Finite Group Databasebeta

← #11662163

Subgroups — #11662163

Order 768.

2750 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5777C212yesmaximal, complemented
2#86235C211yesmaximal, characteristic, complemented
3C2×#5574C211yesmaximal, characteristic, complemented
4C3×#3037C211yesmaximal, characteristic, complemented
5#83966C212yesmaximal, complemented
6#83297C211yesmaximal, characteristic, complemented
7#82441C211yesmaximal, characteristic, complemented
8#80603C214yesmaximal, complemented
9#80602C214yesmaximal, complemented
10#80479C214yesmaximal, complemented
11#80386C214yesmaximal, complemented
12#79055C211yesmaximal, characteristic, complemented
13#79048C211yesmaximal, characteristic, complemented
14#78910C212yesmaximal, complemented
15D3×#417C212yesmaximal, complemented
16#60425—31nomaximal, Sylow
17C2×D3×#41C2212yes—
18C22×#239C2211yescharacteristic
19C2×C3×#137C2212yescomplemented
20C3×#532C2211yescharacteristic
21C2×C3×C4×Q8C2211yescharacteristic, complemented
22#5832C2212yes—
23C2×#949C2212yescomplemented
24C2×Q8×Dic3C2211yescharacteristic, complemented
25C2×#942C2212yescomplemented
26#5777—216no—
27C2×#919C2214yes—
28C2×#918C2214yescomplemented
29C2×#916C2214yes—
30C2×#914C2214yescomplemented
31C2×#908C2212yescomplemented
32C2×D3×M16C2212yes—
33#5724C2212yescomplemented
34#5715C2212yescomplemented
35#5675C2212yescomplemented
36#5674C2212yescomplemented
37#5605—21no—
38#5605—21no—
39#5597—21no—
40#5597—21no—
41#5574—22no—
42#5574—22no—
43#5574C2214yescomplemented
44#5574C2214yescomplemented
45#5547—22no—
46#5547—22no—
47C2×#893—21no—
48C2×#893C2211yescharacteristic, complemented
49C2×D3×C4⋊C4—21no—
50C2×D3×C4⋊C4C2211yescharacteristic
51#5477C2211yescharacteristic
52C2×C4×D12—21no—
53C2×C4×D12C2211yescharacteristic, complemented
54C2×#872—21no—
55C2×#872C2211yescharacteristic
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#5083C2212yescomplemented
69#5072C2212yescomplemented
70#5057C2214yescomplemented
71#5031C2212yescomplemented
72#5028C2214yescomplemented
73#5027C2212yescomplemented
74#4966C2212yescomplemented
75#4924C2211yescharacteristic, complemented
76#4844C2214yescomplemented
77#4843C2212yescomplemented
78#4841C2212yescomplemented
79#4839C2214yescomplemented
80#4839C2214yescomplemented
81#4819C2214yescomplemented
82#4818C2214yescomplemented
83#4803C2214yescomplemented
84D3×#103C2214yescomplemented
85#4787C2214yescomplemented
86#4786C2214yescomplemented
87#4771C2214yescomplemented
88D3×#102C2214yescomplemented
89C2×#575—32no—
90#3449—31no—
91C2×#520—31no—
92#3046—34no—
93#3046—34no—
94#3045—34no—
95#3045—34no—
96#3037—32no—
97#3037—31no—
98#3037D311yescharacteristic, complemented
99#3036—31no—
100#3036—32no—
101#3036—31no—
102#2905—31no—
103C2×#417—32no—
104C2×C3×#41C2312yes—
105C22×C3×Q8C2311yescharacteristic
106D3×#41—28no—
107D3×#41—28no—
108C2×#239—22no—
109C2×#239—24no—
110C2×#239D418yescomplemented
111C2×#239C2312yes—
112C2×#239C2314yes—
113C2×D3×Q8C2312yes—
114C2×#237—22no—
115C2×#237C2312yes—
116C2×D3×D4—22no—
117C2×D3×D4C2312yes—
118C2×#235—22no—
119C2×#235C2312yes—
120C22×D12—21no—
121C22×D12C2311yescharacteristic
122C22×C4×D3—21no—
123C22×C4×D3—21no—
124C22×C4×D3—21no—
125C22×C4×D3—21no—
126C22×C4×D3—22no—
127C22×C4×D3C2311yescharacteristic
128C3×#137—28no—
129C2×C3×Q16C2314yes—
130C2×C3×SD16C2314yes—
131C2×C3×M16C2312yes—
132C3×C4⋊Q8C2311yescharacteristic
133C3×#127C2311yescharacteristic
134C3×#124C2312yes—
135C3×#121—21no—
136C3×#121—21no—
137C3×C4×Q8—21no—
138C3×C4×Q8—21no—
139C3×C4×Q8C2312yes—
140C3×C4×Q8C2312yes—
141C3×C4×D4—21no—
142C3×C4×D4—21no—
143C2×C3×C4⋊C4—21no—
144C2×C3×C4⋊C4C2311yescharacteristic
145C2×C3×C42—21no—
146C2×C3×C42C2311yescharacteristic
147#949—28no—
148#947C2312yes—
149Q8×Dic3—22no—
150Q8×Dic3C2314yes—
151#944C2312yes—
152C2×#216C2314yes—
153#942—28no—
154C2×#215C2314yes—
155C2×#215C2314yes—
156#940C2312yes—
157#939—22no—
158#939—22no—
159#939—22no—
160#939—22no—
161#937—22no—
162#937—22no—
163#936C2312yes—
164C2×#213C2314yes—
165#930—21no—
166#930—21no—
167C4×#67—22no—
168C4×#67—22no—
169C2×(C2×D3)⋊C4—21no—
170C2×(C2×D3)⋊C4—21no—
171C2×(C2×D3)⋊C4D411yescharacteristic
172C2×(C2×D3)⋊C4D411yescharacteristic
173C2×C4⋊Dic3—21no—
174C2×C4⋊Dic3C2311yescharacteristic
175C2×Dic3⋊C4—21no—
176C2×Dic3⋊C4D411yescharacteristic
177C2×Dic3⋊C4D411yescharacteristic
178C2×C4×Dic3—21no—
179C2×C4×Dic3C2311yescharacteristic
180C2×#208C2312yes—
181#919—216no—
182#918—216no—
183#916—216no—
184#914—216no—
185#908—28no—
186D3×M16—28no—
187C2×D24C2314yes—
188C2×#204C2314yes—
189C2×ΓL(1,𝔽25)C2314yes—
190C2×D3×C8C2314yes—
191#896—22no—
192#896—22no—
193#894—22no—
194#894—22no—
195#893—24no—
196#893—24no—
197#893—22no—
198#893C2314yes—
199D3×C4⋊C4—22no—
200D3×C4⋊C4—24no—
201D3×C4⋊C4—24no—
202D3×C4⋊C4C2314yes—
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—
215C4×D12—21no—
216C4×D12—21no—
217C4×D12—24no—
218C4×D12—24no—
219C4×D12C2312yes—
220C4×D12C2312yes—
221#872—24no—
222#872—24no—
223#872D412yes—
224#872D412yes—
225#872C2312yes—
226#872C2312yes—
227#869C2311yescharacteristic
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—
243C22×#41—31no—
244#575—616no—
245C2×#137—32no—
246C2×#137—34no—
247C2×#137C2×D312yescomplemented
248C2×AGL(1,ℤ/8)—32no—
249C2×AGL(1,ℤ/8)—34no—
250C2×AGL(1,ℤ/8)—32no—
251C2×#135—34no—
252C2×#135—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#520—34no—
268#520—34no—
269#520—62no—
270#520—62no—
271C2×C4×Q8—31no—
272C2×C4×Q8C2×D311yescharacteristic, complemented
273C2×C4×D4—31no—
274C2×C4×D4—31no—
275C2×C4×D4—61no—
276C2×C4×D4—61no—
277C2×#117—31no—
278C2×#117—61no—
279C22×C4⋊C4—31no—
280C22×C4⋊C4—61no—
281#464—34no—
282#464—34no—
283#464—34no—
284#464C2×D314yescomplemented
285#463—34no—
286#463—34no—
287#463—34no—
288#463—34no—
289#462—34no—
290#462—32no—
291#462C2×D312yescomplemented
292#461—32no—
293#461—32no—
294#461—34no—
295#460—34no—
296#460—32no—
297#460C2×D312yescomplemented
298#459—32no—
299#459—32no—
300#459—34no—
301#424—34no—
302#424—34no—
303#423—32no—
304#423—31no—
305#423C2×D311yescharacteristic, complemented
306#417—32no—
307#417—32no—
308#417—32no—
309#417—34no—
310#417—34no—
311#417C2×D312yescomplemented
312C2×#103—34no—
313C2×#102—34no—
314C23×D3—21no—
315C23×D3—22no—
316C23×D3C2×D411yescharacteristic
317C3×#41—24no—
318C3×#41—24no—
319C2×C3×Q8—21no—
320C2×C3×Q8—22no—
321C2×C3×Q8C2×D414yes—
322C2×C3×Q8C2412yes—
323C2×C3×Q8C2412yes—
324C2×C3×D4—22no—
325C2×C3×D4—21no—
326C2×C3×D4—21no—
327C2×C3×D4C2412yes—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—22no—
331C22×C3×C4C2×D411yescharacteristic
332C22×C3×C4C2×D411yescharacteristic
333C22×C3×C4C2411yescharacteristic
334C2×#67—22no—
335C2×#67—22no—
336C2×#67—22no—
337C2×#67—22no—
338C2×#67—22no—
339C22×Dic3—21no—
340C22×Dic3—22no—
341C22×Dic3C2×D411yescharacteristic
342C22×Dic3C2×D411yescharacteristic
343C22×Dic3C2×D411yescharacteristic
344#239—216no—
345#239—28no—
346#239—24no—
347#239—24no—
348#239C2×D4116yes—
349D3×Q8—24no—
350D3×Q8—24no—
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—28no—
361C2×D12—24no—
362C2×D12—21no—
363C2×D12—22no—
364C2×D12—22no—
365C2×D12—21no—
366C2×D12—21no—
367C2×D12C2×D414yes—
368C2×D12C2412yes—
369C2×D12C2412yes—
370C2×C4×D3—28no—
371C2×C4×D3—24no—
372C2×C4×D3—22no—
373C2×C4×D3—22no—
374C2×C4×D3—22no—
375C2×C4×D3—24no—
376C2×C4×D3—22no—
377C2×C4×D3—22no—
378C2×C4×D3—24no—
379C2×C4×D3—48no—
380C2×C4×D3—82no—
381C2×C4×D3—82no—
382C2×C4×D3—82no—
383C2×C4×D3C2×D412yes—
384C2×C4×D3C2×D414yes—
385C2×C4×D3#4114yes—
386C2×C4×D3C2412yes—
387C2×Dic6—22no—
388C2×Dic6C2412yes—
389C3×Q16—28no—
390C3×SD16—28no—
391C3×M16—24no—
392C2×C3×C8C2414yes—
393C3×C4⋊C4—22no—
394C3×C4⋊C4—22no—
395C3×C4⋊C4—21no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4—21no—
398C3×C4⋊C4C2412yes—
399C3×C22⋊C4—22no—
400C3×C22⋊C4—22no—
401C3×C42—22no—
402C3×C42—22no—
403C3×C42C2×D411yescharacteristic
404C3×C42C2×D411yescharacteristic
405C3×C42C2411yescharacteristic
406C3×C42C2411yescharacteristic
407#217—22no—
408#217—22no—
409#216—28no—
410#215—28no—
411#215—28no—
412#213—28no—
413(C2×D3)⋊C4—22no—
414(C2×D3)⋊C4—22no—
415(C2×D3)⋊C4—22no—
416(C2×D3)⋊C4—22no—
417(C2×D3)⋊C4—24no—
418(C2×D3)⋊C4—22no—
419(C2×D3)⋊C4—22no—
420(C2×D3)⋊C4C2×D412yes—
421(C2×D3)⋊C4C2×D412yes—
422(C2×D3)⋊C4C2×D412yes—
423(C2×D3)⋊C4C2×D412yes—
424C4⋊Dic3—21no—
425C4⋊Dic3—21no—
426C4⋊Dic3—21no—
427C4⋊Dic3—24no—
428C4⋊Dic3C2412yes—
429Dic3⋊C4—24no—
430Dic3⋊C4—22no—
431Dic3⋊C4—22no—
432Dic3⋊C4C2×D412yes—
433Dic3⋊C4C2×D412yes—
434Dic3⋊C4C2×D412yes—
435Dic3⋊C4C2×D412yes—
436C4×Dic3—24no—
437C4×Dic3C2×D412yes—
438C4×Dic3C2412yes—
439#208—24no—
440C2×C3⋊C8C2414yes—
441D24—28no—
442#204—28no—
443ΓL(1,𝔽25)—28no—
444D3×C8—28no—
445C2×#41—38no—
446C2×#41—34no—
447C2×#41—32no—
448C2×#41—32no—
449C2×#41—32no—
450C2×#41—62no—
451C2×#41—62no—
452C2×#41—62no—
453C2×#41—64no—
454C2×#41—68no—
455C2×#41—68no—
456C2×#41C22×D312yes—
457C22×Q8—32no—
458C22×Q8C22×D311yescharacteristic
459C22×D4—32no—
460C22×D4—31no—
461C22×D4—61no—
462C22×D4—62no—
463C23×C4—31no—
464C23×C4—61no—
465C23×C4—62no—
466C23×C4—61no—
467C23×C4—61no—
468C23×C4—61no—
469#137—28no—
470#137—616no—
471#137—68no—
472AGL(1,ℤ/8)—68no—
473AGL(1,ℤ/8)—616no—
474AGL(1,ℤ/8)—68no—
475#135—616no—
476#135—616no—
477C2×Q16—34no—
478C2×Q16C22×D314yes—
479C2×SD16—34no—
480C2×SD16—34no—
481C2×SD16—34no—
482C2×SD16C22×D314yes—
483C2×D8—34no—
484C2×D8—34no—
485C2×M16—32no—
486C2×M16—34no—
487C2×M16—68no—
488C2×M16C22×D312yes—
489C22×C8—34no—
490C4⋊Q8—32no—
491C4⋊Q8—31no—
492C4⋊Q8C22×D311yescharacteristic
493#127—32no—
494#127—31no—
495#127C22×D311yescharacteristic
496#124—32no—
497#124—32no—
498#124—32no—
499#124C22×D312yes—
500#123—62no—
501#123—62no—
502#123—62no—
503#123—62no—
504C22⋊Q8—62no—
505C22⋊Q8—62no—
506C22⋊Q8—62no—
507C22⋊Q8—62no—
508#121—21no—
509#121—21no—
510#121—62no—
511#121—62no—
512#121—62no—
513#121—62no—
514#121—62no—
515#121—62no—
516#121—61no—
517#121—61no—
518#120—62no—
519#120—62no—
520#120—62no—
521#120—62no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8—34no—
525C4×Q8—62no—
526C4×Q8C22×D312yes—
527C4×Q8C22×D312yes—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—34no—
531C4×D4—32no—
532C4×D4—32no—
533C4×D4—64no—
534C4×D4—64no—
535C4×D4—62no—
536C4×D4—62no—
537C4×D4—62no—
538C4×D4—64no—
539C4×D4—64no—
540C4×D4—61no—
541C4×D4—61no—
542C4×D4—61no—
543C4×D4—61no—
544#117—32no—
545#117—32no—
546#117—32no—
547#117—32no—
548#117—64no—
549#117—64no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—31no—
552C2×C4⋊C4—31no—
553C2×C4⋊C4—31no—
554C2×C4⋊C4—34no—
555C2×C4⋊C4—64no—
556C2×C4⋊C4—64no—
557C2×C4⋊C4—62no—
558C2×C4⋊C4—61no—
559C2×C4⋊C4—61no—
560C2×C4⋊C4C22×D311yescharacteristic
561C2×C22⋊C4—31no—
562C2×C22⋊C4—31no—
563C2×C22⋊C4—61no—
564C2×C22⋊C4—61no—
565C2×C42—21no—
566C2×C42—31no—
567C2×C42—61no—
568C2×C42C22×D311yescharacteristic
569C4⋊C8—34no—
570C4⋊C8—34no—
571C4⋊C8—32no—
572C4⋊C8—32no—
573C4⋊C8C22×D312yes—
574C4⋊C8C22×D312yes—
575#103—34no—
576#103—34no—
577#103—34no—
578#103C22×D314yes—
579#102—34no—
580#102—34no—
581#102—34no—
582#102C22×D314yes—
583C23×C3—22no—
584C23×C3C22×D411yescharacteristic
585C22×D3—24no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—41no—
589C22×D3—41no—
590C22×D3—42no—
591C22×D3—42no—
592C22×D3—44no—
593C22×D3—82no—
594C22×D3—82no—
595C22×D3#12114yes—
596C22×D3C22×D412yes—
597C3×Q8—24no—
598C3×Q8—22no—
599C3×Q8—22no—
600C3×Q8—22no—
601C3×Q8C22×D414yes—
602C3×D4—22no—
603C3×D4—22no—
604C3×D4—44no—
605C3×D4—81no—
606C3×D4—81no—
607C2×C3×C4—24no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—42no—
614C2×C3×C4—44no—
615C2×C3×C4C22×D411yescharacteristic
616C2×C3×C4C22×D411yescharacteristic
617C2×C3×C4C22×D411yescharacteristic
618C2×C3×C4C22×D411yescharacteristic
619C2×C3×C4C22×D411yescharacteristic
620C2×C3×C4C22×D412yes—
621C2×C3×C4C2×#4112yes—
622C2×C3×C4C2511yescharacteristic
623#67—44no—
624#67—44no—
625#67—44no—
626#67—82no—
627#67—82no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—42no—
633C2×Dic3—44no—
634C2×Dic3#12114yes—
635C2×Dic3C22×D412yes—
636C2×Dic3C22×D412yes—
637C2×Dic3C22×D412yes—
638D12—216no—
639D12—24no—
640D12—22no—
641D12—22no—
642D12—22no—
643D12—44no—
644D12—81no—
645D12—81no—
646D12C22×D414yes—
647C4×D3—216no—
648C4×D3—44no—
649C4×D3—44no—
650C4×D3—44no—
651C4×D3—84no—
652C4×D3—82no—
653C4×D3—82no—
654C4×D3—84no—
655C4×D3#12118yes—
656C4×D3C22×D414yes—
657C4×D3C2×#4114yes—
658Dic6—22no—
659Dic6—22no—
660Dic6—44no—
661C3×C8—24no—
662C3⋊C8—24no—
663C24—31no—
664C24—62no—
665C24—61no—
666#41—24no—
667#41—24no—
668#41—316no—
669#41—68no—
670#41—616no—
671#41—64no—
672#41—64no—
673#41—64no—
674#41—64no—
675#41—64no—
676#41—64no—
677#41—128no—
678#41—128no—
679C2×Q8—21no—
680C2×Q8—22no—
681C2×Q8—32no—
682C2×Q8—62no—
683C2×Q8—64no—
684C2×Q8—64no—
685C2×Q8D3×D414yes—
686C2×Q8C23×D312yes—
687C2×Q8C23×D312yes—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—34no—
692C2×D4—32no—
693C2×D4—32no—
694C2×D4—64no—
695C2×D4—68no—
696C2×D4—62no—
697C2×D4—64no—
698C2×D4—64no—
699C2×D4—62no—
700C2×D4—62no—
701C2×D4—62no—
702C2×D4—62no—
703C2×D4—62no—
704C2×D4—61no—
705C2×D4—61no—
706C2×D4—61no—
707C2×D4—62no—
708C2×D4—128no—
709C2×D4C23×D312yes—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—22no—
713C22×C4—31no—
714C22×C4—32no—
715C22×C4—34no—
716C22×C4—34no—
717C22×C4—32no—
718C22×C4—31no—
719C22×C4—31no—
720C22×C4—64no—
721C22×C4—68no—
722C22×C4—62no—
723C22×C4—64no—
724C22×C4—62no—
725C22×C4—64no—
726C22×C4—62no—
727C22×C4—61no—
728C22×C4—62no—
729C22×C4—62no—
730C22×C4—62no—
731C22×C4—128no—
732C22×C4—242no—
733C22×C4—242no—
734C22×C4—242no—
735C22×C4D3×D411yescharacteristic
736C22×C4D3×D411yescharacteristic
737C22×C4C23×D311yescharacteristic
738Q16—28no—
739Q16—68no—
740SD16—28no—
741SD16—68no—
742SD16—68no—
743SD16—68no—
744D8—68no—
745D8—68no—
746M16—24no—
747M16—68no—
748M16—64no—
749C2×C8—34no—
750C2×C8—68no—
751C2×C8C23×D314yes—
752C4⋊C4—22no—
753C4⋊C4—22no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—32no—
758C4⋊C4—32no—
759C4⋊C4—32no—
760C4⋊C4—32no—
761C4⋊C4—32no—
762C4⋊C4—64no—
763C4⋊C4—64no—
764C4⋊C4—62no—
765C4⋊C4—62no—
766C4⋊C4—61no—
767C4⋊C4—61no—
768C4⋊C4—61no—
769C4⋊C4C23×D312yes—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—32no—
773C22⋊C4—32no—
774C22⋊C4—32no—
775C22⋊C4—32no—
776C22⋊C4—64no—
777C22⋊C4—62no—
778C22⋊C4—62no—
779C22⋊C4—62no—
780C22⋊C4—62no—
781C22⋊C4—62no—
782C22⋊C4—62no—
783C22⋊C4—62no—
784C22⋊C4—62no—
785C42—22no—
786C42—22no—
787C42—32no—
788C42—32no—
789C42—64no—
790C42D3×D411yescharacteristic
791C42D3×D411yescharacteristic
792C42C23×D311yescharacteristic
793C42C23×D311yescharacteristic
794C22×C3—21no—
795C22×C3—21no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3C2×#12112yes—
800C22×C3C23×D411yescharacteristic
801C2×D3—22no—
802C2×D3—22no—
803C2×D3—24no—
804C2×D3—44no—
805C2×D3—48no—
806C2×D3—42no—
807C2×D3—42no—
808C2×D3—42no—
809C2×D3—42no—
810C2×D3—42no—
811C2×D3—88no—
812C2×D3C2×#12114yes—
813C3×C4—21no—
814C3×C4—21no—
815C3×C4—21no—
816C3×C4—21no—
817C3×C4—24no—
818C3×C4—42no—
819C3×C4—42no—
820C3×C4C2×#12112yes—
821C3×C4C23×D411yescharacteristic
822C3×C4C22×#4111yescharacteristic
823Dic3—22no—
824Dic3—22no—
825Dic3—42no—
826Dic3—42no—
827Dic3C2×#12114yes—
828C23—22no—
829C23—32no—
830C23—34no—
831C23—62no—
832C23—64no—
833C23—62no—
834C23—121no—
835C23—121no—
836C23—122no—
837C23—122no—
838C23—124no—
839C23—242no—
840C23—242no—
841C23C2×D3×D411yescharacteristic
842Q8—22no—
843Q8—24no—
844Q8—22no—
845Q8—22no—
846Q8—62no—
847Q8—62no—
848Q8—124no—
849Q8C2×D3×D414yes—
850D4—22no—
851D4—22no—
852D4—34no—
853D4—44no—
854D4—616no—
855D4—62no—
856D4—62no—
857D4—62no—
858D4—64no—
859D4—81no—
860D4—81no—
861D4—124no—
862D4—124no—
863D4—124no—
864D4—124no—
865D4—241no—
866D4—241no—
867D4—242no—
868D4—242no—
869C2×C4—22no—
870C2×C4—24no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—32no—
874C2×C4—34no—
875C2×C4—34no—
876C2×C4—34no—
877C2×C4—38no—
878C2×C4—32no—
879C2×C4—32no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—42no—
883C2×C4—44no—
884C2×C4—616no—
885C2×C4—62no—
886C2×C4—62no—
887C2×C4—124no—
888C2×C4—124no—
889C2×C4—124no—
890C2×C4—121no—
891C2×C4—121no—
892C2×C4—122no—
893C2×C4—124no—
894C2×C4—242no—
895C2×C4—242no—
896C2×C4—244no—
897C2×C4—244no—
898C2×C4C2×D3×D411yescharacteristic
899C2×C4C2×D3×D411yescharacteristic
900C2×C4C2×D3×D411yescharacteristic
901C2×C4C2×D3×D411yescharacteristic
902C2×C4C2×D3×D412yes—
903C2×C4C2×D3×D411yescharacteristic
904C2×C4D3×#4112yes—
905C2×C4C24×D311yescharacteristic
906C8—24no—
907C8—64no—
908C2×C3—22no—
909C2×C3—82no—
910C2×C3C22×#12111yescharacteristic
911C2×C3#358511yescharacteristic
912C2×C3#358611yescharacteristic
913D3—24no—
914D3—44no—
915D3—82no—
916C22—21no—
917C22—21no—
918C22—34no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—62no—
923C22—62no—
924C22—64no—
925C22—124no—
926C22—128no—
927C22—122no—
928C22—122no—
929C22—122no—
930C22—122no—
931C22—122no—
932C22—248no—
933C22D3×#12112yes—
934C22C22×D3×D411yescharacteristic
935C4—21no—
936C4—21no—
937C4—21no—
938C4—21no—
939C4—24no—
940C4—34no—
941C4—42no—
942C4—42no—
943C4—62no—
944C4—62no—
945C4—122no—
946C4—122no—
947C4D3×#12112yes—
948C4C22×D3×D411yescharacteristic
949C4C2×D3×#4111yescharacteristic
950C3#6042511yescharacteristic, complemented, Sylow
951C2—22no—
952C2—64no—
953C2—82no—
954C2—124no—
955C2—242no—
956C2C2×D3×#12111yescharacteristic
957C2#8719711yescharacteristic
958C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3037C2
socleC22×C3C23×D4
hypercenter#3037D3
hypocenterC3#60425
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×#5777C2semidirect
2. #86235C2semidirect
3. C2×#5574C2semidirect
4. C3×#3037C2semidirect
5. #83966C2semidirect
6. #83297C2semidirect
7. #82441C2semidirect
8. #80603C2semidirect
9. #80602C2semidirect
10. #80479C2semidirect
11. #80386C2semidirect
12. #79055C2semidirect
13. #79048C2semidirect
14. #78910C2semidirect
15. D3×#417C2semidirect
19. C2×C3×#137C22semidirect
21. C2×C3×C4×Q8C22semidirect
23. C2×#949C22semidirect
24. C2×Q8×Dic3C22semidirect
25. C2×#942C22semidirect
28. C2×#918C22semidirect
30. C2×#914C22semidirect
31. C2×#908C22semidirect
33. #5724C22semidirect
34. #5715C22semidirect
35. #5675C22semidirect
36. #5674C22semidirect
43. #5574C22semidirect
44. #5574C22semidirect
48. C2×#893C22semidirect
53. C2×C4×D12C22semidirect
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. #5083C22semidirect
69. #5072C22semidirect
70. #5057C22semidirect
71. #5031C22semidirect
72. #5028C22semidirect
73. #5027C22semidirect
74. #4966C22semidirect
75. #4924C22semidirect
76. #4844C22semidirect
77. #4843C22semidirect
78. #4841C22semidirect
79. #4839C22semidirect
80. #4839C22semidirect
81. #4819C22semidirect
82. #4818C22semidirect
83. #4803C22semidirect
84. D3×#103C22semidirect
85. #4787C22semidirect
86. #4786C22semidirect
87. #4771C22semidirect
88. D3×#102C22semidirect
98. #3037D3semidirect
110. C2×#239D4semidirect
247. C2×#137C2×D3semidirect
272. C2×C4×Q8C2×D3semidirect
284. #464C2×D3semidirect
291. #462C2×D3semidirect
297. #460C2×D3semidirect
305. #423C2×D3semidirect
311. #417C2×D3semidirect
950. C3#60425semidirect

Maximal subgroups

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

subgroupindex
C2×#57772
#862352
C2×#55742
C3×#30372
#839662
#832972
#824412
#806032
#806022
#804792
#803862
#790552
#790482
#789102
D3×#4172
#604253