Finite Group Databasebeta

← #11865889

Subgroups — #11865889

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
1C3×#5668C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic, complemented
3C2×#63925C211yesmaximal, characteristic, complemented
4C4×D3×D12C211yesmaximal, characteristic, complemented
5#10592756C211yesmaximal, characteristic, complemented
6C3×#5057C211yesmaximal, characteristic, complemented
7#10591565C211yesmaximal, characteristic, complemented
8#10591564C211yesmaximal, characteristic, complemented
9#10591550C211yesmaximal, characteristic, complemented
10#10591429C211yesmaximal, characteristic, complemented
11#10591428C211yesmaximal, characteristic, complemented
12#10591414C211yesmaximal, characteristic, complemented
13#10590356C211yesmaximal, characteristic, complemented
14#10590348C211yesmaximal, characteristic, complemented
15#10590336C211yesmaximal, characteristic, complemented
16#83297—31nomaximal
17#80534—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×C4×D32—21no—
22C32×#124C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24C2×#3753C2211yescharacteristic
25C4×C4⋊(C3⋊D3)C2211yescharacteristic
26C3×#944C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C3×#940C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic
30C3×#884—21no—
31C3×#884—21no—
32C3×#67⋊C4—21no—
33C3×#67⋊C4—21no—
34C3×#875C2211yescharacteristic, complemented
35C3×C4×D12C2211yescharacteristic
36C3×C42×D3C2211yescharacteristic
37#63939—24no—
38#63925—24no—
39D3×(C2×D3)⋊C4—21no—
40C4×#626—21no—
41#63894C2211yescharacteristic
42Dic3×D12C2211yescharacteristic
43D3×C4⋊Dic3C2211yescharacteristic
44#63880—21no—
45C2×#3717C2211yescharacteristic
46C2×#3715C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49C2×#3711C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51#63662C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C3×#532—31no—
64C2×#949—31no—
65C2×#949—31no—
66C2×#914—31no—
67C2×#911—31no—
68#5668D311yescharacteristic, complemented
69C4×D3×D4—31no—
70C2×C4×D12—31no—
71C3×#463—31no—
72#5232—31no—
73#5232—31no—
74#5162—31no—
75#5150—31no—
76#5083—31no—
77#5083—31no—
78#5072—31no—
79#5072—31no—
80#5057—31no—
81#5057—31no—
82#5057—31no—
83#5057—31no—
84#5057—61no—
85#5057D311yescharacteristic, complemented
86#5016—31no—
87#4924—31no—
88#4844—31no—
89#4837—31no—
90#4818—31no—
91#4803—31no—
92#4786—31no—
93#4771—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×#239—22no—
104C3×#239—22no—
105C3×#237—22no—
106C3×#237—22no—
107C2×C3×D12—21no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3D411yescharacteristic
113C2×C3×C4×D3D411yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#626—21no—
117C2×#624—21no—
118C2×D3×Dic3—21no—
119C2×D3×Dic3—21no—
120D3×D12—22no—
121D3×D12D414yescomplemented
122C4×D32—44no—
123C32×C22⋊C4—21no—
124C32×C22⋊C4—21no—
125C32×C42C2311yescharacteristic
126#3755—22no—
127#3753—22no—
128#3752—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#215—22no—
133C3×#213—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×C4×Dic3D411yescharacteristic
141C3×C4×Dic3D411yescharacteristic
142C3×C4×Dic3C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145Dic3⋊Dic3—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148#3717—22no—
149#3715—22no—
150#3714—22no—
151#3713—22no—
152#3711—22no—
153#3711—22no—
154#3036—91noSylow
155C2×C3×#41—31no—
156C2×C3×#41—31no—
157C2×#239C2×D311yescharacteristic
158C2×#237C2×D311yescharacteristic
159C2×D3×D4—31no—
160C22×D12—31no—
161C22×C4×D3—61no—
162C22×C4×D3—61no—
163C2×C3×SD16—31no—
164C2×C3×D8—31no—
165C3×C4⋊Q8—31no—
166C3×#127—31no—
167C3×#124—21no—
168C3×#124—31no—
169C3×#124C2×D311yescharacteristic, complemented
170C3×#124C2×D311yescharacteristic, complemented
171C3×#121—61no—
172C3×#121—61no—
173C3×C4×D4—31no—
174C3×C4×D4—61no—
175C3×C4×D4—61no—
176C2×C3×C42—31no—
177#949—64no—
178#949—64no—
179#944C2×D311yescharacteristic, complemented
180C2×#215—31no—
181C2×#215—31no—
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—61no—
185C2×#215C2×D311yescharacteristic
186#940C2×D311yescharacteristic, complemented
187D4×Dic3—31no—
188C2×#214—31no—
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—61no—
195C2×#213C2×D311yescharacteristic
196C4×#67—61no—
197C2×(C2×D3)⋊C4—61no—
198C2×C4⋊Dic3—31no—
199C2×#208—31no—
200C2×#208—31no—
201#914—64no—
202#911—64no—
203C2×D24—31no—
204C2×#204—31no—
205C2×ΓL(1,𝔽25)—31no—
206C2×ΓL(1,𝔽25)—31no—
207#893—31no—
208D3×C4⋊C4—31no—
209#884—21no—
210#884—21no—
211#67⋊C4—21no—
212#67⋊C4—21no—
213#67⋊C4—61no—
214D3×C22⋊C4—61no—
215#875C2×D311yescharacteristic, complemented
216C4×D12—31no—
217C4×D12—31no—
218C4×D12—31no—
219C4×D12—31no—
220C4×D12—61no—
221C4×D12—61no—
222C4×D12—61no—
223C4×D12C2×D311yescharacteristic
224C42×D3C2×D311yescharacteristic
225C3×C4⋊C8—31no—
226C3×#103—31no—
227C3×#102—31no—
228#835—31no—
229#835—31no—
230#835—31no—
231#835—31no—
232#835—61no—
233#835C2×D311yescharacteristic, complemented
234#832—31no—
235#832—31no—
236#832—31no—
237#832—31no—
238#832—61no—
239#832C2×D311yescharacteristic, complemented
240#821—31no—
241#816—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244#810—31no—
245#809—31no—
246C4⋊(C3⋊C8)—31no—
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—31no—
250C4⋊(C3⋊C8)—61no—
251C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
252C23×C32—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—
262C32×D4—21no—
263C32×D4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2×D411yescharacteristic
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)C2×D412yes—
271C4×C3⋊D3—42no—
272C3×#67—42no—
273C3×#67—42no—
274C3×#67—42no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—42no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—42no—
285C3×D12C2×D412yes—
286C3×C4×D3—22no—
287C3×C4×D3—41no—
288C3×C4×D3—42no—
289C3×C4×D3—42no—
290C3×C4×D3C2×D412yes—
291C3×C4×D3#4112yes—
292C3×Dic6—21no—
293C3×Dic6—21no—
294#626—24no—
295#624—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298C3⋊(C3⋊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—31no—
305C2×C4×D4—91no—
306#463—31no—
307#463—91no—
308#463—91no—
309#463—91no—
310#461—91no—
311#461—91no—
312#459—91no—
313#459—91no—
314#423—91no—
315#417—91no—
316#417—91no—
317C23×D3—61no—
318C23×D3—61no—
319C3×#41—62no—
320C3×#41—62no—
321C3×#41—62no—
322C3×#41—62no—
323C2×C3×Q8—21no—
324C2×C3×Q8—31no—
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×D4—21no—
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C22×C3×C4—61no—
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—21no—
345C2×#67—61no—
346C22×Dic3—21no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349#239—22no—
350#239—22no—
351#237—22no—
352#237—22no—
353D3×D4—34no—
354D3×D4—62no—
355C2×D12—21no—
356C2×D12—31no—
357C2×D12—31no—
358C2×D12—34no—
359C2×D12—61no—
360C2×D12—62no—
361C2×D12—61no—
362C2×D12C22×D311yescharacteristic
363C2×D12C22×D311yescharacteristic
364C2×C4×D3—21no—
365C2×C4×D3—21no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—121no—
373C2×C4×D3—124no—
374C2×C4×D3—124no—
375C2×C4×D3#6711yescharacteristic
376C2×C4×D3#6711yescharacteristic
377C2×C4×D3C22×D311yescharacteristic
378C2×Dic6C22×D311yescharacteristic
379C3×SD16—62no—
380C3×D8—62no—
381C2×C3×C8—31no—
382C2×C3×C8—31no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4—61no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—21no—
390C3×C22⋊C4—41no—
391C3×C22⋊C4—41no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C42—21no—
396C3×C42—31no—
397C3×C42—31no—
398C3×C42—31no—
399C3×C42C22×D311yescharacteristic
400C3×C42C22×D311yescharacteristic
401#217—61no—
402#215—22no—
403#215—62no—
404#215—62no—
405#215—62no—
406#215—62no—
407#215—122no—
408#214—62no—
409#213—22no—
410#213—62no—
411#213—62no—
412#213—62no—
413#213—62no—
414#213—62no—
415#213—122no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—121no—
425C4⋊Dic3—31no—
426C4⋊Dic3—31no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3C22×D311yescharacteristic
430Dic3⋊C4—21no—
431Dic3⋊C4—21no—
432Dic3⋊C4—61no—
433C4×Dic3#6711yescharacteristic
434C4×Dic3#6711yescharacteristic
435C4×Dic3C22×D311yescharacteristic
436#208—62no—
437#208—62no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—61no—
443C2×C3⋊C8—61no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446D24—62no—
447#204—62no—
448ΓL(1,𝔽25)—62no—
449ΓL(1,𝔽25)—62no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32C22×D411yescharacteristic
454C2×C3⋊D3—22no—
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—21no—
468C32×C4—21no—
469C32×C4—41no—
470C32×C4C22×D411yescharacteristic
471C32×C4C2×#4111yescharacteristic
472C3⋊Dic3—41no—
473C3×Dic3—21no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C3×Dic3#12112yes—
477C3×Dic3AGL(1,ℤ/8)12yescomplemented
478C2×#41—31no—
479C2×#41—31no—
480C22×D4—91no—
481C23×C4—181no—
482AGL(1,ℤ/8)—184no—
483AGL(1,ℤ/8)—184no—
484C2×SD16—31no—
485C2×SD16—91no—
486C2×SD16—91no—
487C2×SD16—91no—
488C2×D8—31no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—91no—
492C2×M16—91no—
493C2×M16—91no—
494C4⋊Q8—31no—
495#127—31no—
496#124—31no—
497#124D3211yescharacteristic, complemented
498#121—61no—
499#121—61no—
500C4×D4—31no—
501C4×D4—61no—
502C4×D4—61no—
503C4×D4—91no—
504C4×D4—91no—
505C4×D4—91no—
506C4×D4—181no—
507C4×D4—181no—
508C2×C4⋊C4—91no—
509C2×C22⋊C4—181no—
510C2×C42—31no—
511C4⋊C8—31no—
512C4⋊C8—91no—
513C4⋊C8—91no—
514C4⋊C8—91no—
515#103—31no—
516#103—91no—
517#103—91no—
518#103—91no—
519#102—31no—
520#102—91no—
521#102—91no—
522#102—91no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—31no—
526C23×C3—41no—
527C23×C3—61no—
528C23×C3—61no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—64no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—64no—
535C22×D3—121no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3C2×#6711yescharacteristic
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—21no—
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—32no—
554C3×D4—41no—
555C3×D4—41no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—122no—
560C3×D4—122no—
561C3×D4—122no—
562C3×D4—122no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—31no—
569C2×C3×C4—31no—
570C2×C3×C4—32no—
571C2×C3×C4—32no—
572C2×C3×C4—31no—
573C2×C3×C4—41no—
574C2×C3×C4—62no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—121no—
578C2×C3×C4—122no—
579C2×C3×C4—122no—
580C2×C3×C4—122no—
581C2×C3×C4D3×D411yescharacteristic
582C2×C3×C4D3×D411yescharacteristic
583C2×C3×C4C2×#6711yescharacteristic
584C2×C3×C4C2×#6711yescharacteristic
585C2×C3×C4C23×D311yescharacteristic
586C2×C3×C4C23×D311yescharacteristic
587#67—42no—
588#67—42no—
589#67—42no—
590#67—64no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—42no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—121no—
597C2×Dic3—122no—
598C2×Dic3—122no—
599C2×Dic3C2×#6711yescharacteristic
600C2×Dic3C2×#6711yescharacteristic
601C2×Dic3C2×#6711yescharacteristic
602D12—21no—
603D12—21no—
604D12—21no—
605D12—32no—
606D12—32no—
607D12—42no—
608D12—62no—
609D12—64no—
610D12—61no—
611D12—61no—
612D12—121no—
613D12D3×D412yes—
614C4×D3—22no—
615C4×D3—41no—
616C4×D3—42no—
617C4×D3—42no—
618C4×D3—122no—
619C4×D3—122no—
620C4×D3—122no—
621C4×D3—122no—
622C4×D3—122no—
623C4×D3—122no—
624C4×D3—242no—
625C4×D3D3×D412yes—
626C4×D3#23712yes—
627Dic6—21no—
628Dic6—21no—
629C3×C8—61no—
630C3×C8—61no—
631C3⋊C8—21no—
632C3⋊C8—21no—
633C3⋊C8—61no—
634C3⋊C8—61no—
635C3⋊C8—61no—
636C3⋊C8—61no—
637C3⋊C8—121no—
638C3⋊C8—121no—
639C2×C32—81no—
640C2×C32C2×#12111yescharacteristic
641C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
642C2×C32#57511yescharacteristic
643C3⋊D3—42no—
644C3×D3—22no—
645C3×D3—42no—
646C3×D3—81no—
647C24—181no—
648#41—62no—
649#41—62no—
650#41—62no—
651#41—62no—
652C2×Q8—31no—
653C2×Q8C2×D3211yescharacteristic
654C2×D4—31no—
655C2×D4—31no—
656C2×D4—61no—
657C2×D4—61no—
658C2×D4—61no—
659C2×D4—61no—
660C2×D4—94no—
661C2×D4—91no—
662C2×D4—182no—
663C2×D4—181no—
664C2×D4C2×D3211yescharacteristic
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—181no—
672C22×C4—181no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4—364no—
676SD16—62no—
677SD16—182no—
678SD16—182no—
679SD16—182no—
680D8—62no—
681D8—182no—
682D8—182no—
683D8—182no—
684M16—182no—
685M16—182no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—91no—
689C2×C8—91no—
690C4⋊C4—31no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—91no—
694C4⋊C4—181no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C42—31no—
704C42—31no—
705C42—31no—
706C42C2×D3211yescharacteristic
707C22×C3—21no—
708C22×C3—32no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—62no—
718C22×C3—81no—
719C22×C3—81no—
720C22×C3—81no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3C2×D3×D411yescharacteristic
727C22×C3C22×#6711yescharacteristic
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—22no—
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—128no—
740C2×D3—128no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—241no—
746C2×D3—241no—
747C2×D3#93812yes—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—32no—
755C3×C4—32no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—41no—
760C3×C4—61no—
761C3×C4—81no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4C2×D3×D411yescharacteristic
765C3×C4C2×D3×D411yescharacteristic
766C3×C4C2×#23711yescharacteristic
767C3×C4D3×#4111yescharacteristic
768Dic3—21no—
769Dic3—41no—
770Dic3—41no—
771Dic3—121no—
772Dic3—121no—
773Dic3—241no—
774Dic3#93812yes—
775Dic3#94912yescomplemented
776C32#303611yescharacteristic, complemented, Sylow
777C23—21no—
778C23—31no—
779C23—61no—
780C23—61no—
781C23—184no—
782C23—181no—
783C23—362no—
784C23—362no—
785Q8—21no—
786Q8—21no—
787Q8—61no—
788Q8—61no—
789D4—21no—
790D4—21no—
791D4—32no—
792D4—61no—
793D4—61no—
794D4—61no—
795D4—92no—
796D4—122no—
797D4—122no—
798D4—122no—
799D4—122no—
800D4—184no—
801D4—181no—
802C2×C4—21no—
803C2×C4—31no—
804C2×C4—31no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—31no—
808C2×C4—62no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—121no—
812C2×C4—122no—
813C2×C4—122no—
814C2×C4—122no—
815C2×C4—181no—
816C2×C4—362no—
817C2×C4—362no—
818C2×C4—362no—
819C2×C4—362no—
820C2×C4D3×#6711yescharacteristic
821C2×C4D3×#6711yescharacteristic
822C2×C4C22×D3211yescharacteristic
823C8—61no—
824C8—61no—
825C8—181no—
826C8—181no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—62no—
831C2×C3—81no—
832C2×C3—81no—
833C2×C3—122no—
834C2×C3—161no—
835C2×C3—241no—
836C2×C3D3×#12111yescharacteristic
837C2×C3#576811yescharacteristic
838C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
839C2×C3C2×#93811yescharacteristic
840C2×C3C2×#94911yescharacteristic
841C2×C3#582211yescharacteristic
842D3—22no—
843D3—42no—
844D3—81no—
845D3—122no—
846D3—122no—
847D3—242no—
848C22—32no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—61no—
853C22—61no—
854C22—62no—
855C22—121no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—182no—
861C22—368no—
862C22—361no—
863C22—361no—
864C22C2×D3×#6711yescharacteristic
865C4—21no—
866C4—21no—
867C4—32no—
868C4—32no—
869C4—41no—
870C4—61no—
871C4—121no—
872C4—121no—
873C4—361no—
874C4D32×D411yescharacteristic
875C4D3×#23711yescharacteristic
876C3—21no—
877C3#8053411yescharacteristic, complemented
878C3#8329711yescharacteristic, complemented
879C2—62no—
880C2—81no—
881C2—122no—
882C2—241no—
883C2—362no—
884C2D3×#93811yescharacteristic
885C2D3×#94911yescharacteristic
886C2#1059545311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
hypercenter#124D32
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#5668C2semidirect
2. C2×#63939C2semidirect
3. C2×#63925C2semidirect
4. C4×D3×D12C2semidirect
5. #10592756C2semidirect
6. C3×#5057C2semidirect
7. #10591565C2semidirect
8. #10591564C2semidirect
9. #10591550C2semidirect
10. #10591429C2semidirect
11. #10591428C2semidirect
12. #10591414C2semidirect
13. #10590356C2semidirect
14. #10590348C2semidirect
15. #10590336C2semidirect
22. C32×#124C22semidirect
26. C3×#944C22semidirect
28. C3×#940C22semidirect
34. C3×#875C22semidirect
51. #63662C22semidirect
52. #63659C22semidirect
53. C4⋊(C3⋊(C3⋊C8))C22semidirect
54. C3×#835C22semidirect
55. C3×#832C22semidirect
56. C3×C4⋊(C3⋊C8)C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
68. #5668D3semidirect
85. #5057D3semidirect
121. D3×D12D4semidirect
169. C3×#124C2×D3semidirect
170. C3×#124C2×D3semidirect
179. #944C2×D3semidirect
186. #940C2×D3semidirect
215. #875C2×D3semidirect
233. #835C2×D3semidirect
239. #832C2×D3semidirect
251. C4⋊(C3⋊C8)C2×D3semidirect
477. C3×Dic3AGL(1,ℤ/8)semidirect
497. #124D32semidirect
775. Dic3#949semidirect
776. C32#3036semidirect
877. C3#80534semidirect
878. C3#83297semidirect

Maximal subgroups

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

subgroupindex
C3×#56682
C2×#639392
C2×#639252
C4×D3×D122
#105927562
C3×#50572
#105915652
#105915642
#105915502
#105914292
#105914282
#105914142
#105903562
#105903482
#105903362
#832973
#805343