Finite Group Databasebeta

← #11885816

Subgroups — #11885816

Order 1152.

1146 conjugacy classes of subgroups.

The subgroup lattice has 931 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C211yesmaximal, characteristic, complemented
2#10595428C211yesmaximal, characteristic, complemented
3#10595254C211yesmaximal, characteristic, complemented
4C2×#63926C211yesmaximal, characteristic, complemented
5#10592868C211yesmaximal, characteristic, complemented
6C3×#5165C211yesmaximal, characteristic, complemented
7#10591609C211yesmaximal, characteristic, complemented
8#10591601C211yesmaximal, characteristic, complemented
9#10591588C211yesmaximal, characteristic, complemented
10#10591450C211yesmaximal, characteristic, complemented
11Dic3×#213C211yesmaximal, characteristic, complemented
12#10590943C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590754C211yesmaximal, characteristic, complemented
15#10590720C211yesmaximal, characteristic, complemented
16#83918—31nomaximal
17#80557—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×#237C2211yescharacteristic, complemented
21C2×#3802C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23#64155C2211yescharacteristic
24C2×#3755C2211yescharacteristic, complemented
25C3×#947C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C3×D4×Dic3C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×#916—24no—
31C2×C3×#204C2211yescharacteristic, complemented
32C2×C3×D3×C8C2211yescharacteristic, complemented
33#63981—21no—
34#63978—21no—
35#63966—21no—
36C2×#3722—21no—
37#63926—24no—
38#63922—21no—
39D3×(C2×D3)⋊C4—21no—
40#63909C2211yescharacteristic, complemented
41#63908C2211yescharacteristic, complemented
42#63905—21no—
43C4×#626C2211yescharacteristic
44Dic3×D12C2211yescharacteristic, complemented
45#63885—21no—
46#63871C2211yescharacteristic
47#63864C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51C2×#3710C2211yescharacteristic
52#63659C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63647C2211yescharacteristic
55C3×#835C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58#63575C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5829—31no—
65#5829—31no—
66C2×#916D311yescharacteristic, complemented
67C2×D3×D8—31no—
68C2×D3×D8—31no—
69#5676—31no—
70#5554—31no—
71C3×#463—31no—
72#5238—31no—
73#5238—31no—
74#5191—31no—
75#5188—31no—
76#5169—31no—
77#5169—31no—
78#5169—31no—
79#5169—61no—
80#5165—31no—
81#5165D311yescharacteristic, complemented
82#5158—31no—
83Dic3×D8—31no—
84#5115—31no—
85C8×#67—31no—
86#5059—31no—
87C4×#213—31no—
88#4844—31no—
89#4834—31no—
90#4813—31no—
91#4810—31no—
92#4776—31no—
93#4775—31no—
94C23×C3⋊D3—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99D4×C3⋊D3—22no—
100D4×C3⋊D3—41no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C3×#67—21no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C3×#239—22no—
107C3×#239—41no—
108C3×#237—22no—
109C3×#237—41no—
110C2×C3×D12—21no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#626—21no—
117C2×#626D411yescharacteristic
118C2×#625—21no—
119C2×#625—21no—
120C2×D3×Dic3—21no—
121#3802—22no—
122#3802—41no—
123C32×SD16—22no—
124C2×C32×C8C2311yescharacteristic
125#3755—41no—
126#3752—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128#3750—21no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#217—21no—
131C3×#216—22no—
132C3×#213—22no—
133C3×#213D414yescomplemented
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×#204—22no—
141C3×D3×C8—22no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3D411yescharacteristic
144#3722—21no—
145#3722—21no—
146#3722—21no—
147#3722—21no—
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3D411yescharacteristic
152#3715—41no—
153#3714—22no—
154#3714—22no—
155#3710—22no—
156#3280—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239C2×D311yescharacteristic, complemented
160C2×#237C2×D311yescharacteristic, complemented
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—61no—
166C3×#135—64no—
167C2×C3×Q16—31no—
168C2×C3×SD16—21no—
169C2×C3×SD16—31no—
170C2×C3×SD16C2×D311yescharacteristic, complemented
171C2×C3×SD16C2×D311yescharacteristic, complemented
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C22×C3×C8—31no—
175C3×#124—31no—
176C3×C4×D4—31no—
177#947—31no—
178#947C2×D311yescharacteristic, complemented
179#946—31no—
180#946—31no—
181#946—31no—
182#946—61no—
183C2×#216C2×D311yescharacteristic, complemented
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—61no—
188#939—61no—
189#939—61no—
190#938—31no—
191#937—61no—
192#937—61no—
193D4×Dic3—31no—
194D4×Dic3C2×D311yescharacteristic, complemented
195C2×#214—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213C2×D311yescharacteristic
199C2×#213C2×D311yescharacteristic
200#930—31no—
201#930—31no—
202#930—61no—
203#929—61no—
204#929—61no—
205C4×#67—31no—
206C2×(C2×D3)⋊C4—61no—
207C2×(C2×D3)⋊C4—61no—
208C2×(C2×D3)⋊C4—61no—
209#916—24no—
210D3×D8—64no—
211D3×D8—64no—
212C2×D24—31no—
213C2×D24—31no—
214C2×#204C2×D311yescharacteristic, complemented
215C2×D3×C8—31no—
216C2×D3×C8—31no—
217C2×D3×C8C2×D311yescharacteristic, complemented
218#897—31no—
219#895—31no—
220#886—61no—
221#884—61no—
222#883—61no—
223#882—61no—
224#882—61no—
225D3×C22⋊C4—61no—
226#875—31no—
227C4×D12—31no—
228C4×D12—31no—
229C3×C4⋊C8—31no—
230C3×#103—31no—
231C3×#102—31no—
232#835—31no—
233#835C2×D311yescharacteristic, complemented
234#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#830—31no—
239#821—31no—
240#821—31no—
241#821—61no—
242#821C2×D311yescharacteristic, complemented
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—61no—
247#818—31no—
248#816—31no—
249Dic3⋊C8C2×D311yescharacteristic, complemented
250C8×Dic3—31no—
251#809—31no—
252#807—31no—
253C4×C3⋊C8—31no—
254C23×C32—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—42no—
257C22×C3⋊D3—42no—
258C22×C3⋊D3—81no—
259C22×C3⋊D3C2×D411yescharacteristic
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3C2×D411yescharacteristic
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C32×Q8—21no—
267C32×Q8—21no—
268C32×D4—21no—
269C32×D4C2×D412yes—
270C2×C32×C4—21no—
271C2×C32×C4C2411yescharacteristic
272#638—42no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3C2×D411yescharacteristic
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4×C3⋊D3—21no—
278C4×C3⋊D3—21no—
279C3×#67—42no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3—81no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—42no—
291C3×D12C2×D412yes—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—42no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297#626—22no—
298#626—81no—
299#625—42no—
300#625—81no—
301D3×Dic3—81no—
302C32×C8—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×#135—31no—
307C22×D8—91no—
308#546—91no—
309#546—91no—
310#495—91no—
311#467—91no—
312#466—91no—
313#463—31no—
314#463—91no—
315#450—91no—
316#450—91no—
317#449—91no—
318#449—91no—
319C4×D8—91no—
320C8×D4—91no—
321C23×D3—61no—
322C23×D3—61no—
323C23×D3—61no—
324C23×D3—61no—
325C23×D3—121no—
326C3×#41—62no—
327C3×#41—62no—
328C3×#41—121no—
329C3×#41—121no—
330C2×C3×Q8—21no—
331C2×C3×Q8—31no—
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×D4—21no—
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4C22×D311yescharacteristic
340C2×C3×D4C22×D311yescharacteristic
341C22×C3×C4—31no—
342C22×C3×C4—61no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C2×#67—21no—
346C2×#67—31no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—121no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—61no—
358#239—22no—
359#239—41no—
360#237—22no—
361#237—41no—
362D3×D4—62no—
363D3×D4—62no—
364D3×D4—62no—
365D3×D4—62no—
366D3×D4—122no—
367D3×D4—121no—
368D3×D4—121no—
369D3×D4—121no—
370D3×D4—121no—
371D3×D4—122no—
372C2×D12—21no—
373C2×D12—31no—
374C2×D12—31no—
375C2×D12—31no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—21no—
381C2×C4×D3—31no—
382C2×C4×D3—31no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3C22×D311yescharacteristic
386C2×Dic6C22×D311yescharacteristic
387C3×Q16—62no—
388C3×SD16—22no—
389C3×SD16—22no—
390C3×SD16—42no—
391C3×SD16—62no—
392C3×D8—34no—
393C3×D8—62no—
394C2×C3×C8—21no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C2×C3×C8—62no—
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C3×C4⋊C4—31no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C42—31no—
405#217—21no—
406#217—31no—
407#217—61no—
408#217—61no—
409#216—22no—
410#215—121no—
411#215—121no—
412#215—121no—
413#215—122no—
414#214—121no—
415#213—22no—
416#213—62no—
417#213—62no—
418#213#6714yescomplemented
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—31no—
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—31no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
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—121no—
437C4⋊Dic3—31no—
438C4⋊Dic3—31no—
439C4⋊Dic3—31no—
440C4⋊Dic3—61no—
441C4⋊Dic3—61no—
442C4⋊Dic3C22×D311yescharacteristic
443Dic3⋊C4—31no—
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446Dic3⋊C4—61no—
447Dic3⋊C4—121no—
448C4×Dic3C22×D311yescharacteristic
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8C22×D311yescharacteristic
453C2×C3⋊C8C22×D311yescharacteristic
454D24—62no—
455D24—62no—
456#204—22no—
457D3×C8—22no—
458D3×C8—62no—
459D3×C8—62no—
460C22×C32—22no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—84no—
470C2×C3⋊D3#13512yescomplemented
471C2×C3×D3—22no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480D32—84no—
481C32×C4—41no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3⋊Dic3—21no—
485C3⋊Dic3—41no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—21no—
489C3×Dic3—41no—
490C3×Dic3—41no—
491C2×#41—31no—
492C2×#41—31no—
493C22×D4—91no—
494C22×D4—91no—
495#135—64no—
496C2×Q16—31no—
497C2×SD16—31no—
498C2×SD16—91no—
499C2×SD16—91no—
500C2×SD16D3211yescharacteristic, complemented
501C2×D8—31no—
502C2×D8—31no—
503C2×D8—91no—
504C2×D8—91no—
505C2×D8—184no—
506C22×C8—31no—
507C22×C8—91no—
508#124—31no—
509#124—91no—
510#123—181no—
511#123—181no—
512C22⋊Q8—91no—
513C22⋊Q8—91no—
514#121—91no—
515#121—91no—
516#121—181no—
517#121—181no—
518#120—181no—
519#120—181no—
520C4×D4—31no—
521C4×D4—91no—
522C4×D4—91no—
523C2×C22⋊C4—181no—
524C2×C22⋊C4—181no—
525#107—91no—
526C4⋊C8—31no—
527#103—31no—
528#103—91no—
529#102—31no—
530#102—91no—
531#102—91no—
532#102—91no—
533C22⋊C8—91no—
534C22⋊C8—91no—
535C4×C8—91no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—31no—
539C23×C3—41no—
540C23×C3—61no—
541C23×C3—61no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—31no—
545C22×D3—31no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—121no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—124no—
559C22×D3—242no—
560C22×D3—241no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3—242no—
565C22×D3D3×D411yescharacteristic
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—21no—
570C3×Q8—41no—
571C3×Q8—41no—
572C3×Q8—61no—
573C3×Q8—61no—
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—22no—
577C3×D4—32no—
578C3×D4—41no—
579C3×D4—61no—
580C3×D4—61no—
581C3×D4—61no—
582C3×D4—122no—
583C3×D4—122no—
584C3×D4D3×D412yes—
585C3×D4C2×#6712yes—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—31no—
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—122no—
598C2×C3×C4—122no—
599C2×C3×C4—241no—
600C2×C3×C4C23×D311yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602#67—42no—
603#67—62no—
604#67—122no—
605#67—122no—
606#67—122no—
607#67—122no—
608#67—124no—
609#67—241no—
610#67—241no—
611#67—241no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—31no—
615C2×Dic3—31no—
616C2×Dic3—42no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—61no—
620C2×Dic3—81no—
621C2×Dic3—121no—
622C2×Dic3—241no—
623C2×Dic3D3×D411yescharacteristic
624C2×Dic3D3×D411yescharacteristic
625C2×Dic3D3×D411yescharacteristic
626D12—21no—
627D12—21no—
628D12—21no—
629D12—42no—
630D12—62no—
631D12—62no—
632D12—61no—
633D12—61no—
634D12—61no—
635D12—61no—
636D12—121no—
637D12—241no—
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—241no—
649Dic6—21no—
650Dic6—21no—
651C3×C8—21no—
652C3×C8—21no—
653C3×C8—32no—
654C3×C8—41no—
655C3×C8—61no—
656C3⋊C8—21no—
657C3⋊C8—61no—
658C3⋊C8—61no—
659C3⋊C8—121no—
660C3⋊C8C2×#6712yes—
661C2×C32—42no—
662C2×C32D4211yescharacteristic
663C2×C32C2×#13511yescharacteristic
664C2×C32#57611yescharacteristic
665C3⋊D3—22no—
666C3⋊D3—81no—
667C3×D3—42no—
668C3×D3—41no—
669C3×D3—81no—
670C24—181no—
671C24—181no—
672#41—62no—
673#41—62no—
674#41—121no—
675#41—121no—
676C2×Q8—31no—
677C2×Q8C2×D3211yescharacteristic
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—91no—
683C2×D4—91no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—182no—
688C2×D4—182no—
689C2×D4—181no—
690C2×D4—361no—
691C2×D4—361no—
692C2×D4C2×D3211yescharacteristic
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—91no—
698C22×C4—181no—
699Q16—62no—
700SD16—22no—
701SD16—62no—
702SD16—361no—
703SD16—361no—
704D8—34no—
705D8—62no—
706D8—182no—
707D8—182no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—62no—
711C2×C8—91no—
712C2×C8—182no—
713C2×C8C2×D3211yescharacteristic
714C4⋊C4—31no—
715C4⋊C4—91no—
716C4⋊C4—91no—
717C4⋊C4—181no—
718C4⋊C4—181no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—91no—
723C22⋊C4—91no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C42—31no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—21no—
735C22×C3—42no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—62no—
743C22×C3—61no—
744C22×C3—81no—
745C22×C3—81no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3C2×D3×D411yescharacteristic
752C22×C3C2×D3×D411yescharacteristic
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—22no—
757C2×D3—32no—
758C2×D3—32no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—62no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—61no—
768C2×D3—61no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—122no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—241no—
779C2×D3—241no—
780C2×D3—244no—
781C2×D3—244no—
782C2×D3—244no—
783C2×D3—244no—
784C2×D3—248no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—41no—
788C3×C4—41no—
789C3×C4—61no—
790C3×C4—61no—
791C3×C4—61no—
792C3×C4—81no—
793C3×C4—121no—
794C3×C4—121no—
795C3×C4C2×D3×D411yescharacteristic
796C3×C4#100411yescharacteristic
797C3×C4#100911yescharacteristic
798C3×C4C22×#6711yescharacteristic
799Dic3—21no—
800Dic3—21no—
801Dic3—21no—
802Dic3—41no—
803Dic3—41no—
804Dic3—61no—
805Dic3—61no—
806Dic3—121no—
807Dic3—121no—
808Dic3—121no—
809Dic3—241no—
810C32#328011yescharacteristic, complemented, Sylow
811C23—21no—
812C23—31no—
813C23—61no—
814C23—61no—
815C23—91no—
816C23—181no—
817C23—362no—
818C23—362no—
819C23—362no—
820C23—362no—
821C23—721no—
822C23—721no—
823Q8—21no—
824Q8—21no—
825Q8—61no—
826Q8—61no—
827D4—21no—
828D4—32no—
829D4—61no—
830D4—61no—
831D4—61no—
832D4—122no—
833D4—122no—
834D4—182no—
835D4—181no—
836D4—181no—
837D4—362no—
838D4—362no—
839D4—721no—
840D4—721no—
841D4D3×#6712yes—
842C2×C4—21no—
843C2×C4—31no—
844C2×C4—31no—
845C2×C4—31no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—91no—
851C2×C4—122no—
852C2×C4—122no—
853C2×C4—181no—
854C2×C4—181no—
855C2×C4—181no—
856C2×C4—241no—
857C2×C4—721no—
858C2×C4C22×D3211yescharacteristic
859C8—21no—
860C8—32no—
861C8—61no—
862C8—181no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—42no—
867C2×C3—42no—
868C2×C3—82no—
869C2×C3—122no—
870C2×C3—121no—
871C2×C3—241no—
872C2×C3#560911yescharacteristic
873C2×C3D3×#13511yescharacteristic
874C2×C3D3×#13511yescharacteristic
875C2×C3#576911yescharacteristic
876C2×C3#577411yescharacteristic
877C2×C3D4×#6711yescharacteristic
878D3—41no—
879D3—42no—
880D3—62no—
881D3—62no—
882D3—81no—
883D3—122no—
884D3—242no—
885D3—241no—
886D3—241no—
887C22—22no—
888C22—41no—
889C22—41no—
890C22—61no—
891C22—61no—
892C22—61no—
893C22—62no—
894C22—92no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—181no—
901C22—181no—
902C22—361no—
903C22—361no—
904C22—361no—
905C22—724no—
906C22—724no—
907C22D32×D411yescharacteristic
908C4—41no—
909C4—61no—
910C4—61no—
911C4—61no—
912C4—121no—
913C4—121no—
914C4—181no—
915C4—361no—
916C4#6431411yescharacteristic
917C4C2×D3×#6711yescharacteristic
918C3—21no—
919C3#8055711yescharacteristic, complemented
920C3#8391811yescharacteristic, complemented
921C2—42no—
922C2—121no—
923C2—122no—
924C2—182no—
925C2—241no—
926C2—721no—
927C2#1059474711yescharacteristic
928C2#1059475511yescharacteristic
929C2#1059529111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3280
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×#916C2semidirect
2. #10595428C2semidirect
3. #10595254C2semidirect
4. C2×#63926C2semidirect
5. #10592868C2semidirect
6. C3×#5165C2semidirect
7. #10591609C2semidirect
8. #10591601C2semidirect
9. #10591588C2semidirect
10. #10591450C2semidirect
11. Dic3×#213C2semidirect
12. #10590943C2semidirect
13. #10590826C2semidirect
14. #10590754C2semidirect
15. #10590720C2semidirect
19. C2×C3×#239C22semidirect
20. C2×C3×#237C22semidirect
22. C2×C32×SD16C22semidirect
24. C2×#3755C22semidirect
25. C3×#947C22semidirect
26. C2×C3×#216C22semidirect
27. C3×D4×Dic3C22semidirect
31. C2×C3×#204C22semidirect
32. C2×C3×D3×C8C22semidirect
40. #63909C22semidirect
41. #63908C22semidirect
44. Dic3×D12C22semidirect
47. #63864C22semidirect
48. C2×#3715C22semidirect
52. #63659C22semidirect
53. #63648C22semidirect
55. C3×#835C22semidirect
56. C3×#821C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. #63575C22semidirect
59. #63566C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. Dic3×C3⋊C8C22semidirect
66. C2×#916D3semidirect
81. #5165D3semidirect
133. C3×#213D4semidirect
159. C2×#239C2×D3semidirect
160. C2×#237C2×D3semidirect
170. C2×C3×SD16C2×D3semidirect
171. C2×C3×SD16C2×D3semidirect
178. #947C2×D3semidirect
183. C2×#216C2×D3semidirect
194. D4×Dic3C2×D3semidirect
214. C2×#204C2×D3semidirect
217. C2×D3×C8C2×D3semidirect
233. #835C2×D3semidirect
242. #821C2×D3semidirect
249. Dic3⋊C8C2×D3semidirect
418. #213#67semidirect
470. C2×C3⋊D3#135semidirect
500. C2×SD16D32semidirect
810. C32#3280semidirect
919. C3#80557semidirect
920. C3#83918semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
#105954282
#105952542
C2×#639262
#105928682
C3×#51652
#105916092
#105916012
#105915882
#105914502
Dic3×#2132
#105909432
#105908262
#105907542
#105907202
#839183
#805573