Finite Group Databasebeta

← #11675172

Subgroups — #11675172

Order 768.

1802 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3502C211yesmaximal, characteristic, complemented
2#86259C211yesmaximal, characteristic
3#83704C212yesmaximal, complemented
4#83703C212yesmaximal, complemented
5#83697C214yesmaximal, complemented
6#83691C214yesmaximal, complemented
7#83690C212yesmaximal, complemented
8#83689C212yesmaximal, complemented
9#83476C212yesmaximal, complemented
10#83470C212yesmaximal, complemented
11#83350C211yesmaximal, characteristic, complemented
12#83334C211yesmaximal, characteristic, complemented
13#83328C211yesmaximal, characteristic, complemented
14#82551C212yesmaximal, complemented
15#82547C212yesmaximal, complemented
16#82441C211yesmaximal, characteristic, complemented
17C2×C4×#215C211yesmaximal, characteristic, complemented
18#61327—31nomaximal, Sylow
19C3×Q82—21no—
20C3×Q82C2212yescomplemented
21C3×#557—21no—
22C3×#557—22no—
23C3×#557C2212yescomplemented
24C3×#557C2214yescomplemented
25C3×#544—22no—
26C3×#544C2212yes—
27C3×#533—22no—
28C3×#533C2211yescharacteristic
29C3×#533C2211yescharacteristic
30C3×#519C2212yes—
31C2×C3×C4×Q8C2211yescharacteristic
32C2×#942C2212yes—
33C22×#215C2211yescharacteristic
34#5734—21no—
35#5726—21no—
36#5695—22no—
37#5644—22no—
38#5627—22no—
39#5585C2214yes—
40#5584C2212yes—
41#5577C2212yes—
42#5525C2212yes—
43#5523C2212yes—
44#5477C2211yescharacteristic
45C2×C4×D12C2211yescharacteristic
46C2×#835C2211yescharacteristic
47#5094C2214yescomplemented
48#5093C2211yescharacteristic, complemented
49#5093C2211yescharacteristic, complemented
50#5089C2214yes—
51#5088C2214yes—
52#5088C2211yescharacteristic, complemented
53#5088C2211yescharacteristic, complemented
54#5087C2212yes—
55#5084C2212yes—
56#5084C2214yescomplemented
57#5068C2214yes—
58#5068C2212yescomplemented
59#5068C2212yescomplemented
60#5067C2214yes—
61#5066C2214yes—
62#5066C2214yescomplemented
63#5063C2214yescomplemented
64#5031C2212yescomplemented
65#5030C2214yescomplemented
66C4×#216C2214yescomplemented
67#5028C2214yes—
68#5028C2214yes—
69#5028C2214yescomplemented
70#5027C2214yes—
71#5027C2214yes—
72#5027C2212yescomplemented
73#5026C2214yescomplemented
74C4×#215C2212yes—
75C4×#215C2212yes—
76C4×#215C2212yes—
77C4×#215C2212yes—
78C4×#215C2214yescomplemented
79#5024C2212yescomplemented
80#5024C2212yescomplemented
81Q8×C3⋊C8C2212yescomplemented
82Q8×C3⋊C8C2212yescomplemented
83#5002C2212yes—
84#5002C2212yes—
85#5001C2212yes—
86#4999C2212yes—
87#4997C2212yes—
88#4995C2212yes—
89#4966C2212yes—
90C2×#809C2211yescharacteristic
91C2×#808C2211yescharacteristic
92#4924C2211yescharacteristic
93C2×C4×C3⋊C8C2211yescharacteristic
94#3506—31no—
95#3502D311yescharacteristic, complemented
96#3371—34no—
97#3369—32no—
98#3368—32no—
99#3365—34no—
100#3364—32no—
101#3362—32no—
102#3136—32no—
103#3131—31no—
104#3084—32no—
105#3077—31no—
106#3043—32no—
107#3037—31no—
108#2960—31no—
109#2947—32no—
110C2×C4×SD16—31no—
111C22×C3×Q8C2311yescharacteristic
112C2×#239—22no—
113C2×#235C2312yes—
114C22×D12C2311yescharacteristic
115C22×C4×D3—21no—
116C3×C4⋊Q8—24no—
117C3×C4⋊Q8—22no—
118C3×C4⋊Q8—22no—
119C3×C4⋊Q8—22no—
120C3×C4⋊Q8—24no—
121C3×C4⋊Q8D411yescharacteristic
122C3×C4⋊Q8D411yescharacteristic
123C3×C4⋊Q8C2311yescharacteristic
124C3×C4⋊Q8C2314yes—
125C3×C4⋊Q8C2311yescharacteristic
126C3×#125—24no—
127C3×#125—24no—
128C3×#125—24no—
129C3×#125—22no—
130C3×#125D412yes—
131C3×#125C2314yes—
132C3×#125C2312yes—
133C3×C22⋊Q8—21no—
134C3×C22⋊Q8—21no—
135C3×C22⋊Q8—24no—
136C3×C22⋊Q8D412yes—
137C3×C22⋊Q8D412yes—
138C3×C4×Q8—22no—
139C3×C4×Q8—22no—
140C3×C4×Q8—22no—
141C3×C4×Q8—22no—
142C3×C4×Q8—24no—
143C3×C4×Q8—21no—
144C3×C4×Q8—21no—
145C3×C4×Q8—21no—
146C3×C4×Q8—21no—
147C3×C4×Q8C2312yes—
148C3×C4×Q8C2314yes—
149C3×C4×Q8C2312yes—
150C3×C4×Q8C2314yes—
151C3×C4×Q8C2312yes—
152C3×C4×Q8C2312yes—
153C3×#117—24no—
154C3×#117C2312yes—
155C3×#117C2312yes—
156C2×C3×C4⋊C4—21no—
157C2×C3×C4⋊C4C2311yescharacteristic
158C2×C3×C42—21no—
159C2×C3×C42C2311yescharacteristic
160#947—24no—
161#946—22no—
162C2×#216C2314yes—
163#942—28no—
164C2×#215—24no—
165C2×#215C2312yes—
166C2×#215C2312yes—
167C2×#215C2314yes—
168#930—21no—
169#930—21no—
170C2×(C2×D3)⋊C4—21no—
171C2×C4⋊Dic3C2311yescharacteristic
172C2×#208C2312yes—
173C22×C3⋊C8C2311yescharacteristic
174C22×C3⋊C8C2311yescharacteristic
175#898—24no—
176#895—24no—
177#895—22no—
178#895—22no—
179#895—22no—
180#894—24no—
181#894—24no—
182#893—24no—
183#892—22no—
184#892—22no—
185D3×C4⋊C4—22no—
186#882—24no—
187#67⋊C4—24no—
188#875C2312yes—
189#875C2314yes—
190#874C2311yescharacteristic
191#874C2314yes—
192C4×D12—21no—
193C4×D12—21no—
194C4×D12—21no—
195C4×D12—21no—
196C4×D12C2312yes—
197C4×D12C2312yes—
198C4×D12C2314yes—
199#869C2311yescharacteristic
200C4×Dic6C2314yes—
201#835C2312yes—
202#835C2312yes—
203#810C2314yes—
204#810C2312yes—
205#810C2312yes—
206#810C2312yes—
207#810C2312yes—
208#809C2312yes—
209#809C2312yes—
210#809C2314yes—
211#809C2314yes—
212#809C2314yes—
213#809C2312yes—
214#809C2312yes—
215#809C2312yes—
216#809C2312yes—
217#808C2312yes—
218#808C2312yes—
219#808C2314yes—
220#807C2314yes—
221C4⋊(C3⋊C8)C2312yes—
222C4⋊(C3⋊C8)C2312yes—
223C4⋊(C3⋊C8)C2314yes—
224C4⋊(C3⋊C8)C2314yes—
225#803C2314yes—
226C4×C3⋊C8C2311yescharacteristic
227C4×C3⋊C8C2311yescharacteristic
228C4×C3⋊C8C2311yescharacteristic
229C4×C3⋊C8C2311yescharacteristic
230C4×C3⋊C8C2314yes—
231C2×#137—32no—
232C22×SD16—31no—
233#559—34no—
234Q82—21no—
235Q82C2×D312yescomplemented
236#557—21no—
237#557—22no—
238#557C2×D312yescomplemented
239#557C2×D314yescomplemented
240#556—32no—
241#555—61no—
242#553—62no—
243#550—32no—
244#547—61no—
245#544—22no—
246#544C2×D312yes—
247#538—62no—
248#535—32no—
249#533—22no—
250#533C2×D311yescharacteristic
251#533C2×D311yescharacteristic
252#532—31no—
253#525—62no—
254#520—32no—
255#519C2×D312yes—
256C2×C4×Q8C2×D311yescharacteristic
257C2×C4×D4—31no—
258#490—34no—
259#489—34no—
260#488—34no—
261#488—32no—
262#488—32no—
263#487—31no—
264#487—31no—
265#486—31no—
266#486—34no—
267#486—31no—
268#479—34no—
269#478—34no—
270#478—34no—
271#476—32no—
272#476—34no—
273#475—34no—
274#474—32no—
275#464—34no—
276#464—34no—
277#464—34no—
278#462—32no—
279#460—32no—
280#460—34no—
281#460—34no—
282#446—32no—
283#446—32no—
284C8×Q8—32no—
285C8×Q8—32no—
286#441—34no—
287#440—34no—
288C4×Q16—34no—
289C4×SD16—32no—
290C4×SD16—34no—
291C4×SD16—32no—
292C4×SD16—32no—
293C4×SD16—32no—
294#428—32no—
295C2×#106—31no—
296#424—32no—
297#423—31no—
298#418—32no—
299#417—32no—
300#416—32no—
301#416—32no—
302C2×#103—31no—
303C2×#102—31no—
304#405—32no—
305C2×C4×C8—31no—
306C23×D3—21no—
307C2×C3×Q8—21no—
308C2×C3×Q8—21no—
309C2×C3×Q8—21no—
310C2×C3×Q8—24no—
311C2×C3×Q8—22no—
312C2×C3×Q8C2×D412yes—
313C2×C3×Q8C2×D412yes—
314C2×C3×Q8#4114yescomplemented
315C2×C3×Q8C2412yes—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4C2×D411yescharacteristic
319C22×C3×C4C2×D411yescharacteristic
320C22×C3×C4C2411yescharacteristic
321C2×#67—22no—
322C22×Dic3—21no—
323#239—84no—
324#235—24no—
325#235—24no—
326C2×D12—22no—
327C2×D12—22no—
328C2×D12—21no—
329C2×D12—21no—
330C2×D12—21no—
331C2×D12—24no—
332C2×D12—24no—
333C2×D12C2412yes—
334C2×D12C2412yes—
335C2×C4×D3—22no—
336C2×C4×D3—22no—
337C2×C4×D3—22no—
338C2×C4×D3—24no—
339C2×C4×D3—82no—
340C2×Dic6C2412yes—
341C3×C4⋊C4—22no—
342C3×C4⋊C4—22no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—24no—
345C3×C4⋊C4—24no—
346C3×C4⋊C4—22no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—24no—
350C3×C4⋊C4—24no—
351C3×C4⋊C4—22no—
352C3×C4⋊C4—24no—
353C3×C4⋊C4C2×D412yes—
354C3×C4⋊C4C2×D412yes—
355C3×C4⋊C4C2×D412yes—
356C3×C4⋊C4C2×D414yes—
357C3×C4⋊C4C2×D412yes—
358C3×C4⋊C4C2×D414yes—
359C3×C4⋊C4C2412yes—
360C3×C4⋊C4C2412yes—
361C3×C4⋊C4C2412yes—
362C3×C22⋊C4—22no—
363C3×C22⋊C4C2×D414yes—
364C3×C42—22no—
365C3×C42—22no—
366C3×C42—24no—
367C3×C42—24no—
368C3×C42—22no—
369C3×C42C2×D411yescharacteristic
370C3×C42C2×D411yescharacteristic
371C3×C42C2411yescharacteristic
372C3×C42C2411yescharacteristic
373C3×C42C2414yes—
374#216—28no—
375#215—24no—
376#215—24no—
377#215—28no—
378(C2×D3)⋊C4—22no—
379(C2×D3)⋊C4—22no—
380(C2×D3)⋊C4—22no—
381(C2×D3)⋊C4—22no—
382(C2×D3)⋊C4—24no—
383(C2×D3)⋊C4—24no—
384(C2×D3)⋊C4—24no—
385C4⋊Dic3—21no—
386C4⋊Dic3—21no—
387C4⋊Dic3—21no—
388C4⋊Dic3C2412yes—
389Dic3⋊C4—24no—
390C4×Dic3—24no—
391#208—24no—
392C2×C3⋊C8—22no—
393C2×C3⋊C8—22no—
394C2×C3⋊C8C2411yescharacteristic
395C2×C3⋊C8C2411yescharacteristic
396C2×C3⋊C8C2411yescharacteristic
397C2×C3⋊C8C2411yescharacteristic
398C2×C3⋊C8C2414yes—
399C2×#41—32no—
400C2×#41—62no—
401C22×Q8C22×D311yescharacteristic
402C22×D4—31no—
403C23×C4—61no—
404#137—68no—
405C2×Q16—34no—
406C2×SD16—32no—
407C2×SD16—32no—
408C2×SD16—34no—
409C2×SD16—64no—
410C2×M16—32no—
411C22×C8—31no—
412C22×C8—31no—
413C4⋊Q8—22no—
414C4⋊Q8—24no—
415C4⋊Q8—22no—
416C4⋊Q8—24no—
417C4⋊Q8—22no—
418C4⋊Q8—31no—
419C4⋊Q8#6711yescharacteristic
420C4⋊Q8#6711yescharacteristic
421C4⋊Q8C22×D311yescharacteristic
422C4⋊Q8C22×D311yescharacteristic
423C4⋊Q8C22×D314yes—
424#127—31no—
425#127—34no—
426#126—64no—
427#125—24no—
428#125—24no—
429#125—24no—
430#125—22no—
431#125#6712yes—
432#125C22×D312yes—
433#125C22×D314yes—
434#124—32no—
435#124—34no—
436#124—64no—
437#123—64no—
438#123—64no—
439C22⋊Q8—21no—
440C22⋊Q8—21no—
441C22⋊Q8—24no—
442C22⋊Q8—62no—
443C22⋊Q8#6712yes—
444C22⋊Q8#6712yes—
445#121—61no—
446#121—61no—
447#121—62no—
448#121—62no—
449#121—62no—
450#121—64no—
451#120—64no—
452C4×Q8—22no—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×Q8—24no—
456C4×Q8—22no—
457C4×Q8—21no—
458C4×Q8—21no—
459C4×Q8—21no—
460C4×Q8—21no—
461C4×Q8—34no—
462C4×Q8C22×D312yes—
463C4×Q8C22×D312yes—
464C4×Q8C22×D314yes—
465C4×Q8C22×D314yes—
466C4×Q8C22×D312yes—
467C4×Q8C22×D312yes—
468C4×D4—32no—
469C4×D4—32no—
470C4×D4—34no—
471C4×D4—64no—
472C4×D4—64no—
473C4×D4—61no—
474C4×D4—61no—
475C4×D4—61no—
476C4×D4—61no—
477#117—24no—
478#117—62no—
479#117—62no—
480#117C22×D312yes—
481#117C22×D312yes—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—62no—
485C2×C4⋊C4C22×D311yescharacteristic
486C2×C22⋊C4—61no—
487C2×C42—21no—
488C2×C42C22×D311yescharacteristic
489#107—34no—
490#106—32no—
491#106—32no—
492#106—34no—
493C4⋊C8—32no—
494C4⋊C8—32no—
495C4⋊C8—34no—
496C4⋊C8—34no—
497#103—32no—
498#103—32no—
499#103—32no—
500#103—32no—
501#103—32no—
502#103—32no—
503#103—34no—
504#102—32no—
505#102—32no—
506#102—32no—
507#102—32no—
508#102—32no—
509#102—32no—
510#102—34no—
511#102—34no—
512#102—34no—
513#97—34no—
514C4×C8—31no—
515C4×C8—31no—
516C4×C8—31no—
517C4×C8—31no—
518C4×C8—34no—
519C23×C3C22×D411yescharacteristic
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—42no—
523C22×D3—81no—
524C22×D3—81no—
525C3×Q8—24no—
526C3×Q8—24no—
527C3×Q8—22no—
528C3×Q8—42no—
529C3×Q8—42no—
530C3×Q8—81no—
531C3×Q8—84no—
532C3×Q8C2×#4114yes—
533C2×C3×C4—24no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—41no—
540C2×C3×C4—81no—
541C2×C3×C4C22×D414yes—
542C2×C3×C4C22×D414yes—
543C2×C3×C4C22×D411yescharacteristic
544C2×C3×C4C22×D411yescharacteristic
545C2×C3×C4C22×D411yescharacteristic
546C2×C3×C4C22×D411yescharacteristic
547C2×C3×C4C22×D411yescharacteristic
548C2×C3×C4C2×#4112yes—
549C2×C3×C42−1+412yes—
550C2×C3×C4C2511yescharacteristic
551#67—44no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—81no—
555D12—22no—
556D12—22no—
557D12—22no—
558D12—22no—
559D12—42no—
560D12—42no—
561D12—81no—
562D12—84no—
563D12—84no—
564C4×D3—44no—
565C4×D3—44no—
566C4×D3—82no—
567C4×D3—84no—
568Dic6—22no—
569Dic6—22no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—24no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C24—61no—
576#41—64no—
577#41—64no—
578#41—244no—
579C2×Q8—22no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—24no—
584C2×Q8—32no—
585C2×Q8#23914yescomplemented
586C2×Q8C2×#6712yes—
587C2×Q8C2×#6712yes—
588C2×Q8C23×D312yes—
589C2×D4—32no—
590C2×D4—32no—
591C2×D4—62no—
592C2×D4—62no—
593C2×D4—62no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—64no—
597C2×D4—61no—
598C2×D4—64no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—61no—
602C22×C4—62no—
603C22×C4—62no—
604C22×C4—64no—
605C22×C4—62no—
606C22×C4—242no—
607C22×C4C2×#6711yescharacteristic
608C22×C4C2×#6711yescharacteristic
609C22×C4C23×D311yescharacteristic
610Q16—68no—
611SD16—64no—
612SD16—64no—
613SD16—68no—
614M16—64no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—34no—
620C2×C8—62no—
621C2×C8—62no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—22no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—22no—
633C4⋊C4—24no—
634C4⋊C4—32no—
635C4⋊C4—61no—
636C4⋊C4—64no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4C2×#6712yes—
640C4⋊C4C2×#6712yes—
641C4⋊C4C2×#6712yes—
642C4⋊C4C2×#6714yes—
643C4⋊C4C2×#6714yes—
644C4⋊C4C2×#6712yes—
645C4⋊C4C23×D312yes—
646C4⋊C4C23×D312yes—
647C4⋊C4C23×D312yes—
648C22⋊C4—22no—
649C22⋊C4—62no—
650C22⋊C4—62no—
651C22⋊C4—64no—
652C22⋊C4—64no—
653C22⋊C4—62no—
654C22⋊C4—64no—
655C22⋊C4—62no—
656C22⋊C4C2×#6714yes—
657C42—22no—
658C42—22no—
659C42—24no—
660C42—24no—
661C42—22no—
662C42—64no—
663C42C2×#6711yescharacteristic
664C42C2×#6711yescharacteristic
665C42C23×D311yescharacteristic
666C42C23×D311yescharacteristic
667C42C23×D314yes—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3#54812yes—
671C22×C3C23×D411yescharacteristic
672C2×D3—42no—
673C2×D3—42no—
674C2×D3—42no—
675C2×D3—42no—
676C2×D3—42no—
677C2×D3—42no—
678C2×D3—84no—
679C3×C4—21no—
680C3×C4—24no—
681C3×C4—21no—
682C3×C4—24no—
683C3×C4—21no—
684C3×C4—24no—
685C3×C4—42no—
686C3×C4—42no—
687C3×C4—42no—
688C3×C4#54812yes—
689C3×C4#57712yes—
690C3×C4C22×#4111yescharacteristic
691C3×C4C2×2−1+411yescharacteristic
692Dic3—42no—
693Dic3—42no—
694C23—62no—
695C23—62no—
696C23—122no—
697C23—241no—
698C23—241no—
699C23C22×#6711yescharacteristic
700Q8—22no—
701Q8—24no—
702Q8—24no—
703Q8—42no—
704Q8—42no—
705Q8—62no—
706Q8—62no—
707Q8—81no—
708Q8—84no—
709Q8C2×#23914yes—
710D4—62no—
711D4—62no—
712D4—62no—
713D4—62no—
714D4—124no—
715D4—122no—
716D4—122no—
717D4—244no—
718D4—241no—
719D4—244no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—81no—
730C2×C4—124no—
731C2×C4—124no—
732C2×C4—242no—
733C2×C4—244no—
734C2×C4—241no—
735C2×C4C2×#23912yes—
736C2×C4#100712yes—
737C2×C4C22×#6711yescharacteristic
738C2×C4C22×#6714yes—
739C2×C4C22×#6714yes—
740C2×C4C22×#6711yescharacteristic
741C2×C4C22×#6711yescharacteristic
742C2×C4C22×#6711yescharacteristic
743C2×C4C22×#6711yescharacteristic
744C2×C4C24×D311yescharacteristic
745C8—61no—
746C8—61no—
747C8—64no—
748C8—61no—
749C8—61no—
750C2×C3—22no—
751C2×C3C2×#54811yescharacteristic
752C2×C3C2×#57711yescharacteristic
753C2×C3#358411yescharacteristic
754D3—82no—
755D3—82no—
756C22—21no—
757C22—21no—
758C22—122no—
759C22—122no—
760C22—122no—
761C22—122no—
762C22—122no—
763C22—122no—
764C22—244no—
765C22#581712yes—
766C22C23×#6711yescharacteristic
767C4—21no—
768C4—21no—
769C4—24no—
770C4—24no—
771C4—21no—
772C4—24no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4—122no—
777C4—122no—
778C4#581712yes—
779C4#583712yes—
780C4C22×#23911yescharacteristic
781C4C2×#100711yescharacteristic
782C3#6132711yescharacteristic, complemented, Sylow
783C2—22no—
784C2—242no—
785C2—242no—
786C2C2×#581711yescharacteristic
787C2C2×#583711yescharacteristic
788C2#8729711yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3502C2
socleC22×C3C23×D4
prime radical#86259C2
hypercenter#3502D3
hypocenterC3#61327
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #533 ◁ #3502

Complements

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

NH ≅ G/Ntype
1. C3×#3502C2semidirect
3. #83704C2semidirect
4. #83703C2semidirect
5. #83697C2semidirect
6. #83691C2semidirect
7. #83690C2semidirect
8. #83689C2semidirect
9. #83476C2semidirect
10. #83470C2semidirect
11. #83350C2semidirect
12. #83334C2semidirect
13. #83328C2semidirect
14. #82551C2semidirect
15. #82547C2semidirect
16. #82441C2semidirect
17. C2×C4×#215C2semidirect
20. C3×Q82C22semidirect
23. C3×#557C22semidirect
24. C3×#557C22semidirect
47. #5094C22semidirect
48. #5093C22semidirect
49. #5093C22semidirect
52. #5088C22semidirect
53. #5088C22semidirect
56. #5084C22semidirect
58. #5068C22semidirect
59. #5068C22semidirect
62. #5066C22semidirect
63. #5063C22semidirect
64. #5031C22semidirect
65. #5030C22semidirect
66. C4×#216C22semidirect
69. #5028C22semidirect
72. #5027C22semidirect
73. #5026C22semidirect
78. C4×#215C22semidirect
79. #5024C22semidirect
80. #5024C22semidirect
81. Q8×C3⋊C8C22semidirect
82. Q8×C3⋊C8C22semidirect
95. #3502D3semidirect
235. Q82C2×D3semidirect
238. #557C2×D3semidirect
239. #557C2×D3semidirect
314. C2×C3×Q8#41semidirect
585. C2×Q8#239semidirect
782. C3#61327semidirect

Maximal subgroups

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

subgroupindex
C3×#35022
#862592
#837042
#837032
#836972
#836912
#836902
#836892
#834762
#834702
#833502
#833342
#833282
#825512
#825472
#824412
C2×C4×#2152
#613273