#625—24no—
372#625—44no—
373#625C2×D414yescomplemented
374#624—42no—
375D3×Dic3—28no—
376C2×H(5,𝔽2)—91no—
377C22×#41—91no—
378#550—92no—
379#548—92no—
380#546—92no—
381#546—94no—
382D42—94no—
383D42—92no—
384#537—92no—
385#537—91no—
386#535—91no—
387#535—92no—
388#525—92no—
389#525—91no—
390C2×#121—32no—
391C2×#121—91no—
392#520—91no—
393C24×C3—32no—
394C24×C3—34no—
395C23×D3—32no—
396C23×D3—34no—
397C23×D3—61no—
398C23×D3C22×D312yes—
399C23×D3C22×D314yes—
400C2×C3×D4—22no—
401C2×C3×D4—21no—
402C2×C3×D4—34no—
403C2×C3×D4—34no—
404C2×C3×D4—34no—
405C2×C3×D4—32no—
406C2×C3×D4—34no—
407C2×C3×D4—68no—
408C2×C3×D4—128no—
409C2×C3×D4C22×D314yes—
410C2×C3×D4C22×D312yes—
411C22×C3×C4—21no—
412C22×C3×C4—32no—
413C22×C3×C4—32no—
414C22×C3×C4—32no—
415C22×C3×C4—32no—
416C22×C3×C4—32no—
417C22×C3×C4—34no—
418C22×C3×C4—68no—
419C22×C3×C4C22×D312yes—
420C2×#67—32no—
421C2×#67—34no—
422C2×#67—34no—
423C2×#67—34no—
424C2×#67—34no—
425C2×#67—32no—
426C2×#67—32no—
427C2×#67—32no—
428C2×#67—34no—
429C2×#67—34no—
430C2×#67—34no—
431C2×#67—32no—
432C2×#67—32no—
433C2×#67—32no—
434C2×#67—32no—
435C2×#67—34no—
436C2×#67—62no—
437C2×#67—62no—
438C2×#67—68no—
439C2×#67—616no—
440C2×#67—68no—
441C2×#67—616no—
442C2×#67C22×D314yes—
443C2×#67C22×D314yes—
444C2×#67C22×D314yes—
445C22×Dic3—34no—
446C22×Dic3—32no—
447C22×Dic3—34no—
448C22×Dic3—62no—
449C22×Dic3—61no—
450C22×Dic3C22×D312yes—
451#237—616no—
452#237—68no—
453#237—68no—
454#237—124no—
455D3×D4—28no—
456D3×D4—48no—
457D3×D4—68no—
458D3×D4—616no—
459D3×D4—128no—
460#235—316no—
461#235—68no—
462#235—68no—
463#235—68no—
464#235—68no—
465#235—68no—
466#235—68no—
467#235—68no—
468#235—68no—
469C2×D12—32no—
470C2×D12—32no—
471C2×D12—32no—
472C2×D12—32no—
473C2×D12—34no—
474C2×D12—68no—
475C2×D12C22×D312yes—
476C2×D12C22×D314yes—
477C2×C4×D3—28no—
478C2×C4×D3—32no—
479C2×C4×D3—34no—
480C2×C4×D3—32no—
481C2×C4×D3—32no—
482C2×C4×D3—32no—
483C2×C4×D3—34no—
484C2×C4×D3—61no—
485C2×C4×D3—61no—
486C2×C4×D3—61no—
487C2×C4×D3—61no—
488C2×C4×D3—68no—
489C2×C4×D3—124no—
490C2×C4×D3C22×D312yes—
491C2×C4×D3C22×D312yes—
492C2×C4×D3C22×D312yes—
493C2×C4×D3C22×D314yes—
494C2×C4×D3C22×D312yes—
495C2×Dic6—32no—
496C2×Dic6—32no—
497C2×Dic6—32no—
498C2×Dic6—32no—
499C2×Dic6—32no—
500C2×Dic6—61no—
501C2×Dic6—68no—
502C3×C4⋊C4—21no—
503C3×C4⋊C4—34no—
504C3×C4⋊C4—32no—
505C3×C4⋊C4C22×D312yes—
506C3×C22⋊C4—22no—
507C3×C22⋊C4—34no—
508C3×C22⋊C4—34no—
509C3×C22⋊C4—34no—
510C3×C22⋊C4C22×D314yes—
511#217—34no—
512#217—34no—
513#217—34no—
514#217—34no—
515#217—34no—
516#217—34no—
517#217—62no—
518#217—62no—
519#217C22×D314yes—
520(C2×D3)⋊C4—34no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—34no—
524(C2×D3)⋊C4—34no—
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4—62no—
527(C2×D3)⋊C4—62no—
528(C2×D3)⋊C4C22×D314yes—
529(C2×D3)⋊C4C22×D314yes—
530C4⋊Dic3—34no—
531C4⋊Dic3—32no—
532C4⋊Dic3—34no—
533C4⋊Dic3—62no—
534C4⋊Dic3—61no—
535C4⋊Dic3C22×D312yes—
536Dic3⋊C4—34no—
537Dic3⋊C4—34no—
538Dic3⋊C4—34no—
539Dic3⋊C4—62no—
540Dic3⋊C4C22×D314yes—
541C4×Dic3—34no—
542C4×Dic3—34no—
543C4×Dic3—34no—
544C4×Dic3—62no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—22no—
548C22×C32—22no—
549C22×C32—22no—
550C22×C32H(5,𝔽2)12yescomplemented
551C22×C32C2511yescharacteristic
552C2×C3⋊D3—21no—
553C2×C3⋊D3—21no—
554C2×C3⋊D3—21no—
555C2×C3⋊D3—21no—
556C2×C3⋊D3—21no—
557C2×C3⋊D3—44no—
558C2×C3⋊D3C22×D412yes—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—24no—
562C2×C3×D3—22no—
563C2×C3×D3—24no—
564C2×C3×D3—22no—
565C2×C3×D3—22no—
566C2×C3×D3—24no—
567C2×C3×D3—48no—
568C2×C3×D3—88no—
569C2×C3×D3C22×D414yes—
570D32—84no—
571C32×C4—21no—
572C32×C4—22no—
573C32×C4C22×D412yes—
574C3⋊Dic3—22no—
575C3⋊Dic3—21no—
576C3⋊Dic3—22no—
577C3⋊Dic3C22×D412yes—
578C3×Dic3—22no—
579C3×Dic3—24no—
580C3×Dic3C22×D414yes—
581H(5,𝔽2)—188no—
582C2×#41—91no—
583C2×#41—92no—
584C2×#41—91no—
585C2×#41—91no—
586C2×#41—92no—
587C2×#41—91no—
588C2×#41—92no—
589C2×#41—92no—
590C2×#41—91no—
591C2×#41—188no—
592C22×Q8—91no—
593C22×D4—32no—
594C22×D4—34no—
595C22×D4—92no—
596C22×D4—91no—
597C22×D4—92no—
598C22×D4—94no—
599C22×D4—91no—
600C22×D4—92no—
601C23×C4—32no—
602C23×C4—91no—
603#127—94no—
604#127—92no—
605#124—92no—
606#124—94no—
607#123—94no—
608#123—92no—
609C22⋊Q8—92no—
610C22⋊Q8—94no—
611C22⋊Q8—92no—
612C22⋊Q8—91no—
613C22⋊Q8—91no—
614#121—32no—
615#121—34no—
616#121—32no—
617#121—32no—
618#121—34no—
619#121—92no—
620#121—94no—
621#121—94no—
622#121—92no—
623#121—94no—
624#121—92no—
625#121—94no—
626#121—92no—
627#121—92no—
628#121—91no—
629#121D3211yescharacteristic, complemented
630#120—94no—
631#120—94no—
632#120—94no—
633#120—94no—
634#120—92no—
635C4×Q8—92no—
636C4×D4—94no—
637C4×D4—94no—
638C4×D4—92no—
639C4×D4—94no—
640C4×D4—92no—
641C4×D4—92no—
642#117—92no—
643#117—91no—
644C2×C4⋊C4—32no—
645C2×C4⋊C4—91no—
646C2×C22⋊C4—34no—
647C2×C22⋊C4—92no—
648C23×C3—21no—
649C23×C3—22no—
650C23×C3—32no—
651C23×C3—34no—
652C23×C3—32no—
653C23×C3—64no—
654C23×C3—68no—
655C23×C3—64no—
656C23×C3—122no—
657C23×C3—124no—
658C23×C3—124no—
659C23×C3C23×D314yes—
660C23×C3C23×D312yes—
661C22×D3—24no—
662C22×D3—24no—
663C22×D3—28no—
664C22×D3—32no—
665C22×D3—32no—
666C22×D3—42no—
667C22×D3—44no—
668C22×D3—44no—
669C22×D3—61no—
670C22×D3—61no—
671C22×D3—68no—
672C22×D3—64no—
673C22×D3—64no—
674C22×D3—122no—
675C22×D3—122no—
676C22×D3—124no—
677C22×D3—124no—
678C22×D3—122no—
679C22×D3—122no—
680C22×D3C23×D314yes—
681C22×D3C23×D312yes—
682C22×D3C23×D312yes—
683C3×D4—28no—
684C3×D4—24no—
685C3×D4—42no—
686C3×D4—44no—
687C3×D4—68no—
688C3×D4—68no—
689C3×D4—64no—
690C3×D4—124no—
691C3×D4—124no—
692C2×C3×C4—24no—
693C2×C3×C4—21no—
694C2×C3×C4—22no—
695C2×C3×C4—21no—
696C2×C3×C4—32no—
697C2×C3×C4—38no—
698C2×C3×C4—34no—
699C2×C3×C4—32no—
700C2×C3×C4—42no—
701C2×C3×C4—64no—
702C2×C3×C4—64no—
703C2×C3×C4—64no—
704C2×C3×C4—64no—
705C2×C3×C4—124no—
706C2×C3×C4C23×D314yes—
707C2×C3×C4C23×D312yes—
708C2×C3×C4C23×D312yes—
709#67—28no—
710#67—28no—
711#67—38no—
712#67—38no—
713#67—44no—
714#67—64no—
715#67—64no—
716#67—64no—
717#67—68no—
718#67—64no—
719#67—68no—
720#67—68no—
721#67—64no—
722#67—68no—
723#67—64no—
724#67—124no—
725#67—124no—
726#67—124no—
727#67—124no—
728#67—124no—
729#67—124no—
730C2×Dic3—24no—
731C2×Dic3—32no—
732C2×Dic3—34no—
733C2×Dic3—34no—
734C2×Dic3—32no—
735C2×Dic3—61no—
736C2×Dic3—62no—
737C2×Dic3—62no—
738C2×Dic3—61no—
739C2×Dic3—64no—
740C2×Dic3—68no—
741C2×Dic3—68no—
742C2×Dic3—122no—
743C2×Dic3—124no—
744C2×Dic3C23×D314yes—
745C2×Dic3C23×D312yes—
746C2×Dic3C23×D312yes—
747D12—24no—
748D12—38no—
749D12—44no—
750D12—64no—
751D12—64no—
752D12—64no—
753D12—124no—
754C4×D3—24no—
755C4×D3—24no—
756C4×D3—24no—
757C4×D3—38no—
758C4×D3—44no—
759C4×D3—64no—
760C4×D3—64no—
761C4×D3—64no—
762C4×D3—68no—
763C4×D3—64no—
764C4×D3—122no—
765C4×D3—122no—
766C4×D3—122no—
767C4×D3—124no—
768C4×D3D3×D418yescomplemented
769Dic6—38no—
770Dic6—64no—
771Dic6—64no—
772Dic6—64no—
773Dic6—64no—
774Dic6—122no—
775C2×C32—22no—
776C2×C32—42no—
777C2×C32C23×D411yescharacteristic
778C2×C32C2×H(5,𝔽2)11yescharacteristic
779C2×C32#58511yescharacteristic
780C3⋊D3—22no—
781C3⋊D3—41no—
782C3×D3—24no—
783C3×D3—44no—
784C3×D3—42no—
785C24—32no—
786C24—34no—
787C24—92no—
788C24—91no—
789#41—98no—
790#41—188no—
791#41—188no—
792#41—184no—
793#41—188no—
794#41—184no—
795#41—184no—
796#41—184no—
797#41—188no—
798C2×Q8—91no—
799C2×Q8—92no—
800C2×Q8—91no—
801C2×Q8—91no—
802C2×Q8—184no—
803C2×D4—34no—
804C2×D4—34no—
805C2×D4—34no—
806C2×D4—32no—
807C2×D4—34no—
808C2×D4—68no—
809C2×D4—92no—
810C2×D4—92no—
811C2×D4—92no—
812C2×D4—92no—
813C2×D4—94no—
814C2×D4—91no—
815C2×D4—92no—
816C2×D4—94no—
817C2×D4—92no—
818C2×D4—91no—
819C2×D4—92no—
820C2×D4—94no—
821C2×D4—92no—
822C2×D4—128no—
823C2×D4—188no—
824C2×D4—184no—
825C2×D4—1816no—
826C2×D4—184no—
827C2×D4—188no—
828C2×D4—364no—
829C2×D4C2×D3212yes—
830C2×D4C2×D3211yescharacteristic
831C22×C4—32no—
832C22×C4—32no—
833C22×C4—32no—
834C22×C4—32no—
835C22×C4—32no—
836C22×C4—34no—
837C22×C4—68no—
838C22×C4—92no—
839C22×C4—94no—
840C22×C4—91no—
841C22×C4—91no—
842C22×C4—92no—
843C22×C4—91no—
844C22×C4—91no—
845C22×C4—91no—
846C22×C4—184no—
847C22×C4C2×D3211yescharacteristic
848C4⋊C4—32no—
849C4⋊C4—34no—
850C4⋊C4—92no—
851C4⋊C4—94no—
852C4⋊C4—91no—
853C4⋊C4—92no—
854C4⋊C4—92no—
855C4⋊C4C2×D3211yescharacteristic
856C22⋊C4—34no—
857C22⋊C4—34no—
858C22⋊C4—34no—
859C22⋊C4—94no—
860C22⋊C4—94no—
861C22⋊C4—94no—
862C22⋊C4—94no—
863C22⋊C4—92no—
864C22⋊C4—92no—
865C22⋊C4—92no—
866C22⋊C4—92no—
867C22⋊C4C2×D3212yes—
868C42—94no—
869C42—92no—
870C22×C3—22no—
871C22×C3—22no—
872C22×C3—24no—
873C22×C3—24no—
874C22×C3—24no—
875C22×C3—22no—
876C22×C3—21no—
877C22×C3—34no—
878C22×C3—41no—
879C22×C3—41no—
880C22×C3—42no—
881C22×C3—42no—
882C22×C3—42no—
883C22×C3—62no—
884C22×C3—62no—
885C22×C3—64no—
886C22×C3—62no—
887C22×C3—64no—
888C22×C3—62no—
889C22×C3—62no—
890C22×C3—64no—
891C22×C3—128no—
892C22×C3—248no—
893C22×C3#100414yescomplemented
894C22×C3C24×D312yes—
895C2×D3—22no—
896C2×D3—22no—
897C2×D3—22no—
898C2×D3—24no—
899C2×D3—22no—
900C2×D3—24no—
901C2×D3—22no—
902C2×D3—24no—
903C2×D3—34no—
904C2×D3—48no—
905C2×D3—62no—
906C2×D3—62no—
907C2×D3—62no—
908C2×D3—62no—
909C2×D3—62no—
910C2×D3—62no—
911C2×D3—62no—
912C2×D3—88no—
913C2×D3—121no—
914C2×D3—121no—
915C2×D3—121no—
916C2×D3—121no—
917C2×D3—128no—
918C2×D3—128no—
919C2×D3—248no—
920C2×D3C2×D3×D414yes—
921C3×C4—22no—
922C3×C4—24no—
923C3×C4—22no—
924C3×C4—34no—
925C3×C4—41no—
926C3×C4—42no—
927C3×C4—62no—
928C3×C4—64no—
929C3×C4C2×D3×D414yes—
930Dic3—22no—
931Dic3—24no—
932Dic3—34no—
933Dic3—62no—
934Dic3—62no—
935Dic3—64no—
936Dic3—64no—
937Dic3—122no—
938Dic3—121no—
939Dic3—122no—
940Dic3C2×D3×D414yes—
941C32#348811yescharacteristic, complemented, Sylow
942C23—32no—
943C23—34no—
944C23—32no—
945C23—64no—
946C23—68no—
947C23—64no—
948C23—91no—
949C23—91no—
950C23—122no—
951C23—124no—
952C23—124no—
953C23—182no—
954C23—184no—
955C23—182no—
956C23—361no—
957C23—362no—
958C23—362no—
959C23C22×D3212yes—
960C23C22×D3211yescharacteristic
961Q8—94no—
962Q8—184no—
963Q8—182no—
964Q8—182no—
965D4—24no—
966D4—22no—
967D4—68no—
968D4—68no—
969D4—64no—
970D4—98no—
971D4—94no—
972D4—124no—
973D4—124no—
974D4—184no—
975D4—184no—
976D4—184no—
977D4—184no—
978D4—182no—
979D4—184no—
980D4—188no—
981D4—184no—
982D4—364no—
983D4—362no—
984D4—364no—
985C2×C4—22no—
986C2×C4—32no—
987C2×C4—38no—
988C2×C4—34no—
989C2×C4—32no—
990C2×C4—64no—
991C2×C4—64no—
992C2×C4—64no—
993C2×C4—64no—
994C2×C4—91no—
995C2×C4—94no—
996C2×C4—92no—
997C2×C4—91no—
998C2×C4—92no—
999C2×C4—124no—
1000C2×C4—182no—
1001C2×C4—182no—
1002C2×C4—188no—
1003C2×C4—182no—
1004C2×C4—184no—
1005C2×C4—182no—
1006C2×C4—362no—
1007C2×C4C22×D3212yes—
1008C2×C4C22×D3211yescharacteristic
1009C2×C4C22×D3211yescharacteristic
1010C2×C3—24no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—42no—
1015C2×C3—44no—
1016C2×C3—64no—
1017C2×C3—82no—
1018C2×C3—124no—
1019C2×C3—122no—
1020C2×C3C22×D3×D412yes—
1021C2×C3C2×#100412yes—
1022C2×C3#596412yes—
1023D3—24no—
1024D3—42no—
1025D3—44no—
1026D3—64no—
1027D3—122no—
1028D3—122no—
1029D3—122no—
1030C22—21no—
1031C22—21no—
1032C22—22no—
1033C22—22no—
1034C22—22no—
1035C22—34no—
1036C22—62no—
1037C22—62no—
1038C22—62no—
1039C22—64no—
1040C22—64no—
1041C22—62no—
1042C22—62no—
1043C22—64no—
1044C22—92no—
1045C22—128no—
1046C22—181no—
1047C22—181no—
1048C22—181no—
1049C22—181no—
1050C22—181no—
1051C22—248no—
1052C22—364no—
1053C22—724no—
1054C22#6431312yescomplemented
1055C22C23×D3211yescharacteristic
1056C4—21no—
1057C4—22no—
1058C4—34no—
1059C4—62no—
1060C4—64no—
1061C4—92no—
1062C4—182no—
1063C4—181no—
1064C4—182no—
1065C4D32×D412yes—
1066C3—21no—
1067C3#8594912yescomplemented
1068C2—22no—
1069C2—42no—
1070C2—64no—
1071C2—122no—
1072C2—124no—
1073C2—182no—
1074C2—361no—
1075C2C2×D32×D411yescharacteristic
1076C2C2×#6431311yescharacteristic
1077C2#1059669511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#121C22
hypercenter#121D32
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#64313C2semidirect
2. C22×#3798C2semidirect
3. #10596077C2semidirect
4. C3×D3×#121C2semidirect
5. #10595291C2semidirect
6. #10595240C2semidirect
7. #10595231C2semidirect
8. D4×#625C2semidirect
9. #10595142C2semidirect
10. #10595081C2semidirect
11. #10594892C2semidirect
12. #10594634C2semidirect
13. #10594522C2semidirect
14. #10594509C2semidirect
15. #10594278C2semidirect
16. #10594190C2semidirect
17. #10594183C2semidirect
19. C2×#3830C22semidirect
20. C22×C4×C3⋊D3C22semidirect
21. C2×C3×D3×D4C22semidirect
22. C2×C3×D3×D4C22semidirect
23. C22×C3×C4×D3C22semidirect
24. C2×#3811C22semidirect
25. C2×D3×#67C22semidirect
26. C22×#627C22semidirect
27. C22×#626C22semidirect
28. C22×#625C22semidirect
29. C22×#625C22semidirect
30. C2×#3805C22semidirect
32. C2×#3802C22semidirect
35. C2×#3798C22semidirect
36. C2×#3798C22semidirect
37. C2×#3798C22semidirect
38. C2×#3798C22semidirect
39. C2×#3798C22semidirect
40. C2×#3795C22semidirect
41. C32×#121C22semidirect
42. #64147C22semidirect
43. #64146C22semidirect
44. D4×C3⋊Dic3C22semidirect
45. #64133C22semidirect
46. #64106C22semidirect
47. #64101C22semidirect
48. #64092C22semidirect
49. #64090C22semidirect
50. C3×#939C22semidirect
51. C3×#938C22semidirect
52. C3×#930C22semidirect
53. C3×#895C22semidirect
54. C3×D3×C4⋊C4C22semidirect
55. C3×#884C22semidirect
56. C3×D3×C22⋊C4C22semidirect
57. #63982C22semidirect
58. #63980C22semidirect
59. #63980C22semidirect
60. #63979C22semidirect
61. #63977C22semidirect
62. #63976C22semidirect
63. #63976C22semidirect
64. Dic3×#67C22semidirect
65. #63959C22semidirect
66. #63958C22semidirect
67. #63922C22semidirect
68. #63921C22semidirect
69. #63916C22semidirect
70. #63915C22semidirect
71. #63914C22semidirect
72. #63912C22semidirect
73. #63908C22semidirect
74. #63908C22semidirect
75. #63906C22semidirect
76. #63905C22semidirect
77. #63904C22semidirect
78. C4×#625C22semidirect
79. #63900C22semidirect
80. #63893C22semidirect
81. #63886C22semidirect
82. #63879C22semidirect
83. #63857C22semidirect
84. #63841C22semidirect
85. #63838C22semidirect
103. D3×#121D3semidirect
171. #3798D4semidirect
211. C2×D3×D4C2×D3semidirect
212. C2×D3×D4C2×D3semidirect
226. C22×C4×D3C2×D3semidirect
234. C3×#121C2×D3semidirect
246. #939C2×D3semidirect
253. #938C2×D3semidirect
266. #930C2×D3semidirect
282. #895C2×D3semidirect
288. D3×C4⋊C4C2×D3semidirect
295. #884C2×D3semidirect
305. D3×C22⋊C4C2×D3semidirect
344. C4×C3⋊D3C2×D4semidirect
359. C3×C4×D3C2×D4semidirect
362. #627C2×D4semidirect
367. #626C2×D4semidirect
373. #625C2×D4semidirect
550. C22×C32H(5,𝔽2)semidirect
629. #121D32semidirect
768. C4×D3D3×D4semidirect
893. C22×C3#1004semidirect
941. C32#3488semidirect
1054. C22#64313semidirect
1067. C3#85949semidirect

Maximal subgroups

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

subgroupindex
C2×#643132
C22×#37982
#105960772
C3×D3×#1212
#105952912
#105952402
#105952312
D4×#6252
#105951422
#105950812
#105948922
#105946342
#105945222
#105945092
#105942782
#105941902
#105941832
#859493