Finite Group Databasebeta

← #11906149

Subgroups — #11906149

Order 1152.

3225 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C2×#64320C211yesmaximal, characteristic, complemented
3#10596288C211yesmaximal, characteristic, complemented
4C3×#5817C211yesmaximal, characteristic, complemented
5#10595428C213yesmaximal, complemented
6#10595427C213yesmaximal, complemented
7D3×#947C213yesmaximal, complemented
8#10595409C211yesmaximal, characteristic, complemented
9#10595397C213yesmaximal, complemented
10Dic3×#239C211yesmaximal, characteristic, complemented
11#10595342C211yesmaximal, characteristic, complemented
12#10595070C213yesmaximal, complemented
13#10595067C213yesmaximal, complemented
14#10595064C213yesmaximal, complemented
15#10595003C213yesmaximal, complemented
16#87293—31nomaximal
17#86715—31nomaximal
18C22×C32×Q8C2211yescharacteristic, complemented
19C2×#3832C2211yescharacteristic
20C3×#1007—28no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×#239C2211yescharacteristic
23C2×C3×#239C2213yescomplemented
24C2×C3×D3×Q8C2211yescharacteristic, complemented
25C2×C3×D3×Q8C2213yescomplemented
26C2×C3×#235C2213yescomplemented
27C2×C3×#235C2213yescomplemented
28#64320—28no—
29C2×#3802C2213yes—
30C2×D3×D12C2213yes—
31C2×D3×D12C2213yes—
32C2×#3798C2213yes—
33#64156C2213yescomplemented
34#64155C2213yescomplemented
35Q8×C3⋊Dic3C2211yescharacteristic, complemented
36#64139C2213yescomplemented
37C4×#638C2213yescomplemented
38C3×#947C2213yescomplemented
39C3×#946C2213yescomplemented
40C3×Q8×Dic3C2211yescharacteristic, complemented
41C3×#930C2213yescomplemented
42C3×C4×#67C2213yescomplemented
43#63983C2216yescomplemented
44#63979C2213yescomplemented
45#63971C2213yescomplemented
46#63970C2213yescomplemented
47#63959C2211yescharacteristic, complemented
48#63922C2216yescomplemented
49D3×(C2×D3)⋊C4C2216yescomplemented
50D3×(C2×D3)⋊C4C2216yescomplemented
51#63909C2213yescomplemented
52#63908C2213yescomplemented
53#63907C2216yescomplemented
54#63907C2213yescomplemented
55#63905C2216yescomplemented
56C4×#626C2213yescomplemented
57C4×#625C2213yescomplemented
58#63898C2213yescomplemented
59Dic3×D12C2213yescomplemented
60#63886C2213yescomplemented
61#63885C2213yescomplemented
62C4×D3×Dic3C2213yescomplemented
63#63871C2213yescomplemented
64#63864C2213yescomplemented
65#63863C2213yescomplemented
66#63856C2213yescomplemented
67#63850C2216yescomplemented
68#63841C2213yescomplemented
69#63839C2213yescomplemented
70C2×C3×2−1+4—31no—
71C2×#1009—31no—
72C2×#1009—31no—
73C2×#1007D311yescharacteristic, complemented
74C3×#548—31no—
75#5832—33no—
76#5831—31no—
77#5830—33no—
78#5829—33no—
79#5829—33no—
80#5829—33no—
81#5829—33no—
82Dic3×#41—31no—
83#5817—31no—
84#5817—31no—
85#5817—31no—
86#5817—31no—
87#5817—61no—
88#5817D311yescharacteristic, complemented
89#5816—33no—
90C2×#947—33no—
91#5676—33no—
92D3×#124—33no—
93#5630—33no—
94#5628—33no—
95#5612—33no—
96#5607—33no—
97#5576—31no—
98C4×#239—31no—
99#5550—33no—
100#5548—33no—
101C22×D32C2316yes—
102C2×C32×Q8—24no—
103C2×C32×Q8C2313yes—
104C2×C32×Q8C2311yescharacteristic
105C22×C32×C4C2313yes—
106C2×#638C2313yes—
107#3832—24no—
108C2×C4⋊(C3⋊D3)C2313yes—
109C2×C4×C3⋊D3C2313yes—
110C2×C3×#67C2311yescharacteristic
111C2×C3×#67C2313yes—
112C2×C3×#67C2313yes—
113C3×#239—24no—
114C3×#239—212no—
115C3×#239D418yescomplemented
116C3×D3×Q8—24no—
117C3×D3×Q8—212no—
118C3×#235—212no—
119C3×#235—212no—
120C2×C3×D12C2313yes—
121C2×C3×D12C2313yes—
122C2×C3×D12C2313yes—
123C2×C3×C4×D3C2313yes—
124C2×C3×C4×D3C2316yes—
125C2×C3×C4×D3C2313yes—
126C2×C3×C4×D3C2313yes—
127C2×C3×Dic6C2313yes—
128C2×C3×Dic6C2313yes—
129C2×#627C2311yescharacteristic
130C2×#626C2313yes—
131C2×#626C2313yes—
132C2×#626C2313yes—
133C2×#625C2313yes—
134C2×#625C2313yes—
135C2×D3×Dic3C2313yes—
136C2×D3×Dic3C2313yes—
137#3802—212no—
138D3×D12—212no—
139D3×D12—212no—
140#3798—212no—
141#3757C2311yescharacteristic
142#3752C2316yes—
143#3752C2313yes—
144C4⋊(C3⋊Dic3)C2313yes—
145#3750C2313yes—
146C4×C3⋊Dic3C2313yes—
147C3×#217C2311yescharacteristic
148C3×(C2×D3)⋊C4C2313yes—
149C3×(C2×D3)⋊C4C2316yes—
150C3×C4⋊Dic3C2313yes—
151C3×Dic3⋊C4C2313yes—
152C3×C4×Dic3C2313yes—
153#3724C2313yes—
154Dic3⋊Dic3C2313yes—
155#3722C2316yes—
156#3722C2313yes—
157(C2×D3)⋊Dic3C2316yes—
158(C2×D3)⋊Dic3C2316yes—
159(C2×D3)⋊Dic3C2313yes—
160(C2×D3)⋊Dic3C2311yescharacteristic
161(C2×D3)⋊Dic3C2311yescharacteristic
162Dic32C2313yes—
163Dic32C2311yescharacteristic
164#3500—91noSylow
165C3×2−1+4—68no—
166C2×C3×#41—31no—
167C2×C3×#41—31no—
168C2×C3×#41—33no—
169C2×C3×#41—33no—
170C2×C3×#41—33no—
171C22×C3×Q8—21no—
172C22×C3×Q8—33no—
173C22×C3×Q8—31no—
174C22×C3×Q8C2×D311yescharacteristic, complemented
175C22×C3×Q8C2×D311yescharacteristic, complemented
176#1009—68no—
177#1009—68no—
178#1007—28no—
179C2×#239—31no—
180C2×#239—31no—
181C2×#239—61no—
182C2×#239C2×D311yescharacteristic
183C2×#239C2×D311yescharacteristic
184C2×#239C2×D313yescomplemented
185C2×D3×Q8C2×D313yescomplemented
186C2×D3×Q8C2×D311yescharacteristic, complemented
187C2×D3×D4—33no—
188C2×D3×D4—33no—
189C2×D3×D4—33no—
190C2×D3×D4—33no—
191C2×#235—33no—
192C2×#235—33no—
193C2×#235C2×D313yescomplemented
194C2×#235C2×D313yescomplemented
195C22×D12—33no—
196C22×D12—33no—
197C3×#124—33no—
198C3×C22⋊Q8—33no—
199C3×#121—33no—
200C3×C4×Q8—31no—
201C3×C4×D4—33no—
202#947—33no—
203#947—33no—
204#947—33no—
205#947—33no—
206#947—36no—
207#947—33no—
208#947—63no—
209#947C2×D313yescomplemented
210#946—33no—
211#946—33no—
212#946—33no—
213#946—33no—
214#946—63no—
215#946C2×D313yescomplemented
216Q8×Dic3—31no—
217Q8×Dic3—31no—
218Q8×Dic3—61no—
219Q8×Dic3C2×D311yescharacteristic, complemented
220#944—33no—
221#940—33no—
222#940—33no—
223#939—33no—
224#939—33no—
225#939—33no—
226#939—33no—
227#938—33no—
228#938—33no—
229#937—36no—
230#937—36no—
231#937—36no—
232#936—33no—
233#936—31no—
234D4×Dic3—33no—
235D4×Dic3—33no—
236#930—33no—
237#930—33no—
238#930—33no—
239#930—33no—
240#930—63no—
241#930C2×D313yescomplemented
242#929—36no—
243#929—36no—
244C4×#67—33no—
245C4×#67—33no—
246C4×#67—33no—
247C4×#67—33no—
248C4×#67—33no—
249C4×#67—63no—
250C4×#67C2×D313yescomplemented
251C2×(C2×D3)⋊C4—36no—
252C2×(C2×D3)⋊C4—36no—
253#926—33no—
254#924—33no—
255C2×C4×Dic3—33no—
256#897—33no—
257#895—33no—
258#895—33no—
259#894—36no—
260#893—33no—
261#892—33no—
262#888—33no—
263#885—31no—
264#885—33no—
265#885—36no—
266#884—33no—
267#884—33no—
268#883—36no—
269#882—36no—
270D3×C22⋊C4—36no—
271D3×C22⋊C4—36no—
272#875—33no—
273C4×D12—33no—
274C4×D12—33no—
275C42×D3—33no—
276C23×C32C2411yescharacteristic
277C22×C3⋊D3C2413yes—
278C22×C3×D3C2413yes—
279C22×C3×D3C2411yescharacteristic
280C22×C3×D3C2413yes—
281C2×D32—212no—
282C2×D32—46no—
283C2×D32—46no—
284C32×Q8—26no—
285C32×Q8C2×D414yes—
286C2×C32×C4—26no—
287C2×C32×C4C2413yes—
288C2×C32×C4C2413yes—
289#638—43no—
290C2×C3⋊Dic3C2413yes—
291C2×C3⋊Dic3C2411yescharacteristic
292C2×C3⋊Dic3C2411yescharacteristic
293C4⋊(C3⋊D3)—26no—
294C4×C3⋊D3—26no—
295C3×#67—26no—
296C3×#67—22no—
297C3×#67—43no—
298C2×C3×Dic3C2413yes—
299C2×C3×Dic3C2411yescharacteristic
300C2×C3×Dic3C2413yes—
301C2×C3×Dic3C2411yescharacteristic
302C2×C3×Dic3C2411yescharacteristic
303C3×D12—26no—
304C3×D12—26no—
305C3×D12C2×D4112yes—
306C3×C4×D3—212no—
307C3×C4×D3—26no—
308C3×C4×D3—26no—
309C3×C4×D3C2×D4112yes—
310C3×Dic6—26no—
311C3×Dic6—26no—
312#627—22no—
313#626—26no—
314#626—26no—
315#626—43no—
316#625—26no—
317#625—43no—
318D3×Dic3—43no—
319D3×Dic3—43no—
320C2×2−1+4—31no—
321C2×H(5,𝔽2)—91no—
322#548—31no—
323#548—91no—
324#548—91no—
325#548—91no—
326#546—93no—
327#546—93no—
328#546—93no—
329#546—93no—
330#536—93no—
331#535—93no—
332#532—93no—
333C2×#124—93no—
334C4×#41—91no—
335C23×D3—36no—
336C23×D3—36no—
337C3×#41—38no—
338C3×#41—612no—
339C3×#41—612no—
340C3×#41—612no—
341C3×#41—64no—
342C2×C3×Q8—24no—
343C2×C3×Q8—24no—
344C2×C3×Q8—21no—
345C2×C3×Q8—23no—
346C2×C3×Q8—33no—
347C2×C3×Q8—33no—
348C2×C3×Q8—44no—
349C2×C3×Q8—612no—
350C2×C3×Q8—64no—
351C2×C3×Q8C22×D313yes—
352C2×C3×Q8C22×D313yes—
353C2×C3×Q8C22×D311yescharacteristic
354C2×C3×Q8C22×D311yescharacteristic
355C2×C3×D4—31no—
356C2×C3×D4—33no—
357C2×C3×D4—33no—
358C2×C3×D4—33no—
359C2×C3×D4—33no—
360C2×C3×D4—33no—
361C22×C3×C4—23no—
362C22×C3×C4—33no—
363C22×C3×C4—33no—
364C22×C3×C4—36no—
365C22×C3×C4—33no—
366C22×C3×C4C22×D313yes—
367C22×C3×C4C22×D313yes—
368C2×#67—33no—
369C2×#67—33no—
370C2×#67—33no—
371C2×#67—33no—
372C2×#67—33no—
373C2×#67—33no—
374C2×#67—33no—
375C2×#67—33no—
376C2×#67—33no—
377C2×#67—63no—
378C2×#67C22×D313yes—
379C2×#67C22×D311yescharacteristic
380C2×#67C22×D313yes—
381C22×Dic3—33no—
382C22×Dic3—33no—
383#239—24no—
384#239—212no—
385#239—64no—
386#239—64no—
387#239—124no—
388#239#6718yescomplemented
389D3×Q8—24no—
390D3×Q8—212no—
391D3×D4—612no—
392D3×D4—612no—
393D3×D4—612no—
394D3×D4—612no—
395#235—212no—
396#235—212no—
397#235—612no—
398#235—612no—
399C2×D12—33no—
400C2×D12—33no—
401C2×D12—33no—
402C2×D12—33no—
403C2×D12—33no—
404C2×D12—63no—
405C2×D12—612no—
406C2×D12—612no—
407C2×D12C22×D313yes—
408C2×D12C22×D313yes—
409C2×D12C22×D313yes—
410C2×C4×D3—33no—
411C2×C4×D3—33no—
412C2×C4×D3—33no—
413C2×C4×D3—33no—
414C2×C4×D3—63no—
415C2×C4×D3C22×D313yes—
416C2×C4×D3C22×D316yes—
417C2×C4×D3C22×D313yes—
418C2×C4×D3C22×D313yes—
419C2×Dic6—31no—
420C2×Dic6—31no—
421C2×Dic6C22×D313yes—
422C2×Dic6C22×D313yes—
423C3×C4⋊C4—33no—
424C3×C4⋊C4—33no—
425C3×C22⋊C4—31no—
426C3×C22⋊C4—33no—
427C3×C22⋊C4—36no—
428C3×C42—33no—
429#217—31no—
430#217—31no—
431#217—33no—
432#217—36no—
433#217—36no—
434#217—31no—
435#217—31no—
436#217—61no—
437#217C22×D311yescharacteristic
438(C2×D3)⋊C4—31no—
439(C2×D3)⋊C4—36no—
440(C2×D3)⋊C4—31no—
441(C2×D3)⋊C4—33no—
442(C2×D3)⋊C4—36no—
443(C2×D3)⋊C4—33no—
444(C2×D3)⋊C4—36no—
445(C2×D3)⋊C4—33no—
446(C2×D3)⋊C4—36no—
447(C2×D3)⋊C4—33no—
448(C2×D3)⋊C4—36no—
449(C2×D3)⋊C4—33no—
450(C2×D3)⋊C4—36no—
451(C2×D3)⋊C4—63no—
452(C2×D3)⋊C4—66no—
453(C2×D3)⋊C4C22×D313yes—
454(C2×D3)⋊C4C22×D316yes—
455C4⋊Dic3—33no—
456C4⋊Dic3—33no—
457C4⋊Dic3—33no—
458C4⋊Dic3—63no—
459C4⋊Dic3C22×D313yes—
460Dic3⋊C4—33no—
461Dic3⋊C4—33no—
462Dic3⋊C4—33no—
463Dic3⋊C4—33no—
464Dic3⋊C4—33no—
465Dic3⋊C4—63no—
466Dic3⋊C4C22×D313yes—
467C4×Dic3—33no—
468C4×Dic3—33no—
469C4×Dic3—31no—
470C4×Dic3—33no—
471C4×Dic3—31no—
472C4×Dic3—33no—
473C4×Dic3—63no—
474C4×Dic3C22×D313yes—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32C2511yescharacteristic
479C2×C3⋊D3—23no—
480C2×C3⋊D3—23no—
481C2×C3⋊D3—23no—
482C2×C3×D3—23no—
483C2×C3×D3—23no—
484C2×C3×D3—23no—
485C2×C3×D3—21no—
486C2×C3×D3—21no—
487C2×C3×D3—23no—
488C2×C3×D3—21no—
489C2×C3×D3—23no—
490C2×C3×D3C22×D416yes—
491D32—812no—
492C32×C4—23no—
493C32×C4C22×D416yes—
494C3⋊Dic3—21no—
495C3⋊Dic3—21no—
496C3⋊Dic3—23no—
497C3×Dic3—21no—
498C3×Dic3—23no—
499C3×Dic3—21no—
500C3×Dic3—23no—
501C3×Dic3C22×D412yes—
5022−1+4—68no—
503H(5,𝔽2)—188no—
504C2×#41—31no—
505C2×#41—33no—
506C2×#41—31no—
507C2×#41—33no—
508C2×#41—33no—
509C2×#41—93no—
510C2×#41—91no—
511C22×Q8—33no—
512C22×Q8—31no—
513C22×Q8D3211yescharacteristic, complemented
514C22×D4—93no—
515C22×D4—93no—
516C22×D4—93no—
517C4⋊Q8—93no—
518#127—93no—
519#124—33no—
520#124—93no—
521#124—91no—
522#124—93no—
523#124—96no—
524#124—93no—
525#124—93no—
526#123—96no—
527#123—96no—
528C22⋊Q8—33no—
529C22⋊Q8—93no—
530C22⋊Q8—93no—
531C22⋊Q8—93no—
532#121—33no—
533#121—93no—
534#121—93no—
535#121—93no—
536#121—93no—
537#121—93no—
538#121—93no—
539#121—93no—
540#120—96no—
541#120—96no—
542C4×Q8—31no—
543C4×Q8—91no—
544C4×D4—33no—
545C4×D4—93no—
546C4×D4—93no—
547C4×D4—93no—
548C4×D4—93no—
549C4×D4—93no—
550#117—93no—
551C2×C22⋊C4—96no—
552C2×C22⋊C4—96no—
553C2×C42—93no—
554C23×C3—21no—
555C23×C3—33no—
556C23×C3—33no—
557C23×C3—31no—
558C23×C3C23×D311yescharacteristic
559C23×C3C23×D311yescharacteristic
560C22×D3—33no—
561C22×D3—33no—
562C22×D3—63no—
563C22×D3—612no—
564C22×D3—612no—
565C22×D3—126no—
566C22×D3—126no—
567C22×D3—126no—
568C22×D3—126no—
569C22×D3C23×D313yes—
570C22×D3C23×D311yescharacteristic
571C22×D3C23×D313yes—
572C3×Q8—26no—
573C3×Q8—26no—
574C3×Q8—24no—
575C3×Q8—46no—
576C3×Q8—66no—
577C3×Q8—66no—
578C3×Q8D3×D414yes—
579C3×Q8C2×#6714yes—
580C3×D4—312no—
581C3×D4—66no—
582C3×D4—62no—
583C3×D4—66no—
584C3×D4—66no—
585C3×D4—123no—
586C2×C3×C4—26no—
587C2×C3×C4—26no—
588C2×C3×C4—23no—
589C2×C3×C4—23no—
590C2×C3×C4—31no—
591C2×C3×C4—312no—
592C2×C3×C4—33no—
593C2×C3×C4—31no—
594C2×C3×C4—31no—
595C2×C3×C4—33no—
596C2×C3×C4—46no—
597C2×C3×C4—612no—
598C2×C3×C4—66no—
599C2×C3×C4—66no—
600C2×C3×C4C23×D313yes—
601C2×C3×C4C23×D313yes—
602C2×C3×C4C23×D313yes—
603C2×C3×C4C23×D313yes—
604#67—26no—
605#67—22no—
606#67—43no—
607#67—66no—
608#67—66no—
609#67—66no—
610#67—66no—
611#67—123no—
612#67—123no—
613#67—123no—
614#67—123no—
615#67—123no—
616#67—126no—
617C2×Dic3—31no—
618C2×Dic3—31no—
619C2×Dic3—33no—
620C2×Dic3—33no—
621C2×Dic3—31no—
622C2×Dic3—31no—
623C2×Dic3—61no—
624C2×Dic3—63no—
625C2×Dic3—61no—
626C2×Dic3—123no—
627C2×Dic3—123no—
628C2×Dic3C23×D311yescharacteristic
629C2×Dic3C23×D313yes—
630C2×Dic3C23×D311yescharacteristic
631C2×Dic3C23×D313yes—
632C2×Dic3C23×D311yescharacteristic
633D12—26no—
634D12—26no—
635D12—66no—
636D12—66no—
637D12—66no—
638D12—66no—
639D12—126no—
640D12—123no—
641D12C2×#67112yes—
642C4×D3—212no—
643C4×D3—26no—
644C4×D3—26no—
645C4×D3—66no—
646C4×D3—66no—
647C4×D3—126no—
648C4×D3—123no—
649C4×D3—123no—
650C4×D3C2×#67112yes—
651Dic6—26no—
652Dic6—26no—
653Dic6—62no—
654Dic6—62no—
655C2×C32—41no—
656C2×C32C23×D411yescharacteristic
657C2×C32#58511yescharacteristic
658C2×C32#58511yescharacteristic
659C3⋊D3—43no—
660C3×D3—26no—
661C3×D3—43no—
662C3×D3—41no—
663C24—96no—
664#41—38no—
665#41—612no—
666#41—612no—
667#41—612no—
668#41—64no—
669#41—1812no—
670#41—184no—
671C2×Q8—24no—
672C2×Q8—33no—
673C2×Q8—33no—
674C2×Q8—612no—
675C2×Q8—64no—
676C2×Q8—91no—
677C2×Q8C2×D3213yes—
678C2×Q8C2×D3211yescharacteristic
679C2×D4—33no—
680C2×D4—31no—
681C2×D4—33no—
682C2×D4—33no—
683C2×D4—33no—
684C2×D4—33no—
685C2×D4—93no—
686C2×D4—93no—
687C2×D4—93no—
688C2×D4—93no—
689C2×D4—93no—
690C2×D4—93no—
691C2×D4—93no—
692C2×D4—1812no—
693C2×D4—1812no—
694C2×D4—1812no—
695C22×C4—33no—
696C22×C4—36no—
697C22×C4—33no—
698C22×C4—33no—
699C22×C4—93no—
700C22×C4—93no—
701C22×C4—93no—
702C22×C4C2×D3213yes—
703C4⋊C4—33no—
704C4⋊C4—33no—
705C4⋊C4—93no—
706C4⋊C4—93no—
707C4⋊C4—93no—
708C4⋊C4—93no—
709C22⋊C4—31no—
710C22⋊C4—33no—
711C22⋊C4—36no—
712C22⋊C4—93no—
713C22⋊C4—96no—
714C22⋊C4—93no—
715C22⋊C4—96no—
716C22⋊C4—96no—
717C22⋊C4—91no—
718C22⋊C4—91no—
719C22⋊C4—91no—
720C22⋊C4—93no—
721C22⋊C4—96no—
722C42—33no—
723C42—91no—
724C42—93no—
725C42—93no—
726C22×C3—22no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—36no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—63no—
738C22×C3—63no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—63no—
743C22×C3—63no—
744C22×C3—63no—
745C22×C3C24×D311yescharacteristic
746C22×C3C24×D311yescharacteristic
747C2×D3—23no—
748C2×D3—23no—
749C2×D3—23no—
750C2×D3—23no—
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—23no—
754C2×D3—21no—
755C2×D3—63no—
756C2×D3—63no—
757C2×D3—63no—
758C2×D3—63no—
759C2×D3—63no—
760C2×D3—63no—
761C2×D3—123no—
762C2×D3—123no—
763C2×D3—123no—
764C2×D3—2412no—
765C2×D3—2412no—
766C2×D3C22×#6716yes—
767C3×C4—23no—
768C3×C4—23no—
769C3×C4—26no—
770C3×C4—32no—
771C3×C4—43no—
772C3×C4—63no—
773C3×C4—61no—
774C3×C4—63no—
775C3×C4—61no—
776C3×C4C2×D3×D416yes—
777C3×C4C22×#6716yes—
778Dic3—21no—
779Dic3—23no—
780Dic3—21no—
781Dic3—23no—
782Dic3—61no—
783Dic3—61no—
784Dic3—61no—
785Dic3—63no—
786Dic3—63no—
787Dic3—61no—
788Dic3—121no—
789Dic3—123no—
790Dic3—121no—
791Dic3C22×#6712yes—
792C32#350011yescharacteristic, complemented, Sylow
793C23—33no—
794C23—33no—
795C23—31no—
796C23—93no—
797C23—1812no—
798C23—366no—
799C23—366no—
800C23C22×D3211yescharacteristic
801Q8—26no—
802Q8—66no—
803Q8—66no—
804Q8—182no—
805Q8D3×#6714yes—
806D4—312no—
807D4—66no—
808D4—62no—
809D4—66no—
810D4—66no—
811D4—123no—
812D4—186no—
813D4—186no—
814D4—186no—
815D4—186no—
816D4—363no—
817D4—363no—
818D4—363no—
819C2×C4—26no—
820C2×C4—31no—
821C2×C4—312no—
822C2×C4—31no—
823C2×C4—33no—
824C2×C4—31no—
825C2×C4—33no—
826C2×C4—612no—
827C2×C4—66no—
828C2×C4—66no—
829C2×C4—91no—
830C2×C4—93no—
831C2×C4—91no—
832C2×C4—186no—
833C2×C4—363no—
834C2×C4—363no—
835C2×C4C22×D3213yes—
836C2×C4C22×D3213yes—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—42no—
841C2×C3—41no—
842C2×C3—41no—
843C2×C3—66no—
844C2×C3—121no—
845C2×C3—123no—
846C2×C3C22×D3×D411yescharacteristic
847C2×C3#596411yescharacteristic
848C2×C3#596811yescharacteristic
849C2×C3#596811yescharacteristic
850C2×C3#596811yescharacteristic
851C2×C3C23×#6711yescharacteristic
852D3—26no—
853D3—43no—
854D3—41no—
855D3—123no—
856D3—123no—
857D3—243no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—36no—
862C22—63no—
863C22—63no—
864C22—63no—
865C22—61no—
866C22—61no—
867C22—63no—
868C22—61no—
869C22—63no—
870C22—183no—
871C22—183no—
872C22—183no—
873C22—7212no—
874C22C23×D3211yescharacteristic
875C4—23no—
876C4—32no—
877C4—63no—
878C4—61no—
879C4—63no—
880C4—61no—
881C4—181no—
882C4—183no—
883C4—181no—
884C4C2×D3×#6716yes—
885C3—21no—
886C3#8671511yescharacteristic, complemented
887C3#8729311yescharacteristic, complemented
888C2—41no—
889C2—66no—
890C2—123no—
891C2—121no—
892C2—363no—
893C2#1059668811yescharacteristic
894C2#1059668911yescharacteristic
895C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#3500
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C2×#64320C2semidirect
3. #10596288C2semidirect
4. C3×#5817C2semidirect
5. #10595428C2semidirect
6. #10595427C2semidirect
7. D3×#947C2semidirect
8. #10595409C2semidirect
9. #10595397C2semidirect
10. Dic3×#239C2semidirect
11. #10595342C2semidirect
12. #10595070C2semidirect
13. #10595067C2semidirect
14. #10595064C2semidirect
15. #10595003C2semidirect
18. C22×C32×Q8C22semidirect
23. C2×C3×#239C22semidirect
24. C2×C3×D3×Q8C22semidirect
25. C2×C3×D3×Q8C22semidirect
26. C2×C3×#235C22semidirect
27. C2×C3×#235C22semidirect
33. #64156C22semidirect
34. #64155C22semidirect
35. Q8×C3⋊Dic3C22semidirect
36. #64139C22semidirect
37. C4×#638C22semidirect
38. C3×#947C22semidirect
39. C3×#946C22semidirect
40. C3×Q8×Dic3C22semidirect
41. C3×#930C22semidirect
42. C3×C4×#67C22semidirect
43. #63983C22semidirect
44. #63979C22semidirect
45. #63971C22semidirect
46. #63970C22semidirect
47. #63959C22semidirect
48. #63922C22semidirect
49. D3×(C2×D3)⋊C4C22semidirect
50. D3×(C2×D3)⋊C4C22semidirect
51. #63909C22semidirect
52. #63908C22semidirect
53. #63907C22semidirect
54. #63907C22semidirect
55. #63905C22semidirect
56. C4×#626C22semidirect
57. C4×#625C22semidirect
58. #63898C22semidirect
59. Dic3×D12C22semidirect
60. #63886C22semidirect
61. #63885C22semidirect
62. C4×D3×Dic3C22semidirect
63. #63871C22semidirect
64. #63864C22semidirect
65. #63863C22semidirect
66. #63856C22semidirect
67. #63850C22semidirect
68. #63841C22semidirect
69. #63839C22semidirect
73. C2×#1007D3semidirect
88. #5817D3semidirect
115. C3×#239D4semidirect
174. C22×C3×Q8C2×D3semidirect
175. C22×C3×Q8C2×D3semidirect
184. C2×#239C2×D3semidirect
185. C2×D3×Q8C2×D3semidirect
186. C2×D3×Q8C2×D3semidirect
193. C2×#235C2×D3semidirect
194. C2×#235C2×D3semidirect
209. #947C2×D3semidirect
215. #946C2×D3semidirect
219. Q8×Dic3C2×D3semidirect
241. #930C2×D3semidirect
250. C4×#67C2×D3semidirect
388. #239#67semidirect
513. C22×Q8D32semidirect
792. C32#3500semidirect
886. C3#86715semidirect
887. C3#87293semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C2×#643202
#105962882
C3×#58172
#105954282
#105954272
D3×#9472
#105954092
#105953972
Dic3×#2392
#105953422
#105950702
#105950672
#105950642
#105950032
#872933
#867153