Finite Group Databasebeta

← #11662153

Subgroups — #11662153

Order 768.

2674 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#137C212yesmaximal, complemented
2#86235C211yesmaximal, characteristic
3C2×#5572C211yesmaximal, characteristic, complemented
4C3×#3037C211yesmaximal, characteristic, complemented
5#83966C212yesmaximal, complemented
6#83314C211yesmaximal, characteristic, complemented
7#82441C211yesmaximal, characteristic, complemented
8#80601C214yesmaximal, complemented
9#80600C214yesmaximal, complemented
10#80478C214yesmaximal, complemented
11#80385C214yesmaximal, complemented
12#79067C211yesmaximal, characteristic, complemented
13#79048C211yesmaximal, characteristic, complemented
14#78913C212yesmaximal, complemented
15#78881C212yesmaximal, complemented
16#60424—31nomaximal, Sylow
17C2×D3×#41C2212yes—
18C22×D3×Q8C2211yescharacteristic
19C2×C3×#137C2212yescomplemented
20C3×#532C2211yescharacteristic
21C2×C3×C4×Q8C2211yescharacteristic, complemented
22#5832C2212yes—
23C2×#951C2212yescomplemented
24C2×Q8×Dic3C2211yescharacteristic, complemented
25C2×#942C2212yescomplemented
26D3×#137—216no—
27C2×#918C2214yes—
28C2×D3×Q16C2214yescomplemented
29C2×#915C2214yes—
30C2×D3×SD16C2214yescomplemented
31C2×#909C2212yescomplemented
32C2×D3×M16C2212yes—
33#5724C2212yes—
34#5715C2212yes—
35#5675C2212yes—
36#5674C2212yes—
37#5605—21no—
38#5605—21no—
39#5597—21no—
40#5597—21no—
41#5572—22no—
42#5572—22no—
43#5572C2214yescomplemented
44#5572C2214yescomplemented
45#5547—22no—
46#5547—22no—
47C2×#892—21no—
48C2×#892C2211yescharacteristic
49C2×#887—21no—
50C2×#887C2211yescharacteristic, complemented
51#5477C2211yescharacteristic
52C2×#872—21no—
53C2×#872C2211yescharacteristic
54C2×C4×Dic6—21no—
55C2×C4×Dic6C2211yescharacteristic, complemented
56C3×#464C2214yescomplemented
57C3×#462C2212yescomplemented
58C3×#460C2212yescomplemented
59C3×#423C2211yescharacteristic, complemented
60C3×#417C2212yescomplemented
61#5232C2212yescomplemented
62#5185C2214yescomplemented
63#5182C2214yescomplemented
64#5166C2214yescomplemented
65#5163C2214yescomplemented
66#5133C2212yescomplemented
67#5118C2212yescomplemented
68#5090C2212yescomplemented
69#5075C2212yescomplemented
70#5054C2214yescomplemented
71#5031C2212yescomplemented
72#5028C2214yescomplemented
73#5027C2212yescomplemented
74#4966C2212yescomplemented
75#4924C2211yescharacteristic, complemented
76#4849C2212yescomplemented
77#4848C2212yescomplemented
78#4845C2214yescomplemented
79#4839C2214yescomplemented
80#4839C2214yescomplemented
81#4804C2214yes—
82#4802C2214yescomplemented
83#4798C2214yescomplemented
84#4795C2214yescomplemented
85#4772C2214yes—
86#4770C2214yescomplemented
87#4767C2214yescomplemented
88#4762C2214yescomplemented
89C22×#137—32no—
90#3449—31no—
91C2×#519—31no—
92#3044—34no—
93#3044—34no—
94#3043—34no—
95#3043—34no—
96#3037—31no—
97#3037—32no—
98#3037—32no—
99#3037—31no—
100#3037—31no—
101#3037D311yescharacteristic, complemented
102#2905—31no—
103#2896—32no—
104C2×C3×#41C2312yes—
105C22×C3×Q8C2311yescharacteristic
106D3×#41—28no—
107D3×#41—28no—
108C2×#239C2312yes—
109C2×D3×Q8—22no—
110C2×D3×Q8—24no—
111C2×D3×Q8D418yescomplemented
112C2×D3×Q8C2312yes—
113C2×D3×Q8C2314yes—
114C2×#237—22no—
115C2×#237C2312yes—
116C2×D3×D4—22no—
117C2×D3×D4C2312yes—
118C2×#235—22no—
119C2×#235C2312yes—
120C22×C4×D3—21no—
121C22×C4×D3—22no—
122C22×C4×D3C2311yescharacteristic
123C22×Dic6—21no—
124C22×Dic6C2311yescharacteristic
125C3×#137—28no—
126C2×C3×Q16C2314yes—
127C2×C3×SD16C2314yes—
128C2×C3×M16C2312yes—
129C3×C4⋊Q8C2311yescharacteristic
130C3×#127C2311yescharacteristic
131C3×#124C2312yes—
132C3×#121—21no—
133C3×#121—21no—
134C3×C4×Q8—21no—
135C3×C4×Q8—21no—
136C3×C4×Q8C2312yes—
137C3×C4×Q8C2312yes—
138C3×C4×D4—21no—
139C3×C4×D4—21no—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4C2311yescharacteristic
142C2×C3×C42—21no—
143C2×C3×C42C2311yescharacteristic
144#951—28no—
145#947C2312yes—
146Q8×Dic3—22no—
147Q8×Dic3C2314yes—
148#944C2312yes—
149C2×#216C2314yes—
150C2×#216C2314yes—
151#942—28no—
152C2×#215C2314yes—
153#940C2312yes—
154#939—22no—
155#939—22no—
156#939—22no—
157#939—22no—
158#937—22no—
159#937—22no—
160#936C2312yes—
161C2×#214C2314yes—
162#930—21no—
163#930—21no—
164C4×#67—22no—
165C4×#67—22no—
166C2×(C2×D3)⋊C4—21no—
167C2×(C2×D3)⋊C4D411yescharacteristic
168C2×(C2×D3)⋊C4D411yescharacteristic
169C2×C4⋊Dic3—21no—
170C2×C4⋊Dic3C2311yescharacteristic
171C2×Dic3⋊C4—21no—
172C2×Dic3⋊C4—21no—
173C2×Dic3⋊C4D411yescharacteristic
174C2×Dic3⋊C4D411yescharacteristic
175C2×C4×Dic3—21no—
176C2×C4×Dic3—21no—
177C2×C4×Dic3—21no—
178C2×C4×Dic3—21no—
179C2×C4×Dic3C2311yescharacteristic
180C2×#208C2312yes—
181#918—216no—
182D3×Q16—216no—
183#915—216no—
184D3×SD16—216no—
185#909—28no—
186D3×M16—28no—
187C2×Dic12C2314yes—
188C2×#204C2314yes—
189C2×ΓL(1,𝔽25)C2314yes—
190C2×D3×C8C2314yes—
191#896—22no—
192#896—22no—
193#894—22no—
194#894—22no—
195#892—22no—
196#892—24no—
197#892—24no—
198#892C2314yes—
199#887—24no—
200#887—24no—
201#887—22no—
202#887C2314yes—
203#884—22no—
204#884—22no—
205#883—22no—
206#883—22no—
207#882—22no—
208#882—22no—
209#878—22no—
210#878—22no—
211#875C2312yes—
212#874C2311yescharacteristic
213C4×D12—21no—
214C4×D12—21no—
215#872—24no—
216#872—24no—
217#872D412yes—
218#872D412yes—
219#872C2312yes—
220#872C2312yes—
221#869C2311yescharacteristic
222C4×Dic6—21no—
223C4×Dic6—21no—
224C4×Dic6—24no—
225C4×Dic6—24no—
226C4×Dic6C2312yes—
227C4×Dic6C2312yes—
228C3×C4⋊C8C2312yes—
229C3×C4⋊C8C2312yes—
230C3×#103C2314yes—
231C3×#102C2314yes—
232#835C2314yes—
233#832C2314yes—
234#821C2314yes—
235#816C2314yes—
236Dic3⋊C8C2314yes—
237Dic3⋊C8C2314yes—
238#810C2314yes—
239#809C2314yes—
240C4⋊(C3⋊C8)C2312yes—
241C4⋊(C3⋊C8)C2312yes—
242C22×#41—32no—
243C23×Q8—31no—
244C2×#137—32no—
245C2×#137—32no—
246C2×#137—34no—
247C2×#137—34no—
248C2×#137—32no—
249C2×#137—616no—
250C2×#137C2×D312yescomplemented
251C22×Q16—34no—
252C22×SD16—34no—
253C22×M16—32no—
254#537—61no—
255#537—61no—
256#536—32no—
257#536—32no—
258#535—32no—
259#535—32no—
260#534—61no—
261#534—61no—
262#532—32no—
263#532—31no—
264#532C2×D311yescharacteristic
265#525—62no—
266#525—62no—
267#519—34no—
268#519—34no—
269#519—62no—
270#519—62no—
271C2×C4×Q8—31no—
272C2×C4×Q8—31no—
273C2×C4×Q8—31no—
274C2×C4×Q8—61no—
275C2×C4×Q8—61no—
276C2×C4×Q8C2×D311yescharacteristic, complemented
277C2×#117—31no—
278C2×#117—31no—
279C2×#117—61no—
280C2×#117—61no—
281#464—34no—
282#464—34no—
283#464—34no—
284#464—34no—
285#464—34no—
286#464—34no—
287#464—34no—
288#464C2×D314yescomplemented
289#462—34no—
290#462—32no—
291#462—32no—
292#462—32no—
293#462—34no—
294#462C2×D312yescomplemented
295#460—34no—
296#460—32no—
297#460—32no—
298#460—32no—
299#460—34no—
300#460C2×D312yescomplemented
301#424—34no—
302#424—34no—
303#423—32no—
304#423—31no—
305#423C2×D311yescharacteristic, complemented
306#419—34no—
307#418—34no—
308#417—32no—
309#417—32no—
310#417—32no—
311#417C2×D312yescomplemented
312#416—34no—
313#416—34no—
314C23×D3—22no—
315C23×D3C2×D411yescharacteristic
316C3×#41—24no—
317C3×#41—24no—
318C2×C3×Q8—21no—
319C2×C3×Q8—22no—
320C2×C3×Q8C2×D414yes—
321C2×C3×Q8C2412yes—
322C2×C3×Q8C2412yes—
323C2×C3×D4—22no—
324C2×C3×D4—21no—
325C2×C3×D4—21no—
326C2×C3×D4C2412yes—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—22no—
330C22×C3×C4C2×D411yescharacteristic
331C22×C3×C4C2×D411yescharacteristic
332C22×C3×C4C2411yescharacteristic
333C2×#67—22no—
334C2×#67—22no—
335C2×#67—22no—
336C2×#67—22no—
337C2×#67—22no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—22no—
341C22×Dic3C2×D411yescharacteristic
342C22×Dic3C2×D411yescharacteristic
343C22×Dic3C2×D411yescharacteristic
344#239—24no—
345#239—24no—
346D3×Q8—216no—
347D3×Q8—28no—
348D3×Q8—24no—
349D3×Q8—24no—
350D3×Q8C2×D4116yes—
351#237—24no—
352#237—24no—
353#237—48no—
354D3×D4—24no—
355D3×D4—24no—
356D3×D4—48no—
357#235—24no—
358#235—24no—
359#235—48no—
360C2×D12—22no—
361C2×D12—21no—
362C2×D12—21no—
363C2×D12C2412yes—
364C2×C4×D3—28no—
365C2×C4×D3—24no—
366C2×C4×D3—22no—
367C2×C4×D3—22no—
368C2×C4×D3—22no—
369C2×C4×D3—48no—
370C2×C4×D3C2×D412yes—
371C2×C4×D3C2×D414yes—
372C2×C4×D3#4114yes—
373C2×C4×D3C2412yes—
374C2×Dic6—21no—
375C2×Dic6—22no—
376C2×Dic6—28no—
377C2×Dic6—24no—
378C2×Dic6—22no—
379C2×Dic6C2×D414yes—
380C2×Dic6C2412yes—
381C2×Dic6C2412yes—
382C3×Q16—28no—
383C3×SD16—28no—
384C3×M16—24no—
385C2×C3×C8C2414yes—
386C3×C4⋊C4—22no—
387C3×C4⋊C4—22no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—21no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4C2412yes—
392C3×C22⋊C4—22no—
393C3×C22⋊C4—22no—
394C3×C42—22no—
395C3×C42—22no—
396C3×C42C2×D411yescharacteristic
397C3×C42C2×D411yescharacteristic
398C3×C42C2411yescharacteristic
399C3×C42C2411yescharacteristic
400#217—22no—
401#217—22no—
402#216—28no—
403#216—28no—
404#215—28no—
405#214—28no—
406(C2×D3)⋊C4—24no—
407(C2×D3)⋊C4—22no—
408(C2×D3)⋊C4—22no—
409(C2×D3)⋊C4—22no—
410(C2×D3)⋊C4—22no—
411(C2×D3)⋊C4C2×D412yes—
412(C2×D3)⋊C4C2×D412yes—
413(C2×D3)⋊C4C2×D412yes—
414(C2×D3)⋊C4C2×D412yes—
415C4⋊Dic3—21no—
416C4⋊Dic3—21no—
417C4⋊Dic3—21no—
418C4⋊Dic3—24no—
419C4⋊Dic3C2412yes—
420Dic3⋊C4—22no—
421Dic3⋊C4—22no—
422Dic3⋊C4—24no—
423Dic3⋊C4—22no—
424Dic3⋊C4—22no—
425Dic3⋊C4C2×D412yes—
426Dic3⋊C4C2×D412yes—
427Dic3⋊C4C2×D412yes—
428Dic3⋊C4C2×D412yes—
429C4×Dic3—22no—
430C4×Dic3—22no—
431C4×Dic3—24no—
432C4×Dic3—24no—
433C4×Dic3—24no—
434C4×Dic3C2×D412yes—
435C4×Dic3C2412yes—
436#208—24no—
437C2×C3⋊C8C2414yes—
438Dic12—28no—
439#204—28no—
440ΓL(1,𝔽25)—28no—
441D3×C8—28no—
442C2×#41—32no—
443C2×#41—32no—
444C2×#41—32no—
445C2×#41—62no—
446C2×#41—62no—
447C2×#41—68no—
448C2×#41—68no—
449C2×#41C22×D312yes—
450C22×Q8—38no—
451C22×Q8—34no—
452C22×Q8—32no—
453C22×Q8—31no—
454C22×Q8—61no—
455C22×Q8—62no—
456C22×Q8—64no—
457C22×Q8C22×D311yescharacteristic
458C22×D4—32no—
459C22×D4—62no—
460C23×C4—31no—
461C23×C4—62no—
462C23×C4—61no—
463#137—28no—
464#137—68no—
465#137—616no—
466#137—616no—
467#137—68no—
468#137—68no—
469C2×Q16—34no—
470C2×Q16—34no—
471C2×Q16—34no—
472C2×Q16—616no—
473C2×Q16C22×D314yes—
474C2×SD16—34no—
475C2×SD16—34no—
476C2×SD16—34no—
477C2×SD16—616no—
478C2×SD16C22×D314yes—
479C2×M16—32no—
480C2×M16—34no—
481C2×M16—68no—
482C2×M16C22×D312yes—
483C22×C8—34no—
484C4⋊Q8—32no—
485C4⋊Q8—31no—
486C4⋊Q8C22×D311yescharacteristic
487#127—32no—
488#127—31no—
489#127C22×D311yescharacteristic
490#124—32no—
491#124—32no—
492#124—32no—
493#124C22×D312yes—
494#123—62no—
495#123—62no—
496#123—62no—
497#123—62no—
498C22⋊Q8—62no—
499C22⋊Q8—62no—
500C22⋊Q8—62no—
501C22⋊Q8—62no—
502#121—21no—
503#121—21no—
504#121—62no—
505#121—62no—
506#121—62no—
507#121—62no—
508#121—62no—
509#121—62no—
510#121—61no—
511#121—61no—
512#120—62no—
513#120—62no—
514#120—62no—
515#120—62no—
516C4×Q8—21no—
517C4×Q8—21no—
518C4×Q8—34no—
519C4×Q8—34no—
520C4×Q8—32no—
521C4×Q8—32no—
522C4×Q8—64no—
523C4×Q8—64no—
524C4×Q8—62no—
525C4×Q8—62no—
526C4×Q8—64no—
527C4×Q8—64no—
528C4×Q8—61no—
529C4×Q8—61no—
530C4×Q8C22×D312yes—
531C4×Q8C22×D312yes—
532C4×D4—21no—
533C4×D4—21no—
534C4×D4—62no—
535C4×D4—62no—
536C4×D4—61no—
537C4×D4—61no—
538#117—32no—
539#117—32no—
540#117—32no—
541#117—32no—
542#117—34no—
543#117—64no—
544#117—64no—
545#117—64no—
546#117—64no—
547#117—62no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—31no—
550C2×C4⋊C4—31no—
551C2×C4⋊C4—31no—
552C2×C4⋊C4—61no—
553C2×C4⋊C4—61no—
554C2×C4⋊C4—61no—
555C2×C4⋊C4C22×D311yescharacteristic
556C2×C22⋊C4—31no—
557C2×C22⋊C4—31no—
558C2×C22⋊C4—61no—
559C2×C42—21no—
560C2×C42—31no—
561C2×C42—61no—
562C2×C42—61no—
563C2×C42—61no—
564C2×C42—61no—
565C2×C42C22×D311yescharacteristic
566C4⋊C8—34no—
567C4⋊C8—34no—
568C4⋊C8—32no—
569C4⋊C8—32no—
570C4⋊C8C22×D312yes—
571C4⋊C8C22×D312yes—
572#103—34no—
573#103—34no—
574#103—34no—
575#103C22×D314yes—
576#102—34no—
577#102—34no—
578#102—34no—
579#102C22×D314yes—
580C23×C3—22no—
581C23×C3C22×D411yescharacteristic
582C22×D3—22no—
583C22×D3—41no—
584C22×D3—41no—
585C22×D3—44no—
586C22×D3—82no—
587C22×D3—82no—
588C22×D3#12114yes—
589C22×D3C22×D412yes—
590C3×Q8—24no—
591C3×Q8—22no—
592C3×Q8—22no—
593C3×Q8—22no—
594C3×Q8C22×D414yes—
595C3×D4—22no—
596C3×D4—22no—
597C3×D4—44no—
598C3×D4—81no—
599C3×D4—81no—
600C2×C3×C4—24no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—42no—
607C2×C3×C4—44no—
608C2×C3×C4C22×D411yescharacteristic
609C2×C3×C4C22×D411yescharacteristic
610C2×C3×C4C22×D411yescharacteristic
611C2×C3×C4C22×D411yescharacteristic
612C2×C3×C4C22×D411yescharacteristic
613C2×C3×C4C22×D412yes—
614C2×C3×C4C2×#4112yes—
615C2×C3×C4C2511yescharacteristic
616#67—44no—
617#67—44no—
618#67—44no—
619#67—82no—
620#67—82no—
621C2×Dic3—24no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—42no—
628C2×Dic3—44no—
629C2×Dic3#12114yes—
630C2×Dic3C22×D412yes—
631C2×Dic3C22×D412yes—
632C2×Dic3C22×D412yes—
633D12—22no—
634D12—22no—
635D12—44no—
636D12—81no—
637D12—81no—
638C4×D3—216no—
639C4×D3—44no—
640C4×D3—44no—
641C4×D3—44no—
642C4×D3#12118yes—
643C4×D3C22×D414yes—
644C4×D3C2×#4114yes—
645Dic6—24no—
646Dic6—22no—
647Dic6—216no—
648Dic6—22no—
649Dic6—22no—
650Dic6—44no—
651Dic6C22×D414yes—
652C3×C8—24no—
653C3⋊C8—24no—
654C24—31no—
655C24—62no—
656#41—24no—
657#41—24no—
658#41—64no—
659#41—64no—
660#41—64no—
661#41—64no—
662#41—64no—
663#41—64no—
664#41—128no—
665#41—128no—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—316no—
669C2×Q8—34no—
670C2×Q8—32no—
671C2×Q8—32no—
672C2×Q8—64no—
673C2×Q8—68no—
674C2×Q8—62no—
675C2×Q8—68no—
676C2×Q8—616no—
677C2×Q8—64no—
678C2×Q8—64no—
679C2×Q8—61no—
680C2×Q8—62no—
681C2×Q8D3×D414yes—
682C2×Q8C23×D312yes—
683C2×Q8C23×D312yes—
684C2×D4—22no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—32no—
688C2×D4—62no—
689C2×D4—64no—
690C2×D4—64no—
691C2×D4—62no—
692C2×D4—62no—
693C2×D4—62no—
694C2×D4—62no—
695C2×D4—62no—
696C2×D4—61no—
697C2×D4—61no—
698C2×D4—128no—
699C2×D4C23×D312yes—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—22no—
703C22×C4—31no—
704C22×C4—32no—
705C22×C4—34no—
706C22×C4—34no—
707C22×C4—32no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—62no—
711C22×C4—64no—
712C22×C4—68no—
713C22×C4—62no—
714C22×C4—62no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—62no—
718C22×C4—128no—
719C22×C4D3×D411yescharacteristic
720C22×C4D3×D411yescharacteristic
721C22×C4C23×D311yescharacteristic
722Q16—28no—
723Q16—68no—
724Q16—68no—
725Q16—68no—
726SD16—28no—
727SD16—68no—
728SD16—68no—
729SD16—68no—
730M16—24no—
731M16—68no—
732M16—64no—
733C2×C8—34no—
734C2×C8—68no—
735C2×C8C23×D314yes—
736C4⋊C4—22no—
737C4⋊C4—22no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—32no—
742C4⋊C4—32no—
743C4⋊C4—32no—
744C4⋊C4—32no—
745C4⋊C4—32no—
746C4⋊C4—64no—
747C4⋊C4—64no—
748C4⋊C4—62no—
749C4⋊C4—62no—
750C4⋊C4—61no—
751C4⋊C4—62no—
752C4⋊C4—62no—
753C4⋊C4—61no—
754C4⋊C4—61no—
755C4⋊C4C23×D312yes—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—32no—
759C22⋊C4—32no—
760C22⋊C4—32no—
761C22⋊C4—32no—
762C22⋊C4—62no—
763C22⋊C4—62no—
764C22⋊C4—64no—
765C22⋊C4—62no—
766C22⋊C4—62no—
767C22⋊C4—62no—
768C22⋊C4—62no—
769C42—22no—
770C42—22no—
771C42—32no—
772C42—32no—
773C42—64no—
774C42—64no—
775C42—64no—
776C42—62no—
777C42—62no—
778C42D3×D411yescharacteristic
779C42D3×D411yescharacteristic
780C42C23×D311yescharacteristic
781C42C23×D311yescharacteristic
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—42no—
787C22×C3C2×#12112yes—
788C22×C3C23×D411yescharacteristic
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—44no—
792C2×D3—42no—
793C2×D3—42no—
794C2×D3—42no—
795C2×D3—88no—
796C2×D3C2×#12114yes—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—21no—
800C3×C4—21no—
801C3×C4—24no—
802C3×C4—42no—
803C3×C4—42no—
804C3×C4C2×#12112yes—
805C3×C4C23×D411yescharacteristic
806C3×C4C22×#4111yescharacteristic
807Dic3—22no—
808Dic3—22no—
809Dic3—24no—
810Dic3—42no—
811Dic3—42no—
812Dic3C2×#12114yes—
813C23—22no—
814C23—32no—
815C23—34no—
816C23—62no—
817C23—121no—
818C23—121no—
819C23—124no—
820C23—242no—
821C23—242no—
822C23C2×D3×D411yescharacteristic
823Q8—22no—
824Q8—24no—
825Q8—22no—
826Q8—22no—
827Q8—34no—
828Q8—616no—
829Q8—62no—
830Q8—64no—
831Q8—62no—
832Q8—62no—
833Q8—124no—
834Q8C2×D3×D414yes—
835D4—22no—
836D4—22no—
837D4—44no—
838D4—62no—
839D4—62no—
840D4—81no—
841D4—81no—
842D4—124no—
843D4—124no—
844D4—124no—
845D4—124no—
846D4—241no—
847D4—241no—
848D4—242no—
849D4—242no—
850C2×C4—22no—
851C2×C4—24no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—32no—
855C2×C4—34no—
856C2×C4—34no—
857C2×C4—34no—
858C2×C4—38no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—42no—
864C2×C4—44no—
865C2×C4—616no—
866C2×C4—62no—
867C2×C4—64no—
868C2×C4—62no—
869C2×C4—62no—
870C2×C4—124no—
871C2×C4—124no—
872C2×C4—124no—
873C2×C4—121no—
874C2×C4—121no—
875C2×C4—122no—
876C2×C4—124no—
877C2×C4C2×D3×D411yescharacteristic
878C2×C4C2×D3×D411yescharacteristic
879C2×C4C2×D3×D411yescharacteristic
880C2×C4C2×D3×D411yescharacteristic
881C2×C4C2×D3×D412yes—
882C2×C4C2×D3×D411yescharacteristic
883C2×C4D3×#4112yes—
884C2×C4C24×D311yescharacteristic
885C8—24no—
886C8—64no—
887C2×C3—22no—
888C2×C3—82no—
889C2×C3C22×#12111yescharacteristic
890C2×C3#358611yescharacteristic
891C2×C3#358611yescharacteristic
892D3—24no—
893D3—82no—
894C22—21no—
895C22—21no—
896C22—34no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—62no—
901C22—62no—
902C22—124no—
903C22—122no—
904C22—122no—
905C22—122no—
906C22—248no—
907C22D3×#12112yes—
908C22C22×D3×D411yescharacteristic
909C4—21no—
910C4—21no—
911C4—21no—
912C4—21no—
913C4—24no—
914C4—34no—
915C4—42no—
916C4—42no—
917C4—62no—
918C4—62no—
919C4—64no—
920C4—122no—
921C4—122no—
922C4D3×#12112yes—
923C4C22×D3×D411yescharacteristic
924C4C2×D3×#4111yescharacteristic
925C3#6042411yescharacteristic, complemented, Sylow
926C2—22no—
927C2—64no—
928C2—82no—
929C2—242no—
930C2C2×D3×#12111yescharacteristic
931C2#8719711yescharacteristic
932C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3037C2
socleC22×C3C23×D4
prime radical#86235C2
hypercenter#3037D3
hypocenterC3#60424
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
1. C2×D3×#137C2semidirect
3. C2×#5572C2semidirect
4. C3×#3037C2semidirect
5. #83966C2semidirect
6. #83314C2semidirect
7. #82441C2semidirect
8. #80601C2semidirect
9. #80600C2semidirect
10. #80478C2semidirect
11. #80385C2semidirect
12. #79067C2semidirect
13. #79048C2semidirect
14. #78913C2semidirect
15. #78881C2semidirect
19. C2×C3×#137C22semidirect
21. C2×C3×C4×Q8C22semidirect
23. C2×#951C22semidirect
24. C2×Q8×Dic3C22semidirect
25. C2×#942C22semidirect
28. C2×D3×Q16C22semidirect
30. C2×D3×SD16C22semidirect
31. C2×#909C22semidirect
43. #5572C22semidirect
44. #5572C22semidirect
50. C2×#887C22semidirect
55. C2×C4×Dic6C22semidirect
56. C3×#464C22semidirect
57. C3×#462C22semidirect
58. C3×#460C22semidirect
59. C3×#423C22semidirect
60. C3×#417C22semidirect
61. #5232C22semidirect
62. #5185C22semidirect
63. #5182C22semidirect
64. #5166C22semidirect
65. #5163C22semidirect
66. #5133C22semidirect
67. #5118C22semidirect
68. #5090C22semidirect
69. #5075C22semidirect
70. #5054C22semidirect
71. #5031C22semidirect
72. #5028C22semidirect
73. #5027C22semidirect
74. #4966C22semidirect
75. #4924C22semidirect
76. #4849C22semidirect
77. #4848C22semidirect
78. #4845C22semidirect
79. #4839C22semidirect
80. #4839C22semidirect
82. #4802C22semidirect
83. #4798C22semidirect
84. #4795C22semidirect
86. #4770C22semidirect
87. #4767C22semidirect
88. #4762C22semidirect
101. #3037D3semidirect
111. C2×D3×Q8D4semidirect
250. C2×#137C2×D3semidirect
276. C2×C4×Q8C2×D3semidirect
288. #464C2×D3semidirect
294. #462C2×D3semidirect
300. #460C2×D3semidirect
305. #423C2×D3semidirect
311. #417C2×D3semidirect
925. C3#60424semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#1372
#862352
C2×#55722
C3×#30372
#839662
#833142
#824412
#806012
#806002
#804782
#803852
#790672
#790482
#789132
#788812
#604243