Finite Group Databasebeta

← #11866185

Subgroups — #11866185

Order 1152.

1114 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63795C211yesmaximal, characteristic, complemented
2C2×D3×D24C211yesmaximal, characteristic, complemented
3#10594000C211yesmaximal, characteristic, complemented
4#10593994C211yesmaximal, characteristic, complemented
5#10592543C211yesmaximal, characteristic, complemented
6C3×#4843C211yesmaximal, characteristic, complemented
7C3×#4839C211yesmaximal, characteristic, complemented
8#10590954C211yesmaximal, characteristic, complemented
9#10590939C211yesmaximal, characteristic, complemented
10#10590860C211yesmaximal, characteristic, complemented
11#10590765C211yesmaximal, characteristic, complemented
12#10590755C211yesmaximal, characteristic, complemented
13#10590753C211yesmaximal, characteristic, complemented
14#10590366C211yesmaximal, characteristic, complemented
15#10590355C211yesmaximal, characteristic, complemented
16#80334—31nomaximal
17#79086—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×#3745C2211yescharacteristic
22C2×#3744C2211yescharacteristic, complemented
23#64084C2211yescharacteristic, complemented
24C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C2×C3×D24C2211yescharacteristic
26C2×C3×D24C2211yescharacteristic, complemented
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#874C2211yescharacteristic, complemented
30C3×C4×D12C2211yescharacteristic, complemented
31C3×#872C2211yescharacteristic
32#63922—21no—
33#63922—21no—
34#63921—21no—
35D3×(C2×D3)⋊C4—21no—
36#63911C2211yescharacteristic, complemented
37#63904—21no—
38#63894C2211yescharacteristic, complemented
39Dic3×D12C2211yescharacteristic, complemented
40#63886—21no—
41#63886—21no—
42#63881—21no—
43#63860C2211yescharacteristic, complemented
44#63841C2211yescharacteristic
45C2×#3716C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3714C2211yescharacteristic, complemented
49#63795—24no—
50D3×D24—24no—
51C32×C4⋊C8C2211yescharacteristic, complemented
52#63648C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×#911—31no—
64C2×D3×D8—31no—
65C2×#908—31no—
66C22×D24—31no—
67#5715—31no—
68#5545—31no—
69#5525—31no—
70#5521—31no—
71C3×#459—31no—
72C3×#424—31no—
73#5153—31no—
74#5150—31no—
75#5131—31no—
76#5113—31no—
77#5072—31no—
78#5016—31no—
79#4844—31no—
80#4844—31no—
81#4844—31no—
82#4844—31no—
83#4844—31no—
84#4844—61no—
85#4843—31no—
86#4843—31no—
87#4843—31no—
88#4843D311yescharacteristic, complemented
89#4839D311yescharacteristic, complemented
90#4787—31no—
91#4786—31no—
92#4772—31no—
93#4770—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634C2311yescharacteristic
100C2×C3×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#625—21no—
112C2×#624—21no—
113C2×D3×Dic3—21no—
114C2×D3×Dic3—21no—
115D3×D12—22no—
116D3×D12—22no—
117D3×D12—22no—
118D3×D12D414yescomplemented
119#3795—22no—
120#3795—22no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123C32×C42C2311yescharacteristic
124#3752—21no—
125#3752—21no—
126#3752—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128#3745—22no—
129#3744—22no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4D411yescharacteristic
132C3×(C2×D3)⋊C4D411yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4D411yescharacteristic
135C3×Dic3⋊C4D411yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×D24—22no—
140C3×D24—22no—
141C3×ΓL(1,𝔽25)—22no—
142C3×D3×C8—22no—
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148Dic32—21no—
149#3716—22no—
150#3714—22no—
151#3714—22no—
152#3714—22no—
153#3041—91noSylow
154C2×#237—31no—
155C2×D3×D4—31no—
156C2×D3×D4—31no—
157C2×#235—31no—
158C22×D12—31no—
159C22×D12—31no—
160C2×C3×D8—31no—
161C2×C3×D8—31no—
162C2×C3×M16—31no—
163C22×C3×C8—31no—
164C3×#127—31no—
165C3×C4×D4—31no—
166C3×#117—31no—
167#940—31no—
168#939—61no—
169#939—61no—
170#937—61no—
171#937—61no—
172#936—31no—
173D4×Dic3—31no—
174C2×#214—31no—
175C2×#213—31no—
176C2×#213—31no—
177C2×#213—31no—
178C4×#67—61no—
179C2×(C2×D3)⋊C4—61no—
180#926—31no—
181#911—64no—
182D3×D8—64no—
183#908—64no—
184C2×D24—31no—
185C2×D24—31no—
186C2×D24—31no—
187C2×D24—31no—
188C2×D24—31no—
189C2×D24—61no—
190C2×D24—64no—
191C2×D24C2×D311yescharacteristic
192C2×D24C2×D311yescharacteristic, complemented
193C2×#204—31no—
194C2×#204—31no—
195C2×#204—31no—
196C2×#204—61no—
197C2×ΓL(1,𝔽25)C2×D311yescharacteristic
198C2×D3×C8C2×D311yescharacteristic
199#895—61no—
200#895—61no—
201#893—31no—
202#893—61no—
203#893—61no—
204#892—31no—
205#882—61no—
206#882—61no—
207#67⋊C4—61no—
208D3×C22⋊C4—61no—
209D3×C22⋊C4—61no—
210D3×C22⋊C4—61no—
211#875—31no—
212#875—31no—
213#875—31no—
214#875—61no—
215#874—31no—
216#874C2×D311yescharacteristic, complemented
217C4×D12—31no—
218C4×D12—31no—
219C4×D12—31no—
220C4×D12—31no—
221C4×D12—61no—
222C4×D12C2×D311yescharacteristic, complemented
223#872C2×D311yescharacteristic
224C3×C4⋊C8—21no—
225C3×C4⋊C8—31no—
226C3×C4⋊C8—31no—
227C3×C4⋊C8—31no—
228C3×C4⋊C8C2×D311yescharacteristic, complemented
229C3×C4⋊C8C2×D311yescharacteristic, complemented
230C3×#102—31no—
231C3×#102—31no—
232#832—31no—
233#832—31no—
234#821—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—31no—
239#821—61no—
240#821C2×D311yescharacteristic, complemented
241#821C2×D311yescharacteristic, complemented
242#816—31no—
243#816—31no—
244#816—31no—
245#816—61no—
246Dic3⋊C8C2×D311yescharacteristic, complemented
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#810—31no—
249#809—31no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C2×D32—24no—
258C2×D32—42no—
259C2×D32—81no—
260C2×D32—81no—
261C2×D32—81no—
262C2×D32—81no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)C2×D412yes—
272C4×C3⋊D3—81no—
273#634—21no—
274#634—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—81no—
285C3×D12—81no—
286C3×D12C2×D412yes—
287C3×C4×D3—81no—
288C3×C4×D3C2×D412yes—
289C3×C4×D3#4112yes—
290#626—24no—
291#626—42no—
292#626—81no—
293#626—81no—
294#625—42no—
295#624—81no—
296D3×Dic3—42no—
297D3×Dic3—81no—
298C32×C8—21no—
299C32×C8—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—91no—
303C22×D8—91no—
304#535—91no—
305#518—91no—
306#463—91no—
307#463—91no—
308#463—91no—
309#463—91no—
310#459—31no—
311#459—91no—
312#459—91no—
313#459—91no—
314#424—31no—
315#418—91no—
316#416—91no—
317C23×D3—61no—
318C23×D3—61no—
319C23×D3—61no—
320C23×D3—61no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C22×C3×C4—31no—
327C22×C3×C4—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C22×Dic3—61no—
335C22×Dic3—61no—
336#237—62no—
337#237—62no—
338D3×D4—34no—
339D3×D4—62no—
340D3×D4—62no—
341D3×D4—62no—
342#235—62no—
343#235—62no—
344C2×D12—21no—
345C2×D12—21no—
346C2×D12—31no—
347C2×D12—31no—
348C2×D12—34no—
349C2×D12—31no—
350C2×D12—31no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12—62no—
354C2×D12—62no—
355C2×D12—62no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12C22×D311yescharacteristic
361C2×D12C22×D311yescharacteristic
362C2×D12C22×D311yescharacteristic
363C2×C4×D3—21no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—121no—
371C2×C4×D3C22×D311yescharacteristic
372C2×Dic6—31no—
373C2×Dic6—31no—
374C2×Dic6—61no—
375C3×D8—62no—
376C3×D8—62no—
377C3×M16—62no—
378C2×C3×C8—21no—
379C2×C3×C8—21no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C2×C3×C8—62no—
383C2×C3×C8C22×D311yescharacteristic
384C2×C3×C8C22×D311yescharacteristic
385C2×C3×C8C22×D311yescharacteristic
386C2×C3×C8C22×D311yescharacteristic
387C3×C4⋊C4—31no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—31no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—31no—
392C3×C22⋊C4—61no—
393C3×C42—21no—
394C3×C42—31no—
395C3×C42C22×D311yescharacteristic
396C3×C42C22×D311yescharacteristic
397#217—61no—
398#217—61no—
399#217—61no—
400#217—61no—
401#214—62no—
402#213—62no—
403#213—62no—
404#213—62no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—121no—
419(C2×D3)⋊C4—121no—
420(C2×D3)⋊C4—121no—
421(C2×D3)⋊C4D1211yescharacteristic
422(C2×D3)⋊C4D1211yescharacteristic
423C4⋊Dic3—31no—
424C4⋊Dic3—31no—
425C4⋊Dic3—61no—
426C4⋊Dic3C22×D311yescharacteristic
427Dic3⋊C4D1211yescharacteristic
428Dic3⋊C4D1211yescharacteristic
429C4×Dic3—61no—
430C4×Dic3—61no—
431C4×Dic3C22×D311yescharacteristic
432C2×C3⋊C8C22×D311yescharacteristic
433C2×C3⋊C8C22×D311yescharacteristic
434D24—22no—
435D24—22no—
436D24—62no—
437D24—62no—
438D24—62no—
439D24—62no—
440D24—62no—
441D24—122no—
442#204—62no—
443#204—62no—
444#204—62no—
445#204—122no—
446ΓL(1,𝔽25)—22no—
447D3×C8—22no—
448C22×C32C22×D411yescharacteristic
449C2×C3⋊D3—22no—
450C2×C3⋊D3—41no—
451C2×C3⋊D3—41no—
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—22no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3#12112yes—
467D32—84no—
468D32—84no—
469C32×C4—21no—
470C32×C4—21no—
471C32×C4C22×D411yescharacteristic
472C32×C4C2×#4111yescharacteristic
473C3⋊Dic3—41no—
474C3⋊Dic3—41no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C2×#41—91no—
480C22×D4—91no—
481C22×D4—91no—
482AGL(1,ℤ/8)—184no—
483C2×SD16—91no—
484C2×SD16—91no—
485C2×D8—31no—
486C2×D8—31no—
487C2×D8—91no—
488C2×D8—91no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—184no—
492C2×M16—31no—
493C22×C8—31no—
494#127—31no—
495#127—91no—
496#124—91no—
497#124—91no—
498#121—181no—
499#121—181no—
500#120—181no—
501#120—181no—
502C4×D4—31no—
503C4×D4—91no—
504C4×D4—91no—
505C4×D4—91no—
506C4×D4—181no—
507C4×D4—181no—
508#117—31no—
509#117—91no—
510C2×C22⋊C4—181no—
511C2×C22⋊C4—181no—
512C4⋊C8—31no—
513C4⋊C8—31no—
514C4⋊C8—31no—
515C4⋊C8D3211yescharacteristic, complemented
516#103—91no—
517#103—91no—
518#102—31no—
519#102—31no—
520#102—91no—
521#102—91no—
522#102—91no—
523#102—91no—
524C23×C3—31no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3—61no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—64no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—64no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—121no—
538C22×D3—121no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—241no—
542C22×D3—241no—
543C22×D3—241no—
544C22×D3—241no—
545C22×D3—241no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3—241no—
549C22×D3C2×D1211yescharacteristic
550C3×D4—32no—
551C3×D4—61no—
552C3×D4—61no—
553C3×D4—61no—
554C3×D4—61no—
555C3×D4—61no—
556C3×D4—241no—
557C3×D4—241no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—31no—
562C2×C3×C4—32no—
563C2×C3×C4—32no—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—61no—
567C2×C3×C4—241no—
568C2×C3×C4C2×D1211yescharacteristic
569C2×C3×C4C2×D1211yescharacteristic
570C2×C3×C4D3×D411yescharacteristic
571C2×C3×C4D3×D411yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573C2×C3×C4C23×D311yescharacteristic
574#67—64no—
575#67—122no—
576#67—122no—
577#67—122no—
578#67—241no—
579#67—241no—
580C2×Dic3—21no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—121no—
586C2×Dic3—121no—
587C2×Dic3—122no—
588C2×Dic3—241no—
589C2×Dic3C2×D1211yescharacteristic
590C2×Dic3C2×D1211yescharacteristic
591C2×Dic3C2×D1211yescharacteristic
592D12—21no—
593D12—21no—
594D12—21no—
595D12—21no—
596D12—21no—
597D12—32no—
598D12—32no—
599D12—62no—
600D12—64no—
601D12—61no—
602D12—61no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—81no—
608D12—81no—
609D12—121no—
610D12—121no—
611D12—121no—
612D12—122no—
613D12—241no—
614D12—241no—
615D12D3×D412yes—
616C4×D3—81no—
617C4×D3—122no—
618C4×D3—241no—
619C4×D3—241no—
620C4×D3—241no—
621C4×D3—241no—
622C4×D3—241no—
623C4×D3—242no—
624C4×D3D3×D412yes—
625C4×D3#23912yes—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—61no—
630Dic6—121no—
631Dic6—121no—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—41no—
637C3×C8—41no—
638C3×C8—61no—
639C3×C8—61no—
640C3⋊C8—21no—
641C3⋊C8—21no—
642C2×C32C2×#12111yescharacteristic
643C2×C32#57611yescharacteristic
644C2×C32#57611yescharacteristic
645C3⋊D3—42no—
646C3⋊D3—81no—
647C3×D3—22no—
648C3×D3—42no—
649C3×D3—81no—
650C3×D3—81no—
651C24—181no—
652C24—181no—
653#41—182no—
654#41—182no—
655C2×Q8—91no—
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—61no—
660C2×D4—61no—
661C2×D4—94no—
662C2×D4—91no—
663C2×D4—91no—
664C2×D4—182no—
665C2×D4—182no—
666C2×D4—182no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4—181no—
672C22×C4—31no—
673C22×C4—61no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678SD16—182no—
679SD16—182no—
680D8—62no—
681D8—62no—
682D8—182no—
683D8—182no—
684D8—182no—
685D8—182no—
686M16—62no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—62no—
690C2×C8C2×D3211yescharacteristic
691C2×C8C2×D3211yescharacteristic
692C4⋊C4—31no—
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4—91no—
696C22⋊C4—31no—
697C22⋊C4—31no—
698C22⋊C4—61no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C42—31no—
708C42—181no—
709C42C2×D3211yescharacteristic
710C22×C3—21no—
711C22×C3—32no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—62no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3C22×D1211yescharacteristic
724C22×C3C2×D3×D411yescharacteristic
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—22no—
728C2×D3—41no—
729C2×D3—41no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—62no—
737C2×D3—62no—
738C2×D3—122no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—241no—
750C2×D3—241no—
751C2×D3—241no—
752C2×D3—241no—
753C2×D3—241no—
754C2×D3—244no—
755C2×D3—244no—
756C2×D3—244no—
757C2×D3—244no—
758C2×D3#89512yes—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—21no—
764C3×C4—21no—
765C3×C4—32no—
766C3×C4—41no—
767C3×C4—41no—
768C3×C4—61no—
769C3×C4—61no—
770C3×C4—121no—
771C3×C4C2×D3×D411yescharacteristic
772C3×C4C2×D3×D411yescharacteristic
773C3×C4C2×#23911yescharacteristic
774C3×C4D3×#4111yescharacteristic
775Dic3—21no—
776Dic3—21no—
777Dic3—41no—
778Dic3—121no—
779Dic3—121no—
780Dic3—121no—
781Dic3—121no—
782Dic3—241no—
783Dic3—241no—
784Dic3#89512yes—
785C32#304111yescharacteristic, complemented, Sylow
786C23—31no—
787C23—61no—
788C23—61no—
789C23—61no—
790C23—184no—
791C23—181no—
792C23—181no—
793C23—362no—
794C23—721no—
795C23—721no—
796C23—721no—
797C23—721no—
798Q8—181no—
799Q8—181no—
800D4—32no—
801D4—61no—
802D4—61no—
803D4—61no—
804D4—61no—
805D4—61no—
806D4—92no—
807D4—184no—
808D4—181no—
809D4—181no—
810D4—181no—
811D4—241no—
812D4—241no—
813D4—362no—
814D4—362no—
815D4—721no—
816D4—721no—
817C2×C4—31no—
818C2×C4—32no—
819C2×C4—32no—
820C2×C4—31no—
821C2×C4—31no—
822C2×C4—61no—
823C2×C4—181no—
824C2×C4—181no—
825C2×C4—241no—
826C2×C4—362no—
827C2×C4—721no—
828C2×C4—721no—
829C2×C4—721no—
830C2×C4D3×D1211yescharacteristic
831C2×C4D3×D1211yescharacteristic
832C2×C4C22×D3211yescharacteristic
833C8—21no—
834C8—21no—
835C8—61no—
836C8—61no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—62no—
841C2×C3—122no—
842C2×C3—241no—
843C2×C3—241no—
844C2×C3C2×#89511yescharacteristic
845C2×C3D3×#12111yescharacteristic
846C2×C3#575211yescharacteristic
847C2×C3#575211yescharacteristic
848C2×C3#575711yescharacteristic
849C2×C3#577411yescharacteristic
850D3—22no—
851D3—42no—
852D3—81no—
853D3—81no—
854D3—122no—
855D3—122no—
856D3—242no—
857D3—241no—
858D3—241no—
859D3—481no—
860C22—32no—
861C22—61no—
862C22—61no—
863C22—62no—
864C22—121no—
865C22—121no—
866C22—121no—
867C22—121no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22—182no—
873C22—361no—
874C22—361no—
875C22—361no—
876C22—361no—
877C22—361no—
878C22—724no—
879C22—724no—
880C22C2×D3×D1211yescharacteristic
881C4—21no—
882C4—21no—
883C4—32no—
884C4—61no—
885C4—61no—
886C4—121no—
887C4—361no—
888C4—361no—
889C4D32×D411yescharacteristic
890C4D3×#23911yescharacteristic
891C3—21no—
892C3#7908611yescharacteristic, complemented
893C3#8033411yescharacteristic, complemented
894C2—62no—
895C2—122no—
896C2—241no—
897C2—241no—
898C2—362no—
899C2—721no—
900C2D3×#89511yescharacteristic
901C2#1059467811yescharacteristic
902C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63795C2semidirect
2. C2×D3×D24C2semidirect
3. #10594000C2semidirect
4. #10593994C2semidirect
5. #10592543C2semidirect
6. C3×#4843C2semidirect
7. C3×#4839C2semidirect
8. #10590954C2semidirect
9. #10590939C2semidirect
10. #10590860C2semidirect
11. #10590765C2semidirect
12. #10590755C2semidirect
13. #10590753C2semidirect
14. #10590366C2semidirect
15. #10590355C2semidirect
22. C2×#3744C22semidirect
23. #64084C22semidirect
24. C4×C4⋊(C3⋊D3)C22semidirect
26. C2×C3×D24C22semidirect
29. C3×#874C22semidirect
30. C3×C4×D12C22semidirect
36. #63911C22semidirect
38. #63894C22semidirect
39. Dic3×D12C22semidirect
43. #63860C22semidirect
45. C2×#3716C22semidirect
48. C2×#3714C22semidirect
51. C32×C4⋊C8C22semidirect
52. #63648C22semidirect
53. #63643C22semidirect
54. C3×#821C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
60. #63564C22semidirect
61. #63563C22semidirect
62. #63563C22semidirect
88. #4843D3semidirect
89. #4839D3semidirect
118. D3×D12D4semidirect
192. C2×D24C2×D3semidirect
216. #874C2×D3semidirect
222. C4×D12C2×D3semidirect
228. C3×C4⋊C8C2×D3semidirect
229. C3×C4⋊C8C2×D3semidirect
240. #821C2×D3semidirect
241. #821C2×D3semidirect
246. Dic3⋊C8C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
515. C4⋊C8D32semidirect
785. C32#3041semidirect
892. C3#79086semidirect
893. C3#80334semidirect

Maximal subgroups

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

subgroupindex
C2×#637952
C2×D3×D242
#105940002
#105939942
#105925432
C3×#48432
C3×#48392
#105909542
#105909392
#105908602
#105907652
#105907552
#105907532
#105903662
#105903552
#803343
#790863