Finite Group Databasebeta

← #11675528

Subgroups — #11675528

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×#3503C211yesmaximal, characteristic, complemented
2#86259C211yesmaximal, characteristic, complemented
3#83704C212yesmaximal, complemented
4#83703C212yesmaximal, complemented
5#83691C214yesmaximal, complemented
6#83638C212yesmaximal, complemented
7#83637C212yesmaximal, complemented
8#83569C214yesmaximal, complemented
9#83476C212yesmaximal, complemented
10#83470C212yesmaximal, complemented
11#83330C211yesmaximal, characteristic, complemented
12C2×#5084C211yesmaximal, characteristic, complemented
13#83199C211yesmaximal, characteristic, complemented
14#82565C212yesmaximal, complemented
15#82558C212yesmaximal, complemented
16#82525C211yesmaximal, characteristic, complemented
17C4×#949C211yesmaximal, characteristic, complemented
18#61347—31nomaximal, Sylow
19C3×Q82C2212yescomplemented
20C3×#557C2212yescomplemented
21C3×#554—22no—
22C3×#554C2212yescomplemented
23C3×D4×Q8—22no—
24C3×D4×Q8C2212yescomplemented
25C3×#544—22no—
26C3×#544C2212yes—
27C3×#533—21no—
28C3×#533C2211yescharacteristic
29C2×C3×C4⋊Q8—21no—
30C2×C3×C4⋊Q8C2211yescharacteristic
31C3×#520C2212yes—
32C3×C4×#41C2211yescharacteristic
33C2×#950C2212yes—
34C2×#949C2211yescharacteristic
35#5734—21no—
36#5726—21no—
37#5695—22no—
38#5644—22no—
39#5627—22no—
40#5585C2214yes—
41#5584C2212yes—
42#5577C2212yes—
43#5525C2212yes—
44#5523C2212yes—
45#5477C2211yescharacteristic
46C2×C4×D12C2211yescharacteristic
47#5232C2211yescharacteristic
48#5094C2214yescomplemented
49#5093C2212yescomplemented
50#5089C2214yes—
51#5089C2214yescomplemented
52#5088C2214yes—
53#5088C2212yescomplemented
54#5084C2214yes—
55#5084C2212yes—
56#5084C2212yes—
57#5084C2214yescomplemented
58#5068C2214yes—
59#5067C2214yes—
60#5066C2214yescomplemented
61#5063C2214yescomplemented
62#5031C2211yescharacteristic, complemented
63#5030C2214yescomplemented
64#5028C2214yes—
65#5028C2212yescomplemented
66#5027C2214yes—
67#5027C2211yescharacteristic, complemented
68#5026C2212yes—
69C4×#215C2212yes—
70C4×#215C2214yescomplemented
71#5024C2214yescomplemented
72#5024C2212yescomplemented
73Q8×C3⋊C8C2212yescomplemented
74#5019C2211yescharacteristic, complemented
75C4×#214C2214yescomplemented
76#5016C2214yes—
77#5016C2212yescomplemented
78#5015C2214yes—
79#5015C2211yescharacteristic, complemented
80#5014C2212yes—
81#5014C2214yescomplemented
82C4×#213C2212yes—
83#5002C2212yes—
84#5001C2211yescharacteristic
85#4999C2212yes—
86#4997C2212yes—
87#4995C2211yescharacteristic
88#4966C2212yes—
89#4966C2212yes—
90C2×#809C2212yes—
91C2×#808C2212yes—
92C2×C4⋊(C3⋊C8)C2211yescharacteristic
93C4×#208C2211yescharacteristic
94#3506—31no—
95#3503D311yescharacteristic, complemented
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×#41C2311yescharacteristic
112C22×C3×Q8—22no—
113C22×C3×Q8—21no—
114C2×#239—22no—
115C2×#235C2312yes—
116C22×D12C2311yescharacteristic
117C22×C4×D3—21no—
118C3×C4⋊Q8—22no—
119C3×C4⋊Q8—22no—
120C3×C4⋊Q8—24no—
121C3×C4⋊Q8—22no—
122C3×C4⋊Q8—21no—
123C3×C4⋊Q8—21no—
124C3×C4⋊Q8D411yescharacteristic
125C3×C4⋊Q8D411yescharacteristic
126C3×C4⋊Q8C2312yes—
127C3×C4⋊Q8C2314yes—
128C3×C4⋊Q8C2312yes—
129C3×#125—22no—
130C3×#125—24no—
131C3×#125D412yes—
132C3×#125C2314yes—
133C3×C22⋊Q8—22no—
134C3×C22⋊Q8—22no—
135C3×C22⋊Q8—24no—
136C3×C22⋊Q8—24no—
137C3×C22⋊Q8—24no—
138C3×C22⋊Q8D412yes—
139C3×C22⋊Q8D412yes—
140C3×C4×Q8—22no—
141C3×C4×Q8—22no—
142C3×C4×Q8C2311yescharacteristic
143C3×C4×Q8C2314yes—
144C3×C4×Q8C2311yescharacteristic
145C3×C4×Q8C2312yes—
146C3×C4×Q8C2312yes—
147C3×C4×D4—21no—
148C3×C4×D4—21no—
149C3×C4×D4—24no—
150C3×C4×D4C2311yescharacteristic
151C3×C4×D4C2311yescharacteristic
152C3×C4×D4C2314yes—
153C3×#117—22no—
154C3×#117—21no—
155C3×#117C2311yescharacteristic
156C3×#117C2312yes—
157C2×C3×C4⋊C4—21no—
158C2×C3×C4⋊C4—22no—
159C2×C3×C4⋊C4—22no—
160C2×C3×C4⋊C4C2312yes—
161C2×C3×C42—21no—
162C2×C3×C42C2311yescharacteristic
163#950—28no—
164#949—24no—
165#947—24no—
166#946—22no—
167C2×#216C2312yes—
168C2×#215C2312yes—
169C2×#215C2312yes—
170C2×#214C2312yes—
171C2×#213C2312yes—
172C2×#213C2312yes—
173#930—21no—
174#930—21no—
175C2×(C2×D3)⋊C4—21no—
176C2×C4⋊Dic3C2311yescharacteristic
177C2×#208C2311yescharacteristic
178C2×#208C2311yescharacteristic
179C22×C3⋊C8C2312yes—
180#898—24no—
181#895—24no—
182#895—22no—
183#895—22no—
184#895—22no—
185#894—24no—
186#894—24no—
187#893—24no—
188#892—22no—
189#892—22no—
190D3×C4⋊C4—22no—
191#882—24no—
192#67⋊C4—24no—
193#875C2312yes—
194#875C2314yes—
195#874C2311yescharacteristic
196#874C2314yes—
197C4×D12—21no—
198C4×D12—21no—
199C4×D12—21no—
200C4×D12—21no—
201C4×D12C2312yes—
202C4×D12C2312yes—
203C4×D12C2314yes—
204#869C2311yescharacteristic
205C4×Dic6C2314yes—
206#835C2312yes—
207#832C2312yes—
208#810C2314yes—
209#810C2314yes—
210#810C2312yes—
211#810C2312yes—
212#809C2314yes—
213#809C2314yes—
214#809C2314yes—
215#809C2314yes—
216#809C2312yes—
217#809C2312yes—
218#809C2312yes—
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#559—34no—
236Q82C2×D312yescomplemented
237#557C2×D312yescomplemented
238#556—32no—
239#555—61no—
240#554—22no—
241#554C2×D312yescomplemented
242#553—62no—
243#550—32no—
244D4×Q8—22no—
245D4×Q8C2×D312yescomplemented
246#547—61no—
247#544—22no—
248#544C2×D312yes—
249#538—62no—
250#535—32no—
251#533—21no—
252#533C2×D311yescharacteristic
253#532—31no—
254C2×C4⋊Q8—21no—
255C2×C4⋊Q8C2×D311yescharacteristic
256#525—62no—
257#520—32no—
258#520C2×D312yes—
259C4×#41C2×D311yescharacteristic
260C2×C4×D4—31no—
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—32no—
293C4×SD16—34no—
294C4×SD16—34no—
295C4×D8—32no—
296#428—31no—
297C2×#106—32no—
298#424—32no—
299C2×C4⋊C8—31no—
300#418—31no—
301#417—31no—
302#417—32no—
303#417—32no—
304#416—32no—
305C2×#102—32no—
306#405—32no—
307C4×M16—31no—
308C23×D3—21no—
309C3×#41—22no—
310C3×#41#4114yescomplemented
311C2×C3×Q8—22no—
312C2×C3×Q8—24no—
313C2×C3×Q8—22no—
314C2×C3×Q8—82no—
315C2×C3×Q8—84no—
316C2×C3×Q8C2×D412yes—
317C2×C3×Q8C2×D412yes—
318C2×C3×Q8C2411yescharacteristic
319C2×C3×D4—21no—
320C2×C3×D4C2411yescharacteristic
321C22×C3×C4—21no—
322C22×C3×C4—22no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—24no—
326C22×C3×C4C2×D411yescharacteristic
327C22×C3×C4C2×D411yescharacteristic
328C22×C3×C4C2411yescharacteristic
329C2×#67—22no—
330C22×Dic3—21no—
331#239—84no—
332#235—24no—
333#235—24no—
334C2×D12—22no—
335C2×D12—22no—
336C2×D12—21no—
337C2×D12—21no—
338C2×D12—21no—
339C2×D12—24no—
340C2×D12—24no—
341C2×D12C2412yes—
342C2×D12C2412yes—
343C2×C4×D3—22no—
344C2×C4×D3—22no—
345C2×C4×D3—22no—
346C2×C4×D3—24no—
347C2×C4×D3—82no—
348C2×Dic6C2412yes—
349C3×C4⋊C4—22no—
350C3×C4⋊C4—22no—
351C3×C4⋊C4—24no—
352C3×C4⋊C4—22no—
353C3×C4⋊C4—24no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—24no—
357C3×C4⋊C4—24no—
358C3×C4⋊C4C2×D412yes—
359C3×C4⋊C4C2×D412yes—
360C3×C4⋊C4C2×D412yes—
361C3×C4⋊C4C2×D414yes—
362C3×C4⋊C4C2×D412yes—
363C3×C4⋊C4C2×D414yes—
364C3×C4⋊C4C2411yescharacteristic
365C3×C4⋊C4C2414yes—
366C3×C4⋊C4C2411yescharacteristic
367C3×C22⋊C4—21no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—24no—
371C3×C22⋊C4C2×D414yes—
372C3×C42—21no—
373C3×C42—21no—
374C3×C42—21no—
375C3×C42—24no—
376C3×C42C2×D411yescharacteristic
377C3×C42C2×D411yescharacteristic
378C3×C42C2411yescharacteristic
379C3×C42C2414yes—
380C3×C42C2411yescharacteristic
381#216—24no—
382#215—24no—
383#215—24no—
384#214—24no—
385#213—24no—
386#213—24no—
387(C2×D3)⋊C4—22no—
388(C2×D3)⋊C4—22no—
389(C2×D3)⋊C4—22no—
390(C2×D3)⋊C4—22no—
391(C2×D3)⋊C4—24no—
392(C2×D3)⋊C4—24no—
393(C2×D3)⋊C4—24no—
394C4⋊Dic3—21no—
395C4⋊Dic3—21no—
396C4⋊Dic3—21no—
397C4⋊Dic3C2412yes—
398Dic3⋊C4—24no—
399C4×Dic3—24no—
400#208—22no—
401#208—22no—
402C2×C3⋊C8—24no—
403C2×C3⋊C8C2412yes—
404C2×C3⋊C8C2412yes—
405C2×C3⋊C8C2412yes—
406C2×C3⋊C8C2412yes—
407C2×#41—32no—
408C2×#41—62no—
409C2×#41C22×D311yescharacteristic
410C22×Q8—22no—
411C22×Q8—21no—
412C22×D4—31no—
413C23×C4—61no—
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—22no—
426C4⋊Q8—22no—
427C4⋊Q8—22no—
428C4⋊Q8—24no—
429C4⋊Q8—21no—
430C4⋊Q8—21no—
431C4⋊Q8—31no—
432C4⋊Q8#6711yescharacteristic
433C4⋊Q8#6711yescharacteristic
434C4⋊Q8C22×D312yes—
435C4⋊Q8C22×D312yes—
436C4⋊Q8C22×D314yes—
437#127—31no—
438#127—34no—
439#126—64no—
440#125—22no—
441#125—24no—
442#125#6712yes—
443#125C22×D314yes—
444#124—32no—
445#124—34no—
446#124—64no—
447#123—64no—
448#123—64no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—24no—
452C22⋊Q8—24no—
453C22⋊Q8—24no—
454C22⋊Q8—62no—
455C22⋊Q8#6712yes—
456C22⋊Q8#6712yes—
457#121—61no—
458#121—61no—
459#121—62no—
460#121—62no—
461#121—62no—
462#121—64no—
463#120—64no—
464C4×Q8—22no—
465C4×Q8—22no—
466C4×Q8—34no—
467C4×Q8C22×D311yescharacteristic
468C4×Q8C22×D311yescharacteristic
469C4×Q8C22×D314yes—
470C4×Q8C22×D312yes—
471C4×Q8C22×D312yes—
472C4×D4—21no—
473C4×D4—21no—
474C4×D4—24no—
475C4×D4—32no—
476C4×D4—32no—
477C4×D4—34no—
478C4×D4—64no—
479C4×D4—64no—
480C4×D4—61no—
481C4×D4—61no—
482C4×D4—61no—
483C4×D4—61no—
484C4×D4C22×D311yescharacteristic
485C4×D4C22×D311yescharacteristic
486C4×D4C22×D314yes—
487#117—22no—
488#117—21no—
489#117—62no—
490#117—62no—
491#117C22×D311yescharacteristic
492#117C22×D312yes—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—62no—
498C2×C4⋊C4C22×D312yes—
499C2×C22⋊C4—61no—
500C2×C42—21no—
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—32no—
514#103—34no—
515#103—34no—
516#102—32no—
517#102—34no—
518#102—34no—
519#102—32no—
520#102—32no—
521#102—34no—
522#102—34no—
523#102—32no—
524#102—32no—
525#97—32no—
526#97—34no—
527C4×C8—32no—
528C4×C8—34no—
529C23×C3—21no—
530C23×C3C22×D411yescharacteristic
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—42no—
534C22×D3—81no—
535C22×D3—81no—
536C3×Q8—24no—
537C3×Q8—21no—
538C3×Q8—42no—
539C3×Q8—44no—
540C3×Q8—82no—
541C3×Q8—84no—
542C3×Q8C2×#4112yes—
543C3×D4—24no—
544C3×D4—21no—
545C3×D4C2×#4112yes—
546C2×C3×C4—21no—
547C2×C3×C4—24no—
548C2×C3×C4—22no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—24no—
552C2×C3×C4—41no—
553C2×C3×C4—42no—
554C2×C3×C4—42no—
555C2×C3×C4—84no—
556C2×C3×C4—82no—
557C2×C3×C4C22×D414yes—
558C2×C3×C4C22×D414yes—
559C2×C3×C4C22×D411yescharacteristic
560C2×C3×C4C22×D411yescharacteristic
561C2×C3×C4C22×D411yescharacteristic
562C2×C3×C4C22×D411yescharacteristic
563C2×C3×C4C22×D411yescharacteristic
564C2×C3×C4C2×#4112yes—
565C2×C3×C42−1+412yes—
566C2×C3×C4C2511yescharacteristic
567#67—44no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—81no—
571D12—22no—
572D12—22no—
573D12—22no—
574D12—22no—
575D12—42no—
576D12—42no—
577D12—81no—
578D12—84no—
579D12—84no—
580C4×D3—44no—
581C4×D3—44no—
582C4×D3—82no—
583C4×D3—84no—
584Dic6—22no—
585Dic6—22no—
586C3⋊C8—22no—
587C3⋊C8—22no—
588C3⋊C8—22no—
589C3⋊C8—22no—
590C24—61no—
591#41—22no—
592#41—64no—
593#41—64no—
594#41—244no—
595#41#23914yescomplemented
596C2×Q8—22no—
597C2×Q8—24no—
598C2×Q8—22no—
599C2×Q8—32no—
600C2×Q8—82no—
601C2×Q8—84no—
602C2×Q8C2×#6712yes—
603C2×Q8C2×#6712yes—
604C2×Q8C23×D311yescharacteristic
605C2×D4—21no—
606C2×D4—32no—
607C2×D4—32no—
608C2×D4—62no—
609C2×D4—62no—
610C2×D4—62no—
611C2×D4—61no—
612C2×D4—61no—
613C2×D4—64no—
614C2×D4—61no—
615C2×D4—64no—
616C2×D4C23×D311yescharacteristic
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—24no—
622C22×C4—61no—
623C22×C4—62no—
624C22×C4—62no—
625C22×C4—64no—
626C22×C4—62no—
627C22×C4—242no—
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—22no—
645C4⋊C4—22no—
646C4⋊C4—24no—
647C4⋊C4—22no—
648C4⋊C4—24no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—32no—
654C4⋊C4—61no—
655C4⋊C4—64no—
656C4⋊C4—61no—
657C4⋊C4—61no—
658C4⋊C4C2×#6712yes—
659C4⋊C4C2×#6712yes—
660C4⋊C4C2×#6712yes—
661C4⋊C4C2×#6714yes—
662C4⋊C4C2×#6712yes—
663C4⋊C4C2×#6714yes—
664C4⋊C4C23×D314yes—
665C4⋊C4C23×D311yescharacteristic
666C4⋊C4C23×D311yescharacteristic
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—24no—
671C22⋊C4—62no—
672C22⋊C4—62no—
673C22⋊C4—64no—
674C22⋊C4—64no—
675C22⋊C4—62no—
676C22⋊C4—64no—
677C22⋊C4—62no—
678C22⋊C4C2×#6714yes—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—24no—
683C42—64no—
684C42C2×#6711yescharacteristic
685C42C2×#6711yescharacteristic
686C42C23×D311yescharacteristic
687C42C23×D314yes—
688C42C23×D311yescharacteristic
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—22no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3#54812yes—
695C22×C3C23×D411yescharacteristic
696C2×D3—42no—
697C2×D3—42no—
698C2×D3—42no—
699C2×D3—42no—
700C2×D3—42no—
701C2×D3—42no—
702C2×D3—84no—
703C3×C4—21no—
704C3×C4—24no—
705C3×C4—21no—
706C3×C4—22no—
707C3×C4—21no—
708C3×C4—24no—
709C3×C4—41no—
710C3×C4—44no—
711C3×C4—41no—
712C3×C4#54812yes—
713C3×C4#57712yes—
714C3×C4C22×#4111yescharacteristic
715C3×C4C2×2−1+411yescharacteristic
716Dic3—42no—
717Dic3—42no—
718C23—21no—
719C23—62no—
720C23—62no—
721C23—122no—
722C23—241no—
723C23—241no—
724C23C22×#6711yescharacteristic
725Q8—21no—
726Q8—24no—
727Q8—42no—
728Q8—44no—
729Q8—62no—
730Q8—62no—
731Q8—82no—
732Q8—84no—
733Q8C2×#23912yes—
734D4—24no—
735D4—21no—
736D4—62no—
737D4—62no—
738D4—62no—
739D4—62no—
740D4—124no—
741D4—122no—
742D4—122no—
743D4—244no—
744D4—241no—
745D4—244no—
746D4C2×#23912yes—
747C2×C4—21no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—24no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—84no—
759C2×C4—82no—
760C2×C4—124no—
761C2×C4—124no—
762C2×C4—242no—
763C2×C4—244no—
764C2×C4—241no—
765C2×C4C2×#23912yes—
766C2×C4#100712yes—
767C2×C4C22×#6711yescharacteristic
768C2×C4C22×#6714yes—
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—42no—
781C2×C3C2×#54811yescharacteristic
782C2×C3C2×#57711yescharacteristic
783C2×C3#358511yescharacteristic
784D3—82no—
785D3—82no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—122no—
792C22—122no—
793C22—122no—
794C22—122no—
795C22—122no—
796C22—122no—
797C22—244no—
798C22#581712yes—
799C22C23×#6711yescharacteristic
800C4—22no—
801C4—21no—
802C4—21no—
803C4—24no—
804C4—21no—
805C4—24no—
806C4—41no—
807C4—44no—
808C4—41no—
809C4—122no—
810C4—122no—
811C4#581712yes—
812C4#583712yes—
813C4C22×#23911yescharacteristic
814C4C2×#100711yescharacteristic
815C3#6134711yescharacteristic, complemented, Sylow
816C2—22no—
817C2—42no—
818C2—242no—
819C2—242no—
820C2C2×#581711yescharacteristic
821C2#8727711yescharacteristic
822C2C2×#583711yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3503C2
socleC22×C3C23×D4
hypercenter#3503D3
hypocenterC3#61347
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #533 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. C3×#3503C2semidirect
2. #86259C2semidirect
3. #83704C2semidirect
4. #83703C2semidirect
5. #83691C2semidirect
6. #83638C2semidirect
7. #83637C2semidirect
8. #83569C2semidirect
9. #83476C2semidirect
10. #83470C2semidirect
11. #83330C2semidirect
12. C2×#5084C2semidirect
13. #83199C2semidirect
14. #82565C2semidirect
15. #82558C2semidirect
16. #82525C2semidirect
17. C4×#949C2semidirect
19. C3×Q82C22semidirect
20. C3×#557C22semidirect
22. C3×#554C22semidirect
24. C3×D4×Q8C22semidirect
48. #5094C22semidirect
49. #5093C22semidirect
51. #5089C22semidirect
53. #5088C22semidirect
57. #5084C22semidirect
60. #5066C22semidirect
61. #5063C22semidirect
62. #5031C22semidirect
63. #5030C22semidirect
65. #5028C22semidirect
67. #5027C22semidirect
70. C4×#215C22semidirect
71. #5024C22semidirect
72. #5024C22semidirect
73. Q8×C3⋊C8C22semidirect
74. #5019C22semidirect
75. C4×#214C22semidirect
77. #5016C22semidirect
79. #5015C22semidirect
81. #5014C22semidirect
95. #3503D3semidirect
236. Q82C2×D3semidirect
237. #557C2×D3semidirect
241. #554C2×D3semidirect
245. D4×Q8C2×D3semidirect
310. C3×#41#41semidirect
595. #41#239semidirect
815. C3#61347semidirect

Maximal subgroups

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

subgroupindex
C3×#35032
#862592
#837042
#837032
#836912
#836382
#836372
#835692
#834762
#834702
#833302
C2×#50842
#831992
#825652
#825582
#825252
C4×#9492
#613473