Finite Group Databasebeta

← #11863939

Subgroups — #11863939

Order 1152.

2082 conjugacy classes of subgroups.

The subgroup lattice has 1115 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×D4C211yesmaximal, characteristic, complemented
2C2×C3×#914C211yesmaximal, characteristic, complemented
3#10595424C211yesmaximal, characteristic, complemented
4C2×#63939C211yesmaximal, characteristic, complemented
5#10592868C211yesmaximal, characteristic, complemented
6C3×#5169C211yesmaximal, characteristic, complemented
7#10591652C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591456C211yesmaximal, characteristic, complemented
10#10591447C211yesmaximal, characteristic, complemented
11#10591421C211yesmaximal, characteristic, complemented
12#10590945C211yesmaximal, characteristic, complemented
13#10590944C211yesmaximal, characteristic, complemented
14#10590939C211yesmaximal, characteristic, complemented
15#10590936C211yesmaximal, characteristic, complemented
16#83944—31nomaximal
17#80146—31nomaximal
18C23×D32—21no—
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic, complemented
21C2×C3×D3×D4C2211yescharacteristic
22C2×C3×D3×D4C2211yescharacteristic
23C2×#3811—21no—
24C2×D3×#67—21no—
25C2×D3×#67—21no—
26D32×D4—24no—
27D32×D4—24no—
28C2×#3802C2211yescharacteristic
29C2×D3×D12C2211yescharacteristic
30C2×D3×D12C2211yescharacteristic
31C2×C4×D32C2211yescharacteristic
32C2×C32×SD16C2211yescharacteristic, complemented
33#64155C2211yescharacteristic, complemented
34C2×#3755C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic, complemented
36C2×C3×#215C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C2×C3×#213C2211yescharacteristic, complemented
39C3×#914—24no—
40C2×C3×D24C2211yescharacteristic, complemented
41C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
42#63939—24no—
43#63922—21no—
44#63916C2211yescharacteristic, complemented
45#63908C2211yescharacteristic, complemented
46#63904—21no—
47#63884—21no—
48#63879—21no—
49#63841C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×#3713C2211yescharacteristic, complemented
52C2×#3711C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63647C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C22×D3×D4—31no—
66C22×D3×D4—31no—
67C2×C3×AGL(1,ℤ/8)—31no—
68#5828—31no—
69C2×#949—31no—
70C2×#914—31no—
71C2×#914D311yescharacteristic, complemented
72#5627—31no—
73C3×#450—31no—
74#5217—31no—
75#5215—31no—
76#5169—31no—
77#5169—31no—
78#5169—31no—
79#5169—31no—
80#5169—31no—
81#5169—61no—
82#5169D311yescharacteristic, complemented
83#5156—31no—
84#5156—31no—
85#5156—31no—
86#5156—31no—
87#5131—31no—
88#5126—31no—
89#5046—31no—
90#4773—31no—
91#4773—31no—
92#4770—31no—
93#4770—31no—
94#4732—31no—
95#4726—31no—
96C23×C3⋊D3—21no—
97C23×C3×D3—21no—
98C23×C3×D3—21no—
99C22×D32—28no—
100C22×D32—21no—
101C22×D32—21no—
102C22×D32—21no—
103C22×D32—44no—
104C22×D32—44no—
105C22×D32D411yescharacteristic
106C2×C32×Q8C2311yescharacteristic, complemented
107C2×C32×D4C2311yescharacteristic
108C2×#638—21no—
109D4×C3⋊D3—22no—
110D4×C3⋊D3—22no—
111C2×C4⋊(C3⋊D3)C2311yescharacteristic
112C2×C4×C3⋊D3C2311yescharacteristic
113C2×C3×#67—21no—
114C2×C3×#67—21no—
115C3×#239—22no—
116C3×#239—22no—
117C3×D3×D4—22no—
118C3×D3×D4—22no—
119C3×D3×D4—22no—
120C3×D3×D4D414yescomplemented
121C2×C3×D12—21no—
122C2×C3×D12C2311yescharacteristic
123C2×C3×D12C2311yescharacteristic
124C2×C3×D12C2311yescharacteristic, complemented
125C2×C3×C4×D3—21no—
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×C4×D3C2311yescharacteristic
128#3811—28no—
129D3×#67—28no—
130D3×#67—28no—
131C2×#626—21no—
132C2×#626—21no—
133C2×#626—21no—
134C2×#625—21no—
135C2×#625—21no—
136C2×#624D411yescharacteristic
137C2×D3×Dic3D411yescharacteristic
138C2×D3×Dic3D411yescharacteristic
139#3802—22no—
140#3802—22no—
141D3×D12—22no—
142D3×D12—22no—
143D3×D12—22no—
144D3×D12D414yescomplemented
145C4×D32—22no—
146C4×D32—22no—
147C32×SD16—22no—
148C2×C32×C8C2311yescharacteristic, complemented
149#3755—22no—
150#3752—21no—
151C4⋊(C3⋊Dic3)C2311yescharacteristic, complemented
152#3750—21no—
153C2×C3⋊(C3⋊C8)C2311yescharacteristic, complemented
154C3×#215—22no—
155C3×#215—22no—
156C3×#213—22no—
157C3×(C2×D3)⋊C4—21no—
158C3×C4⋊Dic3C2311yescharacteristic, complemented
159C3×Dic3⋊C4—21no—
160C2×C3×C3⋊C8C2311yescharacteristic, complemented
161C2×C3×C3⋊C8C2311yescharacteristic, complemented
162C3×D24—22no—
163C3×ΓL(1,𝔽25)—22no—
164(C2×D3)⋊Dic3—21no—
165(C2×D3)⋊Dic3—21no—
166(C2×D3)⋊Dic3—21no—
167Dic32—21no—
168#3714—22no—
169#3713—22no—
170#3711—22no—
171#3003—91noSylow
172C24×D3—61no—
173C24×D3—61no—
174C2×C3×#41—31no—
175C22×C3×D4—31no—
176C22×C3×D4—31no—
177C22×#67—61no—
178C22×#67—61no—
179C2×#239C2×D311yescharacteristic, complemented
180C2×D3×D4—31no—
181C2×D3×D4—31no—
182C2×D3×D4—31no—
183C2×D3×D4—31no—
184C2×D3×D4—31no—
185C2×D3×D4—31no—
186C2×D3×D4—61no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×D3×D4—64no—
192C2×D3×D4—64no—
193C2×D3×D4—64no—
194C2×D3×D4—64no—
195C2×D3×D4C2×D311yescharacteristic
196C2×D3×D4C2×D311yescharacteristic
197C22×D12—31no—
198C22×D12—31no—
199C22×C4×D3—31no—
200C22×C4×D3—31no—
201C3×AGL(1,ℤ/8)—64no—
202C2×C3×SD16—21no—
203C2×C3×SD16—31no—
204C2×C3×SD16—31no—
205C2×C3×SD16C2×D311yescharacteristic, complemented
206C2×C3×SD16C2×D311yescharacteristic, complemented
207C2×C3×D8—31no—
208C2×C3×D8—31no—
209C2×C3×M16—31no—
210C3×C22⋊Q8—31no—
211#949—64no—
212#946—31no—
213#946—31no—
214#946—61no—
215#946C2×D311yescharacteristic, complemented
216C2×#215—31no—
217C2×#215—31no—
218C2×#215—61no—
219C2×#215C2×D311yescharacteristic, complemented
220C2×#215C2×D311yescharacteristic, complemented
221#938—31no—
222#938—31no—
223#937—61no—
224#935—61no—
225C2×#213—31no—
226C2×#213—31no—
227C2×#213—31no—
228C2×#213C2×D311yescharacteristic, complemented
229#930—31no—
230C4×#67—61no—
231C4×#67—61no—
232#926—31no—
233C2×#208—31no—
234#914—24no—
235#914—64no—
236C2×D24—31no—
237C2×D24C2×D311yescharacteristic, complemented
238C2×ΓL(1,𝔽25)—31no—
239C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
240#895—31no—
241#894—61no—
242#893—61no—
243#892—31no—
244#882—61no—
245#67⋊C4—61no—
246C3×#102—31no—
247C3×#102—31no—
248C3×C22⋊C8—31no—
249#832—31no—
250#832—31no—
251#832—31no—
252#832—31no—
253#832—31no—
254#832—61no—
255#832C2×D311yescharacteristic, complemented
256#830—31no—
257#821—31no—
258#821—31no—
259#821—31no—
260#821—31no—
261#821—31no—
262#821—61no—
263#821C2×D311yescharacteristic, complemented
264(C2×D3)⋊C8—31no—
265(C2×D3)⋊C8—31no—
266(C2×D3)⋊C8—31no—
267(C2×D3)⋊C8—31no—
268(C2×D3)⋊C8—31no—
269(C2×D3)⋊C8—61no—
270(C2×D3)⋊C8C2×D311yescharacteristic, complemented
271#809—31no—
272#809—31no—
273C23×C32—21no—
274C22×C3⋊D3—24no—
275C22×C3⋊D3—21no—
276C22×C3⋊D3—42no—
277C22×C3⋊D3—42no—
278C22×C3⋊D3C2×D411yescharacteristic
279C22×C3×D3—24no—
280C22×C3×D3—21no—
281C22×C3×D3—21no—
282C22×C3×D3—24no—
283C22×C3×D3—21no—
284C22×C3×D3—42no—
285C22×C3×D3—42no—
286C22×C3×D3—42no—
287C22×C3×D3—42no—
288C22×C3×D3C2×D411yescharacteristic
289C22×C3×D3C2×D411yescharacteristic
290C2×D32—22no—
291C2×D32—22no—
292C2×D32—22no—
293C2×D32—24no—
294C2×D32—24no—
295C2×D32—24no—
296C2×D32—432no—
297C2×D32—42no—
298C2×D32—42no—
299C2×D32—42no—
300C2×D32—42no—
301C2×D32—42no—
302C2×D32—42no—
303C32×Q8—21no—
304C32×Q8—21no—
305C32×D4—21no—
306C32×D4C2×D412yes—
307C2×C32×C4—21no—
308C2×C32×C4C2411yescharacteristic
309#638—24no—
310C2×C3⋊Dic3—21no—
311C2×C3⋊Dic3C2×D411yescharacteristic
312C4⋊(C3⋊D3)—21no—
313C4⋊(C3⋊D3)C2×D412yes—
314C4×C3⋊D3—21no—
315C4×C3⋊D3—21no—
316C3×#67—24no—
317C3×#67—24no—
318C2×C3×Dic3—21no—
319C2×C3×Dic3C2×D411yescharacteristic
320C2×C3×Dic3C2×D411yescharacteristic
321C3×D12—21no—
322C3×D12—21no—
323C3×D12—21no—
324C3×D12—21no—
325C3×D12—42no—
326C3×D12C2×D412yes—
327C3×D12C2×D412yes—
328C3×C4×D3—21no—
329C3×C4×D3—21no—
330C3×C4×D3—42no—
331C3×C4×D3C2×D412yes—
332C3×C4×D3C2×D412yes—
333#626—24no—
334#626—24no—
335#626—42no—
336#625—24no—
337#625—42no—
338#624—22no—
339D3×Dic3—22no—
340D3×Dic3—22no—
341C32×C8—21no—
342C3⋊(C3⋊C8)—21no—
343C3×C3⋊C8—21no—
344C3×C3⋊C8—21no—
345C23×D4—91no—
346C2×AGL(1,ℤ/8)—31no—
347C2×AGL(1,ℤ/8)—91no—
348#525—91no—
349#450—31no—
350#450—91no—
351#450—91no—
352#450—91no—
353#447—91no—
354#447—91no—
355#447—91no—
356#447—91no—
357#418—91no—
358#418—91no—
359#407—91no—
360C24×C3—61no—
361C24×C3—61no—
362C23×D3—21no—
363C23×D3—21no—
364C23×D3—31no—
365C23×D3—31no—
366C23×D3—61no—
367C23×D3—61no—
368C23×D3—61no—
369C23×D3—61no—
370C23×D3—68no—
371C23×D3—68no—
372C23×D3—61no—
373C23×D3—61no—
374C23×D3—61no—
375C23×D3—61no—
376C23×D3—121no—
377C23×D3—124no—
378C23×D3—124no—
379C23×D3—124no—
380C23×D3—124no—
381C3×#41—62no—
382C3×#41—62no—
383C2×C3×Q8—21no—
384C2×C3×Q8C22×D311yescharacteristic, complemented
385C2×C3×Q8C22×D311yescharacteristic, complemented
386C2×C3×D4—21no—
387C2×C3×D4—34no—
388C2×C3×D4—31no—
389C2×C3×D4—31no—
390C2×C3×D4—31no—
391C2×C3×D4—61no—
392C2×C3×D4—62no—
393C2×C3×D4—61no—
394C2×C3×D4—61no—
395C2×C3×D4—62no—
396C2×C3×D4—62no—
397C2×C3×D4C22×D311yescharacteristic
398C2×C3×D4C22×D311yescharacteristic
399C22×C3×C4—31no—
400C22×C3×C4—31no—
401C22×C3×C4—61no—
402C2×#67—21no—
403C2×#67—21no—
404C2×#67—61no—
405C2×#67—61no—
406C2×#67—61no—
407C2×#67—61no—
408C2×#67—61no—
409C2×#67—68no—
410C2×#67—68no—
411C2×#67—61no—
412C2×#67—61no—
413C2×#67—61no—
414C2×#67—61no—
415C2×#67—121no—
416C22×Dic3—31no—
417C22×Dic3—31no—
418#239—22no—
419#239—22no—
420D3×D4—22no—
421D3×D4—22no—
422D3×D4—22no—
423D3×D4—34no—
424D3×D4—62no—
425D3×D4—62no—
426D3×D4—62no—
427D3×D4—62no—
428D3×D4—62no—
429D3×D4—62no—
430D3×D4—68no—
431D3×D4—68no—
432D3×D4—68no—
433D3×D4—68no—
434D3×D4—62no—
435D3×D4—62no—
436D3×D4—62no—
437D3×D4—62no—
438D3×D4—62no—
439D3×D4—122no—
440D3×D4—122no—
441D3×D4#6714yescomplemented
442C2×D12—21no—
443C2×D12—31no—
444C2×D12—31no—
445C2×D12—34no—
446C2×D12—61no—
447C2×D12—62no—
448C2×D12—62no—
449C2×D12—61no—
450C2×D12—61no—
451C2×D12—62no—
452C2×D12—61no—
453C2×D12C22×D311yescharacteristic
454C2×D12C22×D311yescharacteristic
455C2×D12C22×D311yescharacteristic, complemented
456C2×C4×D3—21no—
457C2×C4×D3—31no—
458C2×C4×D3—31no—
459C2×C4×D3—31no—
460C2×C4×D3—31no—
461C2×C4×D3—31no—
462C2×C4×D3—31no—
463C2×C4×D3—61no—
464C2×C4×D3—62no—
465C2×C4×D3—62no—
466C2×C4×D3—62no—
467C2×C4×D3—62no—
468C2×C4×D3C22×D311yescharacteristic
469C2×C4×D3C22×D311yescharacteristic
470C3×SD16—22no—
471C3×SD16—22no—
472C3×SD16—42no—
473C3×SD16—62no—
474C3×SD16—62no—
475C3×D8—62no—
476C3×D8—62no—
477C3×M16—62no—
478C2×C3×C8—21no—
479C2×C3×C8—31no—
480C2×C3×C8—31no—
481C2×C3×C8C22×D311yescharacteristic, complemented
482C2×C3×C8C22×D311yescharacteristic, complemented
483C3×C4⋊C4—31no—
484C3×C4⋊C4—61no—
485C3×C22⋊C4—61no—
486#217—61no—
487#217—61no—
488#217—61no—
489#215—22no—
490#215—22no—
491#215—62no—
492#215—62no—
493#215—122no—
494#213—22no—
495#213—62no—
496#213—62no—
497#213—62no—
498(C2×D3)⋊C4—21no—
499(C2×D3)⋊C4—61no—
500(C2×D3)⋊C4—61no—
501(C2×D3)⋊C4—61no—
502(C2×D3)⋊C4—61no—
503(C2×D3)⋊C4—61no—
504(C2×D3)⋊C4—121no—
505C4⋊Dic3—31no—
506C4⋊Dic3—31no—
507C4⋊Dic3—61no—
508C4⋊Dic3C22×D311yescharacteristic, complemented
509Dic3⋊C4—21no—
510Dic3⋊C4—61no—
511Dic3⋊C4—61no—
512Dic3⋊C4—121no—
513C4×Dic3—61no—
514C4×Dic3—61no—
515#208—62no—
516C2×C3⋊C8—31no—
517C2×C3⋊C8—31no—
518C2×C3⋊C8—61no—
519C2×C3⋊C8C22×D311yescharacteristic, complemented
520C2×C3⋊C8C22×D311yescharacteristic, complemented
521D24—22no—
522D24—62no—
523ΓL(1,𝔽25)—22no—
524ΓL(1,𝔽25)—62no—
525C22×C32—22no—
526C22×C32—41no—
527C22×C32—41no—
528C22×C32C22×D411yescharacteristic
529C2×C3⋊D3—21no—
530C2×C3⋊D3—21no—
531C2×C3⋊D3—22no—
532C2×C3⋊D3—48no—
533C2×C3⋊D3—41no—
534C2×C3⋊D3—41no—
535C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
536C2×C3×D3—21no—
537C2×C3×D3—21no—
538C2×C3×D3—21no—
539C2×C3×D3—21no—
540C2×C3×D3—22no—
541C2×C3×D3—22no—
542C2×C3×D3—48no—
543C2×C3×D3—48no—
544C2×C3×D3—41no—
545C2×C3×D3—41no—
546C2×C3×D3—41no—
547C2×C3×D3—41no—
548C2×C3×D3—41no—
549C2×C3×D3—41no—
550C2×C3×D3—41no—
551C2×C3×D3#12012yes—
552C2×C3×D3AGL(1,ℤ/8)12yescomplemented
553D32—28no—
554D32—48no—
555D32—48no—
556D32—48no—
557C32×C4—41no—
558C32×C4C22×D411yescharacteristic
559C32×C4C22×D411yescharacteristic
560C3⋊Dic3—21no—
561C3⋊Dic3—41no—
562C3×Dic3—21no—
563C3×Dic3—41no—
564C3×Dic3#12012yes—
565C25—181no—
566C2×#41—31no—
567C22×D4—31no—
568C22×D4—31no—
569C22×D4—91no—
570C22×D4—91no—
571C22×D4—91no—
572C22×D4—91no—
573C22×D4—181no—
574C22×D4—181no—
575C22×D4—181no—
576C22×D4—184no—
577C22×D4—184no—
578C23×C4—91no—
579AGL(1,ℤ/8)—64no—
580AGL(1,ℤ/8)—184no—
581C2×SD16—31no—
582C2×SD16—31no—
583C2×SD16—91no—
584C2×SD16D3211yescharacteristic, complemented
585C2×D8—31no—
586C2×D8—31no—
587C2×D8—91no—
588C2×D8—91no—
589C2×M16—31no—
590C2×M16—91no—
591#123—181no—
592C22⋊Q8—31no—
593C22⋊Q8—91no—
594#121—91no—
595#121—91no—
596#120—181no—
597C4×D4—181no—
598C4×D4—181no—
599#117—91no—
600#102—31no—
601#102—31no—
602#102—91no—
603#102—91no—
604#102—91no—
605#102—91no—
606#102—91no—
607#102—91no—
608C22⋊C8—31no—
609C22⋊C8—91no—
610C22⋊C8—91no—
611C22⋊C8—91no—
612C23×C3—21no—
613C23×C3—21no—
614C23×C3—31no—
615C23×C3—31no—
616C23×C3—41no—
617C23×C3—64no—
618C23×C3—64no—
619C23×C3—61no—
620C23×C3—61no—
621C23×C3—61no—
622C23×C3—122no—
623C23×C3—122no—
624C23×C3—122no—
625C23×C3—122no—
626C22×D3—24no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—24no—
630C22×D3—21no—
631C22×D3—31no—
632C22×D3—31no—
633C22×D3—42no—
634C22×D3—42no—
635C22×D3—42no—
636C22×D3—42no—
637C22×D3—61no—
638C22×D3—62no—
639C22×D3—62no—
640C22×D3—62no—
641C22×D3—62no—
642C22×D3—64no—
643C22×D3—64no—
644C22×D3—64no—
645C22×D3—64no—
646C22×D3—64no—
647C22×D3—62no—
648C22×D3—62no—
649C22×D3—64no—
650C22×D3—64no—
651C22×D3—61no—
652C22×D3—61no—
653C22×D3—64no—
654C22×D3—121no—
655C22×D3—124no—
656C22×D3—122no—
657C22×D3—122no—
658C22×D3—122no—
659C22×D3—122no—
660C22×D3—122no—
661C22×D3—122no—
662C22×D3—122no—
663C22×D3—1232no—
664C22×D3—1232no—
665C22×D3—122no—
666C22×D3—122no—
667C22×D3—122no—
668C22×D3—122no—
669C22×D3—122no—
670C22×D3—122no—
671C22×D3—122no—
672C22×D3—122no—
673C22×D3—122no—
674C22×D3—242no—
675C22×D3—242no—
676C22×D3D3×D411yescharacteristic
677C22×D3D3×D411yescharacteristic
678C3×Q8—21no—
679C3×Q8—21no—
680C3×Q8—21no—
681C3×Q8—21no—
682C3×Q8—41no—
683C3×Q8—41no—
684C3×D4—21no—
685C3×D4—21no—
686C3×D4—22no—
687C3×D4—32no—
688C3×D4—32no—
689C3×D4—41no—
690C3×D4—64no—
691C3×D4—64no—
692C3×D4—61no—
693C3×D4—61no—
694C3×D4—61no—
695C3×D4—61no—
696C3×D4—122no—
697C3×D4D3×D412yes—
698C3×D4C2×#6712yes—
699C2×C3×C4—21no—
700C2×C3×C4—21no—
701C2×C3×C4—21no—
702C2×C3×C4—31no—
703C2×C3×C4—32no—
704C2×C3×C4—32no—
705C2×C3×C4—31no—
706C2×C3×C4—41no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—122no—
711C2×C3×C4C23×D311yescharacteristic
712C2×C3×C4C23×D311yescharacteristic
713#67—24no—
714#67—24no—
715#67—64no—
716#67—64no—
717#67—64no—
718#67—64no—
719#67—64no—
720#67—64no—
721#67—124no—
722#67—122no—
723#67—122no—
724#67—122no—
725C2×Dic3—21no—
726C2×Dic3—31no—
727C2×Dic3—31no—
728C2×Dic3—61no—
729C2×Dic3—62no—
730C2×Dic3—62no—
731C2×Dic3—61no—
732C2×Dic3—61no—
733C2×Dic3—121no—
734C2×Dic3D3×D411yescharacteristic
735C2×Dic3D3×D411yescharacteristic
736D12—21no—
737D12—21no—
738D12—21no—
739D12—21no—
740D12—32no—
741D12—32no—
742D12—42no—
743D12—62no—
744D12—64no—
745D12—64no—
746D12—61no—
747D12—61no—
748D12—121no—
749D12—122no—
750D12D3×D412yes—
751D12C2×#6712yes—
752C4×D3—21no—
753C4×D3—21no—
754C4×D3—42no—
755C4×D3—62no—
756C4×D3—62no—
757C4×D3—62no—
758C4×D3—61no—
759C4×D3—61no—
760C4×D3—61no—
761C4×D3—61no—
762C4×D3—62no—
763C4×D3—121no—
764C4×D3—121no—
765C4×D3D3×D412yes—
766C4×D3C2×#6712yes—
767C3×C8—21no—
768C3×C8—21no—
769C3×C8—41no—
770C3×C8—61no—
771C3×C8—61no—
772C3⋊C8—21no—
773C3⋊C8—21no—
774C3⋊C8—61no—
775C3⋊C8—61no—
776C3⋊C8—121no—
777C2×C32—42no—
778C2×C32C2×#12011yescharacteristic
779C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
780C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
781C3⋊D3—22no—
782C3⋊D3—42no—
783C3×D3—22no—
784C3×D3—22no—
785C3×D3—42no—
786C3×D3—42no—
787C3×D3—81no—
788C24—61no—
789C24—61no—
790C24—91no—
791C24—181no—
792C24—181no—
793C24—181no—
794C24—181no—
795C24—188no—
796C24—364no—
797C24—364no—
798#41—62no—
799#41—62no—
800C2×Q8C2×D3211yescharacteristic, complemented
801C2×D4—34no—
802C2×D4—31no—
803C2×D4—31no—
804C2×D4—31no—
805C2×D4—61no—
806C2×D4—62no—
807C2×D4—61no—
808C2×D4—61no—
809C2×D4—62no—
810C2×D4—62no—
811C2×D4—94no—
812C2×D4—91no—
813C2×D4—182no—
814C2×D4—181no—
815C2×D4—181no—
816C2×D4—182no—
817C2×D4—182no—
818C2×D4—181no—
819C2×D4—181no—
820C2×D4—181no—
821C2×D4—182no—
822C2×D4—182no—
823C2×D4—182no—
824C2×D4—188no—
825C2×D4—188no—
826C2×D4—188no—
827C2×D4—182no—
828C2×D4—181no—
829C2×D4C2×D3211yescharacteristic
830C22×C4—31no—
831C22×C4—31no—
832C22×C4—61no—
833C22×C4—91no—
834C22×C4—91no—
835C22×C4—91no—
836C22×C4—91no—
837C22×C4—182no—
838C22×C4—182no—
839SD16—22no—
840SD16—62no—
841SD16—62no—
842SD16—182no—
843D8—62no—
844D8—62no—
845D8—182no—
846D8—182no—
847M16—62no—
848M16—182no—
849C2×C8—31no—
850C2×C8—31no—
851C2×C8—91no—
852C2×C8C2×D3211yescharacteristic, complemented
853C4⋊C4—31no—
854C4⋊C4—61no—
855C4⋊C4—91no—
856C4⋊C4—181no—
857C22⋊C4—61no—
858C22⋊C4—181no—
859C22⋊C4—181no—
860C22⋊C4—181no—
861C22⋊C4—181no—
862C42—181no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—21no—
866C22×C3—32no—
867C22×C3—32no—
868C22×C3—42no—
869C22×C3—41no—
870C22×C3—41no—
871C22×C3—41no—
872C22×C3—41no—
873C22×C3—61no—
874C22×C3—61no—
875C22×C3—61no—
876C22×C3—61no—
877C22×C3—62no—
878C22×C3—62no—
879C22×C3—81no—
880C22×C3—81no—
881C22×C3—128no—
882C22×C3—128no—
883C22×C3—121no—
884C22×C3—121no—
885C22×C3—121no—
886C22×C3—121no—
887C22×C3—121no—
888C22×C3—121no—
889C22×C3—121no—
890C22×C3C2×D3×D411yescharacteristic
891C22×C3C2×D3×D411yescharacteristic
892C2×D3—21no—
893C2×D3—21no—
894C2×D3—21no—
895C2×D3—21no—
896C2×D3—22no—
897C2×D3—22no—
898C2×D3—32no—
899C2×D3—32no—
900C2×D3—48no—
901C2×D3—48no—
902C2×D3—41no—
903C2×D3—41no—
904C2×D3—41no—
905C2×D3—41no—
906C2×D3—41no—
907C2×D3—41no—
908C2×D3—41no—
909C2×D3—62no—
910C2×D3—68no—
911C2×D3—68no—
912C2×D3—61no—
913C2×D3—61no—
914C2×D3—61no—
915C2×D3—61no—
916C2×D3—62no—
917C2×D3—62no—
918C2×D3—121no—
919C2×D3—121no—
920C2×D3—122no—
921C2×D3—128no—
922C2×D3—128no—
923C2×D3—128no—
924C2×D3—128no—
925C2×D3—128no—
926C2×D3—128no—
927C2×D3—128no—
928C2×D3—128no—
929C2×D3—121no—
930C2×D3—121no—
931C2×D3—121no—
932C2×D3—121no—
933C2×D3—248no—
934C2×D3—241no—
935C2×D3—241no—
936C2×D3#91412yescomplemented
937C2×D3#93712yes—
938C3×C4—21no—
939C3×C4—21no—
940C3×C4—32no—
941C3×C4—41no—
942C3×C4—41no—
943C3×C4—61no—
944C3×C4—81no—
945C3×C4—121no—
946C3×C4C2×D3×D411yescharacteristic
947C3×C4C2×D3×D411yescharacteristic
948C3×C4C2×D3×D411yescharacteristic
949C3×C4C22×#6711yescharacteristic
950Dic3—21no—
951Dic3—41no—
952Dic3—61no—
953Dic3—61no—
954Dic3—121no—
955Dic3—121no—
956Dic3—121no—
957Dic3—241no—
958Dic3#93712yes—
959C32#300311yescharacteristic, complemented, Sylow
960C23—21no—
961C23—31no—
962C23—31no—
963C23—64no—
964C23—64no—
965C23—61no—
966C23—61no—
967C23—61no—
968C23—91no—
969C23—122no—
970C23—122no—
971C23—122no—
972C23—122no—
973C23—184no—
974C23—182no—
975C23—182no—
976C23—184no—
977C23—182no—
978C23—184no—
979C23—184no—
980C23—181no—
981C23—362no—
982C23—362no—
983C23—362no—
984C23—362no—
985C23—362no—
986C23—362no—
987C23—362no—
988C23—3632no—
989C23—362no—
990Q8—21no—
991Q8—21no—
992D4—21no—
993D4—32no—
994D4—32no—
995D4—64no—
996D4—64no—
997D4—61no—
998D4—61no—
999D4—61no—
1000D4—61no—
1001D4—92no—
1002D4—122no—
1003D4—184no—
1004D4—184no—
1005D4—184no—
1006D4—184no—
1007D4—181no—
1008D4—362no—
1009D4—362no—
1010D4D3×#6712yes—
1011C2×C4—21no—
1012C2×C4—31no—
1013C2×C4—32no—
1014C2×C4—32no—
1015C2×C4—31no—
1016C2×C4—61no—
1017C2×C4—61no—
1018C2×C4—61no—
1019C2×C4—91no—
1020C2×C4—122no—
1021C2×C4—182no—
1022C2×C4—182no—
1023C2×C4—182no—
1024C2×C4—181no—
1025C2×C4—181no—
1026C2×C4—181no—
1027C2×C4C22×D3211yescharacteristic
1028C8—21no—
1029C8—61no—
1030C8—61no—
1031C8—181no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—42no—
1036C2×C3—42no—
1037C2×C3—62no—
1038C2×C3—62no—
1039C2×C3—82no—
1040C2×C3—122no—
1041C2×C3—122no—
1042C2×C3—241no—
1043C2×C3D3×#12011yescharacteristic
1044C2×C3C2×#91411yescharacteristic
1045C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1046C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1047C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1048C2×C3C2×#93711yescharacteristic
1049D3—22no—
1050D3—22no—
1051D3—42no—
1052D3—42no—
1053D3—62no—
1054D3—62no—
1055D3—81no—
1056D3—122no—
1057D3—122no—
1058D3—122no—
1059D3—242no—
1060C22—22no—
1061C22—32no—
1062C22—32no—
1063C22—41no—
1064C22—41no—
1065C22—61no—
1066C22—61no—
1067C22—61no—
1068C22—61no—
1069C22—62no—
1070C22—62no—
1071C22—92no—
1072C22—128no—
1073C22—128no—
1074C22—121no—
1075C22—121no—
1076C22—121no—
1077C22—121no—
1078C22—121no—
1079C22—121no—
1080C22—121no—
1081C22—188no—
1082C22—181no—
1083C22—181no—
1084C22—182no—
1085C22—368no—
1086C22—368no—
1087C22—368no—
1088C22—368no—
1089C22—361no—
1090C22—361no—
1091C22D32×D411yescharacteristic
1092C4—32no—
1093C4—41no—
1094C4—61no—
1095C4—121no—
1096C4—181no—
1097C4—361no—
1098C4D32×D411yescharacteristic
1099C4C2×D3×#6711yescharacteristic
1100C3—21no—
1101C3#8014611yescharacteristic, complemented
1102C3#8394411yescharacteristic, complemented
1103C2—42no—
1104C2—62no—
1105C2—62no—
1106C2—122no—
1107C2—122no—
1108C2—182no—
1109C2—241no—
1110C2—362no—
1111C2D3×#91411yescharacteristic
1112C2#1059474011yescharacteristic
1113C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3003
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×D32×D4C2semidirect
2. C2×C3×#914C2semidirect
3. #10595424C2semidirect
4. C2×#63939C2semidirect
5. #10592868C2semidirect
6. C3×#5169C2semidirect
7. #10591652C2semidirect
8. #10591651C2semidirect
9. #10591456C2semidirect
10. #10591447C2semidirect
11. #10591421C2semidirect
12. #10590945C2semidirect
13. #10590944C2semidirect
14. #10590939C2semidirect
15. #10590936C2semidirect
20. C2×C3×#239C22semidirect
32. C2×C32×SD16C22semidirect
33. #64155C22semidirect
34. C2×#3755C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#215C22semidirect
37. C2×C3×#215C22semidirect
38. C2×C3×#213C22semidirect
40. C2×C3×D24C22semidirect
41. C2×C3×ΓL(1,𝔽25)C22semidirect
44. #63916C22semidirect
45. #63908C22semidirect
49. #63841C22semidirect
50. C2×#3714C22semidirect
51. C2×#3713C22semidirect
52. C2×#3711C22semidirect
53. #63659C22semidirect
54. #63648C22semidirect
55. #63647C22semidirect
56. C3×#832C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. #63564C22semidirect
60. #63563C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
71. C2×#914D3semidirect
82. #5169D3semidirect
106. C2×C32×Q8C23semidirect
120. C3×D3×D4D4semidirect
124. C2×C3×D12C23semidirect
144. D3×D12D4semidirect
148. C2×C32×C8C23semidirect
151. C4⋊(C3⋊Dic3)C23semidirect
153. C2×C3⋊(C3⋊C8)C23semidirect
158. C3×C4⋊Dic3C23semidirect
160. C2×C3×C3⋊C8C23semidirect
161. C2×C3×C3⋊C8C23semidirect
179. C2×#239C2×D3semidirect
205. C2×C3×SD16C2×D3semidirect
206. C2×C3×SD16C2×D3semidirect
215. #946C2×D3semidirect
219. C2×#215C2×D3semidirect
220. C2×#215C2×D3semidirect
228. C2×#213C2×D3semidirect
237. C2×D24C2×D3semidirect
239. C2×ΓL(1,𝔽25)C2×D3semidirect
255. #832C2×D3semidirect
263. #821C2×D3semidirect
270. (C2×D3)⋊C8C2×D3semidirect
384. C2×C3×Q8C22×D3semidirect
385. C2×C3×Q8C22×D3semidirect
441. D3×D4#67semidirect
455. C2×D12C22×D3semidirect
481. C2×C3×C8C22×D3semidirect
482. C2×C3×C8C22×D3semidirect
508. C4⋊Dic3C22×D3semidirect
519. C2×C3⋊C8C22×D3semidirect
520. C2×C3⋊C8C22×D3semidirect
535. C2×C3⋊D3AGL(1,ℤ/8)semidirect
552. C2×C3×D3AGL(1,ℤ/8)semidirect
584. C2×SD16D32semidirect
800. C2×Q8C2×D32semidirect
852. C2×C8C2×D32semidirect
936. C2×D3#914semidirect
959. C32#3003semidirect
1101. C3#80146semidirect
1102. C3#83944semidirect

Maximal subgroups

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

subgroupindex
C2×D32×D42
C2×C3×#9142
#105954242
C2×#639392
#105928682
C3×#51692
#105916522
#105916512
#105914562
#105914472
#105914212
#105909452
#105909442
#105909392
#105909362
#839443
#801463