Finite Group Databasebeta

← #11905975

Subgroups — #11905975

Order 1152.

3745 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64314C212yesmaximal, complemented
2C3⋊D3×#127C211yesmaximal, characteristic, complemented
3C3×#5716C211yesmaximal, characteristic, complemented
4C3×D3×#127C211yesmaximal, characteristic, complemented
5#10595303C212yesmaximal, complemented
6#10595297C214yesmaximal, complemented
7#10595288C214yesmaximal, complemented
8#10595235C212yesmaximal, complemented
9D4×#626C214yesmaximal, complemented
10#10595168C212yesmaximal, complemented
11#10595143C214yesmaximal, complemented
12D3×#874C211yesmaximal, characteristic, complemented
13#10593970C211yesmaximal, characteristic, complemented
14C4×#3798C211yesmaximal, characteristic, complemented
15#10593907C211yesmaximal, characteristic, complemented
16#86242—31nomaximal
17#86195—31nomaximal
18C2×D4×C3⋊D3C2212yescomplemented
19C2×D4×C3⋊D3C2214yescomplemented
20C2×C3×#237C2212yescomplemented
21C2×C3×D3×D4C2212yescomplemented
22C2×C3×D3×D4C2214yescomplemented
23C2×#3811C2214yescomplemented
24C2×D3×#67C2214yescomplemented
25C22×#626C2214yescomplemented
26C2×#3804C2214yescomplemented
27#64314—216no—
28C2×D3×D12C2212yescomplemented
29C2×D3×D12C2214yescomplemented
30C2×#3799C2212yescomplemented
31C2×#3798C2211yescharacteristic
32C2×#3796C2212yescomplemented
33C32×#127C2211yescharacteristic, complemented
34#64149C2214yescomplemented
35#64149C2212yescomplemented
36#64083C2211yescharacteristic, complemented
37C42×C3⋊D3C2211yescharacteristic, complemented
38C3×#940C2214yescomplemented
39C3×#940C2212yescomplemented
40C3×#938C2214yescomplemented
41C3×#936C2212yescomplemented
42C3×D4×Dic3C2214yescomplemented
43C3×#874C2211yescharacteristic, complemented
44C3×C42×D3C2211yescharacteristic, complemented
45C3×C42×D3C2211yescharacteristic, complemented
46C3×#869C2211yescharacteristic, complemented
47#63983C2218yescomplemented
48#63981C2218yescomplemented
49#63978C2218yescomplemented
50#63977C2218yescomplemented
51#63971C2218yescomplemented
52#63958C2218yescomplemented
53C4×#627C2212yescomplemented
54#63916C2214yescomplemented
55#63911C2214yescomplemented
56#63911C2212yescomplemented
57#63909C2214yescomplemented
58C4×#626C2212yescomplemented
59C4×#626C2212yescomplemented
60C4×#625C2212yescomplemented
61#63898C2214yescomplemented
62#63894C2214yescomplemented
63#63874C2211yescharacteristic, complemented
64#63864C2212yescomplemented
65#63863C2212yescomplemented
66#63855C2211yescharacteristic, complemented
67#63855C2211yescharacteristic, complemented
68C2×#1009—32no—
69C2×#1004—32no—
70C3×#532—31no—
71C2×C3×#127—31no—
72#5830—32no—
73#5805—32no—
74D4×#67—34no—
75D4×#67—34no—
76#5725—31no—
77#5725—31no—
78#5718—34no—
79#5717—34no—
80#5716—31no—
81#5716D311yescharacteristic, complemented
82#5715—32no—
83#5715—32no—
84D3×#127—31no—
85D3×#127—31no—
86D3×#127—31no—
87D3×#127—61no—
88D3×#127D311yescharacteristic, complemented
89#5674—32no—
90#5674—32no—
91#5609—34no—
92#5609—34no—
93#5553—34no—
94D4×D12—34no—
95#5477—31no—
96C2×#874—31no—
97C4×#235—31no—
98C4×#235—31no—
99C23×C3⋊D3C2314yes—
100C23×C3×D3C2314yes—
101C22×D32C2314yes—
102C2×C32×D4C2314yes—
103C2×C32×D4C2312yes—
104C2×#638C2314yes—
105C2×#638C2318yes—
106D4×C3⋊D3—28no—
107D4×C3⋊D3—48no—
108C2×C4⋊(C3⋊D3)C2312yes—
109C2×C4⋊(C3⋊D3)C2314yes—
110C2×C4×C3⋊D3C2312yes—
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C3×#67C2314yes—
113C2×C3×#67C2314yes—
114C2×C3×#67C2318yes—
115C22×C3×Dic3C2314yes—
116C3×#237—28no—
117C3×D3×D4—28no—
118C3×D3×D4—48no—
119C2×C3×D12C2312yes—
120C2×C3×D12C2314yes—
121C2×C3×C4×D3C2312yes—
122C2×C3×C4×D3C2312yes—
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×Dic6C2312yes—
126#3811—216no—
127D3×#67—216no—
128C2×#627C2311yescharacteristic
129C2×#626—216no—
130C2×#626C2314yes—
131C2×#626C2314yes—
132C2×#626C2314yes—
133C2×#626C2318yes—
134C2×#626C2311yescharacteristic
135C2×#626C2311yescharacteristic
136C2×#625C2311yescharacteristic
137C2×#624C2314yes—
138#3804—216no—
139C2×D3×Dic3C2314yes—
140D3×D12—28no—
141D3×D12—48no—
142#3799—28no—
143#3798D418yescomplemented
144#3796—28no—
145C32×C42C2311yescharacteristic
146C4×C3⋊Dic3C2311yescharacteristic
147C4×C3⋊Dic3C2312yes—
148C3×#217C2318yes—
149C3×C4⋊Dic3C2314yes—
150C3×C4×Dic3C2312yes—
151C3×C4×Dic3C2311yescharacteristic
152C3×C4×Dic3C2311yescharacteristic
153C3×C4×Dic3C2312yes—
154#3724C2312yes—
155Dic3⋊Dic3C2312yes—
156Dic3⋊Dic3C2312yes—
157#3722C2318yes—
158#3722C2312yes—
159(C2×D3)⋊Dic3C2312yes—
160(C2×D3)⋊Dic3C2312yes—
161(C2×D3)⋊Dic3C2318yes—
162#3498—91noSylow
163C2×C3×#41—32no—
164C22×C3×D4—32no—
165C22×C3×D4—34no—
166C22×#67—34no—
167C22×#67—34no—
168#1009—616no—
169C2×#239—32no—
170C2×#239—32no—
171#1004—616no—
172C2×#237—34no—
173C2×#237—32no—
174C2×#237C2×D312yescomplemented
175C2×D3×D4—34no—
176C2×D3×D4—32no—
177C2×D3×D4—32no—
178C2×D3×D4—34no—
179C2×D3×D4—34no—
180C2×D3×D4—34no—
181C2×D3×D4—34no—
182C2×D3×D4—32no—
183C2×D3×D4—34no—
184C2×D3×D4—62no—
185C2×D3×D4—64no—
186C2×D3×D4C2×D312yescomplemented
187C2×D3×D4C2×D314yescomplemented
188C2×#235—34no—
189C2×#235—31no—
190C2×#235—31no—
191C2×#235—32no—
192C22×D12—34no—
193C22×D12—32no—
194C22×D12—34no—
195C3×C4⋊Q8—31no—
196C3×#127—21no—
197C3×#127—32no—
198C3×#127—34no—
199C3×#127—31no—
200C3×#127C2×D311yescharacteristic, complemented
201C3×#127C2×D311yescharacteristic, complemented
202C3×#124—32no—
203C3×#121—34no—
204C3×C4×D4—34no—
205C2×C3×C42—31no—
206C2×C3×C42—31no—
207#953—38no—
208#947—32no—
209#947—32no—
210#940—32no—
211#940—32no—
212#940—34no—
213#940—34no—
214#940—32no—
215#940—34no—
216#940—62no—
217#940—64no—
218#940C2×D312yescomplemented
219#940C2×D314yescomplemented
220#939—38no—
221#939—38no—
222#938—38no—
223#938—34no—
224#938C2×D314yescomplemented
225#937—38no—
226#937—38no—
227#937—38no—
228#936—32no—
229#936C2×D312yescomplemented
230D4×Dic3—34no—
231D4×Dic3C2×D314yescomplemented
232#930—38no—
233#930—34no—
234C4×#67—32no—
235C4×#67—32no—
236C4×#67—32no—
237C4×#67—32no—
238#926—31no—
239#926—31no—
240#895—34no—
241#895—34no—
242#893—34no—
243#893—34no—
244#884—38no—
245#884—38no—
246#882—38no—
247#882—38no—
248#875—32no—
249#874—32no—
250#874—34no—
251#874—31no—
252#874—31no—
253#874—61no—
254#874C2×D311yescharacteristic, complemented
255C4×D12—32no—
256C4×D12—32no—
257C4×D12—34no—
258#872—31no—
259#872—31no—
260#872—31no—
261#872—31no—
262C42×D3—31no—
263C42×D3—31no—
264C42×D3—61no—
265C42×D3C2×D311yescharacteristic, complemented
266C42×D3C2×D311yescharacteristic, complemented
267#869C2×D311yescharacteristic, complemented
268C4×Dic6—32no—
269C4×Dic6—32no—
270C23×C32C2414yes—
271C22×C3⋊D3—28no—
272C22×C3⋊D3—48no—
273C22×C3⋊D3C2414yes—
274C22×C3⋊D3C2411yescharacteristic
275C22×C3×D3—28no—
276C22×C3×D3—48no—
277C22×C3×D3C2414yes—
278C22×C3×D3C2411yescharacteristic
279C22×C3×D3C2411yescharacteristic
280C2×D32—28no—
281C2×D32—48no—
282C32×D4—24no—
283C32×D4—28no—
284C2×C32×C4C2411yescharacteristic
285C2×C32×C4C2412yes—
286#638—28no—
287#638—48no—
288C2×C3⋊Dic3C2412yes—
289C2×C3⋊Dic3C2411yescharacteristic
290C4⋊(C3⋊D3)—24no—
291C4⋊(C3⋊D3)—28no—
292C4×C3⋊D3—24no—
293C4×C3⋊D3C2×D414yescomplemented
294C3×#67—28no—
295C3×#67—28no—
296C3×#67—48no—
297C2×C3×Dic3—28no—
298C2×C3×Dic3C2414yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2411yescharacteristic
302C2×C3×Dic3C2411yescharacteristic
303C3×D12—24no—
304C3×D12—28no—
305C3×C4×D3—24no—
306C3×C4×D3—24no—
307C3×C4×D3C2×D414yescomplemented
308C3×C4×D3C2×D414yescomplemented
309C3×Dic6—24no—
310#627C2×D414yescomplemented
311#626—28no—
312#626—28no—
313#626—28no—
314#626—48no—
315#626C2×D414yescomplemented
316#626C2×D414yescomplemented
317#625C2×D414yescomplemented
318#624—28no—
319D3×Dic3—28no—
320C2×H(5,𝔽2)—92no—
321#550—94no—
322D42—94no—
323D42—94no—
324D42—94no—
325#535—92no—
326#535—92no—
327#535—92no—
328#532—31no—
329#532—91no—
330#532—91no—
331C2×#127—31no—
332C2×#127—91no—
333C2×#127—91no—
334C4×#41—91no—
335C24×C3—34no—
336C23×D3—34no—
337C23×D3—34no—
338C23×D3—34no—
339C23×D3—34no—
340C23×D3—64no—
341C23×D3C22×D314yes—
342C3×#41—68no—
343C2×C3×Q8—32no—
344C2×C3×D4—24no—
345C2×C3×D4—22no—
346C2×C3×D4—34no—
347C2×C3×D4—34no—
348C2×C3×D4—38no—
349C2×C3×D4—34no—
350C2×C3×D4—32no—
351C2×C3×D4—68no—
352C2×C3×D4—128no—
353C2×C3×D4C22×D314yes—
354C2×C3×D4C22×D312yes—
355C2×C3×D4C22×D314yes—
356C2×C3×D4C22×D312yes—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—34no—
360C22×C3×C4—32no—
361C22×C3×C4—32no—
362C2×#67—31no—
363C2×#67—31no—
364C2×#67—34no—
365C2×#67—34no—
366C2×#67—38no—
367C2×#67—38no—
368C2×#67—31no—
369C2×#67—31no—
370C2×#67—34no—
371C2×#67—34no—
372C2×#67—34no—
373C2×#67—38no—
374C2×#67—64no—
375C2×#67—68no—
376C2×#67—616no—
377C2×#67—616no—
378C2×#67C22×D314yes—
379C2×#67C22×D314yes—
380C2×#67C22×D318yes—
381C22×Dic3—34no—
382C22×Dic3C22×D314yes—
383#239—68no—
384#239—68no—
385#237—28no—
386#237—68no—
387#237—616no—
388D3×D4—28no—
389D3×D4—48no—
390D3×D4—68no—
391D3×D4—68no—
392D3×D4—616no—
393D3×D4—616no—
394D3×D4—616no—
395D3×D4—68no—
396D3×D4—128no—
397D3×D4—128no—
398D3×D4—128no—
399D3×D4—128no—
400D3×D4—1216no—
401#235—38no—
402#235—38no—
403#235—68no—
404#235—616no—
405C2×D12—31no—
406C2×D12—31no—
407C2×D12—34no—
408C2×D12—34no—
409C2×D12—34no—
410C2×D12—34no—
411C2×D12—34no—
412C2×D12—32no—
413C2×D12—32no—
414C2×D12—38no—
415C2×D12—64no—
416C2×D12—62no—
417C2×D12—68no—
418C2×D12—616no—
419C2×D12—128no—
420C2×D12C22×D314yes—
421C2×D12C22×D312yes—
422C2×C4×D3—31no—
423C2×C4×D3—31no—
424C2×C4×D3—34no—
425C2×C4×D3—32no—
426C2×C4×D3—32no—
427C2×C4×D3—34no—
428C2×C4×D3—34no—
429C2×C4×D3—61no—
430C2×C4×D3—62no—
431C2×C4×D3C22×D312yes—
432C2×C4×D3C22×D312yes—
433C2×C4×D3C22×D311yescharacteristic
434C2×C4×D3C22×D311yescharacteristic
435C2×Dic6—31no—
436C2×Dic6—31no—
437C2×Dic6C22×D312yes—
438C3×C4⋊C4—34no—
439C3×C22⋊C4—38no—
440C3×C42—21no—
441C3×C42—32no—
442C3×C42—32no—
443C3×C42—31no—
444C3×C42—31no—
445C3×C42C22×D311yescharacteristic
446C3×C42C22×D311yescharacteristic
447#217—32no—
448#217—32no—
449#217—38no—
450#217C22×D318yes—
451(C2×D3)⋊C4—32no—
452(C2×D3)⋊C4—32no—
453(C2×D3)⋊C4—38no—
454(C2×D3)⋊C4—32no—
455(C2×D3)⋊C4—32no—
456(C2×D3)⋊C4—38no—
457(C2×D3)⋊C4—38no—
458C4⋊Dic3—32no—
459C4⋊Dic3—32no—
460C4⋊Dic3C22×D314yes—
461Dic3⋊C4—32no—
462Dic3⋊C4—32no—
463Dic3⋊C4—32no—
464Dic3⋊C4—32no—
465C4×Dic3—32no—
466C4×Dic3—32no—
467C4×Dic3—31no—
468C4×Dic3—31no—
469C4×Dic3—61no—
470C4×Dic3—62no—
471C4×Dic3C22×D312yes—
472C4×Dic3C22×D312yes—
473C4×Dic3C22×D311yescharacteristic
474C4×Dic3C22×D311yescharacteristic
475C22×C32—24no—
476C22×C32—28no—
477C22×C32C2511yescharacteristic
478C2×C3⋊D3—22no—
479C2×C3⋊D3—24no—
480C2×C3⋊D3—28no—
481C2×C3⋊D3—88no—
482C2×C3⋊D3C22×D412yes—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—24no—
486C2×C3×D3—28no—
487C2×C3×D3—88no—
488C2×C3×D3C22×D412yes—
489C2×C3×D3C22×D412yes—
490D32—88no—
491C32×C4C22×D412yes—
492C32×C4H(5,𝔽2)14yescomplemented
493C3⋊Dic3—22no—
494C3⋊Dic3C22×D412yes—
495C3×Dic3—24no—
496C3×Dic3—22no—
497C3×Dic3—22no—
498C3×Dic3C22×D412yes—
499C3×Dic3C22×D412yes—
500H(5,𝔽2)—1816no—
501C2×#41—32no—
502C2×#41—91no—
503C2×#41—94no—
504C2×#41—92no—
505C2×#41—92no—
506C22×D4—32no—
507C22×D4—34no—
508C22×D4—92no—
509C22×D4—94no—
510C22×D4—94no—
511C22×D4—94no—
512C22×D4—94no—
513C22×D4—92no—
514C22×D4—94no—
515C4⋊Q8—31no—
516#127—32no—
517#127—34no—
518#127—31no—
519#127—92no—
520#127—94no—
521#127—92no—
522#127—94no—
523#127—91no—
524#127D3211yescharacteristic, complemented
525#124—32no—
526#124—92no—
527#124—92no—
528#121—34no—
529#121—98no—
530#121—98no—
531#121—94no—
532#121—94no—
533#121—98no—
534#120—98no—
535#120—98no—
536#120—98no—
537C4×Q8—92no—
538C4×D4—34no—
539C4×D4—94no—
540C4×D4—92no—
541C4×D4—92no—
542C4×D4—94no—
543C4×D4—92no—
544#117—91no—
545#117—91no—
546#117—91no—
547C2×C42—31no—
548C2×C42—31no—
549C2×C42—91no—
550C23×C3—24no—
551C23×C3—31no—
552C23×C3—31no—
553C23×C3—34no—
554C23×C3—68no—
555C23×C3—128no—
556C23×C3C23×D314yes—
557C23×C3C23×D314yes—
558C22×D3—28no—
559C22×D3—31no—
560C22×D3—31no—
561C22×D3—34no—
562C22×D3—34no—
563C22×D3—48no—
564C22×D3—61no—
565C22×D3—64no—
566C22×D3—68no—
567C22×D3—68no—
568C22×D3—68no—
569C22×D3—68no—
570C22×D3—128no—
571C22×D3—128no—
572C22×D3—128no—
573C22×D3—128no—
574C22×D3—128no—
575C22×D3—1216no—
576C22×D3C23×D314yes—
577C22×D3C23×D311yescharacteristic
578C22×D3C23×D311yescharacteristic
579C3×Q8—64no—
580C3×D4—24no—
581C3×D4—24no—
582C3×D4—28no—
583C3×D4—28no—
584C3×D4—44no—
585C3×D4—48no—
586C3×D4—68no—
587C3×D4—68no—
588C3×D4—64no—
589C3×D4—68no—
590C3×D4—128no—
591C2×C3×C4—21no—
592C2×C3×C4—22no—
593C2×C3×C4—31no—
594C2×C3×C4—31no—
595C2×C3×C4—34no—
596C2×C3×C4—34no—
597C2×C3×C4—32no—
598C2×C3×C4—32no—
599C2×C3×C4—34no—
600C2×C3×C4—68no—
601C2×C3×C4—64no—
602C2×C3×C4—64no—
603C2×C3×C4C23×D311yescharacteristic
604C2×C3×C4C23×D311yescharacteristic
605C2×C3×C4C23×D312yes—
606C2×C3×C4C23×D312yes—
607#67—28no—
608#67—28no—
609#67—34no—
610#67—34no—
611#67—34no—
612#67—34no—
613#67—48no—
614#67—68no—
615#67—68no—
616#67—68no—
617#67—68no—
618#67—68no—
619#67—128no—
620#67—128no—
621#67—128no—
622#67—128no—
623#67—1216no—
624C2×Dic3—28no—
625C2×Dic3—31no—
626C2×Dic3—31no—
627C2×Dic3—32no—
628C2×Dic3—32no—
629C2×Dic3—61no—
630C2×Dic3—62no—
631C2×Dic3—68no—
632C2×Dic3C23×D312yes—
633C2×Dic3C23×D312yes—
634C2×Dic3C23×D314yes—
635C2×Dic3C23×D311yescharacteristic
636C2×Dic3C23×D311yescharacteristic
637D12—24no—
638D12—28no—
639D12—34no—
640D12—34no—
641D12—68no—
642D12—68no—
643D12—68no—
644D12—64no—
645D12—64no—
646D12—68no—
647D12—68no—
648D12—124no—
649D12—128no—
650D12—128no—
651C4×D3—24no—
652C4×D3—24no—
653C4×D3—34no—
654C4×D3—34no—
655C4×D3—64no—
656C4×D3—68no—
657C4×D3—68no—
658C4×D3—68no—
659C4×D3—64no—
660C4×D3—64no—
661C4×D3—68no—
662C4×D3D3×D414yescomplemented
663C4×D3D3×D414yescomplemented
664Dic6—24no—
665Dic6—34no—
666Dic6—34no—
667C2×C32—44no—
668C2×C32C23×D411yescharacteristic
669C2×C32C2×H(5,𝔽2)12yes—
670C3⋊D3—22no—
671C3⋊D3—44no—
672C3×D3—22no—
673C3×D3—22no—
674C3×D3—44no—
675C24—34no—
676C24—94no—
677C24—94no—
678#41—68no—
679#41—98no—
680#41—188no—
681#41—1816no—
682#41—188no—
683C2×Q8—32no—
684C2×Q8—91no—
685C2×D4—34no—
686C2×D4—34no—
687C2×D4—38no—
688C2×D4—34no—
689C2×D4—32no—
690C2×D4—68no—
691C2×D4—91no—
692C2×D4—91no—
693C2×D4—94no—
694C2×D4—94no—
695C2×D4—94no—
696C2×D4—98no—
697C2×D4—91no—
698C2×D4—94no—
699C2×D4—98no—
700C2×D4—94no—
701C2×D4—92no—
702C2×D4—128no—
703C2×D4—188no—
704C2×D4—1816no—
705C2×D4—188no—
706C2×D4—1816no—
707C2×D4—1816no—
708C2×D4—368no—
709C2×D4—368no—
710C2×D4C2×D3214yes—
711C2×D4C2×D3212yes—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—34no—
715C22×C4—32no—
716C22×C4—32no—
717C22×C4—94no—
718C22×C4—94no—
719C22×C4—91no—
720C22×C4—92no—
721C4⋊C4—34no—
722C4⋊C4—92no—
723C4⋊C4—92no—
724C4⋊C4—92no—
725C22⋊C4—38no—
726C22⋊C4—92no—
727C22⋊C4—98no—
728C22⋊C4—92no—
729C22⋊C4—92no—
730C22⋊C4—98no—
731C42—31no—
732C42—31no—
733C42—32no—
734C42—32no—
735C42—91no—
736C42—92no—
737C42C2×D3211yescharacteristic
738C22×C3—24no—
739C22×C3—24no—
740C22×C3—28no—
741C22×C3—28no—
742C22×C3—21no—
743C22×C3—32no—
744C22×C3—32no—
745C22×C3—44no—
746C22×C3—48no—
747C22×C3—62no—
748C22×C3—62no—
749C22×C3—64no—
750C22×C3—68no—
751C22×C3—248no—
752C22×C3C24×D311yescharacteristic
753C22×C3C24×D311yescharacteristic
754C2×D3—22no—
755C2×D3—22no—
756C2×D3—24no—
757C2×D3—28no—
758C2×D3—32no—
759C2×D3—32no—
760C2×D3—62no—
761C2×D3—64no—
762C2×D3—62no—
763C2×D3—62no—
764C2×D3—64no—
765C2×D3—64no—
766C2×D3—68no—
767C2×D3—68no—
768C2×D3—88no—
769C2×D3—124no—
770C2×D3—128no—
771C2×D3—248no—
772C2×D3—248no—
773C2×D3—248no—
774C2×D3—248no—
775C2×D3—2416no—
776C2×D3C2×D3×D412yes—
777C2×D3C2×D3×D412yes—
778C3×C4—22no—
779C3×C4—24no—
780C3×C4—32no—
781C3×C4—32no—
782C3×C4—64no—
783C3×C4—62no—
784C3×C4—62no—
785C3×C4C2×D3×D412yes—
786C3×C4C2×D3×D412yes—
787C3×C4#100414yescomplemented
788C3×C4#100914yescomplemented
789Dic3—24no—
790Dic3—22no—
791Dic3—22no—
792Dic3—32no—
793Dic3—32no—
794Dic3—62no—
795Dic3—64no—
796Dic3—62no—
797Dic3—62no—
798Dic3C2×D3×D412yes—
799Dic3C2×D3×D412yes—
800C32#349811yescharacteristic, complemented, Sylow
801C23—31no—
802C23—31no—
803C23—34no—
804C23—68no—
805C23—91no—
806C23—94no—
807C23—128no—
808C23—188no—
809C23—188no—
810C23—368no—
811C23—368no—
812C23C22×D3214yes—
813Q8—64no—
814Q8—94no—
815D4—24no—
816D4—28no—
817D4—68no—
818D4—68no—
819D4—64no—
820D4—68no—
821D4—94no—
822D4—94no—
823D4—94no—
824D4—128no—
825D4—188no—
826D4—188no—
827D4—188no—
828D4—188no—
829D4—184no—
830D4—188no—
831D4—368no—
832D4—368no—
833C2×C4—31no—
834C2×C4—31no—
835C2×C4—34no—
836C2×C4—34no—
837C2×C4—32no—
838C2×C4—32no—
839C2×C4—34no—
840C2×C4—68no—
841C2×C4—64no—
842C2×C4—64no—
843C2×C4—91no—
844C2×C4—94no—
845C2×C4—92no—
846C2×C4—188no—
847C2×C4—188no—
848C2×C4—184no—
849C2×C4C22×D3211yescharacteristic
850C2×C4C22×D3212yes—
851C2×C3—21no—
852C2×C3—22no—
853C2×C3—44no—
854C2×C3—44no—
855C2×C3—62no—
856C2×C3—62no—
857C2×C3—84no—
858C2×C3—124no—
859C2×C3C22×D3×D411yescharacteristic
860C2×C3C22×D3×D411yescharacteristic
861C2×C3C2×#100412yes—
862C2×C3C2×#100912yes—
863D3—22no—
864D3—22no—
865D3—44no—
866D3—64no—
867D3—62no—
868D3—62no—
869D3—124no—
870D3—124no—
871D3—244no—
872C22—24no—
873C22—28no—
874C22—32no—
875C22—32no—
876C22—62no—
877C22—62no—
878C22—64no—
879C22—68no—
880C22—92no—
881C22—182no—
882C22—184no—
883C22—188no—
884C22—248no—
885C22—728no—
886C22—728no—
887C22C23×D3211yescharacteristic
888C4—32no—
889C4—32no—
890C4—64no—
891C4—62no—
892C4—62no—
893C4—92no—
894C4—182no—
895C4D32×D412yes—
896C4#6431414yescomplemented
897C3—21no—
898C3#8619511yescharacteristic, complemented
899C3#8624211yescharacteristic, complemented
900C2—44no—
901C2—62no—
902C2—62no—
903C2—124no—
904C2—182no—
905C2—364no—
906C2C2×D32×D411yescharacteristic
907C2C2×#6431412yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#127C22
hypercenter#127D32
hypocenterC32#3498
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C2×#64314C2semidirect
2. C3⋊D3×#127C2semidirect
3. C3×#5716C2semidirect
4. C3×D3×#127C2semidirect
5. #10595303C2semidirect
6. #10595297C2semidirect
7. #10595288C2semidirect
8. #10595235C2semidirect
9. D4×#626C2semidirect
10. #10595168C2semidirect
11. #10595143C2semidirect
12. D3×#874C2semidirect
13. #10593970C2semidirect
14. C4×#3798C2semidirect
15. #10593907C2semidirect
18. C2×D4×C3⋊D3C22semidirect
19. C2×D4×C3⋊D3C22semidirect
20. C2×C3×#237C22semidirect
21. C2×C3×D3×D4C22semidirect
22. C2×C3×D3×D4C22semidirect
23. C2×#3811C22semidirect
24. C2×D3×#67C22semidirect
25. C22×#626C22semidirect
26. C2×#3804C22semidirect
28. C2×D3×D12C22semidirect
29. C2×D3×D12C22semidirect
30. C2×#3799C22semidirect
32. C2×#3796C22semidirect
33. C32×#127C22semidirect
34. #64149C22semidirect
35. #64149C22semidirect
36. #64083C22semidirect
37. C42×C3⋊D3C22semidirect
38. C3×#940C22semidirect
39. C3×#940C22semidirect
40. C3×#938C22semidirect
41. C3×#936C22semidirect
42. C3×D4×Dic3C22semidirect
43. C3×#874C22semidirect
44. C3×C42×D3C22semidirect
45. C3×C42×D3C22semidirect
46. C3×#869C22semidirect
47. #63983C22semidirect
48. #63981C22semidirect
49. #63978C22semidirect
50. #63977C22semidirect
51. #63971C22semidirect
52. #63958C22semidirect
53. C4×#627C22semidirect
54. #63916C22semidirect
55. #63911C22semidirect
56. #63911C22semidirect
57. #63909C22semidirect
58. C4×#626C22semidirect
59. C4×#626C22semidirect
60. C4×#625C22semidirect
61. #63898C22semidirect
62. #63894C22semidirect
63. #63874C22semidirect
64. #63864C22semidirect
65. #63863C22semidirect
66. #63855C22semidirect
67. #63855C22semidirect
81. #5716D3semidirect
88. D3×#127D3semidirect
143. #3798D4semidirect
174. C2×#237C2×D3semidirect
186. C2×D3×D4C2×D3semidirect
187. C2×D3×D4C2×D3semidirect
200. C3×#127C2×D3semidirect
201. C3×#127C2×D3semidirect
218. #940C2×D3semidirect
219. #940C2×D3semidirect
224. #938C2×D3semidirect
229. #936C2×D3semidirect
231. D4×Dic3C2×D3semidirect
254. #874C2×D3semidirect
265. C42×D3C2×D3semidirect
266. C42×D3C2×D3semidirect
267. #869C2×D3semidirect
293. C4×C3⋊D3C2×D4semidirect
307. C3×C4×D3C2×D4semidirect
308. C3×C4×D3C2×D4semidirect
310. #627C2×D4semidirect
315. #626C2×D4semidirect
316. #626C2×D4semidirect
317. #625C2×D4semidirect
492. C32×C4H(5,𝔽2)semidirect
524. #127D32semidirect
662. C4×D3D3×D4semidirect
663. C4×D3D3×D4semidirect
787. C3×C4#1004semidirect
788. C3×C4#1009semidirect
800. C32#3498semidirect
896. C4#64314semidirect
898. C3#86195semidirect
899. C3#86242semidirect

Maximal subgroups

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

subgroupindex
C2×#643142
C3⋊D3×#1272
C3×#57162
C3×D3×#1272
#105953032
#105952972
#105952882
#105952352
D4×#6262
#105951682
#105951432
D3×#8742
#105939702
C4×#37982
#105939072
#862423
#861953