Finite Group Databasebeta

← #11884022

Subgroups — #11884022

Order 1152.

1164 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
2#10595402C211yesmaximal, characteristic, complemented
3#10595288C211yesmaximal, characteristic, complemented
4C2×#63794C211yesmaximal, characteristic, complemented
5#10592875C211yesmaximal, characteristic, complemented
6C3×#5174C211yesmaximal, characteristic, complemented
7#10591651C211yesmaximal, characteristic, complemented
8#10591584C211yesmaximal, characteristic, complemented
9#10591570C211yesmaximal, characteristic, complemented
10#10591521C211yesmaximal, characteristic, complemented
11#10591448C211yesmaximal, characteristic, complemented
12#10591444C211yesmaximal, characteristic, complemented
13#10590832C211yesmaximal, characteristic, complemented
14#10590779C211yesmaximal, characteristic, complemented
15#10590722C211yesmaximal, characteristic, complemented
16#83864—31nomaximal
17#80834—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic, complemented
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22C2×#3799C2211yescharacteristic, complemented
23C2×C32×SD16C2211yescharacteristic, complemented
24#64156C2211yescharacteristic, complemented
25C2×#3755C2211yescharacteristic, complemented
26#64149C2211yescharacteristic
27C2×#3753C2211yescharacteristic, complemented
28C2×#3745C2211yescharacteristic, complemented
29C3×#946C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic
31C3×#938C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic, complemented
33C3×D3×SD16—24no—
34C2×C3×#204C2211yescharacteristic
35C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
36C2×C3×D3×C8C2211yescharacteristic, complemented
37#63983—21no—
38#63977—21no—
39#63971—21no—
40#63909C2211yescharacteristic
41#63909C2211yescharacteristic, complemented
42#63907—21no—
43#63906—21no—
44#63904—21no—
45C4×#625C2211yescharacteristic
46#63898C2211yescharacteristic
47#63888—21no—
48#63843C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic
51#63794—24no—
52#63642C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#818C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, 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×#908—31no—
69#5633—31no—
70#5609—31no—
71C3×#468—31no—
72#5227—31no—
73#5217—31no—
74#5176—31no—
75#5176—31no—
76#5176—61no—
77#5174D311yescharacteristic, complemented
78#5172—31no—
79#5169—31no—
80#5165—31no—
81#5164—31no—
82#5163—31no—
83#5127—31no—
84#5115—31no—
85#5111—31no—
86#5046—31no—
87#5037—31no—
88#4889—31no—
89#4883—31no—
90#4819—31no—
91#4806—31no—
92#4773—31no—
93#4762—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C2×#638—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C3×D3×Q8—22no—
105C3×D3×Q8—41no—
106C3×D3×D4—22no—
107C3×D3×D4—41no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6—21no—
113C2×C3×Dic6C2311yescharacteristic
114D3×#67—44no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#625D411yescharacteristic
120C2×#624—21no—
121C2×D3×Dic3—21no—
122D3×D12—22no—
123D3×D12—41no—
124#3799—22no—
125#3799—41no—
126C32×SD16—22no—
127C2×C32×C8C2311yescharacteristic
128#3755—41no—
129#3753—41no—
130#3752—21no—
131#3752—21no—
132C4×C3⋊Dic3C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134#3745—22no—
135C3×#217—21no—
136C3×#215—22no—
137C3×#214—22no—
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3C2311yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C3×#204D414yescomplemented
145C3×ΓL(1,𝔽25)—22no—
146C3×D3×C8—22no—
147#3724D411yescharacteristic
148Dic3⋊Dic3—21no—
149#3722—21no—
150#3722—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3D411yescharacteristic
153(C2×D3)⋊Dic3D411yescharacteristic
154Dic32—21no—
155#3717—22no—
156#3714—22no—
157#3265—91noSylow
158C22×C3×Q8—31no—
159C22×C3×D4—31no—
160C22×#67—61no—
161C2×#239—31no—
162C2×D3×Q8C2×D311yescharacteristic, complemented
163C2×D3×D4—31no—
164C2×D3×D4—61no—
165C2×D3×D4C2×D311yescharacteristic
166C2×#235—31no—
167C22×D12—31no—
168C2×C3×SD16—21no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—64no—
173C2×C3×SD16C2×D311yescharacteristic, complemented
174C2×C3×SD16C2×D311yescharacteristic, complemented
175C2×C3×M16—31no—
176C22×C3×C8—31no—
177C3×C22⋊Q8—31no—
178C3×#121—31no—
179#953—61no—
180#947—31no—
181#947—31no—
182#947—61no—
183#947—61no—
184#946—61no—
185#946C2×D311yescharacteristic, complemented
186Q8×Dic3—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—61no—
191C2×#215C2×D311yescharacteristic
192#940—31no—
193#940—31no—
194#940—61no—
195#939—61no—
196#938C2×D311yescharacteristic
197#937—61no—
198#937—61no—
199D4×Dic3—31no—
200C2×#214C2×D311yescharacteristic, complemented
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—61no—
205#930—31no—
206#930—31no—
207#930—61no—
208C4×#67—31no—
209C4×#67—31no—
210C4×#67—61no—
211#914—64no—
212D3×SD16—24no—
213#908—64no—
214C2×D24—31no—
215C2×D24—31no—
216C2×D24—31no—
217C2×D24—61no—
218C2×#204—31no—
219C2×#204C2×D311yescharacteristic
220C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
221C2×D3×C8C2×D311yescharacteristic, complemented
222#896—61no—
223#895—31no—
224#895—31no—
225#893—31no—
226#893—61no—
227#887—31no—
228#885—61no—
229#884—61no—
230#884—61no—
231#882—61no—
232C3×#107—31no—
233C3×#103—31no—
234C3×#102—31no—
235#835—31no—
236#835C2×D311yescharacteristic, complemented
237#832—31no—
238#832C2×D311yescharacteristic, complemented
239#830—31no—
240#830—31no—
241#821—31no—
242#821—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245#818C2×D311yescharacteristic, complemented
246#815—31no—
247#815—31no—
248#815—61no—
249Dic3⋊C8—31no—
250Dic3⋊C8—31no—
251#810—31no—
252#809—31no—
253#809—31no—
254#809—31no—
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—81no—
262C22×C3×D3C2×D411yescharacteristic
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—
274#638—81no—
275C2×C3⋊Dic3C2×D411yescharacteristic
276C2×C3⋊Dic3C2×D411yescharacteristic
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—21no—
279C4⋊(C3⋊D3)—21no—
280C4⋊(C3⋊D3)—21no—
281C3×#67—42no—
282C3×#67—42no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12C2×D412yes—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—42no—
295C3×Dic6—21no—
296C3×Dic6—42no—
297C3×Dic6C2×D412yescomplemented
298#626—42no—
299#626—42no—
300#626—42no—
301#626—42no—
302#625—22no—
303#624—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—91no—
314#468—31no—
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—61no—
338C2×C3×D4—62no—
339C2×C3×D4—61no—
340C2×C3×D4—121no—
341C2×C3×D4C22×D311yescharacteristic
342C2×C3×D4C22×D311yescharacteristic
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—61no—
346C2×#67—21no—
347C2×#67—21no—
348C2×#67—31no—
349C2×#67—31no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—121no—
359C2×#67—121no—
360C2×#67—124no—
361C22×Dic3—61no—
362#239—62no—
363#239—121no—
364D3×Q8—22no—
365D3×Q8—41no—
366D3×D4—22no—
367D3×D4—41no—
368D3×D4—62no—
369D3×D4—121no—
370D3×D4—124no—
371#235—62no—
372#235—121no—
373C2×D12—31no—
374C2×D12—31no—
375C2×D12—31no—
376C2×D12—31no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—62no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12—61no—
384C2×D12—121no—
385C2×D12C22×D311yescharacteristic
386C2×C4×D3—21no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—61no—
390C2×C4×D3C22×D311yescharacteristic
391C2×C4×D3C22×D311yescharacteristic
392C2×Dic6—21no—
393C2×Dic6C22×D311yescharacteristic
394C3×SD16—22no—
395C3×SD16—22no—
396C3×SD16—34no—
397C3×SD16—42no—
398C3×SD16—62no—
399C3×SD16—62no—
400C3×M16—62no—
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×C4⋊C4—31no—
408C3×C4⋊C4—31no—
409C3×C4⋊C4—61no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412#217—21no—
413#217—31no—
414#217—31no—
415#217—61no—
416#215—22no—
417#215—62no—
418#215—121no—
419#215—121no—
420#215—122no—
421#214—22no—
422#213—62no—
423#213—121no—
424#213—121no—
425#213—122no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—31no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—61no—
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—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—121no—
439(C2×D3)⋊C4—121no—
440C4⋊Dic3—61no—
441C4⋊Dic3C22×D311yescharacteristic
442C4⋊Dic3C22×D311yescharacteristic
443Dic3⋊C4—21no—
444Dic3⋊C4—31no—
445Dic3⋊C4—31no—
446Dic3⋊C4—61no—
447C4×Dic3—31no—
448C4×Dic3—31no—
449C4×Dic3—61no—
450C4×Dic3—61no—
451C4×Dic3—61no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—61no—
455C2×C3⋊C8C22×D311yescharacteristic
456C2×C3⋊C8C22×D311yescharacteristic
457D24—62no—
458D24—62no—
459D24—62no—
460D24—122no—
461#204—62no—
462#204#6714yescomplemented
463ΓL(1,𝔽25)—22no—
464D3×C8—22no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32C22×D411yescharacteristic
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—22no—
479C2×C3×D3—21no—
480C2×C3×D3—21no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—84no—
484C2×C3×D3AGL(1,ℤ/8)12yescomplemented
485D32—84no—
486C32×C4—41no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—21no—
490C3⋊Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—22no—
493C3×Dic3—21no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41—91no—
497C22×Q8—31no—
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—64no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16D3211yescharacteristic, complemented
509C2×D8—91no—
510C2×D8—91no—
511C2×D8—91no—
512C2×M16—31no—
513C22×C8—31no—
514#127—91no—
515#124—91no—
516#124—181no—
517C22⋊Q8—31no—
518C22⋊Q8—181no—
519#121—31no—
520#121—91no—
521#121—91no—
522#121—181no—
523#121—181no—
524#120—181no—
525#120—181no—
526C4×Q8—91no—
527C4×D4—91no—
528C4×D4—91no—
529C4×D4—181no—
530#107—31no—
531C4⋊C8—91no—
532#103—31no—
533#103—91no—
534#102—31no—
535#102—91no—
536#102—91no—
537#102—91no—
538C22⋊C8—91no—
539C22⋊C8—91no—
540#97—91no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—31no—
544C23×C3—31no—
545C23×C3—41no—
546C23×C3—61no—
547C23×C3—122no—
548C23×C3—122no—
549C23×C3—241no—
550C22×D3—21no—
551C22×D3—42no—
552C22×D3—42no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—81no—
558C22×D3—121no—
559C22×D3—121no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—241no—
565C22×D3—241no—
566C22×D3D3×D411yescharacteristic
567C22×D3D3×D411yescharacteristic
568C3×Q8—21no—
569C3×Q8—21no—
570C3×Q8—21no—
571C3×Q8—21no—
572C3×Q8—32no—
573C3×Q8—41no—
574C3×Q8—41no—
575C3×Q8—61no—
576C3×Q8—122no—
577C3×D4—21no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—21no—
581C3×D4—32no—
582C3×D4—41no—
583C3×D4—41no—
584C3×D4—61no—
585C3×D4—122no—
586C3×D4—122no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—31no—
591C2×C3×C4—31no—
592C2×C3×C4—41no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—122no—
601C2×C3×C4C23×D311yescharacteristic
602C2×C3×C4C23×D311yescharacteristic
603#67—42no—
604#67—42no—
605#67—62no—
606#67—62no—
607#67—122no—
608#67—122no—
609#67—122no—
610#67—122no—
611#67—122no—
612#67—122no—
613#67—242no—
614#67—241no—
615#67—241no—
616#67—242no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—31no—
621C2×Dic3—31no—
622C2×Dic3—31no—
623C2×Dic3—31no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—122no—
627C2×Dic3D3×D411yescharacteristic
628C2×Dic3D3×D411yescharacteristic
629D12—21no—
630D12—61no—
631D12—61no—
632D12—61no—
633D12—61no—
634D12—61no—
635D12—61no—
636D12—61no—
637D12—61no—
638D12—121no—
639D12—121no—
640D12—121no—
641D12—121no—
642D12—122no—
643D12—122no—
644D12—122no—
645D12—122no—
646D12C2×#6712yes—
647C4×D3—21no—
648C4×D3—21no—
649C4×D3—21no—
650C4×D3—21no—
651C4×D3—42no—
652C4×D3—122no—
653C4×D3—122no—
654C4×D3—122no—
655Dic6—21no—
656Dic6—42no—
657Dic6C2×#6712yescomplemented
658C3×C8—22no—
659C3×C8—61no—
660C3×C8—61no—
661C3×C8D3×D412yescomplemented
662C3×C8C2×#6712yescomplemented
663C3⋊C8—21no—
664C3⋊C8—21no—
665C3⋊C8—62no—
666C3⋊C8—61no—
667C3⋊C8—61no—
668C2×C32—81no—
669C2×C32D4211yescharacteristic
670C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
671C2×C32#57711yescharacteristic
672C3⋊D3—81no—
673C3⋊D3—81no—
674C3×D3—22no—
675C3×D3—41no—
676C3×D3—42no—
677C24—61no—
678C24—181no—
679#41—182no—
680#41—361no—
681C2×Q8—31no—
682C2×Q8—61no—
683C2×Q8—62no—
684C2×Q8—121no—
685C2×Q8C2×D3211yescharacteristic
686C2×D4—31no—
687C2×D4—61no—
688C2×D4—62no—
689C2×D4—61no—
690C2×D4—91no—
691C2×D4—91no—
692C2×D4—91no—
693C2×D4—121no—
694C2×D4—181no—
695C2×D4—182no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—181no—
701C2×D4—361no—
702C2×D4—364no—
703C2×D4C2×D3211yescharacteristic
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—61no—
707C22×C4—181no—
708C22×C4—181no—
709SD16—22no—
710SD16—34no—
711SD16—62no—
712SD16—62no—
713SD16—182no—
714SD16—361no—
715D8—182no—
716D8—182no—
717D8—361no—
718M16—62no—
719C2×C8—31no—
720C2×C8—31no—
721C2×C8—62no—
722C2×C8—91no—
723C2×C8C2×D3211yescharacteristic
724C4⋊C4—31no—
725C4⋊C4—31no—
726C4⋊C4—61no—
727C4⋊C4—91no—
728C4⋊C4—181no—
729C22⋊C4—61no—
730C22⋊C4—61no—
731C22⋊C4—91no—
732C22⋊C4—91no—
733C22⋊C4—181no—
734C22⋊C4—181no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C42—91no—
739C42—181no—
740C22×C3—21no—
741C22×C3—32no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—61no—
749C22×C3—61no—
750C22×C3—61no—
751C22×C3—61no—
752C22×C3—61no—
753C22×C3—62no—
754C22×C3—81no—
755C22×C3—81no—
756C22×C3—81no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—244no—
760C22×C3C2×D3×D411yescharacteristic
761C22×C3C2×D3×D411yescharacteristic
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—21no—
766C2×D3—22no—
767C2×D3—21no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—84no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—241no—
784C2×D3—241no—
785C2×D3—241no—
786C2×D3—241no—
787C2×D3—241no—
788C2×D3—241no—
789C2×D3—244no—
790C2×D3—244no—
791C2×D3#91412yescomplemented
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—41no—
795C3×C4—41no—
796C3×C4—61no—
797C3×C4—62no—
798C3×C4—61no—
799C3×C4—81no—
800C3×C4—121no—
801C3×C4—121no—
802C3×C4C2×D3×D411yescharacteristic
803C3×C4#100411yescharacteristic
804C3×C4#100911yescharacteristic
805C3×C4C22×#6711yescharacteristic
806Dic3—22no—
807Dic3—21no—
808Dic3—21no—
809Dic3—41no—
810Dic3—41no—
811Dic3—61no—
812Dic3—61no—
813Dic3—61no—
814Dic3—61no—
815Dic3—121no—
816Dic3—121no—
817C32#326511yescharacteristic, complemented, Sylow
818C23—21no—
819C23—31no—
820C23—31no—
821C23—61no—
822C23—122no—
823C23—122no—
824C23—181no—
825C23—181no—
826C23—241no—
827C23—362no—
828C23—362no—
829C23—721no—
830Q8—21no—
831Q8—21no—
832Q8—32no—
833Q8—61no—
834Q8—122no—
835D4—21no—
836D4—21no—
837D4—32no—
838D4—61no—
839D4—122no—
840D4—122no—
841D4—182no—
842D4—181no—
843D4—181no—
844D4—181no—
845D4—181no—
846D4—362no—
847D4—362no—
848D4—362no—
849D4—362no—
850D4—362no—
851D4—721no—
852C2×C4—21no—
853C2×C4—31no—
854C2×C4—31no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—91no—
863C2×C4—91no—
864C2×C4—122no—
865C2×C4—362no—
866C2×C4—362no—
867C2×C4C22×D3211yescharacteristic
868C8—61no—
869C8—61no—
870C8—181no—
871C8D3×#6712yescomplemented
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—62no—
876C2×C3—81no—
877C2×C3—81no—
878C2×C3—121no—
879C2×C3—122no—
880C2×C3—161no—
881C2×C3#560911yescharacteristic
882C2×C3C2×#91411yescharacteristic
883C2×C3#576211yescharacteristic
884C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
885C2×C3#577811yescharacteristic
886C2×C3D4×#6711yescharacteristic
887D3—22no—
888D3—42no—
889D3—41no—
890D3—241no—
891D3—241no—
892D3—241no—
893D3—241no—
894D3—481no—
895D3—481no—
896C22—32no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—61no—
901C22—61no—
902C22—61no—
903C22—61no—
904C22—61no—
905C22—62no—
906C22—121no—
907C22—121no—
908C22—244no—
909C22—361no—
910C22—361no—
911C22—361no—
912C22—361no—
913C22—361no—
914C22—361no—
915C22—724no—
916C22D32×D411yescharacteristic
917C4—41no—
918C4—61no—
919C4—61no—
920C4—62no—
921C4—121no—
922C4—121no—
923C4—181no—
924C4—181no—
925C4#6431411yescharacteristic
926C4C2×D3×#6711yescharacteristic
927C3—21no—
928C3#8083411yescharacteristic, complemented
929C3#8386411yescharacteristic, complemented
930C2—62no—
931C2—81no—
932C2—121no—
933C2—122no—
934C2—721no—
935C2—721no—
936C2D3×#91411yescharacteristic
937C2#1059475111yescharacteristic
938C2#1059528811yescharacteristic
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. #10595402C2semidirect
3. #10595288C2semidirect
4. C2×#63794C2semidirect
5. #10592875C2semidirect
6. C3×#5174C2semidirect
7. #10591651C2semidirect
8. #10591584C2semidirect
9. #10591570C2semidirect
10. #10591521C2semidirect
11. #10591448C2semidirect
12. #10591444C2semidirect
13. #10590832C2semidirect
14. #10590779C2semidirect
15. #10590722C2semidirect
18. C2×C3×D3×Q8C22semidirect
22. C2×#3799C22semidirect
23. C2×C32×SD16C22semidirect
24. #64156C22semidirect
25. C2×#3755C22semidirect
27. C2×#3753C22semidirect
28. C2×#3745C22semidirect
29. C3×#946C22semidirect
32. C2×C3×#214C22semidirect
35. C2×C3×ΓL(1,𝔽25)C22semidirect
36. C2×C3×D3×C8C22semidirect
41. #63909C22semidirect
48. #63843C22semidirect
49. C2×#3717C22semidirect
52. #63642C22semidirect
53. C3×#835C22semidirect
54. C3×#832C22semidirect
55. C3×#818C22semidirect
56. #63572C22semidirect
57. #63565C22semidirect
58. #63564C22semidirect
59. #63564C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
67. C2×D3×SD16D3semidirect
77. #5174D3semidirect
144. C3×#204D4semidirect
162. C2×D3×Q8C2×D3semidirect
173. C2×C3×SD16C2×D3semidirect
174. C2×C3×SD16C2×D3semidirect
185. #946C2×D3semidirect
200. C2×#214C2×D3semidirect
220. C2×ΓL(1,𝔽25)C2×D3semidirect
221. C2×D3×C8C2×D3semidirect
236. #835C2×D3semidirect
238. #832C2×D3semidirect
245. #818C2×D3semidirect
297. C3×Dic6C2×D4semidirect
305. C32×C8C2×D4semidirect
462. #204#67semidirect
484. C2×C3×D3AGL(1,ℤ/8)semidirect
508. C2×SD16D32semidirect
657. Dic6C2×#67semidirect
661. C3×C8D3×D4semidirect
662. C3×C8C2×#67semidirect
791. C2×D3#914semidirect
817. C32#3265semidirect
871. C8D3×#67semidirect
928. C3#80834semidirect
929. 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
#105954022
#105952882
C2×#637942
#105928752
C3×#51742
#105916512
#105915842
#105915702
#105915212
#105914482
#105914442
#105908322
#105907792
#105907222
#838643
#808343