Finite Group Databasebeta

← #11905953

Subgroups — #11905953

Order 1152.

3651 conjugacy classes of subgroups.

The subgroup lattice has 1031 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64313C212yesmaximal, complemented
2#10596067C211yesmaximal, characteristic, complemented
3C3×#5609C212yesmaximal, complemented
4#10595287C214yesmaximal, complemented
5D3×#940C212yesmaximal, complemented
6#10595239C212yesmaximal, complemented
7D4×#625C211yesmaximal, characteristic, complemented
8#10595144C211yesmaximal, characteristic, complemented
9D12×#67C212yesmaximal, complemented
10C2×#63914C211yesmaximal, characteristic, complemented
11C4×#3805C211yesmaximal, characteristic, complemented
12#10594618C211yesmaximal, characteristic, complemented
13#10594520C211yesmaximal, characteristic, complemented
14#10594367C212yesmaximal, complemented
15#10594271C212yesmaximal, complemented
16#10594269C214yesmaximal, complemented
17#10594190C212yesmaximal, complemented
18#86608—32nomaximal
19C2×#3830C2212yescomplemented
20C2×C3×D3×D4C2214yescomplemented
21C2×C3×D3×D4C2212yescomplemented
22C22×C3×D12C2212yescomplemented
23C2×D3×#67C2214yescomplemented
24C2×D3×#67C2214yescomplemented
25C2×D3×#67C2214yescomplemented
26C22×#625C2212yescomplemented
27C22×#625C2212yescomplemented
28C22×#625C2212yescomplemented
29C2×#3805C2211yescharacteristic
30C2×#3805C2212yescomplemented
31#64313—216no—
32C2×#3802C2212yescomplemented
33C2×D3×D12C2212yescomplemented
34C2×#3798C2212yescomplemented
35C2×#3795C2214yescomplemented
36C32×#121C2211yescharacteristic, complemented
37#64149C2211yescharacteristic, complemented
38#64148C2212yescomplemented
39D4×C3⋊Dic3C2211yescharacteristic, complemented
40#64139C2211yescharacteristic, complemented
41C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
42#64102C2211yescharacteristic, complemented
43#64097C2211yescharacteristic, complemented
44#64094C2212yescomplemented
45#64090C2212yescomplemented
46C3×#940C2212yescomplemented
47C3×#937C2214yescomplemented
48C3×C4×#67C2212yescomplemented
49C3×#895C2212yescomplemented
50C3×#893C2212yescomplemented
51C3×#884C2214yescomplemented
52C3×#882C2214yescomplemented
53#63980C2212yescomplemented
54#63980C2212yescomplemented
55#63979C2214yescomplemented
56#63979C2214yescomplemented
57#63977C2214yescomplemented
58#63976C2214yescomplemented
59#67⋊Dic3C2212yescomplemented
60#63970C2214yescomplemented
61#63957C2211yescharacteristic, complemented
62#63922C2214yescomplemented
63#63922C2214yescomplemented
64C4×#627C2211yescharacteristic, complemented
65#63914C2211yescharacteristic, complemented
66#63914C2212yescomplemented
67#63914C2212yescomplemented
68#63914C2211yescharacteristic, complemented
69#63914C2212yescomplemented
70#63913C2214yescomplemented
71#63912C2212yescomplemented
72#63912C2212yescomplemented
73#63911C2212yescomplemented
74#63908C2212yescomplemented
75#63906C2214yescomplemented
76#63902C2211yescharacteristic, complemented
77C4×#625C2211yescharacteristic, complemented
78Dic3×D12C2212yescomplemented
79#63886C2214yescomplemented
80#63885C2214yescomplemented
81#63879C2214yescomplemented
82#63878C2212yescomplemented
83C4×D3×Dic3C2212yescomplemented
84#63838C2211yescharacteristic, complemented
85C2×#1004—34no—
86C3×D42—32no—
87C2×#940—32no—
88C2×#940—32no—
89D4×#67—32no—
90D4×#67—34no—
91D4×#67—32no—
92#5718—32no—
93D3×#127—32no—
94#5609—32no—
95#5609D312yescomplemented
96#5607—34no—
97#5599—34no—
98#5596—32no—
99#5596—32no—
100#5596—61no—
101#5592—34no—
102#5592—34no—
103#5590—34no—
104#5590—34no—
105#5553—32no—
106D4×D12—32no—
107#5548—32no—
108C4×#237—32no—
109C23×C3×D3C2314yes—
110C23×C3×D3C2314yes—
111C22×D32C2314yes—
112C2×C32×D4C2312yes—
113C2×C32×D4C2311yescharacteristic
114C22×C32×C4C2311yescharacteristic
115C2×#638C2312yes—
116C2×#638C2312yes—
117C2×#638C2312yes—
118C22×C3⋊Dic3C2312yes—
119C22×C3⋊Dic3C2311yescharacteristic
120C22×C3⋊Dic3C2311yescharacteristic
121#3830—28no—
122C2×C4⋊(C3⋊D3)C2311yescharacteristic
123C2×C4×C3⋊D3C2312yes—
124C2×#634C2312yes—
125C2×C3×#67C2314yes—
126C2×C3×#67C2314yes—
127C2×C3×#67C2314yes—
128C2×C3×#67C2312yes—
129C3×D3×D4—216no—
130C3×D3×D4—44no—
131C2×C3×D12—44no—
132C2×C3×D12C2314yes—
133C2×C3×D12C2312yes—
134C2×C3×D12C2312yes—
135C2×C3×D12C2314yes—
136C2×C3×C4×D3C2314yes—
137C2×C3×C4×D3C2312yes—
138D3×#67—216no—
139D3×#67—216no—
140D3×#67—48no—
141C2×#627C2311yescharacteristic
142C2×#626C2314yes—
143C2×#626C2314yes—
144C2×#626C2314yes—
145C2×#625—28no—
146C2×#625—28no—
147C2×#625—44no—
148C2×#625C2314yes—
149C2×#625C2314yes—
150C2×#625C2312yes—
151C2×#625C2312yes—
152C2×#625C2314yes—
153C2×#625C2312yes—
154C2×#625C2312yes—
155C2×#625C2311yescharacteristic
156#3805—28no—
157#3805D418yescomplemented
158C2×D3×Dic3C2314yes—
159C2×D3×Dic3C2312yes—
160C2×D3×Dic3C2312yes—
161#3802—28no—
162D3×D12—44no—
163#3798—28no—
164#3795—216no—
165C32×C4⋊C4C2311yescharacteristic
166C32×C22⋊C4C2312yes—
167#3757C2312yes—
168#3752C2312yes—
169#3752C2312yes—
170C4⋊(C3⋊Dic3)C2311yescharacteristic
171#3750C2312yes—
172C4×C3⋊Dic3C2311yescharacteristic
173C4×C3⋊Dic3C2311yescharacteristic
174C4×C3⋊Dic3C2311yescharacteristic
175C4×C3⋊Dic3C2311yescharacteristic
176C3×#217C2312yes—
177C3×(C2×D3)⋊C4C2312yes—
178C3×(C2×D3)⋊C4C2314yes—
179C3×(C2×D3)⋊C4C2314yes—
180C3×Dic3⋊C4C2312yes—
181C3×C4×Dic3C2312yes—
182#3724C2311yescharacteristic
183#3724C2311yescharacteristic
184Dic3⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2312yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2314yes—
188Dic32C2312yes—
189Dic32C2312yes—
190#3498—91noSylow
191C22×C3×D4—34no—
192C22×C3×D4—32no—
193C22×C3×D4—32no—
194C22×#67—34no—
195C22×#67—34no—
196C22×#67—34no—
197C22×#67—34no—
198C22×#67—34no—
199C22×#67—34no—
200#1004—632no—
201C2×#237—32no—
202C2×#237—34no—
203C2×#237—34no—
204C2×#237—34no—
205C2×#237—62no—
206C2×D3×D4—34no—
207C2×D3×D4—34no—
208C2×D3×D4—34no—
209C2×D3×D4—34no—
210C2×D3×D4—32no—
211C2×D3×D4C2×D314yescomplemented
212C2×D3×D4C2×D312yescomplemented
213C2×#235—34no—
214C2×#235—34no—
215C22×D12—32no—
216C22×D12C2×D312yescomplemented
217C3×#127—32no—
218C3×#121—21no—
219C3×#121—32no—
220C3×#121—34no—
221C3×#121C2×D312yescomplemented
222C3×#120—34no—
223C3×#120—34no—
224C3×C4×D4—32no—
225C3×C4×D4—32no—
226#953—34no—
227#953—34no—
228#940—32no—
229#940—34no—
230#940—34no—
231#940—34no—
232#940—34no—
233#940—32no—
234#940—32no—
235#940—32no—
236#940—32no—
237#940—34no—
238#940—34no—
239#940—32no—
240#940—61no—
241#940C2×D312yescomplemented
242#939—34no—
243#939—34no—
244#939—34no—
245#939—34no—
246#939—34no—
247#939—34no—
248#939—62no—
249#938—34no—
250#938—32no—
251#937—34no—
252#937—34no—
253#937—34no—
254#937C2×D314yescomplemented
255D4×Dic3—32no—
256D4×Dic3—32no—
257D4×Dic3—32no—
258D4×Dic3—61no—
259#930—32no—
260#930—32no—
261#930—34no—
262#930—61no—
263C4×#67—32no—
264C4×#67—34no—
265C4×#67C2×D312yescomplemented
266C2×C4×Dic3—32no—
267C2×C4×Dic3—32no—
268C2×C4×Dic3—61no—
269#895—34no—
270#895C2×D312yescomplemented
271#893—32no—
272#893—61no—
273#893C2×D312yescomplemented
274#892—32no—
275#888—32no—
276#888—61no—
277#887—32no—
278#885—34no—
279#885—34no—
280#885—34no—
281#885—62no—
282#884—34no—
283#884—34no—
284#884—34no—
285#884—34no—
286#884C2×D314yescomplemented
287#882—34no—
288#882—34no—
289#882—34no—
290#882C2×D314yescomplemented
291#67⋊C4—32no—
292#67⋊C4—34no—
293#67⋊C4—34no—
294#67⋊C4—32no—
295#67⋊C4—62no—
296#877—32no—
297#877—32no—
298#874—32no—
299C4×D12—32no—
300C42×D3—32no—
301C4×Dic6—32no—
302C23×C32C2412yes—
303C23×C32C2411yescharacteristic
304C22×C3⋊D3C2412yes—
305C22×C3×D3—28no—
306C22×C3×D3—28no—
307C22×C3×D3—44no—
308C22×C3×D3—44no—
309C22×C3×D3—44no—
310C22×C3×D3—44no—
311C22×C3×D3C2414yes—
312C22×C3×D3C2414yes—
313C22×C3×D3C2412yes—
314C2×D32—28no—
315C2×D32—44no—
316C2×D32—44no—
317C32×D4—24no—
318C32×D4—22no—
319C2×C32×C4—22no—
320C2×C32×C4C2411yescharacteristic
321C2×C32×C4C2412yes—
322C2×C32×C4C2411yescharacteristic
323#638—24no—
324#638—24no—
325#638—24no—
326C2×C3⋊Dic3—24no—
327C2×C3⋊Dic3—22no—
328C2×C3⋊Dic3C2×D414yescomplemented
329C2×C3⋊Dic3C2412yes—
330C2×C3⋊Dic3C2411yescharacteristic
331C2×C3⋊Dic3C2411yescharacteristic
332C2×C3⋊Dic3C2411yescharacteristic
333C2×C3⋊Dic3C2411yescharacteristic
334C4⋊(C3⋊D3)—22no—
335C4×C3⋊D3—24no—
336#634—24no—
337C3×#67—28no—
338C3×#67—44no—
339C3×#67—44no—
340C3×#67C2×D418yescomplemented
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C3×D12—28no—
345C3×D12—24no—
346C3×D12—24no—
347C3×D12—44no—
348C3×C4×D3—24no—
349C3×C4×D3—28no—
350#627C2×D414yescomplemented
351#626—28no—
352#626—44no—
353#626—44no—
354#625—28no—
355#625—28no—
356#625—24no—
357#625—24no—
358#625—28no—
359#625—42no—
360#625—42no—
361#625C2×D414yescomplemented
362D3×Dic3—24no—
363D3×Dic3—28no—
364D3×Dic3C2×D418yescomplemented
365C2×H(5,𝔽2)—92no—
366#550—91no—
367#550—92no—
368#550—91no—
369D42—32no—
370D42—92no—
371D42—92no—
372D42—94no—
373D42—91no—
374D42—91no—
375#535—92no—
376#535—94no—
377#532—92no—
378#532—91no—
379C2×#127—92no—
380C2×#127—91no—
381C4×#41—91no—
382C24×C3—34no—
383C24×C3—34no—
384C23×D3—34no—
385C23×D3—34no—
386C23×D3C22×D314yes—
387C23×D3C22×D314yes—
388C2×C3×D4—21no—
389C2×C3×D4—22no—
390C2×C3×D4—32no—
391C2×C3×D4—34no—
392C2×C3×D4—34no—
393C2×C3×D4—34no—
394C2×C3×D4—32no—
395C2×C3×D4—34no—
396C2×C3×D4—32no—
397C2×C3×D4—34no—
398C2×C3×D4—616no—
399C2×C3×D4—124no—
400C2×C3×D4—124no—
401C2×C3×D4C22×D312yes—
402C2×C3×D4C22×D314yes—
403C22×C3×C4—21no—
404C22×C3×C4—32no—
405C22×C3×C4—34no—
406C22×C3×C4C22×D312yes—
407C2×#67—32no—
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—34no—
411C2×#67—34no—
412C2×#67—34no—
413C2×#67—34no—
414C2×#67—34no—
415C2×#67—34no—
416C2×#67—34no—
417C2×#67—34no—
418C2×#67—34no—
419C2×#67—34no—
420C2×#67—34no—
421C2×#67—34no—
422C2×#67—34no—
423C2×#67—34no—
424C2×#67—62no—
425C2×#67—62no—
426C2×#67—62no—
427C2×#67—616no—
428C2×#67—616no—
429C2×#67—616no—
430C2×#67—616no—
431C2×#67—128no—
432C2×#67—128no—
433C2×#67C22×D314yes—
434C2×#67C22×D314yes—
435C2×#67C22×D314yes—
436C2×#67C22×D312yes—
437C22×Dic3—32no—
438C22×Dic3—32no—
439C22×Dic3—32no—
440C22×Dic3—34no—
441C22×Dic3—32no—
442C22×Dic3—34no—
443C22×Dic3—61no—
444C22×Dic3—62no—
445C22×Dic3—61no—
446#237—316no—
447#237—616no—
448#237—616no—
449#237—616no—
450#237—128no—
451D3×D4—216no—
452D3×D4—44no—
453D3×D4—616no—
454D3×D4—616no—
455D3×D4—616no—
456D3×D4—124no—
457D3×D4—128no—
458#235—616no—
459#235—616no—
460C2×D12—34no—
461C2×D12—32no—
462C2×D12—34no—
463C2×D12—34no—
464C2×D12—44no—
465C2×D12—61no—
466C2×D12—124no—
467C2×D12C22×D312yes—
468C2×D12C22×D312yes—
469C2×D12C22×D314yes—
470C2×D12C22×D314yes—
471C2×C4×D3—32no—
472C2×C4×D3—32no—
473C2×C4×D3—34no—
474C2×C4×D3—34no—
475C2×C4×D3—62no—
476C2×C4×D3C22×D312yes—
477C2×C4×D3C22×D314yes—
478C2×Dic6—32no—
479C2×Dic6—34no—
480C2×Dic6—62no—
481C3×C4⋊C4—21no—
482C3×C4⋊C4—32no—
483C3×C4⋊C4C22×D312yes—
484C3×C22⋊C4—22no—
485C3×C22⋊C4—32no—
486C3×C22⋊C4—32no—
487C3×C22⋊C4—34no—
488C3×C22⋊C4—34no—
489C3×C22⋊C4C22×D314yes—
490C3×C42—32no—
491#217—34no—
492#217—32no—
493#217—34no—
494#217—34no—
495#217—62no—
496#217C22×D312yes—
497(C2×D3)⋊C4—34no—
498(C2×D3)⋊C4—32no—
499(C2×D3)⋊C4—34no—
500(C2×D3)⋊C4—34no—
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—62no—
503(C2×D3)⋊C4—62no—
504(C2×D3)⋊C4C22×D312yes—
505(C2×D3)⋊C4C22×D314yes—
506(C2×D3)⋊C4C22×D314yes—
507C4⋊Dic3—32no—
508C4⋊Dic3—32no—
509C4⋊Dic3—61no—
510Dic3⋊C4—34no—
511Dic3⋊C4—32no—
512Dic3⋊C4—32no—
513Dic3⋊C4—32no—
514Dic3⋊C4—62no—
515Dic3⋊C4C22×D312yes—
516C4×Dic3—32no—
517C4×Dic3—32no—
518C4×Dic3—32no—
519C4×Dic3—32no—
520C4×Dic3—32no—
521C4×Dic3—32no—
522C4×Dic3—32no—
523C4×Dic3—32no—
524C4×Dic3—61no—
525C4×Dic3—61no—
526C4×Dic3—61no—
527C4×Dic3—61no—
528C4×Dic3C22×D312yes—
529C22×C32—21no—
530C22×C32—21no—
531C22×C32—22no—
532C22×C32—22no—
533C22×C32—22no—
534C22×C32C22×D412yes—
535C22×C32C2511yescharacteristic
536C2×C3⋊D3—22no—
537C2×C3⋊D3—22no—
538C2×C3⋊D3—22no—
539C2×C3×D3—22no—
540C2×C3×D3—22no—
541C2×C3×D3—24no—
542C2×C3×D3—24no—
543C2×C3×D3—24no—
544C2×C3×D3—24no—
545C2×C3×D3—24no—
546C2×C3×D3—24no—
547C2×C3×D3—88no—
548C2×C3×D3—88no—
549C2×C3×D3C22×D414yes—
550D32—88no—
551C32×C4—22no—
552C32×C4—21no—
553C32×C4H(5,𝔽2)12yescomplemented
554C3⋊Dic3—22no—
555C3⋊Dic3—21no—
556C3⋊Dic3C22×D412yes—
557C3⋊Dic3C22×D412yes—
558C3⋊Dic3H(5,𝔽2)12yescomplemented
559C3×Dic3—22no—
560C3×Dic3—22no—
561C3×Dic3C22×D414yes—
562H(5,𝔽2)—1816no—
563C2×#41—92no—
564C2×#41—94no—
565C2×#41—91no—
566C2×#41—92no—
567C2×#41—92no—
568C22×D4—34no—
569C22×D4—32no—
570C22×D4—32no—
571C22×D4—92no—
572C22×D4—92no—
573C22×D4—94no—
574C22×D4—94no—
575C22×D4—94no—
576C22×D4—92no—
577C22×D4—92no—
578C22×D4—92no—
579C4⋊Q8—91no—
580#127—32no—
581#127—92no—
582#127—92no—
583#127—94no—
584#127—92no—
585#127—94no—
586#127—91no—
587#127—91no—
588#127—92no—
589#127—91no—
590#124—94no—
591#124—92no—
592#121—32no—
593#121—34no—
594#121—92no—
595#121—92no—
596#121—94no—
597#121—94no—
598#121—94no—
599#121—92no—
600#121—94no—
601#121—92no—
602#121—92no—
603#121—92no—
604#121—91no—
605#121D3211yescharacteristic, complemented
606#120—34no—
607#120—34no—
608#120—94no—
609#120—94no—
610#120—94no—
611#120—94no—
612C4×Q8—91no—
613C4×Q8—91no—
614C4×D4—32no—
615C4×D4—32no—
616C4×D4—92no—
617C4×D4—91no—
618C4×D4—94no—
619C4×D4—92no—
620C4×D4—91no—
621C4×D4—91no—
622C4×D4—91no—
623C4×D4—92no—
624#117—91no—
625#117—92no—
626C2×C42—92no—
627C2×C42—91no—
628C23×C3—21no—
629C23×C3—22no—
630C23×C3—32no—
631C23×C3—34no—
632C23×C3—34no—
633C23×C3—68no—
634C23×C3—68no—
635C23×C3—124no—
636C23×C3—124no—
637C23×C3—124no—
638C23×C3—124no—
639C23×C3C23×D314yes—
640C23×C3C23×D312yes—
641C22×D3—28no—
642C22×D3—28no—
643C22×D3—34no—
644C22×D3—44no—
645C22×D3—44no—
646C22×D3—44no—
647C22×D3—44no—
648C22×D3—62no—
649C22×D3—68no—
650C22×D3—68no—
651C22×D3—124no—
652C22×D3—124no—
653C22×D3—124no—
654C22×D3—124no—
655C22×D3C23×D314yes—
656C22×D3C23×D314yes—
657C22×D3C23×D312yes—
658C3×D4—28no—
659C3×D4—24no—
660C3×D4—38no—
661C3×D4—42no—
662C3×D4—44no—
663C3×D4—68no—
664C3×D4—68no—
665C3×D4—64no—
666C3×D4—64no—
667C3×D4—124no—
668C3×D4—124no—
669C3×D4—124no—
670C2×C3×C4—24no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—22no—
674C2×C3×C4—32no—
675C2×C3×C4—32no—
676C2×C3×C4—32no—
677C2×C3×C4—42no—
678C2×C3×C4—68no—
679C2×C3×C4—64no—
680C2×C3×C4C23×D312yes—
681C2×C3×C4C23×D314yes—
682C2×C3×C4C23×D312yes—
683#67—28no—
684#67—38no—
685#67—44no—
686#67—44no—
687#67—68no—
688#67—68no—
689#67—68no—
690#67—68no—
691#67—68no—
692#67—68no—
693#67—68no—
694#67—68no—
695#67—68no—
696#67—68no—
697#67—68no—
698#67—68no—
699#67—124no—
700#67—124no—
701#67—124no—
702#67—124no—
703#67—124no—
704#67—124no—
705#67—124no—
706#67D3×D418yescomplemented
707C2×Dic3—38no—
708C2×Dic3—32no—
709C2×Dic3—32no—
710C2×Dic3—32no—
711C2×Dic3—38no—
712C2×Dic3—32no—
713C2×Dic3—34no—
714C2×Dic3—64no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—62no—
720C2×Dic3—64no—
721C2×Dic3—68no—
722C2×Dic3—64no—
723C2×Dic3—68no—
724C2×Dic3—124no—
725C2×Dic3—122no—
726C2×Dic3C23×D312yes—
727C2×Dic3C23×D312yes—
728C2×Dic3C23×D312yes—
729D12—28no—
730D12—24no—
731D12—24no—
732D12—44no—
733D12—68no—
734D12—64no—
735D12—122no—
736D12—124no—
737D12—124no—
738C4×D3—24no—
739C4×D3—28no—
740C4×D3—38no—
741C4×D3—68no—
742C4×D3—64no—
743C4×D3—68no—
744C4×D3—124no—
745Dic6—38no—
746Dic6—68no—
747Dic6—124no—
748C2×C32—22no—
749C2×C32—42no—
750C2×C32C23×D411yescharacteristic
751C2×C32C2×H(5,𝔽2)11yescharacteristic
752C2×C32C2×H(5,𝔽2)11yescharacteristic
753C3⋊D3—42no—
754C3×D3—24no—
755C3×D3—44no—
756C3×D3—44no—
757C24—34no—
758C24—34no—
759C24—94no—
760#41—98no—
761#41—188no—
762#41—1816no—
763#41—188no—
764#41—188no—
765C2×Q8—91no—
766C2×Q8—92no—
767C2×D4—32no—
768C2×D4—34no—
769C2×D4—34no—
770C2×D4—34no—
771C2×D4—32no—
772C2×D4—32no—
773C2×D4—34no—
774C2×D4—34no—
775C2×D4—616no—
776C2×D4—94no—
777C2×D4—94no—
778C2×D4—94no—
779C2×D4—91no—
780C2×D4—94no—
781C2×D4—94no—
782C2×D4—92no—
783C2×D4—92no—
784C2×D4—94no—
785C2×D4—92no—
786C2×D4—92no—
787C2×D4—92no—
788C2×D4—92no—
789C2×D4—92no—
790C2×D4—91no—
791C2×D4—124no—
792C2×D4—124no—
793C2×D4—1816no—
794C2×D4—188no—
795C2×D4—1816no—
796C2×D4—188no—
797C2×D4—188no—
798C2×D4—364no—
799C2×D4—368no—
800C2×D4—364no—
801C2×D4C2×D3211yescharacteristic
802C2×D4C2×D3212yes—
803C22×C4—32no—
804C22×C4—34no—
805C22×C4—92no—
806C22×C4—92no—
807C22×C4—94no—
808C22×C4—91no—
809C22×C4—91no—
810C22×C4—92no—
811C22×C4—92no—
812C22×C4C2×D3211yescharacteristic
813C4⋊C4—32no—
814C4⋊C4—91no—
815C4⋊C4—91no—
816C4⋊C4—92no—
817C4⋊C4—92no—
818C4⋊C4—91no—
819C4⋊C4C2×D3211yescharacteristic
820C22⋊C4—32no—
821C22⋊C4—32no—
822C22⋊C4—34no—
823C22⋊C4—34no—
824C22⋊C4—92no—
825C22⋊C4—94no—
826C22⋊C4—94no—
827C22⋊C4—92no—
828C22⋊C4—92no—
829C22⋊C4—92no—
830C22⋊C4C2×D3212yes—
831C42—32no—
832C42—92no—
833C42—92no—
834C42—91no—
835C42—91no—
836C42—91no—
837C42—91no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—24no—
841C22×C3—24no—
842C22×C3—24no—
843C22×C3—22no—
844C22×C3—21no—
845C22×C3—34no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—42no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—64no—
854C22×C3—64no—
855C22×C3—64no—
856C22×C3—64no—
857C22×C3—64no—
858C22×C3—64no—
859C22×C3—248no—
860C22×C3—248no—
861C22×C3C2×D3×D414yes—
862C22×C3C24×D312yes—
863C2×D3—22no—
864C2×D3—22no—
865C2×D3—24no—
866C2×D3—24no—
867C2×D3—24no—
868C2×D3—24no—
869C2×D3—24no—
870C2×D3—24no—
871C2×D3—64no—
872C2×D3—64no—
873C2×D3—64no—
874C2×D3—88no—
875C2×D3—88no—
876C2×D3—122no—
877C2×D3—122no—
878C2×D3—122no—
879C2×D3—248no—
880C2×D3—248no—
881C2×D3C2×D3×D414yes—
882C3×C4—24no—
883C3×C4—22no—
884C3×C4—22no—
885C3×C4—34no—
886C3×C4—42no—
887C3×C4—41no—
888C3×C4—62no—
889C3×C4—62no—
890C3×C4#100414yescomplemented
891Dic3—22no—
892Dic3—22no—
893Dic3—34no—
894Dic3—34no—
895Dic3—34no—
896Dic3—62no—
897Dic3—62no—
898Dic3—62no—
899Dic3—64no—
900Dic3—62no—
901Dic3—122no—
902Dic3—121no—
903Dic3C2×D3×D414yes—
904C32#349811yescharacteristic, complemented, Sylow
905C23—32no—
906C23—34no—
907C23—34no—
908C23—68no—
909C23—68no—
910C23—92no—
911C23—124no—
912C23—124no—
913C23—124no—
914C23—124no—
915C23—188no—
916C23—364no—
917C23—364no—
918C23C22×D3212yes—
919C23C22×D3211yescharacteristic
920Q8—94no—
921Q8—184no—
922D4—24no—
923D4—22no—
924D4—38no—
925D4—68no—
926D4—68no—
927D4—64no—
928D4—64no—
929D4—94no—
930D4—124no—
931D4—124no—
932D4—124no—
933D4—188no—
934D4—184no—
935D4—184no—
936D4—188no—
937D4—184no—
938D4—184no—
939D4—188no—
940D4—188no—
941D4—184no—
942D4—182no—
943D4—364no—
944D4—364no—
945D4—362no—
946D4—362no—
947C2×C4—22no—
948C2×C4—32no—
949C2×C4—32no—
950C2×C4—32no—
951C2×C4—68no—
952C2×C4—64no—
953C2×C4—98no—
954C2×C4—94no—
955C2×C4—91no—
956C2×C4—91no—
957C2×C4—91no—
958C2×C4—91no—
959C2×C4—92no—
960C2×C4—184no—
961C2×C4—188no—
962C2×C4—184no—
963C2×C4—184no—
964C2×C4—182no—
965C2×C4C22×D3211yescharacteristic
966C2×C4C22×D3212yes—
967C2×C4C22×D3211yescharacteristic
968C2×C3—24no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—21no—
972C2×C3—42no—
973C2×C3—44no—
974C2×C3—64no—
975C2×C3—82no—
976C2×C3—124no—
977C2×C3—124no—
978C2×C3C22×D3×D412yes—
979C2×C3C2×#100412yes—
980C2×C3D3×H(5,𝔽2)12yes—
981D3—24no—
982D3—44no—
983D3—44no—
984D3—124no—
985D3—242no—
986C22—21no—
987C22—21no—
988C22—22no—
989C22—22no—
990C22—22no—
991C22—34no—
992C22—62no—
993C22—62no—
994C22—64no—
995C22—64no—
996C22—64no—
997C22—64no—
998C22—64no—
999C22—64no—
1000C22—182no—
1001C22—182no—
1002C22—182no—
1003C22—248no—
1004C22—248no—
1005C22—728no—
1006C22D32×D412yes—
1007C22C23×D3211yescharacteristic
1008C4—22no—
1009C4—21no—
1010C4—34no—
1011C4—62no—
1012C4—62no—
1013C4—92no—
1014C4—92no—
1015C4—92no—
1016C4—182no—
1017C4—181no—
1018C4#6431312yescomplemented
1019C3—21no—
1020C3#8660812yescomplemented
1021C2—22no—
1022C2—42no—
1023C2—64no—
1024C2—124no—
1025C2—124no—
1026C2—362no—
1027C2C2×D32×D411yescharacteristic
1028C2C2×#6431311yescharacteristic
1029C2#1059669211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#121C22
hypercenter#121D32
hypocenterC32#3498
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. #10596067C2semidirect
3. C3×#5609C2semidirect
4. #10595287C2semidirect
5. D3×#940C2semidirect
6. #10595239C2semidirect
7. D4×#625C2semidirect
8. #10595144C2semidirect
9. D12×#67C2semidirect
10. C2×#63914C2semidirect
11. C4×#3805C2semidirect
12. #10594618C2semidirect
13. #10594520C2semidirect
14. #10594367C2semidirect
15. #10594271C2semidirect
16. #10594269C2semidirect
17. #10594190C2semidirect
19. C2×#3830C22semidirect
20. C2×C3×D3×D4C22semidirect
21. C2×C3×D3×D4C22semidirect
22. C22×C3×D12C22semidirect
23. C2×D3×#67C22semidirect
24. C2×D3×#67C22semidirect
25. C2×D3×#67C22semidirect
26. C22×#625C22semidirect
27. C22×#625C22semidirect
28. C22×#625C22semidirect
30. C2×#3805C22semidirect
32. C2×#3802C22semidirect
33. C2×D3×D12C22semidirect
34. C2×#3798C22semidirect
35. C2×#3795C22semidirect
36. C32×#121C22semidirect
37. #64149C22semidirect
38. #64148C22semidirect
39. D4×C3⋊Dic3C22semidirect
40. #64139C22semidirect
41. C2×C4×C3⋊Dic3C22semidirect
42. #64102C22semidirect
43. #64097C22semidirect
44. #64094C22semidirect
45. #64090C22semidirect
46. C3×#940C22semidirect
47. C3×#937C22semidirect
48. C3×C4×#67C22semidirect
49. C3×#895C22semidirect
50. C3×#893C22semidirect
51. C3×#884C22semidirect
52. C3×#882C22semidirect
53. #63980C22semidirect
54. #63980C22semidirect
55. #63979C22semidirect
56. #63979C22semidirect
57. #63977C22semidirect
58. #63976C22semidirect
59. #67⋊Dic3C22semidirect
60. #63970C22semidirect
61. #63957C22semidirect
62. #63922C22semidirect
63. #63922C22semidirect
64. C4×#627C22semidirect
65. #63914C22semidirect
66. #63914C22semidirect
67. #63914C22semidirect
68. #63914C22semidirect
69. #63914C22semidirect
70. #63913C22semidirect
71. #63912C22semidirect
72. #63912C22semidirect
73. #63911C22semidirect
74. #63908C22semidirect
75. #63906C22semidirect
76. #63902C22semidirect
77. C4×#625C22semidirect
78. Dic3×D12C22semidirect
79. #63886C22semidirect
80. #63885C22semidirect
81. #63879C22semidirect
82. #63878C22semidirect
83. C4×D3×Dic3C22semidirect
84. #63838C22semidirect
95. #5609D3semidirect
157. #3805D4semidirect
211. C2×D3×D4C2×D3semidirect
212. C2×D3×D4C2×D3semidirect
216. C22×D12C2×D3semidirect
221. C3×#121C2×D3semidirect
241. #940C2×D3semidirect
254. #937C2×D3semidirect
265. C4×#67C2×D3semidirect
270. #895C2×D3semidirect
273. #893C2×D3semidirect
286. #884C2×D3semidirect
290. #882C2×D3semidirect
328. C2×C3⋊Dic3C2×D4semidirect
340. C3×#67C2×D4semidirect
350. #627C2×D4semidirect
361. #625C2×D4semidirect
364. D3×Dic3C2×D4semidirect
553. C32×C4H(5,𝔽2)semidirect
558. C3⋊Dic3H(5,𝔽2)semidirect
605. #121D32semidirect
706. #67D3×D4semidirect
890. C3×C4#1004semidirect
904. C32#3498semidirect
1018. C4#64313semidirect
1020. C3#86608semidirect

Maximal subgroups

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

subgroupindex
C2×#643132
#105960672
C3×#56092
#105952872
D3×#9402
#105952392
D4×#6252
#105951442
D12×#672
C2×#639142
C4×#38052
#105946182
#105945202
#105943672
#105942712
#105942692
#105941902
#866083