Finite Group Databasebeta

← #11675520

Subgroups — #11675520

Order 768.

1846 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3506C211yesmaximal, characteristic, complemented
2#86281C211yesmaximal, characteristic, complemented
3#83718C214yesmaximal, complemented
4#83715C214yesmaximal, complemented
5#83677C212yesmaximal, complemented
6#83667C212yesmaximal, complemented
7#83586C212yesmaximal, complemented
8#83581C212yesmaximal, complemented
9#83385C212yesmaximal, complemented
10#83380C212yesmaximal, complemented
11#83330C211yesmaximal, characteristic, complemented
12#83296C211yesmaximal, characteristic, complemented
13#83283C211yesmaximal, characteristic, complemented
14#82560C212yesmaximal, complemented
15#82558C212yesmaximal, complemented
16C2×#5008C211yesmaximal, characteristic, complemented
17C4×#932C211yesmaximal, characteristic, complemented
18#61347—31nomaximal, Sylow
19C3×#559C2214yes—
20C3×#556C2212yes—
21C3×#555—21no—
22C3×#553—22no—
23C3×#550C2212yes—
24C3×#547—21no—
25C3×#538—22no—
26C3×#535C2212yes—
27C3×#533C2211yescharacteristic
28C3×#532C2211yescharacteristic
29C3×#525—22no—
30C3×#520C2212yes—
31C2×C3×C4×D4C2211yescharacteristic
32C2×#950C2212yes—
33C2×#932C2211yescharacteristic
34#5728—21no—
35D3×C4⋊Q8—21no—
36#5689—22no—
37#5635—22no—
38#5632—22no—
39#5579C2212yescomplemented
40Q8×D12C2212yescomplemented
41#5567C2212yescomplemented
42Q8×Dic6C2212yescomplemented
43#5523C2212yes—
44#5519C2212yes—
45C4×#235C2211yescharacteristic
46C2×#869C2211yescharacteristic
47#5233C2212yes—
48#5232C2212yes—
49#5232C2212yes—
50#5215C2211yescharacteristic
51C2×#832C2212yes—
52#5090C2211yescharacteristic, complemented
53#5083C2211yescharacteristic, complemented
54#5079C2212yescomplemented
55#5075C2214yes—
56#5075C2211yescharacteristic, complemented
57#5072C2214yes—
58#5072C2211yescharacteristic, complemented
59#5071C2214yes—
60#5070C2214yes—
61#5070C2212yescomplemented
62#5057C2214yes—
63#5057C2212yescomplemented
64#5056C2214yes—
65#5055C2214yes—
66#5055C2214yescomplemented
67#5054C2214yes—
68#5054C2212yescomplemented
69#5030C2214yescomplemented
70C4×#215C2214yescomplemented
71#5024C2214yescomplemented
72#5024C2212yescomplemented
73Q8×C3⋊C8C2212yescomplemented
74#5022C2214yescomplemented
75#5020C2214yescomplemented
76#5018C2212yes—
77C4×#214C2212yes—
78C4×#214C2214yescomplemented
79#5014C2212yes—
80#5014C2214yescomplemented
81C4×#213C2212yes—
82#5009C2214yescomplemented
83#5008C2214yes—
84#5008C2212yes—
85#5008C2212yes—
86#5008C2214yescomplemented
87#4999C2212yes—
88#4997C2212yes—
89#4966C2211yescharacteristic
90#4964C2211yescharacteristic
91C2×#808C2212yes—
92C2×C4⋊(C3⋊C8)C2211yescharacteristic
93C4×#208C2211yescharacteristic
94#3506D311yescharacteristic, complemented
95#3503—31no—
96#3373—34no—
97#3371—34no—
98#3369—32no—
99#3366—32no—
100#3362—32no—
101#3360—32no—
102#3141—31no—
103#3136—32no—
104#3084—32no—
105C2×#476—31no—
106#3045—32no—
107#3035—31no—
108#2962—31no—
109#2952—32no—
110C4×AGL(1,ℤ/8)—31no—
111C2×C3×#41—22no—
112C2×C3×#41C2312yes—
113C22×C3×D4C2311yescharacteristic
114C23×C3×C4—21no—
115C2×D3×Q8—22no—
116C2×#235C2311yescharacteristic
117C22×Dic6—21no—
118C3×C4⋊Q8D411yescharacteristic
119C3×C4⋊Q8D411yescharacteristic
120C3×C4⋊Q8C2311yescharacteristic
121C3×#127C2314yes—
122C3×#127C2311yescharacteristic
123C3×#126—24no—
124C3×#125D412yes—
125C3×#124—24no—
126C3×#124C2312yes—
127C3×#124C2314yes—
128C3×#123—24no—
129C3×#123—24no—
130C3×C22⋊Q8—22no—
131C3×C22⋊Q8D412yes—
132C3×C22⋊Q8D412yes—
133C3×#121—21no—
134C3×#121—21no—
135C3×#121—22no—
136C3×#121—22no—
137C3×#121—22no—
138C3×#121—24no—
139C3×#120—24no—
140C3×C4×Q8C2314yes—
141C3×C4×Q8C2312yes—
142C3×C4×Q8C2312yes—
143C3×C4×D4—24no—
144C3×C4×D4—24no—
145C3×C4×D4—21no—
146C3×C4×D4—21no—
147C3×C4×D4—21no—
148C3×C4×D4—21no—
149C3×C4×D4C2312yes—
150C3×C4×D4C2314yes—
151C3×C4×D4C2312yes—
152C3×#117—22no—
153C3×#117—22no—
154C3×#117C2312yes—
155C2×C3×C4⋊C4—22no—
156C2×C3×C4⋊C4C2311yescharacteristic
157C2×C3×C22⋊C4—21no—
158C2×C3×C42C2311yescharacteristic
159#950—28no—
160#946—22no—
161Q8×Dic3—22no—
162#944—22no—
163C2×#216C2312yes—
164C2×#215C2312yes—
165C2×#214C2312yes—
166C2×#214C2312yes—
167#932—24no—
168C2×#213C2312yes—
169C2×#213C2312yes—
170C4×#67—21no—
171C4×#67—21no—
172#926C2311yescharacteristic
173C2×C4⋊Dic3—21no—
174C2×C4⋊Dic3C2312yes—
175C2×#208C2311yescharacteristic
176C2×#208C2311yescharacteristic
177C22×C3⋊C8C2312yes—
178#897—22no—
179#897—24no—
180#896—24no—
181#892—22no—
182D3×C4⋊C4—22no—
183D3×C4⋊C4—22no—
184#890—22no—
185#889—24no—
186#888—24no—
187#888—22no—
188#888—22no—
189#887—22no—
190#67⋊C4—24no—
191#878—24no—
192C4×D12C2311yescharacteristic
193C4×D12C2311yescharacteristic
194C4×D12C2314yes—
195#872—21no—
196C42×D3—21no—
197#870C2314yes—
198#869—21no—
199#869—21no—
200#869C2312yes—
201#869C2312yes—
202#869C2314yes—
203C4×Dic6C2311yescharacteristic
204C4×Dic6C2311yescharacteristic
205C4×Dic6C2314yes—
206#835C2314yes—
207#835C2314yes—
208#835C2312yes—
209#835C2312yes—
210#832C2314yes—
211#832C2314yes—
212#832C2312yes—
213#832C2312yes—
214#832C2314yes—
215#832C2314yes—
216#832C2312yes—
217#832C2312yes—
218#810C2312yes—
219#809C2312yes—
220#808C2314yes—
221#808C2314yes—
222#808C2312yes—
223#807C2312yes—
224C4⋊(C3⋊C8)C2311yescharacteristic
225C4⋊(C3⋊C8)C2312yes—
226C4⋊(C3⋊C8)C2311yescharacteristic
227C4⋊(C3⋊C8)C2314yes—
228C4⋊(C3⋊C8)C2314yes—
229#803C2312yes—
230#803C2314yes—
231C4×C3⋊C8C2312yes—
232C4×C3⋊C8C2314yes—
233C2×AGL(1,ℤ/8)—31no—
234C2×#135—32no—
235#559C2×D314yes—
236Q82—32no—
237#557—32no—
238#556C2×D312yes—
239#555—21no—
240#554—32no—
241#554—62no—
242#553—22no—
243#550C2×D312yes—
244D4×Q8—32no—
245D4×Q8—62no—
246#547—21no—
247#544—32no—
248#544—62no—
249#538—22no—
250#535C2×D312yes—
251#533—61no—
252#533C2×D311yescharacteristic
253#532C2×D311yescharacteristic
254C2×C4⋊Q8—31no—
255C2×C4⋊Q8—61no—
256#525—22no—
257#520—32no—
258#520C2×D312yes—
259C4×#41—31no—
260C2×C4×D4C2×D311yescharacteristic
261#490—34no—
262#489—34no—
263#489—34no—
264#488—34no—
265#487—32no—
266#486—32no—
267#486—34no—
268#479—34no—
269#478—34no—
270#476—34no—
271#476—32no—
272#476—32no—
273#476—34no—
274#475—34no—
275#464—34no—
276#464—32no—
277#463—34no—
278#463—32no—
279#462—31no—
280#461—31no—
281#460—31no—
282#460—34no—
283#459—31no—
284#459—34no—
285#446—32no—
286#446—34no—
287C8×Q8—32no—
288#442—34no—
289#442—32no—
290#441—34no—
291#440—32no—
292C4×SD16—34no—
293C4×SD16—32no—
294C4×SD16—34no—
295C4×D8—32no—
296#428—31no—
297C2×#106—32no—
298#424—32no—
299C2×C4⋊C8—31no—
300#418—31no—
301#417—32no—
302#417—32no—
303#417—31no—
304#416—32no—
305C2×#102—32no—
306#405—32no—
307C4×M16—31no—
308C24×C3—21no—
309C3×#41—24no—
310C3×#41—24no—
311C3×#41—84no—
312C2×C3×Q8C2×D412yes—
313C2×C3×Q8C2×D412yes—
314C2×C3×Q8C2412yes—
315C2×C3×D4—22no—
316C2×C3×D4—21no—
317C2×C3×D4—21no—
318C2×C3×D4—24no—
319C2×C3×D4—21no—
320C2×C3×D4—24no—
321C2×C3×D4—22no—
322C2×C3×D4—22no—
323C2×C3×D4C2412yes—
324C2×C3×D4C2412yes—
325C22×C3×C4—21no—
326C22×C3×C4—22no—
327C22×C3×C4—22no—
328C22×C3×C4—24no—
329C22×C3×C4—22no—
330C22×C3×C4—82no—
331C22×C3×C4C2×D411yescharacteristic
332C22×C3×C4C2×D411yescharacteristic
333C22×C3×C4C2411yescharacteristic
334C2×#67—21no—
335C22×Dic3—22no—
336D3×Q8—84no—
337#235—22no—
338#235#4114yescomplemented
339C2×D12C2411yescharacteristic
340C2×C4×D3—21no—
341C2×C4×D3—21no—
342C2×C4×D3—21no—
343C2×C4×D3—24no—
344C2×Dic6—22no—
345C2×Dic6—22no—
346C2×Dic6—24no—
347C2×Dic6—82no—
348C2×Dic6C2411yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—24no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4C2×D412yes—
354C3×C4⋊C4C2×D412yes—
355C3×C4⋊C4C2×D412yes—
356C3×C4⋊C4C2×D414yes—
357C3×C4⋊C4C2×D414yes—
358C3×C4⋊C4C2×D412yes—
359C3×C4⋊C4C2412yes—
360C3×C22⋊C4—22no—
361C3×C22⋊C4—22no—
362C3×C22⋊C4—24no—
363C3×C22⋊C4—24no—
364C3×C22⋊C4—22no—
365C3×C22⋊C4—24no—
366C3×C22⋊C4—22no—
367C3×C22⋊C4C2×D414yes—
368C3×C42—24no—
369C3×C42C2×D411yescharacteristic
370C3×C42C2×D411yescharacteristic
371C3×C42C2411yescharacteristic
372C3×C42C2414yes—
373C3×C42C2411yescharacteristic
374#217—21no—
375#216—24no—
376#215—24no—
377#214—24no—
378#214—24no—
379#213—24no—
380#213—24no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—24no—
384C4⋊Dic3—22no—
385C4⋊Dic3—22no—
386C4⋊Dic3—22no—
387C4⋊Dic3—24no—
388C4⋊Dic3C2411yescharacteristic
389C4⋊Dic3C2411yescharacteristic
390C4⋊Dic3C2414yes—
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—24no—
394Dic3⋊C4—24no—
395Dic3⋊C4—24no—
396C4×Dic3—21no—
397C4×Dic3—21no—
398C4×Dic3—24no—
399C4×Dic3—21no—
400#208—22no—
401#208—22no—
402C2×C3⋊C8—24no—
403C2×C3⋊C8C2412yes—
404C2×C3⋊C8C2412yes—
405C2×C3⋊C8C2412yes—
406C2×C3⋊C8C2412yes—
407C2×#41—22no—
408C2×#41—31no—
409C2×#41C22×D312yes—
410C22×Q8—62no—
411C22×Q8—61no—
412C22×D4C22×D311yescharacteristic
413C23×C4—21no—
414AGL(1,ℤ/8)—64no—
415#135—68no—
416C2×Q16—32no—
417C2×SD16—32no—
418C2×SD16—32no—
419C2×SD16—32no—
420C2×D8—32no—
421C2×D8—32no—
422C2×M16—31no—
423C2×M16—31no—
424C22×C8—32no—
425C4⋊Q8—32no—
426C4⋊Q8—32no—
427C4⋊Q8—34no—
428C4⋊Q8—62no—
429C4⋊Q8—62no—
430C4⋊Q8—62no—
431C4⋊Q8—64no—
432C4⋊Q8—61no—
433C4⋊Q8—61no—
434C4⋊Q8#6711yescharacteristic
435C4⋊Q8#6711yescharacteristic
436C4⋊Q8C22×D311yescharacteristic
437#127C22×D311yescharacteristic
438#127C22×D314yes—
439#126—24no—
440#125—34no—
441#125—62no—
442#125—64no—
443#125#6712yes—
444#124—24no—
445#124C22×D312yes—
446#124C22×D314yes—
447#123—24no—
448#123—24no—
449C22⋊Q8—22no—
450C22⋊Q8—62no—
451C22⋊Q8—62no—
452C22⋊Q8—64no—
453C22⋊Q8—64no—
454C22⋊Q8—64no—
455C22⋊Q8#6712yes—
456C22⋊Q8#6712yes—
457#121—21no—
458#121—21no—
459#121—22no—
460#121—22no—
461#121—22no—
462#121—24no—
463#120—24no—
464C4×Q8—31no—
465C4×Q8—31no—
466C4×Q8—34no—
467C4×Q8—62no—
468C4×Q8—62no—
469C4×Q8C22×D314yes—
470C4×Q8C22×D312yes—
471C4×Q8C22×D312yes—
472C4×D4—24no—
473C4×D4—24no—
474C4×D4—21no—
475C4×D4—21no—
476C4×D4—21no—
477C4×D4—21no—
478C4×D4—31no—
479C4×D4—31no—
480C4×D4—34no—
481C4×D4—61no—
482C4×D4—61no—
483C4×D4—64no—
484C4×D4C22×D312yes—
485C4×D4C22×D312yes—
486C4×D4C22×D314yes—
487#117—22no—
488#117—22no—
489#117—31no—
490#117—62no—
491#117—61no—
492#117C22×D312yes—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—32no—
495C2×C4⋊C4—61no—
496C2×C4⋊C4—62no—
497C2×C4⋊C4—62no—
498C2×C4⋊C4C22×D311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C42—61no—
501C2×C42C22×D311yescharacteristic
502#107—32no—
503#106—34no—
504#106—34no—
505#106—32no—
506C4⋊C8—31no—
507C4⋊C8—31no—
508C4⋊C8—32no—
509C4⋊C8—34no—
510C4⋊C8—34no—
511#103—32no—
512#103—32no—
513#103—34no—
514#103—34no—
515#103—32no—
516#102—34no—
517#102—34no—
518#102—32no—
519#102—32no—
520#102—34no—
521#102—34no—
522#102—32no—
523#102—32no—
524#102—32no—
525#97—32no—
526#97—34no—
527C4×C8—32no—
528C4×C8—34no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—42no—
532C23×C3—81no—
533C23×C3—81no—
534C23×C3C22×D411yescharacteristic
535C22×D3—21no—
536C3×Q8—24no—
537C3×Q8—22no—
538C3×Q8—22no—
539C3×Q8—42no—
540C3×D4—22no—
541C3×D4—22no—
542C3×D4—22no—
543C3×D4—22no—
544C3×D4—44no—
545C3×D4—42no—
546C3×D4—42no—
547C3×D4—81no—
548C3×D4—84no—
549C3×D4—84no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—41no—
554C2×C3×C4—44no—
555C2×C3×C4—44no—
556C2×C3×C4—82no—
557C2×C3×C4—84no—
558C2×C3×C4—81no—
559C2×C3×C4C22×D414yes—
560C2×C3×C4C22×D411yescharacteristic
561C2×C3×C4C22×D414yes—
562C2×C3×C4C22×D411yescharacteristic
563C2×C3×C4C22×D411yescharacteristic
564C2×C3×C4C22×D411yescharacteristic
565C2×C3×C4C22×D411yescharacteristic
566C2×C3×C4C2×#4112yes—
567C2×C3×C42−1+412yes—
568C2×C3×C4C2511yescharacteristic
569#67—24no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—24no—
574C2×Dic3—82no—
575D12—21no—
576D12C2×#4112yes—
577C4×D3—24no—
578C4×D3—42no—
579C4×D3—42no—
580C4×D3—84no—
581Dic6—21no—
582Dic6—44no—
583Dic6—82no—
584Dic6—84no—
585Dic6C2×#4112yes—
586C3⋊C8—22no—
587C3⋊C8—22no—
588C3⋊C8—22no—
589C3⋊C8—22no—
590C24—21no—
591#41—24no—
592#41—24no—
593#41—34no—
594#41—62no—
595#41—84no—
596C2×Q8—31no—
597C2×Q8—62no—
598C2×Q8—64no—
599C2×Q8—62no—
600C2×Q8—242no—
601C2×Q8—244no—
602C2×Q8C2×#6712yes—
603C2×Q8C2×#6712yes—
604C2×Q8C23×D312yes—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—24no—
611C2×D4—21no—
612C2×D4—24no—
613C2×D4—31no—
614C2×D4—61no—
615C2×D4C23×D312yes—
616C2×D4C23×D312yes—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—24no—
621C22×C4—22no—
622C22×C4—61no—
623C22×C4—62no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—64no—
627C22×C4—82no—
628C22×C4C2×#6711yescharacteristic
629C22×C4C2×#6711yescharacteristic
630C22×C4C23×D311yescharacteristic
631Q16—64no—
632SD16—64no—
633SD16—64no—
634SD16—64no—
635D8—64no—
636D8—64no—
637M16—62no—
638M16—62no—
639C2×C8—32no—
640C2×C8—32no—
641C2×C8—32no—
642C2×C8—32no—
643C2×C8—64no—
644C4⋊C4—21no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—34no—
649C4⋊C4—31no—
650C4⋊C4—31no—
651C4⋊C4—62no—
652C4⋊C4—62no—
653C4⋊C4—64no—
654C4⋊C4—64no—
655C4⋊C4—62no—
656C4⋊C4—61no—
657C4⋊C4—61no—
658C4⋊C4—64no—
659C4⋊C4—64no—
660C4⋊C4C2×#6712yes—
661C4⋊C4C2×#6712yes—
662C4⋊C4C2×#6712yes—
663C4⋊C4C2×#6714yes—
664C4⋊C4C2×#6712yes—
665C4⋊C4C2×#6714yes—
666C4⋊C4C23×D312yes—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—22no—
672C22⋊C4—24no—
673C22⋊C4—22no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—64no—
678C22⋊C4C2×#6714yes—
679C42—24no—
680C42—61no—
681C42—61no—
682C42—61no—
683C42—64no—
684C42C2×#6711yescharacteristic
685C42C2×#6711yescharacteristic
686C42C23×D311yescharacteristic
687C42C23×D314yes—
688C42C23×D311yescharacteristic
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—84no—
698C22×C3#54812yes—
699C22×C3C23×D411yescharacteristic
700C2×D3—22no—
701C2×D3—41no—
702C2×D3—41no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—24no—
706C3×C4—21no—
707C3×C4—24no—
708C3×C4—42no—
709C3×C4—42no—
710C3×C4#54812yes—
711C3×C4#57712yes—
712C3×C4C22×#4111yescharacteristic
713C3×C4C2×2−1+411yescharacteristic
714Dic3—22no—
715Dic3—44no—
716Dic3—41no—
717Dic3—41no—
718C23—22no—
719C23—22no—
720C23—42no—
721C23—61no—
722C23—81no—
723C23—81no—
724C23C22×#6711yescharacteristic
725Q8—24no—
726Q8—22no—
727Q8—22no—
728Q8—32no—
729Q8—42no—
730Q8—61no—
731Q8—124no—
732Q8—242no—
733Q8—244no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—32no—
739D4—44no—
740D4—42no—
741D4—42no—
742D4—64no—
743D4—61no—
744D4—84no—
745D4—81no—
746D4—84no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—41no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—61no—
754C2×C4—64no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—64no—
758C2×C4—82no—
759C2×C4—84no—
760C2×C4—81no—
761C2×C4—122no—
762C2×C4—122no—
763C2×C4—244no—
764C2×C4—242no—
765C2×C4D3×#4112yes—
766C2×C4#101012yes—
767C2×C4C22×#6714yes—
768C2×C4C22×#6711yescharacteristic
769C2×C4C22×#6714yes—
770C2×C4C22×#6711yescharacteristic
771C2×C4C22×#6711yescharacteristic
772C2×C4C22×#6711yescharacteristic
773C2×C4C22×#6711yescharacteristic
774C2×C4C24×D311yescharacteristic
775C8—62no—
776C8—62no—
777C8—62no—
778C8—62no—
779C2×C3—22no—
780C2×C3—82no—
781C2×C3—82no—
782C2×C3C2×#54811yescharacteristic
783C2×C3C2×#57711yescharacteristic
784C2×C3#358511yescharacteristic
785D3—42no—
786C22—21no—
787C22—21no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—62no—
795C22—84no—
796C22—121no—
797C22—121no—
798C22#583112yes—
799C22C23×#6711yescharacteristic
800C4—21no—
801C4—21no—
802C4—24no—
803C4—21no—
804C4—24no—
805C4—42no—
806C4—42no—
807C4—62no—
808C4—121no—
809C4—124no—
810C4—121no—
811C4#583112yes—
812C4#583612yes—
813C4C2×D3×#4111yescharacteristic
814C4C2×#101011yescharacteristic
815C3#6134711yescharacteristic, complemented, Sylow
816C2—22no—
817C2—82no—
818C2—82no—
819C2—122no—
820C2C2×#583111yescharacteristic
821C2C2×#583611yescharacteristic
822C2#8729811yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3506C2
socleC22×C3C23×D4
hypercenter#3506D3
hypocenterC3#61347
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #533 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. C3×#3506C2semidirect
2. #86281C2semidirect
3. #83718C2semidirect
4. #83715C2semidirect
5. #83677C2semidirect
6. #83667C2semidirect
7. #83586C2semidirect
8. #83581C2semidirect
9. #83385C2semidirect
10. #83380C2semidirect
11. #83330C2semidirect
12. #83296C2semidirect
13. #83283C2semidirect
14. #82560C2semidirect
15. #82558C2semidirect
16. C2×#5008C2semidirect
17. C4×#932C2semidirect
39. #5579C22semidirect
40. Q8×D12C22semidirect
41. #5567C22semidirect
42. Q8×Dic6C22semidirect
52. #5090C22semidirect
53. #5083C22semidirect
54. #5079C22semidirect
56. #5075C22semidirect
58. #5072C22semidirect
61. #5070C22semidirect
63. #5057C22semidirect
66. #5055C22semidirect
68. #5054C22semidirect
69. #5030C22semidirect
70. C4×#215C22semidirect
71. #5024C22semidirect
72. #5024C22semidirect
73. Q8×C3⋊C8C22semidirect
74. #5022C22semidirect
75. #5020C22semidirect
78. C4×#214C22semidirect
80. #5014C22semidirect
82. #5009C22semidirect
86. #5008C22semidirect
94. #3506D3semidirect
338. #235#41semidirect
815. C3#61347semidirect

Maximal subgroups

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

subgroupindex
C3×#35062
#862812
#837182
#837152
#836772
#836672
#835862
#835812
#833852
#833802
#833302
#832962
#832832
#825602
#825582
C2×#50082
C4×#9322
#613473