Finite Group Databasebeta

← #11664117

Subgroups — #11664117

Order 768.

2134 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5827C211yesmaximal, characteristic, complemented
2#85936C211yesmaximal, characteristic, complemented
3C3×#3006C211yesmaximal, characteristic, complemented
4#84080C211yesmaximal, characteristic, complemented
5#83936C212yesmaximal, complemented
6#83930C212yesmaximal, complemented
7C2×#5034C211yesmaximal, characteristic, complemented
8#80075C214yesmaximal, complemented
9#80072C214yesmaximal, complemented
10#80031C212yesmaximal, complemented
11#80028C212yesmaximal, complemented
12#79990C212yesmaximal, complemented
13#79989C212yesmaximal, complemented
14#78873C212yesmaximal, complemented
15#78869C212yesmaximal, complemented
16#78622C211yesmaximal, characteristic, complemented
17#78621C211yesmaximal, characteristic, complemented
18#60588—31nomaximal, Sylow
19C22×C3×#41C2211yescharacteristic
20C2×C3×AGL(1,ℤ/8)C2212yes—
21C2×C3×#121C2211yescharacteristic
22#5827—21no—
23#5827—21no—
24#5827—22no—
25#5827C2212yes—
26#5827C2212yes—
27#5827C2214yescomplemented
28C2×#950C2212yes—
29C2×Q8×Dic3C2212yescomplemented
30#5806—22no—
31#5805C2211yescharacteristic, complemented
32#5798C2211yescharacteristic, complemented
33C2×D4×Dic3—22no—
34C2×D4×Dic3C2212yescomplemented
35#5791C2211yescharacteristic
36C2×#926—21no—
37C2×#926C2211yescharacteristic
38C22×C4⋊Dic3—21no—
39C22×C4⋊Dic3C2211yescharacteristic
40#5619C2212yescomplemented
41#5618—21no—
42#5616—21no—
43#5614—21no—
44#5611—21no—
45#5603C2212yescomplemented
46#5600C2212yes—
47#5596C2212yes—
48#5504C2211yescharacteristic, complemented
49#5500C2211yescharacteristic, complemented
50#5495—22no—
51C3×#449C2214yes—
52C3×#448C2212yes—
53C3×#447C2212yes—
54C3×#417C2212yes—
55C3×#407C2211yescharacteristic
56#5239C2212yescomplemented
57#5238C2212yescomplemented
58#5233C2212yes—
59#5228C2211yescharacteristic, complemented
60#5227C2211yescharacteristic, complemented
61#5218C2211yescharacteristic, complemented
62#5217C2211yescharacteristic, complemented
63C2×#832C2212yescomplemented
64C2×#830C2211yescharacteristic
65#5166C2214yescomplemented
66#5164C2214yescomplemented
67#5163C2214yescomplemented
68Dic3×SD16C2214yescomplemented
69#5153C2214yescomplemented
70#5152C2214yescomplemented
71#5150C2214yescomplemented
72Dic3×D8C2214yescomplemented
73#5133C2212yescomplemented
74#5122C2212yescomplemented
75#5121C2212yescomplemented
76#5119C2212yescomplemented
77#5034C2212yes—
78#5034C2212yes—
79#5034C2214yescomplemented
80C2×#808C2212yescomplemented
81#4796C2214yescomplemented
82#4791C2214yescomplemented
83#4789C2214yescomplemented
84#4788C2214yescomplemented
85#4785C2214yescomplemented
86#4766C2214yescomplemented
87#4761C2214yescomplemented
88#4758C2214yescomplemented
89#4736C2212yescomplemented
90#4735C2212yescomplemented
91#4722C2212yescomplemented
92#4721C2212yescomplemented
93#4720C2214yescomplemented
94#4719C2212yescomplemented
95#4718C2212yescomplemented
96#3494—31no—
97C2×#520—31no—
98#3125—34no—
99#3119—34no—
100#3117—32no—
101#3109—32no—
102#3105—32no—
103#3103—32no—
104#3092—31no—
105C2×#481—31no—
106#3084—32no—
107#3045—32no—
108#3006D311yescharacteristic, complemented
109#3002—31no—
110#2952—32no—
111#2946—32no—
112#2924—31no—
113C2×C3×#41—28no—
114C2×C3×#41—21no—
115C2×C3×#41—21no—
116C2×C3×#41C2312yes—
117C2×C3×#41C2312yes—
118C22×C3×Q8C2311yescharacteristic
119C22×C3×D4—21no—
120C22×C3×D4—21no—
121C22×C3×D4C2311yescharacteristic
122C22×C3×D4C2311yescharacteristic
123C23×C3×C4—21no—
124C23×C3×C4C2311yescharacteristic
125C23×Dic3—21no—
126C23×Dic3—22no—
127C2×#237—22no—
128C2×#235C2311yescharacteristic
129C3×AGL(1,ℤ/8)—28no—
130C2×C3×SD16C2314yes—
131C2×C3×D8C2314yes—
132C2×C3×M16C2312yes—
133C3×#121—21no—
134C3×#121—21no—
135C3×#121C2312yes—
136C3×#121C2312yes—
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C22⋊C4—21no—
139#953—21no—
140#953—22no—
141C2×#217—22no—
142C2×#217—22no—
143C2×#217D412yes—
144#950—28no—
145Q8×Dic3—22no—
146Q8×Dic3—22no—
147Q8×Dic3C2314yes—
148Q8×Dic3C2314yes—
149C2×#216C2312yes—
150C2×#215C2312yes—
151#940C2312yes—
152#939—22no—
153#939—22no—
154#938—22no—
155#938—21no—
156#938—21no—
157#936—22no—
158#936C2312yes—
159#935—22no—
160#935—22no—
161D4×Dic3—22no—
162D4×Dic3—24no—
163D4×Dic3—24no—
164D4×Dic3—24no—
165D4×Dic3—24no—
166D4×Dic3—21no—
167D4×Dic3—21no—
168D4×Dic3—22no—
169D4×Dic3—22no—
170D4×Dic3C2312yes—
171D4×Dic3C2314yes—
172D4×Dic3C2314yes—
173D4×Dic3C2312yes—
174C2×#214C2312yes—
175C2×#213C2312yes—
176#930C2311yescharacteristic
177#930C2311yescharacteristic
178#929—21no—
179C4×#67—21no—
180C4×#67—21no—
181C4×#67—22no—
182#926—22no—
183#926—22no—
184#926—24no—
185#926D412yes—
186#926D411yescharacteristic
187#926D411yescharacteristic
188#926C2311yescharacteristic
189#926C2311yescharacteristic
190#926C2312yes—
191#926C2311yescharacteristic
192C2×C4⋊Dic3—21no—
193C2×C4⋊Dic3—21no—
194C2×C4⋊Dic3—21no—
195C2×C4⋊Dic3—22no—
196C2×C4⋊Dic3—22no—
197C2×C4⋊Dic3—22no—
198C2×C4⋊Dic3—24no—
199C2×C4⋊Dic3D411yescharacteristic
200C2×C4⋊Dic3D411yescharacteristic
201C2×C4⋊Dic3C2312yes—
202C2×C4⋊Dic3C2312yes—
203C2×C4⋊Dic3C2312yes—
204#924—22no—
205#924C2311yescharacteristic
206#924C2311yescharacteristic
207C2×C4×Dic3—22no—
208C2×C4×Dic3C2312yes—
209C22×C3⋊C8C2312yes—
210#893C2312yes—
211#892—21no—
212D3×C4⋊C4—21no—
213#890—21no—
214#890C2312yes—
215#888—21no—
216#888C2312yes—
217#887C2312yes—
218#886—22no—
219#885—22no—
220#883—22no—
221#67⋊C4—22no—
222#879—22no—
223#879—22no—
224#878—22no—
225#877—22no—
226C3×#103C2314yes—
227C3×#102C2314yes—
228C3×C22⋊C8C2312yes—
229C3×C22⋊C8C2312yes—
230#835C2312yes—
231#835C2312yes—
232#832C2312yes—
233#832C2314yes—
234#832C2314yes—
235#832C2312yes—
236#830C2311yescharacteristic
237#830C2311yescharacteristic
238#830C2312yes—
239#821C2314yes—
240#818C2314yes—
241#817C2314yes—
242#816C2314yes—
243#815C2314yes—
244Dic3⋊C8C2314yes—
245Dic3⋊C8C2314yes—
246C8×Dic3C2314yes—
247#808C2314yes—
248#808C2314yes—
249C22×#41C2×D311yescharacteristic
250C2×AGL(1,ℤ/8)C2×D312yes—
251C2×#135—32no—
252#555—61no—
253#553—61no—
254#553—61no—
255#551—62no—
256#547—61no—
257#546—62no—
258#544—31no—
259#542—32no—
260#540—32no—
261#535—31no—
262#532—32no—
263#529—32no—
264#525—31no—
265C2×#121C2×D311yescharacteristic
266#520—32no—
267#520—34no—
268#520—32no—
269#520—31no—
270#520—62no—
271#520—61no—
272#520—61no—
273#518—31no—
274C2×C4×Q8—32no—
275C2×C4×D4—32no—
276C2×C4×D4—62no—
277C2×#117—31no—
278C2×#117—61no—
279C22×C4⋊C4—31no—
280C22×C4⋊C4—61no—
281#484—32no—
282#483—32no—
283#481—32no—
284#481—32no—
285#481—34no—
286#481—32no—
287#480—32no—
288#479—34no—
289#478—34no—
290#476—34no—
291#475—34no—
292#464—34no—
293#463—34no—
294#460—34no—
295#459—34no—
296#452—32no—
297#451—31no—
298#450—31no—
299#449—32no—
300#449C2×D314yes—
301#448—31no—
302#448C2×D312yes—
303#447—31no—
304#447C2×D312yes—
305#442—34no—
306#442—34no—
307#441—34no—
308#440—34no—
309C4×SD16—34no—
310C4×SD16—34no—
311C4×SD16—34no—
312C4×D8—34no—
313#433—34no—
314#432—32no—
315#431—32no—
316#428—32no—
317C2×#106—32no—
318#424—32no—
319#417—32no—
320#417C2×D312yes—
321#416—32no—
322C2×#102—32no—
323#407C2×D311yescharacteristic
324C2×C22⋊C8—31no—
325#405—32no—
326C24×C3—21no—
327C24×C3—21no—
328C24×C3C2×D411yescharacteristic
329C3×#41—28no—
330C3×#41—28no—
331C3×#41—24no—
332C3×#41—24no—
333C3×#41—24no—
334C3×#41#4118yescomplemented
335C2×C3×Q8—24no—
336C2×C3×Q8—21no—
337C2×C3×Q8C2412yes—
338C2×C3×D4—28no—
339C2×C3×D4—22no—
340C2×C3×D4—22no—
341C2×C3×D4—24no—
342C2×C3×D4—22no—
343C2×C3×D4—22no—
344C2×C3×D4—21no—
345C2×C3×D4—21no—
346C2×C3×D4—24no—
347C2×C3×D4—82no—
348C2×C3×D4C2412yes—
349C2×C3×D4C2412yes—
350C22×C3×C4—28no—
351C22×C3×C4—21no—
352C22×C3×C4—22no—
353C22×C3×C4—22no—
354C22×C3×C4—24no—
355C22×C3×C4—21no—
356C22×C3×C4C2×D411yescharacteristic
357C22×C3×C4C2×D411yescharacteristic
358C22×C3×C4C2×D411yescharacteristic
359C22×C3×C4C2411yescharacteristic
360C22×C3×C4C2411yescharacteristic
361C22×C3×C4C2411yescharacteristic
362C2×#67—21no—
363C2×#67—21no—
364C2×#67—21no—
365C2×#67—22no—
366C2×#67—22no—
367C22×Dic3—22no—
368C22×Dic3—22no—
369C22×Dic3—22no—
370C22×Dic3—22no—
371C22×Dic3—22no—
372C22×Dic3—24no—
373C22×Dic3—24no—
374C22×Dic3—84no—
375C22×Dic3—82no—
376C22×Dic3C2×D412yes—
377C22×Dic3C2×D412yes—
378#237—84no—
379#235—24no—
380C2×D12C2411yescharacteristic
381C2×C4×D3—21no—
382C2×C4×D3—22no—
383C2×Dic6—22no—
384C2×Dic6C2411yescharacteristic
385C3×SD16—28no—
386C3×D8—28no—
387C3×M16—24no—
388C2×C3×C8C2414yes—
389C3×C4⋊C4—21no—
390C3×C4⋊C4C2412yes—
391C3×C22⋊C4—22no—
392C3×C22⋊C4—22no—
393#217—21no—
394#217—21no—
395#217—21no—
396#217—22no—
397#217—22no—
398#217—22no—
399#217—22no—
400#217—24no—
401#217—24no—
402#217C2×D412yes—
403#217C2×D412yes—
404#217C2×D412yes—
405#217C2×D412yes—
406#216—24no—
407#215—24no—
408#214—24no—
409#213—24no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—22no—
413C4⋊Dic3—22no—
414C4⋊Dic3—22no—
415C4⋊Dic3—22no—
416C4⋊Dic3—22no—
417C4⋊Dic3—24no—
418C4⋊Dic3—24no—
419C4⋊Dic3C2×D412yes—
420C4⋊Dic3C2×D412yes—
421C4⋊Dic3C2×D411yescharacteristic
422C4⋊Dic3C2×D411yescharacteristic
423C4⋊Dic3C2×D411yescharacteristic
424C4⋊Dic3C2×D411yescharacteristic
425C4⋊Dic3C2414yes—
426C4⋊Dic3C2411yescharacteristic
427C4⋊Dic3C2411yescharacteristic
428Dic3⋊C4—21no—
429Dic3⋊C4—21no—
430Dic3⋊C4—22no—
431Dic3⋊C4—22no—
432Dic3⋊C4—22no—
433C4×Dic3—21no—
434C4×Dic3—22no—
435C4×Dic3—24no—
436C4×Dic3—24no—
437C4×Dic3C2×D412yes—
438C4×Dic3C2×D412yes—
439C4×Dic3C2412yes—
440C4×Dic3C2412yes—
441C2×C3⋊C8—24no—
442C2×C3⋊C8C2412yes—
443C2×C3⋊C8C2412yes—
444C2×#41—28no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—31no—
448C2×#41—62no—
449C2×#41C22×D312yes—
450C2×#41C22×D312yes—
451C22×Q8C22×D311yescharacteristic
452C22×D4—21no—
453C22×D4—21no—
454C22×D4C22×D311yescharacteristic
455C22×D4C22×D311yescharacteristic
456C23×C4—21no—
457C23×C4—62no—
458C23×C4—61no—
459C23×C4C22×D311yescharacteristic
460AGL(1,ℤ/8)—28no—
461#135—68no—
462C2×Q16—32no—
463C2×SD16—32no—
464C2×SD16—32no—
465C2×SD16C22×D314yes—
466C2×D8—32no—
467C2×D8C22×D314yes—
468C2×M16C22×D312yes—
469C22×C8—32no—
470C4⋊Q8—32no—
471C4⋊Q8—61no—
472#127—32no—
473#126—62no—
474#126—62no—
475#125—32no—
476#125—61no—
477#124—32no—
478#124—62no—
479#124—62no—
480#123—62no—
481#123—62no—
482#123—62no—
483#123—62no—
484#123—61no—
485C22⋊Q8—31no—
486C22⋊Q8—31no—
487C22⋊Q8—62no—
488C22⋊Q8—62no—
489#121—21no—
490#121—21no—
491#121—31no—
492#121—31no—
493#121—62no—
494#121—62no—
495#121—61no—
496#121—61no—
497#121—62no—
498#121C22×D312yes—
499#121C22×D312yes—
500#120—62no—
501#120—61no—
502C4×Q8—34no—
503C4×Q8—34no—
504C4×Q8—32no—
505C4×Q8—62no—
506C4×Q8—62no—
507C4×D4—34no—
508C4×D4—34no—
509C4×D4—32no—
510C4×D4—32no—
511C4×D4—32no—
512C4×D4—62no—
513C4×D4—62no—
514C4×D4—62no—
515C4×D4—62no—
516C4×D4—64no—
517C4×D4—64no—
518C4×D4—64no—
519C4×D4—64no—
520C4×D4—61no—
521C4×D4—61no—
522C4×D4—62no—
523C4×D4—61no—
524C4×D4—61no—
525#117—32no—
526#117—31no—
527#117—31no—
528#117—31no—
529#117—31no—
530#117—32no—
531#117—31no—
532#117—62no—
533#117—61no—
534#117—62no—
535#117—62no—
536#117—64no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—32no—
540C2×C4⋊C4—32no—
541C2×C4⋊C4—32no—
542C2×C4⋊C4—61no—
543C2×C4⋊C4—62no—
544C2×C4⋊C4—62no—
545C2×C4⋊C4—64no—
546C2×C4⋊C4—62no—
547C2×C4⋊C4—61no—
548C2×C4⋊C4—61no—
549C2×C4⋊C4—61no—
550C2×C4⋊C4C22×D311yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—32no—
553C2×C22⋊C4—62no—
554C2×C22⋊C4—62no—
555C2×C42—32no—
556C2×C42—62no—
557#107—34no—
558#106—34no—
559#106—34no—
560#106—34no—
561C4⋊C8—34no—
562C4⋊C8—34no—
563#103—32no—
564#103—32no—
565#103—34no—
566#103C22×D314yes—
567#102—34no—
568#102—34no—
569#102—32no—
570#102—32no—
571#102—34no—
572#102C22×D314yes—
573C22⋊C8—31no—
574C22⋊C8—31no—
575C22⋊C8—32no—
576C22⋊C8C22×D312yes—
577C22⋊C8C22×D312yes—
578#97—34no—
579C4×C8—34no—
580C23×C3—24no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—41no—
586C23×C3—42no—
587C23×C3—42no—
588C23×C3—42no—
589C23×C3—81no—
590C23×C3—81no—
591C23×C3C22×D411yescharacteristic
592C23×C3C22×D411yescharacteristic
593C23×C3C22×D411yescharacteristic
594C22×D3—21no—
595C3×Q8—24no—
596C3×Q8—22no—
597C3×Q8C2×#4114yes—
598C3×D4—28no—
599C3×D4—24no—
600C3×D4—28no—
601C3×D4—22no—
602C3×D4—24no—
603C3×D4—44no—
604C3×D4—42no—
605C3×D4—82no—
606C3×D4C2×#4114yes—
607C2×C3×C4—24no—
608C2×C3×C4—28no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—28no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—81no—
618C2×C3×C4C22×D411yescharacteristic
619C2×C3×C4C22×D411yescharacteristic
620C2×C3×C4C22×D411yescharacteristic
621C2×C3×C4C2×#4114yes—
622C2×C3×C4C2511yescharacteristic
623#67—42no—
624#67—42no—
625#67—82no—
626#67—82no—
627#67—81no—
628C2×Dic3—24no—
629C2×Dic3—21no—
630C2×Dic3—24no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—42no—
634C2×Dic3—44no—
635C2×Dic3—82no—
636C2×Dic3—82no—
637C2×Dic3—84no—
638C2×Dic3—84no—
639C2×Dic3—82no—
640C2×Dic3—82no—
641C2×Dic3C22×D412yes—
642C2×Dic3C22×D412yes—
643C2×Dic3C22×D412yes—
644C2×Dic3C22×D412yes—
645D12—22no—
646C4×D3—42no—
647C4×D3—82no—
648Dic6—22no—
649Dic6—82no—
650C3×C8—24no—
651C3⋊C8—22no—
652C3⋊C8—22no—
653C24—21no—
654C24—21no—
655C24D3×D411yescharacteristic
656#41—28no—
657#41—28no—
658#41—24no—
659#41—24no—
660#41—24no—
661#41—64no—
662#41—244no—
663#41#23718yescomplemented
664C2×Q8—24no—
665C2×Q8—21no—
666C2×Q8—31no—
667C2×Q8—62no—
668C2×Q8C23×D312yes—
669C2×D4—28no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—24no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—24no—
678C2×D4—31no—
679C2×D4—62no—
680C2×D4—62no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—82no—
685C2×D4C23×D312yes—
686C2×D4C23×D312yes—
687C22×C4—28no—
688C22×C4—21no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—24no—
692C22×C4—21no—
693C22×C4—32no—
694C22×C4—32no—
695C22×C4—62no—
696C22×C4—62no—
697C22×C4—62no—
698C22×C4—64no—
699C22×C4—64no—
700C22×C4—62no—
701C22×C4—62no—
702C22×C4—62no—
703C22×C4—61no—
704C22×C4—244no—
705C22×C4—242no—
706C22×C4D3×D411yescharacteristic
707C22×C4D3×D411yescharacteristic
708C22×C4D3×D411yescharacteristic
709C22×C4C23×D311yescharacteristic
710C22×C4C23×D311yescharacteristic
711C22×C4C23×D311yescharacteristic
712Q16—64no—
713SD16—28no—
714SD16—64no—
715SD16—64no—
716D8—28no—
717D8—64no—
718M16—24no—
719C2×C8—32no—
720C2×C8—32no—
721C2×C8—64no—
722C2×C8C23×D314yes—
723C4⋊C4—21no—
724C4⋊C4—31no—
725C4⋊C4—31no—
726C4⋊C4—32no—
727C4⋊C4—31no—
728C4⋊C4—31no—
729C4⋊C4—32no—
730C4⋊C4—34no—
731C4⋊C4—31no—
732C4⋊C4—31no—
733C4⋊C4—64no—
734C4⋊C4—64no—
735C4⋊C4—62no—
736C4⋊C4—62no—
737C4⋊C4—62no—
738C4⋊C4—62no—
739C4⋊C4—62no—
740C4⋊C4—62no—
741C4⋊C4—62no—
742C4⋊C4—61no—
743C4⋊C4—61no—
744C4⋊C4C23×D312yes—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—32no—
748C22⋊C4—32no—
749C22⋊C4—32no—
750C22⋊C4—32no—
751C22⋊C4—62no—
752C22⋊C4—64no—
753C22⋊C4—64no—
754C22⋊C4—62no—
755C22⋊C4—62no—
756C22⋊C4—62no—
757C22⋊C4—62no—
758C22⋊C4—61no—
759C22⋊C4—61no—
760C22⋊C4—61no—
761C22⋊C4—61no—
762C22⋊C4—61no—
763C42—32no—
764C42—32no—
765C42—32no—
766C42—32no—
767C42—64no—
768C42—64no—
769C42—62no—
770C42—61no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—24no—
778C22×C3—21no—
779C22×C3—44no—
780C22×C3—48no—
781C22×C3—42no—
782C22×C3—42no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—162no—
787C22×C3#52512yes—
788C22×C3#57712yes—
789C22×C3C23×D411yescharacteristic
790C2×D3—41no—
791C2×D3—41no—
792C2×D3—41no—
793C3×C4—21no—
794C3×C4—24no—
795C3×C4—21no—
796C3×C4—42no—
797C3×C4#52512yes—
798C3×C4C22×#4112yes—
799Dic3—22no—
800Dic3—22no—
801Dic3—22no—
802Dic3—22no—
803Dic3—44no—
804Dic3—41no—
805Dic3—41no—
806Dic3—41no—
807C23—24no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—41no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—61no—
817C23—81no—
818C23—81no—
819C23C2×D3×D411yescharacteristic
820C23C2×D3×D411yescharacteristic
821C23C2×D3×D411yescharacteristic
822Q8—24no—
823Q8—22no—
824Q8—62no—
825Q8—242no—
826Q8C2×#23714yes—
827D4—28no—
828D4—24no—
829D4—28no—
830D4—22no—
831D4—24no—
832D4—44no—
833D4—42no—
834D4—62no—
835D4—82no—
836D4—122no—
837D4—122no—
838D4—242no—
839D4—242no—
840D4—241no—
841D4C2×#23714yes—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—28no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—64no—
857C2×C4—61no—
858C2×C4—64no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—81no—
862C2×C4—122no—
863C2×C4—124no—
864C2×C4—122no—
865C2×C4—242no—
866C2×C4—244no—
867C2×C4—244no—
868C2×C4—242no—
869C2×C4—242no—
870C2×C4—242no—
871C2×C4—242no—
872C2×C4C2×D3×D411yescharacteristic
873C2×C4C2×D3×D411yescharacteristic
874C2×C4C2×D3×D411yescharacteristic
875C2×C4C2×#23714yes—
876C2×C4C24×D311yescharacteristic
877C8—24no—
878C8—62no—
879C8—62no—
880C2×C3—22no—
881C2×C3—22no—
882C2×C3—41no—
883C2×C3—44no—
884C2×C3—82no—
885C2×C3C2×#52511yescharacteristic
886C2×C3C2×#57711yescharacteristic
887C2×C3#358511yescharacteristic
888D3—81no—
889C22—21no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—24no—
895C22—21no—
896C22—21no—
897C22—44no—
898C22—48no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—162no—
908C22#558612yes—
909C22#577512yes—
910C22C22×D3×D411yescharacteristic
911C4—21no—
912C4—24no—
913C4—21no—
914C4—42no—
915C4—62no—
916C4—62no—
917C4—62no—
918C4—62no—
919C4—121no—
920C4—121no—
921C4—124no—
922C4—121no—
923C4#558612yes—
924C4C22×#23712yes—
925C3#6058811yescharacteristic, complemented, Sylow
926C2—22no—
927C2—22no—
928C2—41no—
929C2—44no—
930C2—82no—
931C2—241no—
932C2C2×#558611yescharacteristic
933C2C2×#577511yescharacteristic
934C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3006C2
socleC22×C3C23×D4
hypercenter#3006D3
hypocenterC3#60588
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3006

Complements

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

NH ≅ G/Ntype
1. C2×#5827C2semidirect
2. #85936C2semidirect
3. C3×#3006C2semidirect
4. #84080C2semidirect
5. #83936C2semidirect
6. #83930C2semidirect
7. C2×#5034C2semidirect
8. #80075C2semidirect
9. #80072C2semidirect
10. #80031C2semidirect
11. #80028C2semidirect
12. #79990C2semidirect
13. #79989C2semidirect
14. #78873C2semidirect
15. #78869C2semidirect
16. #78622C2semidirect
17. #78621C2semidirect
27. #5827C22semidirect
29. C2×Q8×Dic3C22semidirect
31. #5805C22semidirect
32. #5798C22semidirect
34. C2×D4×Dic3C22semidirect
40. #5619C22semidirect
45. #5603C22semidirect
48. #5504C22semidirect
49. #5500C22semidirect
56. #5239C22semidirect
57. #5238C22semidirect
59. #5228C22semidirect
60. #5227C22semidirect
61. #5218C22semidirect
62. #5217C22semidirect
63. C2×#832C22semidirect
65. #5166C22semidirect
66. #5164C22semidirect
67. #5163C22semidirect
68. Dic3×SD16C22semidirect
69. #5153C22semidirect
70. #5152C22semidirect
71. #5150C22semidirect
72. Dic3×D8C22semidirect
73. #5133C22semidirect
74. #5122C22semidirect
75. #5121C22semidirect
76. #5119C22semidirect
79. #5034C22semidirect
80. C2×#808C22semidirect
81. #4796C22semidirect
82. #4791C22semidirect
83. #4789C22semidirect
84. #4788C22semidirect
85. #4785C22semidirect
86. #4766C22semidirect
87. #4761C22semidirect
88. #4758C22semidirect
89. #4736C22semidirect
90. #4735C22semidirect
91. #4722C22semidirect
92. #4721C22semidirect
93. #4720C22semidirect
94. #4719C22semidirect
95. #4718C22semidirect
108. #3006D3semidirect
334. C3×#41#41semidirect
663. #41#237semidirect
925. C3#60588semidirect

Maximal subgroups

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

subgroupindex
C2×#58272
#859362
C3×#30062
#840802
#839362
#839302
C2×#50342
#800752
#800722
#800312
#800282
#799902
#799892
#788732
#788692
#786222
#786212
#605883