Finite Group Databasebeta

← #11865888

Subgroups — #11865888

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595360C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic, complemented
3C2×#63794C211yesmaximal, characteristic, complemented
4D3×#893C211yesmaximal, characteristic, complemented
5#10592518C211yesmaximal, characteristic, complemented
6C3×#4818C211yesmaximal, characteristic, complemented
7C3×#4803C211yesmaximal, characteristic, complemented
8#10591570C211yesmaximal, characteristic, complemented
9#10591565C211yesmaximal, characteristic, complemented
10#10590765C211yesmaximal, characteristic, complemented
11#10590750C211yesmaximal, characteristic, complemented
12#10590663C211yesmaximal, characteristic, complemented
13#10590609C211yesmaximal, characteristic, complemented
14#10590547C211yesmaximal, characteristic, complemented
15#10590540C211yesmaximal, characteristic, complemented
16#80428—31nomaximal
17#78910—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×C4×D32—21no—
21C2×#3799C2211yescharacteristic
22#64156C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24C2×#3745C2211yescharacteristic
25#64102C2211yescharacteristic
26C3×#944C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
30C3×#893C2211yescharacteristic
31C3×D3×C4⋊C4C2211yescharacteristic
32#63939—24no—
33D3×(C2×D3)⋊C4—21no—
34#63911C2211yescharacteristic, complemented
35#63904—21no—
36#63904—21no—
37#63904—21no—
38#63898C2211yescharacteristic
39#63894C2211yescharacteristic
40#63886—21no—
41#63886—21no—
42#63881—21no—
43C4×D3×Dic3C2211yescharacteristic
44#63863C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic
46C2×#3714C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49C2×#3711C2211yescharacteristic
50#63794—24no—
51C32×#103C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63572C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#5832—31no—
64C2×#949—31no—
65C2×#914—31no—
66C2×#914—31no—
67C2×#908—31no—
68#5725—31no—
69C4×D3×D4—31no—
70C2×#893—31no—
71C3×#461—31no—
72C3×#417—31no—
73#5165—31no—
74#5165—31no—
75#5118—31no—
76#5083—31no—
77#5015—31no—
78#4966—31no—
79#4843—31no—
80#4837—31no—
81#4819—31no—
82#4819—31no—
83#4819—31no—
84#4819—31no—
85#4819—61no—
86#4818—31no—
87#4818D311yescharacteristic, complemented
88#4803—31no—
89#4803D311yescharacteristic, complemented
90#4787—31no—
91#4787—31no—
92#4786—31no—
93#4786—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C3×#239—22no—
100C3×#239—22no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#624—21no—
114C2×#624—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3D411yescharacteristic
117C2×D3×Dic3D411yescharacteristic
118D3×D12—22no—
119D3×D12D414yescomplemented
120C4×D32—44no—
121#3799—22no—
122#3799—22no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125#3755—22no—
126#3752—21no—
127#3752—21no—
128#3752—21no—
129C4×C3⋊Dic3C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131#3745—22no—
132C3×#215—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×#204—22no—
142C3×ΓL(1,𝔽25)—22no—
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147Dic32D411yescharacteristic
148Dic32D411yescharacteristic
149#3717—22no—
150#3714—22no—
151#3714—22no—
152#3713—22no—
153#3711—22no—
154#3036—91noSylow
155C2×C3×#41—31no—
156C2×#239—31no—
157C2×#239C2×D311yescharacteristic
158C2×D3×D4—31no—
159C2×#235—31no—
160C22×D12—31no—
161C22×C4×D3—61no—
162C22×C4×D3—61no—
163C2×C3×SD16—31no—
164C2×C3×SD16—31no—
165C2×C3×M16—31no—
166C3×C4⋊Q8—31no—
167C3×C4×D4—31no—
168C2×C3×C4⋊C4—31no—
169#949—64no—
170#947—31no—
171#947—31no—
172#947—31no—
173#947—61no—
174#944C2×D311yescharacteristic, complemented
175C2×#215—31no—
176C2×#215—31no—
177C2×#215—31no—
178C2×#215—61no—
179C2×#215C2×D311yescharacteristic
180#940—31no—
181#939—61no—
182#939—61no—
183#936—31no—
184D4×Dic3—31no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—31no—
189C4×#67—61no—
190C4×#67—61no—
191C4×#67—61no—
192C2×(C2×D3)⋊C4—61no—
193C2×C4×Dic3—31no—
194C2×#208—31no—
195#914—64no—
196#914—64no—
197#908—64no—
198C2×D24—31no—
199C2×D24—31no—
200C2×D24—31no—
201C2×D24—31no—
202C2×D24—61no—
203C2×#204—31no—
204C2×#204C2×D311yescharacteristic
205C2×ΓL(1,𝔽25)—31no—
206C2×ΓL(1,𝔽25)C2×D311yescharacteristic
207#895—61no—
208#895—61no—
209#893—31no—
210#893—31no—
211#893—31no—
212#893—31no—
213#893—61no—
214#893—61no—
215#893—61no—
216#893—61no—
217#893—61no—
218#893C2×D311yescharacteristic
219D3×C4⋊C4C2×D311yescharacteristic
220#67⋊C4—61no—
221D3×C22⋊C4—61no—
222#874—31no—
223C4×D12—31no—
224C42×D3—31no—
225C3×C4⋊C8—31no—
226C3×#103—21no—
227C3×#103—31no—
228C3×#103—31no—
229C3×#103C2×D311yescharacteristic, complemented
230C3×#103C2×D311yescharacteristic, complemented
231C3×#102—31no—
232C3×#102—31no—
233#835—31no—
234#835C2×D311yescharacteristic, complemented
235#821—31no—
236#821C2×D311yescharacteristic, complemented
237Dic3⋊C8—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—61no—
243Dic3⋊C8C2×D311yescharacteristic, complemented
244#810—31no—
245#810C2×D311yescharacteristic, complemented
246#809—31no—
247#809—31no—
248#809—31no—
249#809—61no—
250#809C2×D311yescharacteristic, complemented
251C4⋊(C3⋊C8)—31no—
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—42no—
260C32×Q8—21no—
261C32×Q8—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3C2×D411yescharacteristic
266C2×C3⋊Dic3C2×D411yescharacteristic
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)C2×D412yes—
271C4×C3⋊D3—42no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—42no—
281C3×D12C2×D412yes—
282C3×C4×D3—42no—
283C3×C4×D3—42no—
284C3×C4×D3—42no—
285C3×C4×D3C2×D412yes—
286C3×C4×D3#4112yes—
287C3×Dic6—21no—
288C3×Dic6—21no—
289#626—24no—
290#626—42no—
291#626—42no—
292#626—42no—
293#624—42no—
294#624—42no—
295D3×Dic3—22no—
296D3×Dic3—41no—
297D3×Dic3—42no—
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—91no—
303C2×AGL(1,ℤ/8)—91no—
304#532—91no—
305C2×C4×D4—91no—
306#463—91no—
307#463—91no—
308#463—91no—
309#463—91no—
310#461—31no—
311#461—91no—
312#459—91no—
313#459—91no—
314#423—91no—
315#417—31no—
316#417—91no—
317C23×D3—61no—
318C23×D3—61no—
319C3×#41—62no—
320C3×#41—62no—
321C2×C3×Q8—21no—
322C2×C3×Q8—31no—
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C22×C3×C4—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C22×Dic3—31no—
337C22×Dic3—31no—
338C22×Dic3—61no—
339#239—22no—
340#239—22no—
341#239—62no—
342#239—62no—
343D3×D4—34no—
344D3×D4—62no—
345#235—62no—
346#235—62no—
347C2×D12—21no—
348C2×D12—31no—
349C2×D12—31no—
350C2×D12—34no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—62no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12C22×D311yescharacteristic
361C2×D12C22×D311yescharacteristic
362C2×C4×D3—21no—
363C2×C4×D3—21no—
364C2×C4×D3—21no—
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—121no—
375C2×C4×D3—124no—
376C2×C4×D3—124no—
377C2×C4×D3C22×D311yescharacteristic
378C2×Dic6C22×D311yescharacteristic
379C3×SD16—62no—
380C3×SD16—62no—
381C3×M16—62no—
382C2×C3×C8—21no—
383C2×C3×C8—31no—
384C2×C3×C8—31no—
385C2×C3×C8C22×D311yescharacteristic
386C2×C3×C8C22×D311yescharacteristic
387C3×C4⋊C4—21no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C4⋊C4C22×D311yescharacteristic
394C3×C22⋊C4—61no—
395C3×C42—31no—
396#217—61no—
397#217—61no—
398#217—61no—
399#215—22no—
400#215—62no—
401#215—62no—
402#215—62no—
403#215—122no—
404#213—62no—
405#213—62no—
406#213—62no—
407#213—62no—
408(C2×D3)⋊C4—21no—
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—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—121no—
421(C2×D3)⋊C4—121no—
422(C2×D3)⋊C4—121no—
423C4⋊Dic3C22×D311yescharacteristic
424Dic3⋊C4—21no—
425Dic3⋊C4—21no—
426Dic3⋊C4—21no—
427C4×Dic3—31no—
428C4×Dic3—31no—
429C4×Dic3—31no—
430C4×Dic3—31no—
431C4×Dic3—31no—
432C4×Dic3—31no—
433C4×Dic3—61no—
434C4×Dic3C22×D311yescharacteristic
435#208—62no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—61no—
439C2×C3⋊C8C22×D311yescharacteristic
440C2×C3⋊C8C22×D311yescharacteristic
441D24—62no—
442D24—62no—
443D24—62no—
444D24—62no—
445D24—122no—
446#204—22no—
447#204—62no—
448ΓL(1,𝔽25)—22no—
449ΓL(1,𝔽25)—62no—
450C22×C32C22×D411yescharacteristic
451C2×C3⋊D3—22no—
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—22no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3#12112yes—
466D32—48no—
467C32×C4—41no—
468C32×C4—41no—
469C32×C4C22×D411yescharacteristic
470C32×C4C2×#4111yescharacteristic
471C3⋊Dic3—21no—
472C3⋊Dic3—21no—
473C3×Dic3—21no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C3×Dic3#12112yes—
477C3×Dic3AGL(1,ℤ/8)12yescomplemented
478C2×#41—31no—
479C2×#41—91no—
480C22×D4—91no—
481C23×C4—181no—
482AGL(1,ℤ/8)—184no—
483AGL(1,ℤ/8)—184no—
484C2×SD16—31no—
485C2×SD16—31no—
486C2×SD16—91no—
487C2×SD16—91no—
488C2×D8—91no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—91no—
492C2×M16—31no—
493C2×M16—91no—
494C4⋊Q8—31no—
495#127—91no—
496#124—91no—
497#124—91no—
498#121—181no—
499#121—181no—
500C4×D4—31no—
501C4×D4—91no—
502C4×D4—91no—
503C4×D4—91no—
504C4×D4—181no—
505C4×D4—181no—
506C4×D4—181no—
507C4×D4—181no—
508C2×C4⋊C4—31no—
509C2×C22⋊C4—181no—
510C2×C42—91no—
511C4⋊C8—31no—
512C4⋊C8—91no—
513C4⋊C8—91no—
514C4⋊C8—91no—
515#103—31no—
516#103—31no—
517#103—91no—
518#103D3211yescharacteristic, complemented
519#102—31no—
520#102—31no—
521#102—91no—
522#102—91no—
523C23×C3—31no—
524C23×C3—61no—
525C23×C3—61no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—64no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—64no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—121no—
535C22×D3—121no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3D3×D411yescharacteristic
541C3×Q8—21no—
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—41no—
546C3×Q8—41no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×D4—32no—
550C3×D4—61no—
551C3×D4—61no—
552C3×D4—61no—
553C3×D4—122no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—31no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—122no—
569C2×C3×C4—122no—
570C2×C3×C4—122no—
571C2×C3×C4C23×D311yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573#67—64no—
574#67—122no—
575#67—122no—
576#67—122no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—31no—
580C2×Dic3—31no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—62no—
586C2×Dic3—121no—
587C2×Dic3—122no—
588C2×Dic3D3×D411yescharacteristic
589C2×Dic3D3×D411yescharacteristic
590C2×Dic3D3×D411yescharacteristic
591D12—21no—
592D12—21no—
593D12—21no—
594D12—32no—
595D12—32no—
596D12—42no—
597D12—62no—
598D12—64no—
599D12—61no—
600D12—61no—
601D12—61no—
602D12—61no—
603D12—61no—
604D12—61no—
605D12—121no—
606D12—121no—
607D12—121no—
608D12—122no—
609D12—122no—
610D12—122no—
611D12D3×D412yes—
612C4×D3—42no—
613C4×D3—42no—
614C4×D3—42no—
615C4×D3—62no—
616C4×D3—122no—
617C4×D3—122no—
618C4×D3—122no—
619C4×D3—122no—
620C4×D3—121no—
621C4×D3—122no—
622C4×D3—122no—
623C4×D3—122no—
624C4×D3—242no—
625C4×D3#23512yes—
626C4×D3D3×D412yes—
627Dic6—21no—
628Dic6—21no—
629C3×C8—21no—
630C3×C8—21no—
631C3×C8—41no—
632C3×C8—61no—
633C3×C8—61no—
634C3⋊C8—21no—
635C3⋊C8—21no—
636C3⋊C8—61no—
637C3⋊C8—61no—
638C3⋊C8—121no—
639C2×C32C2×#12111yescharacteristic
640C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
641C2×C32#57511yescharacteristic
642C3⋊D3—42no—
643C3⋊D3—81no—
644C3×D3—22no—
645C3×D3—42no—
646C3×D3—81no—
647C24—181no—
648#41—62no—
649#41—62no—
650#41—182no—
651#41—182no—
652C2×Q8—31no—
653C2×Q8C2×D3211yescharacteristic
654C2×D4—31no—
655C2×D4—31no—
656C2×D4—61no—
657C2×D4—94no—
658C2×D4—91no—
659C2×D4—91no—
660C2×D4—182no—
661C2×D4—181no—
662C2×D4—181no—
663C2×D4—181no—
664C2×D4—181no—
665C22×C4—31no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—91no—
670C22×C4—91no—
671C22×C4—181no—
672C22×C4—181no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4—364no—
676SD16—62no—
677SD16—62no—
678SD16—182no—
679SD16—182no—
680D8—182no—
681D8—182no—
682D8—182no—
683D8—182no—
684M16—62no—
685M16—182no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—91no—
689C2×C8C2×D3211yescharacteristic
690C4⋊C4—31no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4C2×D3211yescharacteristic
695C22⋊C4—61no—
696C22⋊C4—181no—
697C22⋊C4—181no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C42—31no—
704C42—91no—
705C42—91no—
706C42—91no—
707C22×C3—21no—
708C22×C3—32no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—62no—
712C22×C3—121no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3C2×D3×D411yescharacteristic
718C22×C3C2×D3×D411yescharacteristic
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—22no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—41no—
726C2×D3—41no—
727C2×D3—62no—
728C2×D3—62no—
729C2×D3—122no—
730C2×D3—128no—
731C2×D3—128no—
732C2×D3—121no—
733C2×D3—121no—
734C2×D3—121no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—241no—
743C2×D3—241no—
744C2×D3—241no—
745C2×D3—241no—
746C2×D3—241no—
747C2×D3#88412yes—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—32no—
751C3×C4—32no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—61no—
757C3×C4—81no—
758C3×C4—81no—
759C3×C4—121no—
760C3×C4—121no—
761C3×C4C2×#23511yescharacteristic
762C3×C4C2×D3×D411yescharacteristic
763C3×C4C2×D3×D411yescharacteristic
764C3×C4D3×#4111yescharacteristic
765Dic3—21no—
766Dic3—41no—
767Dic3—41no—
768Dic3—61no—
769Dic3—61no—
770Dic3—61no—
771Dic3—61no—
772Dic3—121no—
773Dic3—121no—
774Dic3#88412yes—
775Dic3#91412yescomplemented
776C32#303611yescharacteristic, complemented, Sylow
777C23—31no—
778C23—61no—
779C23—61no—
780C23—184no—
781C23—181no—
782C23—181no—
783C23—362no—
784C23—362no—
785Q8—21no—
786Q8—21no—
787Q8—61no—
788Q8—61no—
789D4—32no—
790D4—61no—
791D4—61no—
792D4—61no—
793D4—92no—
794D4—122no—
795D4—184no—
796D4—181no—
797D4—181no—
798D4—181no—
799D4—362no—
800D4—362no—
801D4—362no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—31no—
805C2×C4—31no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—31no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—91no—
812C2×C4—91no—
813C2×C4—122no—
814C2×C4—122no—
815C2×C4—122no—
816C2×C4—182no—
817C2×C4—362no—
818C2×C4—362no—
819C2×C4—362no—
820C2×C4—361no—
821C2×C4—362no—
822C2×C4C22×D3211yescharacteristic
823C8—21no—
824C8—61no—
825C8—61no—
826C8—181no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—62no—
831C2×C3—122no—
832C2×C3—241no—
833C2×C3C2×#88411yescharacteristic
834C2×C3D3×#12111yescharacteristic
835C2×C3C2×#91411yescharacteristic
836C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
837C2×C3#577711yescharacteristic
838C2×C3#577711yescharacteristic
839D3—22no—
840D3—42no—
841D3—81no—
842D3—122no—
843D3—122no—
844D3—242no—
845D3—241no—
846D3—241no—
847D3—481no—
848C22—32no—
849C22—61no—
850C22—61no—
851C22—62no—
852C22—121no—
853C22—121no—
854C22—121no—
855C22—121no—
856C22—121no—
857C22—182no—
858C22—368no—
859C22—361no—
860C22—361no—
861C22—361no—
862C22—361no—
863C22—361no—
864C22D32×D411yescharacteristic
865C4—32no—
866C4—32no—
867C4—41no—
868C4—41no—
869C4—61no—
870C4—121no—
871C4—121no—
872C4—181no—
873C4—181no—
874C4D3×#23511yescharacteristic
875C4D32×D411yescharacteristic
876C3—21no—
877C3#7891011yescharacteristic, complemented
878C3#8042811yescharacteristic, complemented
879C2—62no—
880C2—122no—
881C2—241no—
882C2—362no—
883C2—721no—
884C2D3×#88411yescharacteristic
885C2D3×#91411yescharacteristic
886C2#1059476211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595360C2semidirect
2. C2×#63939C2semidirect
3. C2×#63794C2semidirect
4. D3×#893C2semidirect
5. #10592518C2semidirect
6. C3×#4818C2semidirect
7. C3×#4803C2semidirect
8. #10591570C2semidirect
9. #10591565C2semidirect
10. #10590765C2semidirect
11. #10590750C2semidirect
12. #10590663C2semidirect
13. #10590609C2semidirect
14. #10590547C2semidirect
15. #10590540C2semidirect
22. #64156C22semidirect
26. C3×#944C22semidirect
34. #63911C22semidirect
44. #63863C22semidirect
51. C32×#103C22semidirect
52. #63641C22semidirect
53. #63636C22semidirect
54. C3×#835C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#809C22semidirect
59. #63572C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63565C22semidirect
62. #63564C22semidirect
87. #4818D3semidirect
89. #4803D3semidirect
119. D3×D12D4semidirect
174. #944C2×D3semidirect
229. C3×#103C2×D3semidirect
230. C3×#103C2×D3semidirect
234. #835C2×D3semidirect
236. #821C2×D3semidirect
243. Dic3⋊C8C2×D3semidirect
245. #810C2×D3semidirect
250. #809C2×D3semidirect
477. C3×Dic3AGL(1,ℤ/8)semidirect
518. #103D32semidirect
775. Dic3#914semidirect
776. C32#3036semidirect
877. C3#78910semidirect
878. C3#80428semidirect

Maximal subgroups

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

subgroupindex
#105953602
C2×#639392
C2×#637942
D3×#8932
#105925182
C3×#48182
C3×#48032
#105915702
#105915652
#105907652
#105907502
#105906632
#105906092
#105905472
#105905402
#804283
#789103