Finite Group Databasebeta

← #11884024

Subgroups — #11884024

Order 1152.

1152 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
2#10595401C211yesmaximal, characteristic, complemented
3#10595293C211yesmaximal, characteristic, complemented
4C2×#63798C211yesmaximal, characteristic, complemented
5#10592873C211yesmaximal, characteristic, complemented
6C3×#5176C211yesmaximal, characteristic, complemented
7#10591652C211yesmaximal, characteristic, complemented
8#10591583C211yesmaximal, characteristic, complemented
9#10591567C211yesmaximal, characteristic, complemented
10#10591520C211yesmaximal, characteristic, complemented
11#10591447C211yesmaximal, characteristic, complemented
12#10591438C211yesmaximal, characteristic, complemented
13#10590831C211yesmaximal, characteristic, complemented
14#10590766C211yesmaximal, characteristic, complemented
15#10590726C211yesmaximal, characteristic, complemented
16#83864—31nomaximal
17#81857—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic, complemented
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×#67—21no—
21C2×#3802C2211yescharacteristic
22C2×#3796C2211yescharacteristic, complemented
23C2×C32×SD16C2211yescharacteristic, complemented
24#64155C2211yescharacteristic, complemented
25#64147C2211yescharacteristic
26C2×#3743C2211yescharacteristic, complemented
27C3×#947C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic, complemented
30C3×#940C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic, complemented
32C2×C3×#213C2211yescharacteristic, complemented
33C3×D3×SD16—24no—
34C2×C3×D24C2211yescharacteristic, complemented
35C2×C3×#204C2211yescharacteristic
36C2×C3×D3×C8C2211yescharacteristic, complemented
37#63983—21no—
38#63976—21no—
39#63970—21no—
40#63908C2211yescharacteristic
41#63908C2211yescharacteristic, complemented
42#63907—21no—
43#63906—21no—
44C4×#626C2211yescharacteristic
45Dic3×D12C2211yescharacteristic
46#63887—21no—
47#63879—21no—
48Dic3×Dic6C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic
51#63798—24no—
52#63662C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63645C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C22×C3×SD16—31no—
64#5817—31no—
65D4×#67—31no—
66C2×#914—31no—
67C2×D3×SD16D311yescharacteristic, complemented
68C2×#911—31no—
69#5717—31no—
70#5677—31no—
71C3×#496—31no—
72#5227—31no—
73#5217—31no—
74#5176D311yescharacteristic, complemented
75#5174—31no—
76#5174—31no—
77#5174—61no—
78#5172—31no—
79#5170—31no—
80#5169—31no—
81#5169—31no—
82#5165—31no—
83#5164—31no—
84#5163—31no—
85#5158—31no—
86#5157—31no—
87#5156—31no—
88#5115—31no—
89#5111—31no—
90#5075—31no—
91#5057—31no—
92#4710—31no—
93#4706—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C3×D3×Q8—22no—
104C3×D3×Q8—41no—
105C3×D3×D4—22no—
106C3×D3×D4—41no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6—21no—
113C2×C3×Dic6C2311yescharacteristic
114D3×#67—44no—
115C2×#626—21no—
116C2×#626D411yescharacteristic
117C2×#625—21no—
118C2×#625—21no—
119C2×#625—21no—
120C2×D3×Dic3—21no—
121C2×D3×Dic3—21no—
122#3802—22no—
123#3802—41no—
124#3796—22no—
125#3796—41no—
126C32×SD16—22no—
127C2×C32×C8C2311yescharacteristic
128#3757—21no—
129#3752—21no—
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132#3750—21no—
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134#3743—22no—
135C3×#215—22no—
136C3×#215—41no—
137C3×#214—22no—
138C3×#213—41no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×C4×Dic3C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C3×D24—22no—
145C3×#204D414yescomplemented
146C3×D3×C8—22no—
147Dic3⋊Dic3—21no—
148Dic3⋊Dic3D411yescharacteristic
149#3722D411yescharacteristic
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3—21no—
153(C2×D3)⋊Dic3D411yescharacteristic
154Dic32—21no—
155#3715—22no—
156#3713—22no—
157#3265—91noSylow
158C22×C3×Q8—31no—
159C22×C3×D4—31no—
160C22×#67—61no—
161C2×#239—31no—
162C2×D3×Q8C2×D311yescharacteristic, complemented
163C2×#237—31no—
164C2×D3×D4—31no—
165C2×D3×D4—31no—
166C2×D3×D4—61no—
167C2×D3×D4C2×D311yescharacteristic
168C2×C3×SD16—21no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—64no—
174C2×C3×SD16C2×D311yescharacteristic, complemented
175C2×C3×SD16C2×D311yescharacteristic, complemented
176C2×C3×D8—31no—
177C2×C3×D8—31no—
178C22×C3×C8—31no—
179C3×#127—31no—
180C3×#124—31no—
181#953—61no—
182#947—61no—
183#947C2×D311yescharacteristic, complemented
184#946—31no—
185#946—31no—
186#946—61no—
187#946—61no—
188Q8×Dic3—31no—
189C2×#215—31no—
190C2×#215C2×D311yescharacteristic
191C2×#215C2×D311yescharacteristic, complemented
192#940C2×D311yescharacteristic
193#939—61no—
194#938—31no—
195#938—31no—
196#938—31no—
197#938—31no—
198#938—61no—
199#938—61no—
200#937—61no—
201#937—61no—
202#937—61no—
203D4×Dic3—31no—
204C2×#214—31no—
205C2×#214C2×D311yescharacteristic, complemented
206C2×#213—31no—
207C2×#213—31no—
208C2×#213C2×D311yescharacteristic, complemented
209#930—31no—
210#930—31no—
211#930—61no—
212C4×#67—31no—
213C4×#67—61no—
214#914—64no—
215D3×SD16—24no—
216#911—64no—
217C2×D24C2×D311yescharacteristic, complemented
218C2×#204C2×D311yescharacteristic
219C2×ΓL(1,𝔽25)—31no—
220C2×ΓL(1,𝔽25)—31no—
221C2×ΓL(1,𝔽25)—61no—
222C2×D3×C8C2×D311yescharacteristic, complemented
223#885—61no—
224#884—61no—
225#67⋊C4—61no—
226#878—61no—
227C4×D12—31no—
228C4×D12—31no—
229C4×Dic6—31no—
230C3×#97—31no—
231#835—31no—
232#835—31no—
233#835—31no—
234#835—61no—
235#832—31no—
236#832—31no—
237#832—31no—
238#832—31no—
239#832—31no—
240#832—61no—
241#830—31no—
242#821—31no—
243#821—31no—
244#821—31no—
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—31no—
247(C2×D3)⋊C8—31no—
248#818—31no—
249#818—31no—
250#818—61no—
251#816—31no—
252#815C2×D311yescharacteristic, complemented
253Dic3⋊C8—31no—
254C4⋊(C3⋊C8)—31no—
255C23×C32—21no—
256C22×C3⋊D3C2×D411yescharacteristic
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×D4—21no—
270C32×D4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C2411yescharacteristic
273#638—42no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3C2×D411yescharacteristic
277C4×C3⋊D3—21no—
278C4×C3⋊D3—21no—
279C3×#67—42no—
280C3×#67—42no—
281C3×#67—81no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12C2×D412yes—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—42no—
295C3×Dic6—21no—
296C3×Dic6—42no—
297C3×Dic6C2×D412yescomplemented
298#626—22no—
299#626—42no—
300#625—42no—
301#625—42no—
302#625—42no—
303D3×Dic3—42no—
304D3×Dic3—42no—
305C32×C8C2×D412yescomplemented
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—31no—
311#548—91no—
312D42—91no—
313#496—31no—
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—
328C2×C3×Q8—21no—
329C2×C3×Q8—31no—
330C2×C3×Q8—61no—
331C2×C3×Q8—62no—
332C2×C3×Q8—121no—
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×Q8C22×D311yescharacteristic
335C2×C3×D4—21no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—31no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—62no—
343C2×C3×D4—121no—
344C2×C3×D4C22×D311yescharacteristic
345C2×C3×D4C22×D311yescharacteristic
346C22×C3×C4—31no—
347C22×C3×C4—61no—
348C2×#67—21no—
349C2×#67—21no—
350C2×#67—21no—
351C2×#67—31no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—121no—
362C2×#67—124no—
363C22×Dic3—61no—
364C22×Dic3—61no—
365#239—62no—
366#239—121no—
367D3×Q8—22no—
368D3×Q8—41no—
369#237—62no—
370#237—121no—
371D3×D4—22no—
372D3×D4—41no—
373D3×D4—62no—
374D3×D4—62no—
375D3×D4—121no—
376D3×D4—121no—
377D3×D4—124no—
378C2×D12—31no—
379C2×D12—61no—
380C2×D12C22×D311yescharacteristic
381C2×D12C22×D311yescharacteristic
382C2×D12C22×D311yescharacteristic
383C2×C4×D3—21no—
384C2×C4×D3—31no—
385C2×C4×D3—31no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3C22×D311yescharacteristic
390C2×Dic6—21no—
391C2×Dic6C22×D311yescharacteristic
392C3×SD16—22no—
393C3×SD16—22no—
394C3×SD16—34no—
395C3×SD16—42no—
396C3×SD16—62no—
397C3×SD16—62no—
398C3×SD16—121no—
399C3×D8—62no—
400C3×D8—121no—
401C2×C3×C8—21no—
402C2×C3×C8—31no—
403C2×C3×C8—31no—
404C2×C3×C8—62no—
405C2×C3×C8C22×D311yescharacteristic
406C2×C3×C8C22×D311yescharacteristic
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C42—31no—
410#217—31no—
411#217—61no—
412#217—61no—
413#217—61no—
414#217—61no—
415#217—61no—
416#217—121no—
417#215—22no—
418#215—41no—
419#215—62no—
420#214—22no—
421#214—62no—
422#213—41no—
423#213—62no—
424#213—62no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—31no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—121no—
436C4⋊Dic3—31no—
437C4⋊Dic3—31no—
438C4⋊Dic3—31no—
439C4⋊Dic3—31no—
440C4⋊Dic3—31no—
441C4⋊Dic3—61no—
442C4⋊Dic3—61no—
443C4⋊Dic3—61no—
444Dic3⋊C4—31no—
445Dic3⋊C4—61no—
446Dic3⋊C4—61no—
447Dic3⋊C4—61no—
448Dic3⋊C4—121no—
449C4×Dic3—61no—
450C4×Dic3—61no—
451C4×Dic3C22×D311yescharacteristic
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—61no—
455C2×C3⋊C8C22×D311yescharacteristic
456C2×C3⋊C8C22×D311yescharacteristic
457D24—22no—
458#204#6714yescomplemented
459ΓL(1,𝔽25)—62no—
460ΓL(1,𝔽25)—62no—
461ΓL(1,𝔽25)—122no—
462D3×C8—22no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—22no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—84no—
482C2×C3×D3AGL(1,ℤ/8)12yescomplemented
483D32—84no—
484C32×C4—41no—
485C32×C4C22×D411yescharacteristic
486C32×C4H(5,𝔽2)11yescharacteristic
487C3⋊Dic3—21no—
488C3⋊Dic3—41no—
489C3⋊Dic3—41no—
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C2×#41—91no—
495C22×Q8—31no—
496C22×D4—31no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—31no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—64no—
505C2×SD16—91no—
506C2×SD16D3211yescharacteristic, complemented
507C2×D8—31no—
508C2×D8—31no—
509C2×D8—91no—
510C2×M16—91no—
511C22×C8—31no—
512#127—31no—
513#124—31no—
514#124—181no—
515C22⋊Q8—91no—
516C22⋊Q8—181no—
517#121—91no—
518#121—91no—
519#121—91no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—91no—
525C4×D4—91no—
526C4×D4—91no—
527C4×D4—181no—
528#107—91no—
529C4⋊C8—91no—
530#103—91no—
531#103—91no—
532#102—91no—
533#102—91no—
534#102—91no—
535#102—91no—
536C22⋊C8—91no—
537C22⋊C8—91no—
538#97—31no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—31no—
542C23×C3—41no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—122no—
547C23×C3—122no—
548C23×C3—241no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—31no—
553C22×D3—31no—
554C22×D3—42no—
555C22×D3—42no—
556C22×D3—61no—
557C22×D3—81no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3D3×D411yescharacteristic
565C3×Q8—21no—
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—32no—
570C3×Q8—41no—
571C3×Q8—41no—
572C3×Q8—61no—
573C3×Q8—122no—
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—32no—
579C3×D4—41no—
580C3×D4—41no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—61no—
584C3×D4—61no—
585C3×D4—61no—
586C3×D4—122no—
587C3×D4—122no—
588C3×D4—241no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—31no—
593C2×C3×C4—31no—
594C2×C3×C4—31no—
595C2×C3×C4—41no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—122no—
600C2×C3×C4C23×D311yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602#67—42no—
603#67—42no—
604#67—62no—
605#67—81no—
606#67—122no—
607#67—122no—
608#67—122no—
609#67—122no—
610#67—122no—
611#67—122no—
612#67—122no—
613#67—122no—
614#67—122no—
615#67—242no—
616C2×Dic3—21no—
617C2×Dic3—31no—
618C2×Dic3—31no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—121no—
625C2×Dic3—121no—
626C2×Dic3—122no—
627C2×Dic3—122no—
628C2×Dic3D3×D411yescharacteristic
629C2×Dic3D3×D411yescharacteristic
630C2×Dic3D3×D411yescharacteristic
631D12—21no—
632D12—21no—
633D12—21no—
634D12—21no—
635D12—21no—
636D12—62no—
637D12—122no—
638D12C2×#6712yes—
639C4×D3—21no—
640C4×D3—21no—
641C4×D3—42no—
642C4×D3—61no—
643C4×D3—61no—
644C4×D3—61no—
645C4×D3—61no—
646C4×D3—121no—
647C4×D3—121no—
648C4×D3—122no—
649C4×D3—122no—
650Dic6—21no—
651Dic6—42no—
652Dic6C2×#6712yescomplemented
653C3×C8—22no—
654C3×C8—61no—
655C3×C8—61no—
656C3×C8D3×D412yescomplemented
657C3×C8C2×#6712yescomplemented
658C3⋊C8—21no—
659C3⋊C8—21no—
660C3⋊C8—61no—
661C3⋊C8—61no—
662C3⋊C8—121no—
663C2×C32—81no—
664C2×C32D4211yescharacteristic
665C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
666C2×C32#57711yescharacteristic
667C3⋊D3—41no—
668C3×D3—22no—
669C3×D3—42no—
670C3×D3—81no—
671C3×D3—81no—
672C24—61no—
673C24—181no—
674#41—182no—
675#41—361no—
676C2×Q8—31no—
677C2×Q8—61no—
678C2×Q8—62no—
679C2×Q8—121no—
680C2×Q8C2×D3211yescharacteristic
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—62no—
688C2×D4—91no—
689C2×D4—121no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—182no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—361no—
697C2×D4—364no—
698C2×D4C2×D3211yescharacteristic
699C22×C4—31no—
700C22×C4—61no—
701C22×C4—91no—
702C22×C4—181no—
703C22×C4—181no—
704SD16—22no—
705SD16—34no—
706SD16—62no—
707SD16—62no—
708SD16—121no—
709SD16—182no—
710D8—62no—
711D8—121no—
712D8—182no—
713M16—182no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—62no—
717C2×C8—91no—
718C2×C8C2×D3211yescharacteristic
719C4⋊C4—91no—
720C4⋊C4—91no—
721C4⋊C4—91no—
722C4⋊C4—181no—
723C4⋊C4—181no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—91no—
727C22⋊C4—91no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C42—31no—
734C42—181no—
735C22×C3—21no—
736C22×C3—32no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—62no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—244no—
758C22×C3C2×D3×D411yescharacteristic
759C22×C3C2×D3×D411yescharacteristic
760C2×D3—21no—
761C2×D3—21no—
762C2×D3—22no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—84no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—244no—
782C2×D3—244no—
783C2×D3#91412yescomplemented
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—41no—
787C3×C4—41no—
788C3×C4—62no—
789C3×C4—61no—
790C3×C4—61no—
791C3×C4—61no—
792C3×C4—81no—
793C3×C4C2×D3×D411yescharacteristic
794C3×C4#100411yescharacteristic
795C3×C4#100411yescharacteristic
796C3×C4C22×#6711yescharacteristic
797Dic3—21no—
798Dic3—21no—
799Dic3—22no—
800Dic3—21no—
801Dic3—61no—
802Dic3—61no—
803Dic3—121no—
804Dic3—121no—
805Dic3—121no—
806Dic3—121no—
807Dic3—121no—
808Dic3—241no—
809Dic3—241no—
810C32#326511yescharacteristic, complemented, Sylow
811C23—21no—
812C23—31no—
813C23—61no—
814C23—61no—
815C23—61no—
816C23—91no—
817C23—122no—
818C23—122no—
819C23—241no—
820C23—362no—
821C23—362no—
822C23—721no—
823Q8—21no—
824Q8—21no—
825Q8—32no—
826Q8—61no—
827Q8—122no—
828D4—21no—
829D4—21no—
830D4—32no—
831D4—61no—
832D4—61no—
833D4—61no—
834D4—61no—
835D4—61no—
836D4—122no—
837D4—122no—
838D4—182no—
839D4—241no—
840D4—362no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—362no—
845C2×C4—21no—
846C2×C4—31no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—91no—
853C2×C4—122no—
854C2×C4—181no—
855C2×C4—181no—
856C2×C4—181no—
857C2×C4—181no—
858C2×C4—362no—
859C2×C4—362no—
860C2×C4C22×D3211yescharacteristic
861C8—61no—
862C8—61no—
863C8—181no—
864C8D3×#6712yescomplemented
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—62no—
869C2×C3—81no—
870C2×C3—81no—
871C2×C3—122no—
872C2×C3—161no—
873C2×C3—241no—
874C2×C3—241no—
875C2×C3#571711yescharacteristic
876C2×C3C2×#91411yescharacteristic
877C2×C3#576211yescharacteristic
878C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
879C2×C3#577511yescharacteristic
880C2×C3D4×#6711yescharacteristic
881D3—22no—
882D3—42no—
883D3—81no—
884D3—81no—
885D3—121no—
886D3—121no—
887D3—241no—
888C22—32no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—61no—
893C22—61no—
894C22—62no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—181no—
904C22—181no—
905C22—181no—
906C22—244no—
907C22—724no—
908C22D32×D411yescharacteristic
909C4—41no—
910C4—61no—
911C4—61no—
912C4—61no—
913C4—62no—
914C4—181no—
915C4—361no—
916C4—361no—
917C4#6431311yescharacteristic
918C4C2×D3×#6711yescharacteristic
919C3—21no—
920C3#8185711yescharacteristic, complemented
921C3#8386411yescharacteristic, complemented
922C2—62no—
923C2—81no—
924C2—122no—
925C2—241no—
926C2—241no—
927C2—361no—
928C2D3×#91411yescharacteristic
929C2#1059474911yescharacteristic
930C2#1059529311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3265
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×C3×D3×SD16C2semidirect
2. #10595401C2semidirect
3. #10595293C2semidirect
4. C2×#63798C2semidirect
5. #10592873C2semidirect
6. C3×#5176C2semidirect
7. #10591652C2semidirect
8. #10591583C2semidirect
9. #10591567C2semidirect
10. #10591520C2semidirect
11. #10591447C2semidirect
12. #10591438C2semidirect
13. #10590831C2semidirect
14. #10590766C2semidirect
15. #10590726C2semidirect
18. C2×C3×D3×Q8C22semidirect
22. C2×#3796C22semidirect
23. C2×C32×SD16C22semidirect
24. #64155C22semidirect
26. C2×#3743C22semidirect
27. C3×#947C22semidirect
29. C2×C3×#215C22semidirect
31. C2×C3×#214C22semidirect
32. C2×C3×#213C22semidirect
34. C2×C3×D24C22semidirect
36. C2×C3×D3×C8C22semidirect
41. #63908C22semidirect
48. Dic3×Dic6C22semidirect
49. C2×#3715C22semidirect
52. #63662C22semidirect
53. #63659C22semidirect
54. #63645C22semidirect
55. C3×#815C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
61. #63557C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
67. C2×D3×SD16D3semidirect
74. #5176D3semidirect
145. C3×#204D4semidirect
162. C2×D3×Q8C2×D3semidirect
174. C2×C3×SD16C2×D3semidirect
175. C2×C3×SD16C2×D3semidirect
183. #947C2×D3semidirect
191. C2×#215C2×D3semidirect
205. C2×#214C2×D3semidirect
208. C2×#213C2×D3semidirect
217. C2×D24C2×D3semidirect
222. C2×D3×C8C2×D3semidirect
252. #815C2×D3semidirect
297. C3×Dic6C2×D4semidirect
305. C32×C8C2×D4semidirect
458. #204#67semidirect
482. C2×C3×D3AGL(1,ℤ/8)semidirect
506. C2×SD16D32semidirect
652. Dic6C2×#67semidirect
656. C3×C8D3×D4semidirect
657. C3×C8C2×#67semidirect
783. C2×D3#914semidirect
810. C32#3265semidirect
864. C8D3×#67semidirect
920. C3#81857semidirect
921. C3#83864semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×SD162
#105954012
#105952932
C2×#637982
#105928732
C3×#51762
#105916522
#105915832
#105915672
#105915202
#105914472
#105914382
#105908312
#105907662
#105907262
#838643
#818573