Finite Group Databasebeta

← #11883950

Subgroups — #11883950

Order 1152.

1171 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5817C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3C2×#63939C211yesmaximal, characteristic, complemented
4D12×#67C211yesmaximal, characteristic, complemented
5#10592926C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591619C211yesmaximal, characteristic, complemented
8#10591617C211yesmaximal, characteristic, complemented
9#10591587C211yesmaximal, characteristic, complemented
10#10591586C211yesmaximal, characteristic, complemented
11#10591567C211yesmaximal, characteristic, complemented
12#10591566C211yesmaximal, characteristic, complemented
13#10591164C211yesmaximal, characteristic, complemented
14#10591160C211yesmaximal, characteristic, complemented
15#10591155C211yesmaximal, characteristic, complemented
16#83864—31nomaximal
17#83542—31nomaximal
18C22×C32×Q8C2211yescharacteristic, complemented
19C2×C3×#239C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic
21C2×D3×#67—21no—
22C2×D3×D12C2211yescharacteristic
23C2×#3755C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic, complemented
25#64139C2211yescharacteristic
26C3×#947—21no—
27C3×#947C2211yescharacteristic, complemented
28C3×#946—21no—
29C3×#946C2211yescharacteristic, complemented
30C3×Q8×Dic3C2211yescharacteristic, complemented
31C2×C3×#215—24no—
32C2×C3×#215C2211yescharacteristic
33C2×C3×#215C2211yescharacteristic
34C2×C3×#215C2211yescharacteristic, complemented
35C2×C3×#215C2211yescharacteristic, complemented
36C3×#930—21no—
37C3×#930C2211yescharacteristic, complemented
38C3×C4×#67—21no—
39C3×C4×#67C2211yescharacteristic
40C22×C3×C3⋊C8C2211yescharacteristic, complemented
41#63977—21no—
42#63939—24no—
43#63922—21no—
44#63911C2211yescharacteristic
45#63908C2211yescharacteristic
46Dic3×D12C2211yescharacteristic
47#63886—21no—
48C2×#3714C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic
50C2×#3713C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63657C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C22×C3×SD16—31no—
64C3×#548—31no—
65C2×#949—31no—
66#5817D311yescharacteristic, complemented
67C22×#215D311yescharacteristic, complemented
68D4×#67—31no—
69C2×#914—31no—
70D4×D12—31no—
71#5238—31no—
72#5227—31no—
73#5227—31no—
74#5227—61no—
75#5217—31no—
76#5176—31no—
77#5174—31no—
78#5172—31no—
79#5169—31no—
80#5165—31no—
81#5164—31no—
82#5163—31no—
83#5115—31no—
84#5111—31no—
85#5058—31no—
86#5057—31no—
87#5049—31no—
88#5046—31no—
89#5038—31no—
90#5036—31no—
91#5027—31no—
92#5026—31no—
93#5011—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×Q8—21no—
97C2×C32×Q8—22no—
98C2×C32×Q8—41no—
99C2×C32×Q8C2311yescharacteristic
100C2×C32×Q8C2311yescharacteristic
101C22×C32×C4—21no—
102C22×C32×C4C2311yescharacteristic
103C2×#638—21no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C3×#67—21no—
106C2×C3×#67D411yescharacteristic
107C3×#239—22no—
108C3×#239—41no—
109C2×C3×D12—22no—
110C2×C3×D12—21no—
111C2×C3×D12—21no—
112C2×C3×D12—41no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118D3×#67—44no—
119C2×#626—21no—
120C2×#626—21no—
121C2×#626—21no—
122C2×#625—21no—
123C2×D3×Dic3—21no—
124D3×D12—22no—
125D3×D12—41no—
126#3755—22no—
127#3755—41no—
128#3752—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#217D411yescharacteristic
133C3×#215—22no—
134C3×#215—22no—
135C3×#215—22no—
136C3×#215D414yescomplemented
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×C4⋊Dic3—21no—
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4D411yescharacteristic
146C3×C4×Dic3—21no—
147C3×C4×Dic3C2311yescharacteristic
148C2×C3×C3⋊C8—22no—
149C2×C3×C3⋊C8C2311yescharacteristic
150C2×C3×C3⋊C8C2311yescharacteristic
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3—21no—
153#3714—22no—
154#3713—22no—
155#3713—41no—
156#3711—22no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C22×C3×Q8—21no—
160C22×C3×Q8C2×D311yescharacteristic, complemented
161C22×C3×Q8C2×D311yescharacteristic, complemented
162C22×C3×D4—31no—
163C22×#67—61no—
164C2×#239C2×D311yescharacteristic, complemented
165C2×D3×D4—31no—
166C2×D3×D4—61no—
167C22×D12—31no—
168C22×D12C2×D311yescharacteristic
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—64no—
174C22×C3×C8—31no—
175C3×#124—31no—
176C3×#124—61no—
177C3×C22⋊Q8—31no—
178C3×C22⋊Q8—61no—
179C3×#121—31no—
180C3×#121—61no—
181C3×C4×Q8—31no—
182C3×C4×D4—31no—
183C3×C4×D4—61no—
184#953—61no—
185#949—64no—
186#947—21no—
187#947C2×D311yescharacteristic, complemented
188#946—21no—
189#946C2×D311yescharacteristic, complemented
190Q8×Dic3C2×D311yescharacteristic, complemented
191C2×#215—24no—
192C2×#215—31no—
193C2×#215—31no—
194C2×#215—31no—
195C2×#215—31no—
196C2×#215—61no—
197C2×#215—61no—
198C2×#215C2×D311yescharacteristic
199C2×#215C2×D311yescharacteristic
200C2×#215C2×D311yescharacteristic, complemented
201C2×#215C2×D311yescharacteristic, complemented
202#940—31no—
203#939—61no—
204#938—31no—
205#937—61no—
206D4×Dic3—31no—
207C2×#213—31no—
208C2×#213—31no—
209C2×#213—31no—
210C2×#213—31no—
211C2×#213—31no—
212#930—21no—
213#930—31no—
214#930—31no—
215#930—31no—
216#930—61no—
217#930C2×D311yescharacteristic, complemented
218C4×#67—21no—
219C4×#67C2×D311yescharacteristic
220C2×#208—31no—
221C22×C3⋊C8C2×D311yescharacteristic, complemented
222#914—64no—
223C2×D24—31no—
224C2×ΓL(1,𝔽25)—31no—
225#895—61no—
226#882—61no—
227#882—61no—
228#874—31no—
229C4×D12—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—31no—
234#835—61no—
235#835—61no—
236#832—31no—
237#832—31no—
238#832—31no—
239#830—31no—
240#830—31no—
241#830—31no—
242#830—61no—
243#821—31no—
244#821—31no—
245(C2×D3)⋊C8—31no—
246#818—31no—
247#815—31no—
248Dic3⋊C8—31no—
249#809—31no—
250#809—31no—
251#809—31no—
252#807—31no—
253C4⋊(C3⋊C8)—31no—
254#803—31no—
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—81no—
263C22×C3×D3C2×D411yescharacteristic
264C2×D32—42no—
265C2×D32—42no—
266C2×D32—81no—
267C32×Q8—21no—
268C32×Q8—21no—
269C32×Q8—21no—
270C32×Q8—42no—
271C32×Q8C2×D412yescomplemented
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—42no—
277C2×C32×C4C2×D411yescharacteristic
278C2×C32×C4C2411yescharacteristic
279#638—42no—
280C2×C3⋊Dic3—21no—
281C4⋊(C3⋊D3)—21no—
282C4⋊(C3⋊D3)—21no—
283C3×#67—22no—
284C3×#67—42no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—21no—
294C3×D12—42no—
295C3×D12—42no—
296C3×D12C2×D412yes—
297C3×C4×D3—21no—
298C3×C4×D3—21no—
299C3×C4×D3—42no—
300#626—42no—
301#626—42no—
302#626—81no—
303#625—42no—
304D3×Dic3—42no—
305C3⋊(C3⋊C8)—21no—
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—31no—
311#548—31no—
312D42—91no—
313#496—91no—
314#468—91no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C24×C3—61no—
325C23×D3—21no—
326C23×D3—61no—
327C23×D3—61no—
328C3×#41—62no—
329C3×#41—121no—
330C2×C3×Q8—21no—
331C2×C3×Q8—21no—
332C2×C3×Q8—22no—
333C2×C3×Q8—22no—
334C2×C3×Q8—21no—
335C2×C3×Q8—21no—
336C2×C3×Q8—41no—
337C2×C3×Q8—42no—
338C2×C3×Q8—41no—
339C2×C3×Q8—41no—
340C2×C3×Q8—42no—
341C2×C3×Q8C22×D311yescharacteristic
342C2×C3×Q8C22×D311yescharacteristic
343C2×C3×Q8C22×D311yescharacteristic
344C2×C3×Q8C22×D311yescharacteristic
345C2×C3×D4—31no—
346C2×C3×D4—31no—
347C2×C3×D4—31no—
348C2×C3×D4—31no—
349C2×C3×D4—62no—
350C2×C3×D4—61no—
351C2×C3×D4—61no—
352C2×C3×D4—61no—
353C2×C3×D4—121no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—21no—
357C22×C3×C4—31no—
358C22×C3×C4—41no—
359C22×C3×C4—61no—
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C2×#67—21no—
363C2×#67—61no—
364C2×#67—61no—
365C2×#67—61no—
366C2×#67—61no—
367C2×#67—61no—
368C2×#67—61no—
369C2×#67—61no—
370C2×#67—121no—
371C2×#67—124no—
372C2×#67#6711yescharacteristic
373C22×Dic3—61no—
374#239—22no—
375#239—41no—
376D3×D4—62no—
377D3×D4—121no—
378D3×D4—124no—
379C2×D12—22no—
380C2×D12—21no—
381C2×D12—21no—
382C2×D12—31no—
383C2×D12—31no—
384C2×D12—41no—
385C2×D12—61no—
386C2×D12—62no—
387C2×D12—61no—
388C2×D12—61no—
389C2×D12—61no—
390C2×D12—121no—
391C2×D12C22×D311yescharacteristic
392C2×D12C22×D311yescharacteristic
393C2×D12C22×D311yescharacteristic
394C2×C4×D3—21no—
395C2×C4×D3—61no—
396C2×C4×D3C22×D311yescharacteristic
397C3×SD16—34no—
398C3×SD16—62no—
399C3×SD16—62no—
400C3×SD16—62no—
401C2×C3×C8—31no—
402C2×C3×C8—31no—
403C2×C3×C8—62no—
404C3×C4⋊C4—31no—
405C3×C4⋊C4—31no—
406C3×C4⋊C4—61no—
407C3×C4⋊C4—61no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—31no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C22⋊C4—61no—
414C3×C42—31no—
415C3×C42—61no—
416#217—61no—
417#217—61no—
418#217#6711yescharacteristic
419#215—22no—
420#215—22no—
421#215—22no—
422#215—62no—
423#215—62no—
424#215—122no—
425#215—121no—
426#215—121no—
427#215—122no—
428#215#6714yescomplemented
429#213—62no—
430#213—62no—
431#213—62no—
432#213—121no—
433#213—121no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4—21no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4—121no—
443(C2×D3)⋊C4#6711yescharacteristic
444C4⋊Dic3—21no—
445C4⋊Dic3—31no—
446C4⋊Dic3—31no—
447C4⋊Dic3—61no—
448C4⋊Dic3C22×D311yescharacteristic
449Dic3⋊C4—21no—
450Dic3⋊C4#6711yescharacteristic
451C4×Dic3—21no—
452C4×Dic3C22×D311yescharacteristic
453#208—62no—
454C2×C3⋊C8—22no—
455C2×C3⋊C8—31no—
456C2×C3⋊C8—31no—
457C2×C3⋊C8—31no—
458C2×C3⋊C8—31no—
459C2×C3⋊C8—61no—
460C2×C3⋊C8—61no—
461C2×C3⋊C8C22×D311yescharacteristic
462C2×C3⋊C8C22×D311yescharacteristic
463D24—62no—
464ΓL(1,𝔽25)—62no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32AGL(1,ℤ/8)12yescomplemented
468C22×C32C22×D411yescharacteristic
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3×D3—22no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—84no—
485D32—84no—
486C32×C4—22no—
487C32×C4—21no—
488C32×C4—41no—
489C32×C4C22×D411yescharacteristic
490C32×C4H(5,𝔽2)11yescharacteristic
491C3⋊Dic3—41no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—41no—
496C2×#41—31no—
497C22×Q8D3211yescharacteristic, complemented
498C22×D4—31no—
499C22×D4—91no—
500C22×D4—181no—
501AGL(1,ℤ/8)—184no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—31no—
505C2×SD16—31no—
506C2×SD16—64no—
507C2×SD16—91no—
508C2×SD16—91no—
509C2×D8—91no—
510C2×D8—91no—
511C2×D8—91no—
512C2×M16—91no—
513C22×C8—31no—
514#127—91no—
515#124—31no—
516#124—61no—
517C22⋊Q8—31no—
518C22⋊Q8—61no—
519#121—31no—
520#121—61no—
521#121—91no—
522#121—91no—
523#121—181no—
524#120—181no—
525#120—181no—
526C4×Q8—31no—
527C4×D4—31no—
528C4×D4—61no—
529C4×D4—91no—
530#107—91no—
531C4⋊C8—91no—
532#103—91no—
533#103—91no—
534#102—91no—
535#102—91no—
536#102—91no—
537#102—91no—
538C22⋊C8—91no—
539C22⋊C8—91no—
540#97—91no—
541C23×C3—21no—
542C23×C3—31no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—122no—
547C23×C3—122no—
548C23×C3—241no—
549C23×C3D3×D411yescharacteristic
550C23×C3C2×#6711yescharacteristic
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—42no—
555C22×D3—42no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—81no—
559C22×D3—121no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—241no—
565C22×D3—241no—
566C22×D3C2×#6711yescharacteristic
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—22no—
570C3×Q8—21no—
571C3×Q8—21no—
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—22no—
575C3×Q8—41no—
576C3×Q8—41no—
577C3×Q8—42no—
578C3×Q8—42no—
579C3×Q8—44no—
580C3×Q8D3×D412yescomplemented
581C3×Q8C2×#6712yescomplemented
582C3×D4—32no—
583C3×D4—62no—
584C3×D4—61no—
585C3×D4—61no—
586C3×D4—61no—
587C3×D4—61no—
588C3×D4—61no—
589C3×D4—122no—
590C3×D4—122no—
591C3×D4—122no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—31no—
603C2×C3×C4—31no—
604C2×C3×C4—31no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—42no—
610C2×C3×C4—42no—
611C2×C3×C4—44no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—122no—
616C2×C3×C4D3×D411yescharacteristic
617C2×C3×C4C2×#6711yescharacteristic
618C2×C3×C4C23×D311yescharacteristic
619C2×C3×C4C23×D311yescharacteristic
620#67—22no—
621#67—42no—
622#67—122no—
623#67—122no—
624#67—122no—
625#67—122no—
626#67—122no—
627#67—122no—
628#67—242no—
629#67—241no—
630C2×Dic3—21no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—121no—
634C2×Dic3—122no—
635C2×Dic3C2×#6711yescharacteristic
636C2×Dic3C2×#6711yescharacteristic
637C2×Dic3C2×#6711yescharacteristic
638D12—21no—
639D12—21no—
640D12—21no—
641D12—21no—
642D12—21no—
643D12—42no—
644D12—42no—
645D12—61no—
646D12—61no—
647D12—61no—
648D12—61no—
649D12—121no—
650D12—121no—
651D12—122no—
652D12—122no—
653D12—241no—
654D12C2×#6712yes—
655C4×D3—21no—
656C4×D3—21no—
657C4×D3—42no—
658C4×D3—122no—
659C3×C8—32no—
660C3×C8—61no—
661C3⋊C8—21no—
662C3⋊C8—61no—
663C3⋊C8—61no—
664C3⋊C8—61no—
665C3⋊C8—61no—
666C3⋊C8—121no—
667C3⋊C8—121no—
668C3⋊C8C2×#6712yescomplemented
669C2×C32—22no—
670C2×C32D4211yescharacteristic
671C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
672C2×C32#57711yescharacteristic
673C3⋊D3—81no—
674C3×D3—41no—
675C3×D3—42no—
676C3×D3—81no—
677C3×D3—81no—
678C24—61no—
679C24—181no—
680#41—62no—
681#41—121no—
682C2×Q8—21no—
683C2×Q8—22no—
684C2×Q8—41no—
685C2×Q8C2×D3211yescharacteristic
686C2×Q8C2×D3211yescharacteristic
687C2×D4—31no—
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—31no—
691C2×D4—62no—
692C2×D4—61no—
693C2×D4—61no—
694C2×D4—61no—
695C2×D4—91no—
696C2×D4—121no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—182no—
701C2×D4—181no—
702C2×D4—181no—
703C2×D4—361no—
704C2×D4—364no—
705C22×C4—21no—
706C22×C4—31no—
707C22×C4—61no—
708C22×C4—181no—
709C22×C4C2×D3211yescharacteristic
710SD16—34no—
711SD16—62no—
712SD16—62no—
713SD16—62no—
714SD16—182no—
715SD16—361no—
716D8—182no—
717D8—182no—
718D8—361no—
719M16—182no—
720C2×C8—31no—
721C2×C8—31no—
722C2×C8—62no—
723C2×C8—91no—
724C2×C8—91no—
725C4⋊C4—31no—
726C4⋊C4—31no—
727C4⋊C4—61no—
728C4⋊C4—61no—
729C4⋊C4—91no—
730C22⋊C4—31no—
731C22⋊C4—31no—
732C22⋊C4—61no—
733C22⋊C4—61no—
734C22⋊C4—61no—
735C22⋊C4—61no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C42—31no—
740C42—61no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—22no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—61no—
750C22×C3—61no—
751C22×C3—62no—
752C22×C3—61no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3—244no—
762C22×C3#91412yescomplemented
763C22×C3#94912yescomplemented
764C22×C3C2×D3×D411yescharacteristic
765C22×C3C22×#6711yescharacteristic
766C2×D3—21no—
767C2×D3—22no—
768C2×D3—21no—
769C2×D3—21no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—84no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—241no—
786C2×D3—241no—
787C2×D3—241no—
788C2×D3—244no—
789C2×D3—244no—
790C3×C4—22no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—22no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—41no—
797C3×C4—42no—
798C3×C4—42no—
799C3×C4—41no—
800C3×C4—41no—
801C3×C4—61no—
802C3×C4—61no—
803C3×C4—61no—
804C3×C4—121no—
805C3×C4C2×D3×D411yescharacteristic
806C3×C4#100411yescharacteristic
807C3×C4#100411yescharacteristic
808C3×C4C22×#6711yescharacteristic
809Dic3—21no—
810Dic3—21no—
811Dic3—21no—
812Dic3—41no—
813Dic3—121no—
814Dic3—121no—
815Dic3—241no—
816C32#326511yescharacteristic, complemented, Sylow
817C23—31no—
818C23—61no—
819C23—61no—
820C23—61no—
821C23—122no—
822C23—122no—
823C23—181no—
824C23—241no—
825C23—362no—
826C23—362no—
827C23—721no—
828C23D3×#6711yescharacteristic
829Q8—21no—
830Q8—21no—
831Q8—21no—
832Q8—42no—
833Q8D3×#6712yescomplemented
834D4—32no—
835D4—62no—
836D4—61no—
837D4—61no—
838D4—61no—
839D4—61no—
840D4—61no—
841D4—122no—
842D4—122no—
843D4—122no—
844D4—181no—
845D4—181no—
846D4—362no—
847D4—362no—
848D4—362no—
849D4—362no—
850D4—721no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—31no—
856C2×C4—31no—
857C2×C4—31no—
858C2×C4—42no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—122no—
863C2×C4—181no—
864C2×C4—362no—
865C2×C4D3×#6711yescharacteristic
866C2×C4C22×D3211yescharacteristic
867C8—32no—
868C8—61no—
869C8—181no—
870C8—181no—
871C2×C3—22no—
872C2×C3—22no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—42no—
877C2×C3—122no—
878C2×C3—121no—
879C2×C3—241no—
880C2×C3—241no—
881C2×C3C2×#91411yescharacteristic
882C2×C3#576211yescharacteristic
883C2×C3D4×#6711yescharacteristic
884C2×C3D4×#6711yescharacteristic
885C2×C3C2×#94911yescharacteristic
886C2×C3#583711yescharacteristic
887D3—41no—
888D3—42no—
889D3—81no—
890D3—81no—
891D3—241no—
892D3—241no—
893D3—481no—
894C22—21no—
895C22—21no—
896C22—61no—
897C22—62no—
898C22—61no—
899C22—61no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—244no—
909C22—361no—
910C22—361no—
911C22—361no—
912C22—724no—
913C22#6393912yescomplemented
914C22C2×D3×#6711yescharacteristic
915C4—21no—
916C4—22no—
917C4—41no—
918C4—61no—
919C4—61no—
920C4—61no—
921C4—121no—
922C4—361no—
923C4C2×D3×#6711yescharacteristic
924C4#6433011yescharacteristic
925C3—21no—
926C3#8354211yescharacteristic, complemented
927C3#8386411yescharacteristic, complemented
928C2—22no—
929C2—121no—
930C2—122no—
931C2—241no—
932C2—241no—
933C2—721no—
934C2C2×#6393911yescharacteristic
935C2#1059531811yescharacteristic
936C2#67211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
hypercenterC22×Q8D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5817C2semidirect
2. C22×C3×#215C2semidirect
3. C2×#63939C2semidirect
4. D12×#67C2semidirect
5. #10592926C2semidirect
6. #10591651C2semidirect
7. #10591619C2semidirect
8. #10591617C2semidirect
9. #10591587C2semidirect
10. #10591586C2semidirect
11. #10591567C2semidirect
12. #10591566C2semidirect
13. #10591164C2semidirect
14. #10591160C2semidirect
15. #10591155C2semidirect
18. C22×C32×Q8C22semidirect
19. C2×C3×#239C22semidirect
23. C2×#3755C22semidirect
24. C2×#3755C22semidirect
27. C3×#947C22semidirect
29. C3×#946C22semidirect
30. C3×Q8×Dic3C22semidirect
34. C2×C3×#215C22semidirect
35. C2×C3×#215C22semidirect
37. C3×#930C22semidirect
40. C22×C3×C3⋊C8C22semidirect
48. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3711C22semidirect
52. #63662C22semidirect
53. #63662C22semidirect
54. #63657C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63564C22semidirect
58. #63563C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
66. #5817D3semidirect
67. C22×#215D3semidirect
136. C3×#215D4semidirect
160. C22×C3×Q8C2×D3semidirect
161. C22×C3×Q8C2×D3semidirect
164. C2×#239C2×D3semidirect
187. #947C2×D3semidirect
189. #946C2×D3semidirect
190. Q8×Dic3C2×D3semidirect
200. C2×#215C2×D3semidirect
201. C2×#215C2×D3semidirect
217. #930C2×D3semidirect
221. C22×C3⋊C8C2×D3semidirect
271. C32×Q8C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
428. #215#67semidirect
467. C22×C32AGL(1,ℤ/8)semidirect
497. C22×Q8D32semidirect
580. C3×Q8D3×D4semidirect
581. C3×Q8C2×#67semidirect
668. C3⋊C8C2×#67semidirect
762. C22×C3#914semidirect
763. C22×C3#949semidirect
816. C32#3265semidirect
833. Q8D3×#67semidirect
913. C22#63939semidirect
926. C3#83542semidirect
927. C3#83864semidirect

Maximal subgroups

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

subgroupindex
C3×#58172
C22×C3×#2152
C2×#639392
D12×#672
#105929262
#105916512
#105916192
#105916172
#105915872
#105915862
#105915672
#105915662
#105911642
#105911602
#105911552
#838643
#835423