Finite Group Databasebeta

← #11865887

Subgroups — #11865887

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595363C211yesmaximal, characteristic, complemented
2C2×#63941C211yesmaximal, characteristic, complemented
3C2×#63798C211yesmaximal, characteristic, complemented
4#10594605C211yesmaximal, characteristic, complemented
5#10592502C211yesmaximal, characteristic, complemented
6C3×#4819C211yesmaximal, characteristic, complemented
7C3×#4818C211yesmaximal, characteristic, complemented
8#10591567C211yesmaximal, characteristic, complemented
9#10591564C211yesmaximal, characteristic, complemented
10#10590754C211yesmaximal, characteristic, complemented
11#10590753C211yesmaximal, characteristic, complemented
12#10590666C211yesmaximal, characteristic, complemented
13#10590612C211yesmaximal, characteristic, complemented
14#10590547C211yesmaximal, characteristic, complemented
15#10590534C211yesmaximal, characteristic, complemented
16#80534—31nomaximal
17#80428—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×C4×D32—21no—
21C2×#3796C2211yescharacteristic
22C2×#3743C2211yescharacteristic
23C4⋊C4×C3⋊D3C2211yescharacteristic
24C3×#947C2211yescharacteristic, complemented
25C3×#944C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic
28C2×C3×D24C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic
30C3×#893C2211yescharacteristic
31C3×#893C2211yescharacteristic
32#63941—24no—
33#63921—21no—
34#63911C2211yescharacteristic, complemented
35#63910—21no—
36#63910—21no—
37Dic3×D12C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39C4×#624C2211yescharacteristic
40#63881—21no—
41#63881—21no—
42#63879—21no—
43#63879—21no—
44#63864C2211yescharacteristic, complemented
45C2×#3715C2211yescharacteristic
46C2×#3714C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49C2×#3712C2211yescharacteristic
50#63798—24no—
51C32×#103C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×#914—31no—
65C2×#914—31no—
66C2×#911—31no—
67#5725—31no—
68#5668—31no—
69C4×D3×D4—31no—
70C4×D3×D4—31no—
71C3×#463—31no—
72C3×#461—31no—
73#5165—31no—
74#5165—31no—
75#5162—31no—
76#5150—31no—
77#5083—31no—
78#5057—31no—
79#5016—31no—
80#5015—31no—
81#4844—31no—
82#4843—31no—
83#4837—31no—
84#4837—31no—
85#4819—31no—
86#4819D311yescharacteristic, complemented
87#4818D311yescharacteristic, complemented
88#4803—31no—
89#4803—31no—
90#4803—31no—
91#4803—61no—
92#4786—31no—
93#4771—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96#3832—22no—
97#3832—22no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×Dic6C2311yescharacteristic
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#625—21no—
113C2×#624D411yescharacteristic
114C2×#624D411yescharacteristic
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118#3802—22no—
119#3802D414yescomplemented
120C4×D32—44no—
121#3796—22no—
122#3796—22no—
123C2×C32×C8C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128#3743—22no—
129C3×#215—22no—
130C3×#215—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×C4×Dic3C2311yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×D24—22no—
142C3×#204—22no—
143#3722—21no—
144#3722—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147Dic32D411yescharacteristic
148Dic32D411yescharacteristic
149#3715—22no—
150#3714—22no—
151#3714—22no—
152#3713—22no—
153#3712—22no—
154#3036—91noSylow
155C2×#239—31no—
156C2×#239—31no—
157C2×#239—31no—
158C2×#239—61no—
159C2×#237—31no—
160C2×D3×D4—31no—
161C2×D3×D4—31no—
162C22×C4×D3—61no—
163C22×C4×D3—61no—
164C2×C3×SD16—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×D8—31no—
168C3×C4⋊Q8—31no—
169C3×#124—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172#947—31no—
173#947C2×D311yescharacteristic, complemented
174#944C2×D311yescharacteristic, complemented
175C2×#215—31no—
176C2×#215C2×D311yescharacteristic
177C2×#215C2×D311yescharacteristic
178#940—31no—
179D4×Dic3—31no—
180D4×Dic3—31no—
181C2×#214—31no—
182C2×#213—31no—
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—31no—
186C4×#67—61no—
187C4×#67—61no—
188#914—64no—
189#914—64no—
190#914—64no—
191#911—64no—
192C2×D24—31no—
193C2×D24—31no—
194C2×D24C2×D311yescharacteristic
195C2×#204C2×D311yescharacteristic
196C2×ΓL(1,𝔽25)—31no—
197C2×ΓL(1,𝔽25)—31no—
198C2×ΓL(1,𝔽25)—31no—
199C2×ΓL(1,𝔽25)—31no—
200C2×ΓL(1,𝔽25)—61no—
201#895—61no—
202#895—61no—
203#893—61no—
204#893—61no—
205#893C2×D311yescharacteristic
206#893C2×D311yescharacteristic
207D3×C4⋊C4—31no—
208D3×C4⋊C4—31no—
209D3×C4⋊C4—61no—
210#884—61no—
211#884—61no—
212#67⋊C4—61no—
213#67⋊C4—61no—
214#67⋊C4—61no—
215#67⋊C4—61no—
216D3×C22⋊C4—61no—
217D3×C22⋊C4—61no—
218#875—31no—
219#874—31no—
220C4×D12—31no—
221C4×D12—31no—
222C42×D3—31no—
223C42×D3—31no—
224C3×C4⋊C8—31no—
225C3×C4⋊C8—31no—
226C3×#103—21no—
227C3×#103—31no—
228C3×#103C2×D311yescharacteristic, complemented
229C3×#103C2×D311yescharacteristic, complemented
230C3×#102—31no—
231#835—31no—
232#835—31no—
233#835—31no—
234#835—61no—
235#832—31no—
236#821—31no—
237#821—31no—
238#821—31no—
239#821—61no—
240#816—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8C2×D311yescharacteristic, complemented
244Dic3⋊C8C2×D311yescharacteristic, complemented
245#810C2×D311yescharacteristic, complemented
246#809—31no—
247#809—31no—
248#809—61no—
249#809C2×D311yescharacteristic, complemented
250C4⋊(C3⋊C8)—31no—
251C4⋊(C3⋊C8)—31no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3C2×D411yescharacteristic
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
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⋊Dic3—21no—
266C2×C3⋊Dic3C2×D411yescharacteristic
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—42no—
270C4×C3⋊D3—42no—
271C4×C3⋊D3—42no—
272C4×C3⋊D3C2×D412yes—
273C4×C3⋊D3#4112yes—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C2×D411yescharacteristic
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×D12C2×D412yes—
284C3×D12C2×D412yes—
285C3×C4×D3—42no—
286C3×C4×D3—42no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289#626—42no—
290#626—42no—
291#626—42no—
292#625—24no—
293#624—22no—
294#624—41no—
295D3×Dic3—42no—
296D3×Dic3—42no—
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—31no—
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—91no—
316#417—91no—
317C23×D3—61no—
318C23×D3—61no—
319C2×C3×Q8—21no—
320C2×C3×Q8—31no—
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3—61no—
336#239—62no—
337#239—62no—
338#239—62no—
339#239—62no—
340#239—62no—
341#239—62no—
342#239—64no—
343#239—122no—
344#237—62no—
345#237—62no—
346D3×D4—34no—
347D3×D4—34no—
348D3×D4—62no—
349D3×D4—62no—
350C2×D12—31no—
351C2×D12—31no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—121no—
359C2×D12C22×D311yescharacteristic
360C2×D12C22×D311yescharacteristic
361C2×D12C22×D311yescharacteristic
362C2×C4×D3—21no—
363C2×C4×D3—21no—
364C2×C4×D3—31no—
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—31no—
368C2×C4×D3—31no—
369C2×C4×D3—31no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—121no—
379C2×C4×D3—121no—
380C2×C4×D3—124no—
381C2×C4×D3—124no—
382C2×Dic6C22×D311yescharacteristic
383C3×SD16—62no—
384C3×SD16—62no—
385C3×SD16—62no—
386C3×D8—62no—
387C2×C3×C8—21no—
388C2×C3×C8—31no—
389C2×C3×C8—31no—
390C2×C3×C8C22×D311yescharacteristic
391C2×C3×C8C22×D311yescharacteristic
392C3×C4⋊C4—21no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4—61no—
395C3×C4⋊C4C22×D311yescharacteristic
396C3×C4⋊C4C22×D311yescharacteristic
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C42—31no—
402C3×C42—31no—
403#217—61no—
404#217—61no—
405#215—22no—
406#215—22no—
407#215—62no—
408#214—62no—
409#213—62no—
410#213—62no—
411#213—62no—
412#213—62no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423C4⋊Dic3—31no—
424C4⋊Dic3—31no—
425C4⋊Dic3—61no—
426Dic3⋊C4—21no—
427Dic3⋊C4—21no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—121no—
431C4×Dic3—31no—
432C4×Dic3—31no—
433C4×Dic3—31no—
434C4×Dic3—31no—
435C4×Dic3C22×D311yescharacteristic
436C4×Dic3C22×D311yescharacteristic
437C2×C3⋊C8—31no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—61no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442D24—22no—
443D24—62no—
444D24—62no—
445#204—22no—
446ΓL(1,𝔽25)—62no—
447ΓL(1,𝔽25)—62no—
448ΓL(1,𝔽25)—62no—
449ΓL(1,𝔽25)—62no—
450ΓL(1,𝔽25)—122no—
451C22×C32C22×D411yescharacteristic
452C2×C3⋊D3—21no—
453C2×C3⋊D3—21no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3#12112yes—
458C2×C3×D3—22no—
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—41no—
466C2×C3×D3—41no—
467D32—48no—
468C32×C4—41no—
469C32×C4—41no—
470C32×C4C22×D411yescharacteristic
471C32×C4C2×#4111yescharacteristic
472C3⋊Dic3—41no—
473C3⋊Dic3#12112yes—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—41no—
478C3×Dic3AGL(1,ℤ/8)12yescomplemented
479C2×#41—91no—
480C2×#41—91no—
481C22×D4—91no—
482C23×C4—181no—
483AGL(1,ℤ/8)—184no—
484AGL(1,ℤ/8)—184no—
485C2×SD16—31no—
486C2×SD16—31no—
487C2×SD16—31no—
488C2×SD16—91no—
489C2×D8—31no—
490C2×D8—91no—
491C2×D8—91no—
492C2×D8—91no—
493C2×M16—91no—
494C2×M16—91no—
495C4⋊Q8—31no—
496#127—91no—
497#124—31no—
498#124—91no—
499#121—181no—
500#121—181no—
501C4×D4—31no—
502C4×D4—31no—
503C4×D4—91no—
504C4×D4—91no—
505C4×D4—181no—
506C4×D4—181no—
507C4×D4—181no—
508C4×D4—181no—
509C2×C4⋊C4—91no—
510C2×C22⋊C4—181no—
511C2×C42—91no—
512C4⋊C8—31no—
513C4⋊C8—31no—
514C4⋊C8—91no—
515C4⋊C8—91no—
516#103—31no—
517#103—91no—
518#103—91no—
519#103D3211yescharacteristic, complemented
520#102—31no—
521#102—91no—
522#102—91no—
523#102—91no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—31no—
531C22×D3—31no—
532C22×D3—61no—
533C22×D3—64no—
534C22×D3—64no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—121no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—122no—
542C3×Q8—22no—
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—41no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×D4—32no—
551C3×D4—32no—
552C3×D4—61no—
553C3×D4—61no—
554C3×D4—61no—
555C3×D4—61no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—61no—
568C2×C3×C4—122no—
569C2×C3×C4—122no—
570C2×C3×C4C23×D311yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572#67—64no—
573#67—64no—
574#67—122no—
575#67—122no—
576#67—122no—
577C2×Dic3—21no—
578C2×Dic3—31no—
579C2×Dic3—31no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—121no—
584C2×Dic3—122no—
585C2×Dic3—122no—
586C2×Dic3—122no—
587C2×Dic3D3×D411yescharacteristic
588C2×Dic3D3×D411yescharacteristic
589C2×Dic3D3×D411yescharacteristic
590C2×Dic3D3×D411yescharacteristic
591D12—21no—
592D12—21no—
593D12—21no—
594D12—21no—
595D12—62no—
596D12—61no—
597D12—61no—
598D12—61no—
599D12—61no—
600D12—121no—
601D12—122no—
602D12—122no—
603D12—122no—
604D12—124no—
605D12—122no—
606D12—122no—
607D12D3×D412yes—
608D12D3×D412yes—
609C4×D3—32no—
610C4×D3—32no—
611C4×D3—32no—
612C4×D3—32no—
613C4×D3—42no—
614C4×D3—42no—
615C4×D3—62no—
616C4×D3—62no—
617C4×D3—62no—
618C4×D3—62no—
619C4×D3—121no—
620C4×D3—121no—
621C4×D3—122no—
622C4×D3—122no—
623C4×D3—122no—
624C4×D3—124no—
625C4×D3—122no—
626C4×D3—122no—
627C4×D3—122no—
628C4×D3—122no—
629C4×D3—242no—
630Dic6—21no—
631Dic6—21no—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—41no—
635C3×C8—61no—
636C3×C8—61no—
637C3⋊C8—21no—
638C3⋊C8—21no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C2×C32C2×#12111yescharacteristic
643C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
644C2×C32#57511yescharacteristic
645C3⋊D3—22no—
646C3⋊D3—81no—
647C3×D3—42no—
648C3×D3—42no—
649C3×D3—81no—
650C24—181no—
651#41—182no—
652#41—182no—
653#41—182no—
654#41—182no—
655C2×Q8—31no—
656C2×Q8C2×D3211yescharacteristic
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—31no—
660C2×D4—94no—
661C2×D4—91no—
662C2×D4—181no—
663C2×D4—181no—
664C2×D4—181no—
665C2×D4—181no—
666C2×D4—182no—
667C2×D4—181no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—91no—
671C22×C4—91no—
672C22×C4—91no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678C22×C4—364no—
679SD16—62no—
680SD16—62no—
681SD16—62no—
682SD16—182no—
683D8—62no—
684D8—182no—
685D8—182no—
686D8—182no—
687M16—182no—
688M16—182no—
689C2×C8—31no—
690C2×C8—31no—
691C2×C8—91no—
692C2×C8C2×D3211yescharacteristic
693C4⋊C4—61no—
694C4⋊C4—61no—
695C4⋊C4—91no—
696C4⋊C4—181no—
697C4⋊C4C2×D3211yescharacteristic
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C42—31no—
707C42—31no—
708C42—91no—
709C42—91no—
710C22×C3—21no—
711C22×C3—62no—
712C22×C3—62no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3C2×D3×D411yescharacteristic
721C22×C3C2×D3×D411yescharacteristic
722C2×D3—22no—
723C2×D3—22no—
724C2×D3—32no—
725C2×D3—32no—
726C2×D3—41no—
727C2×D3—41no—
728C2×D3—41no—
729C2×D3—41no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—62no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—61no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—128no—
741C2×D3—128no—
742C2×D3—122no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—241no—
750C2×D3—241no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—32no—
754C3×C4—42no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—61no—
760C3×C4—61no—
761C3×C4—61no—
762C3×C4—81no—
763C3×C4—121no—
764C3×C4C2×D3×D411yescharacteristic
765C3×C4C2×D3×D411yescharacteristic
766C3×C4D3×#4111yescharacteristic
767C3×C4D3×#4111yescharacteristic
768Dic3—21no—
769Dic3—21no—
770Dic3—21no—
771Dic3—32no—
772Dic3—32no—
773Dic3—41no—
774Dic3—62no—
775Dic3—121no—
776Dic3—121no—
777Dic3—241no—
778Dic3#91412yescomplemented
779C32#303611yescharacteristic, complemented, Sylow
780C23—61no—
781C23—61no—
782C23—61no—
783C23—91no—
784C23—184no—
785C23—181no—
786C23—362no—
787C23—362no—
788Q8—21no—
789Q8—21no—
790Q8—61no—
791Q8—61no—
792D4—32no—
793D4—32no—
794D4—61no—
795D4—61no—
796D4—61no—
797D4—61no—
798D4—184no—
799D4—181no—
800D4—181no—
801D4—362no—
802D4—362no—
803D4—362no—
804D4—362no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—61no—
812C2×C4—91no—
813C2×C4—92no—
814C2×C4—92no—
815C2×C4—122no—
816C2×C4—122no—
817C2×C4—182no—
818C2×C4—181no—
819C2×C4—362no—
820C2×C4—362no—
821C2×C4—362no—
822C2×C4—361no—
823C2×C4—362no—
824C2×C4—362no—
825C2×C4C22×D3211yescharacteristic
826C8—21no—
827C8—61no—
828C8—61no—
829C8—181no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—122no—
834C2×C3—122no—
835C2×C3—241no—
836C2×C3D3×#12111yescharacteristic
837C2×C3D3×#12111yescharacteristic
838C2×C3C2×#91411yescharacteristic
839C2×C3#576811yescharacteristic
840C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
841C2×C3#577711yescharacteristic
842D3—42no—
843D3—42no—
844D3—62no—
845D3—62no—
846D3—81no—
847D3—122no—
848D3—242no—
849D3—241no—
850D3—241no—
851C22—62no—
852C22—62no—
853C22—92no—
854C22—121no—
855C22—121no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—181no—
862C22—181no—
863C22—368no—
864C22—361no—
865C22—361no—
866C22—361no—
867C22D32×D411yescharacteristic
868C4—32no—
869C4—41no—
870C4—41no—
871C4—61no—
872C4—61no—
873C4—61no—
874C4—92no—
875C4—121no—
876C4—361no—
877C4#6430611yescharacteristic
878C4D32×D411yescharacteristic
879C3—21no—
880C3#8042811yescharacteristic, complemented
881C3#8053411yescharacteristic, complemented
882C2—122no—
883C2—122no—
884C2—182no—
885C2—241no—
886C2—721no—
887C2#1059426511yescharacteristic
888C2D3×#91411yescharacteristic
889C2#1059476311yescharacteristic
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. #10595363C2semidirect
2. C2×#63941C2semidirect
3. C2×#63798C2semidirect
4. #10594605C2semidirect
5. #10592502C2semidirect
6. C3×#4819C2semidirect
7. C3×#4818C2semidirect
8. #10591567C2semidirect
9. #10591564C2semidirect
10. #10590754C2semidirect
11. #10590753C2semidirect
12. #10590666C2semidirect
13. #10590612C2semidirect
14. #10590547C2semidirect
15. #10590534C2semidirect
24. C3×#947C22semidirect
25. C3×#944C22semidirect
34. #63911C22semidirect
44. #63864C22semidirect
51. C32×#103C22semidirect
52. #63662C22semidirect
53. #63648C22semidirect
54. #63636C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#809C22semidirect
59. Dic3⋊(C3⋊C8)C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63566C22semidirect
62. #63563C22semidirect
86. #4819D3semidirect
87. #4818D3semidirect
119. #3802D4semidirect
173. #947C2×D3semidirect
174. #944C2×D3semidirect
228. C3×#103C2×D3semidirect
229. C3×#103C2×D3semidirect
243. Dic3⋊C8C2×D3semidirect
244. Dic3⋊C8C2×D3semidirect
245. #810C2×D3semidirect
249. #809C2×D3semidirect
478. C3×Dic3AGL(1,ℤ/8)semidirect
519. #103D32semidirect
778. Dic3#914semidirect
779. C32#3036semidirect
880. C3#80428semidirect
881. C3#80534semidirect

Maximal subgroups

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

subgroupindex
#105953632
C2×#639412
C2×#637982
#105946052
#105925022
C3×#48192
C3×#48182
#105915672
#105915642
#105907542
#105907532
#105906662
#105906122
#105905472
#105905342
#805343
#804283