Finite Group Databasebeta

← #11885817

Subgroups — #11885817

Order 1152.

1185 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
1C2×#64125C211yesmaximal, characteristic, complemented
2#10595431C211yesmaximal, characteristic, complemented
3#10595246C211yesmaximal, characteristic, complemented
4C2×D3×#213C211yesmaximal, characteristic, complemented
5C3×#5169C211yesmaximal, characteristic, complemented
6C3×#5165C211yesmaximal, characteristic, complemented
7#10591606C211yesmaximal, characteristic, complemented
8#10591596C211yesmaximal, characteristic, complemented
9#10591593C211yesmaximal, characteristic, complemented
10#10591457C211yesmaximal, characteristic, complemented
11#10591400C211yesmaximal, characteristic, complemented
12#10590946C211yesmaximal, characteristic, complemented
13#10590906C211yesmaximal, characteristic, complemented
14#10590860C211yesmaximal, characteristic, complemented
15#10590839C211yesmaximal, characteristic, complemented
16#80557—31nomaximal
17#80168—31nomaximal
18C2×#3832C2211yescharacteristic, complemented
19C2×#3830C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic
21C2×D3×D12C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23C2×#3756C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic
25#64125—24no—
26C2×#3744C2211yescharacteristic, complemented
27C2×C8×C3⋊D3C2211yescharacteristic, complemented
28C3×#947C2211yescharacteristic, complemented
29C3×#946C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic, complemented
31C3×D4×Dic3C2211yescharacteristic, complemented
32C2×C3×#213C2211yescharacteristic
33#63978—21no—
34#63977—21no—
35#63962—21no—
36C2×(C2×D3)⋊Dic3—21no—
37D3×#213—24no—
38#63923—21no—
39#63921—21no—
40#63916C2211yescharacteristic, complemented
41#63916C2211yescharacteristic, complemented
42#63910—21no—
43C4×#626C2211yescharacteristic
44#63894C2211yescharacteristic, complemented
45#63860C2211yescharacteristic, complemented
46#63857C2211yescharacteristic
47#63853—21no—
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58#63576C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63#5806—31no—
64C22×#213—31no—
65C2×#916—31no—
66C2×#916—31no—
67C2×#916—61no—
68C2×D3×D8—31no—
69#5676—31no—
70#5630—31no—
71#5554—31no—
72C3×#463—31no—
73C3×#450—31no—
74#5172—31no—
75#5169D311yescharacteristic, complemented
76#5168—31no—
77#5165D311yescharacteristic, complemented
78#5158—31no—
79#5059—31no—
80#5051—31no—
81C4×#213—31no—
82#4844—31no—
83#4834—31no—
84#4813—31no—
85#4810—31no—
86#4787—31no—
87#4781—31no—
88#4776—31no—
89#4775—31no—
90#4775—31no—
91#4756—31no—
92#4731—31no—
93#67⋊C8—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C22×C3⋊Dic3—21no—
100#3832—22no—
101#3832—41no—
102#3830—22no—
103#3830—41no—
104C2×C4⋊(C3⋊D3)—21no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×C4×C3⋊D3C2311yescharacteristic
108C2×#634C2311yescharacteristic
109C2×C3×#67—21no—
110C22×C3×Dic3—21no—
111C3×D3×D4—22no—
112C3×D3×D4—41no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#626D411yescharacteristic
120C2×#624—21no—
121D3×D12—22no—
122D3×D12—41no—
123C32×SD16—22no—
124C2×C32×C8C2311yescharacteristic
125#3756—22no—
126#3753D414yescomplemented
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128#3744—22no—
129C8×C3⋊D3—22no—
130C3×#217—21no—
131C3×#215—41no—
132C3×#213—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3D411yescharacteristic
144#3722—21no—
145#3722D411yescharacteristic
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3D411yescharacteristic
152#3716—41no—
153#3714—22no—
154#3713—22no—
155D3×C3⋊C8—22no—
156#3280—91noSylow
157C22×C3×D4—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#239—61no—
161C2×#237—31no—
162C2×#237—31no—
163C2×#237—61no—
164C2×D3×D4—31no—
165C2×D3×D4C2×D311yescharacteristic
166C22×D12—31no—
167C2×C3×SD16—21no—
168C2×C3×SD16—31no—
169C2×C3×SD16C2×D311yescharacteristic, complemented
170C2×C3×SD16C2×D311yescharacteristic, complemented
171C2×C3×D8—31no—
172C3×#124—31no—
173C3×C22⋊Q8—31no—
174C3×C4×D4—31no—
175#953—61no—
176C2×#217—61no—
177#947C2×D311yescharacteristic, complemented
178#946C2×D311yescharacteristic
179C2×#216—31no—
180C2×#216—31no—
181C2×#216—61no—
182C2×#215C2×D311yescharacteristic, complemented
183#939—61no—
184#938—31no—
185#938—31no—
186#936—31no—
187#935—61no—
188D4×Dic3C2×D311yescharacteristic, complemented
189C2×#214—31no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—61no—
196C2×#213—64no—
197C2×#213C2×D311yescharacteristic
198#930—61no—
199C4×#67—31no—
200C2×(C2×D3)⋊C4—61no—
201#924—31no—
202C22×C3⋊C8—31no—
203#916—64no—
204#916—64no—
205#916—68no—
206D3×D8—64no—
207C2×D24—31no—
208C2×#204—31no—
209C2×#204—31no—
210C2×#204—31no—
211C2×#204—61no—
212C2×D3×C8—31no—
213C2×D3×C8—31no—
214C2×D3×C8—31no—
215C2×D3×C8—61no—
216#897—31no—
217#895—31no—
218#895—31no—
219#895—61no—
220#894—61no—
221#893—31no—
222#886—61no—
223#884—61no—
224#883—61no—
225#882—61no—
226#882—61no—
227#882—61no—
228D3×C22⋊C4—61no—
229D3×C22⋊C4—61no—
230#875—31no—
231C4×D12—31no—
232C4×D12—31no—
233C3×C4⋊C8—31no—
234C3×#103—31no—
235C3×#102—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×C22⋊C8—31no—
239#835C2×D311yescharacteristic, complemented
240#832C2×D311yescharacteristic, complemented
241#821—31no—
242#821C2×D311yescharacteristic, complemented
243#821C2×D311yescharacteristic, complemented
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8C2×D311yescharacteristic
247#816—31no—
248Dic3⋊C8C2×D311yescharacteristic, complemented
249C8×Dic3—31no—
250#810—31no—
251#809—31no—
252#807—31no—
253#807—31no—
254C4×C3⋊C8—31no—
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3C2×D411yescharacteristic
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×D4C2×D412yes—
271C2×C32×C4—21no—
272C2×C32×C4C2411yescharacteristic
273#638—42no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—42no—
276C2×C3⋊Dic3C2×D411yescharacteristic
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—42no—
279C4⋊(C3⋊D3)C2×D412yes—
280C4×C3⋊D3—21no—
281C4×C3⋊D3—21no—
282C4×C3⋊D3—42no—
283#634—21no—
284#634—21no—
285C3×#67—42no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—81no—
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D411yescharacteristic
292C3×D12—21no—
293C3×D12—21no—
294C3×D12—21no—
295C3×D12—21no—
296C3×C4×D3—21no—
297C3×C4×D3—21no—
298#626—22no—
299#626—42no—
300#626—81no—
301#626—81no—
302#624—81no—
303C32×C8—21no—
304C3⋊(C3⋊C8)C2×D412yes—
305C3×C3⋊C8—21no—
306C3×C3⋊C8—21no—
307C2×#135—91no—
308C22×D8—91no—
309#546—91no—
310#546—91no—
311#495—91no—
312#467—91no—
313#466—91no—
314#463—31no—
315#463—91no—
316#450—31no—
317#450—91no—
318#449—91no—
319#449—91no—
320C4×D8—91no—
321C8×D4—91no—
322C24×C3—61no—
323C23×D3—21no—
324C23×D3—61no—
325C23×D3—61no—
326C2×C3×Q8—21no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—62no—
334C2×C3×D4—121no—
335C2×C3×D4C22×D311yescharacteristic
336C2×C3×D4C22×D311yescharacteristic
337C22×C3×C4—31no—
338C22×C3×C4—61no—
339C2×#67—21no—
340C2×#67—31no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—121no—
347C22×Dic3—21no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3—121no—
351#239—62no—
352#239—62no—
353#239—64no—
354#239—121no—
355#239—121no—
356#239—122no—
357#237—64no—
358#237—62no—
359#237—62no—
360#237—121no—
361#237—121no—
362#237—122no—
363D3×D4—22no—
364D3×D4—41no—
365D3×D4—62no—
366D3×D4—121no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—61no—
371C2×D12—62no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—121no—
378C2×D12—121no—
379C2×D12C22×D311yescharacteristic
380C2×D12C22×D311yescharacteristic
381C2×C4×D3—31no—
382C2×C4×D3—31no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3—121no—
389C2×C4×D3C22×D311yescharacteristic
390C2×Dic6—31no—
391C2×Dic6—31no—
392C2×Dic6—61no—
393C3×SD16—24no—
394C3×SD16—22no—
395C3×SD16—22no—
396C3×SD16—121no—
397C3×D8—62no—
398C2×C3×C8—21no—
399C2×C3×C8—31no—
400C2×C3×C8—31no—
401C2×C3×C8C22×D311yescharacteristic
402C2×C3×C8C22×D311yescharacteristic
403C3×C4⋊C4—31no—
404C3×C4⋊C4—31no—
405C3×C4⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C42—31no—
411#217—21no—
412#217—31no—
413#217—61no—
414#217—61no—
415#217—61no—
416#217—61no—
417#217—61no—
418#216—62no—
419#216—62no—
420#216—64no—
421#215—41no—
422#214—121no—
423#213—22no—
424#213—34no—
425#213—34no—
426#213—64no—
427#213—62no—
428#213—62no—
429#213—62no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—31no—
434(C2×D3)⋊C4—31no—
435(C2×D3)⋊C4—31no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4—61no—
443C4⋊Dic3—31no—
444C4⋊Dic3—61no—
445C4⋊Dic3C22×D311yescharacteristic
446C4⋊Dic3C22×D311yescharacteristic
447Dic3⋊C4—21no—
448Dic3⋊C4—31no—
449Dic3⋊C4—61no—
450C4×Dic3C22×D311yescharacteristic
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—61no—
454C2×C3⋊C8—62no—
455C2×C3⋊C8C22×D311yescharacteristic
456C2×C3⋊C8C22×D311yescharacteristic
457D24—62no—
458#204—62no—
459#204—62no—
460#204—64no—
461#204—121no—
462D3×C8—62no—
463D3×C8—62no—
464D3×C8—62no—
465D3×C8—64no—
466C22×C32—22no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C22×D411yescharacteristic
470C2×C3⋊D3—21no—
471C2×C3⋊D3—22no—
472C2×C3⋊D3—21no—
473C2×C3⋊D3—21no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—41no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
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—
485C2×C3×D3#13512yescomplemented
486D32—84no—
487C32×C4—41no—
488C32×C4C22×D411yescharacteristic
489C32×C4H(5,𝔽2)11yescharacteristic
490C3⋊Dic3—21no—
491C3⋊Dic3—41no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—41no—
496C3×Dic3—41no—
497C2×#41—91no—
498C2×#41—91no—
499C22×D4—31no—
500C22×D4—91no—
501#135—184no—
502C2×Q16—91no—
503C2×SD16—31no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16D3211yescharacteristic, complemented
507C2×D8—31no—
508C2×D8—91no—
509C2×D8—91no—
510C2×D8—91no—
511C2×D8—184no—
512C22×C8—91no—
513C22×C8—91no—
514#124—31no—
515#124—91no—
516#123—181no—
517#123—181no—
518C22⋊Q8—31no—
519C22⋊Q8—91no—
520#121—91no—
521#121—91no—
522#121—181no—
523#121—181no—
524#120—181no—
525#120—181no—
526C4×D4—31no—
527C4×D4—91no—
528C4×D4—91no—
529C2×C22⋊C4—181no—
530C2×C22⋊C4—181no—
531#107—91no—
532C4⋊C8—31no—
533#103—31no—
534#103—91no—
535#102—31no—
536#102—31no—
537#102—31no—
538#102—91no—
539C22⋊C8—31no—
540C22⋊C8—91no—
541C4×C8—91no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—31no—
545C23×C3—41no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—122no—
549C23×C3—122no—
550C23×C3—241no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—31no—
554C22×D3—31no—
555C22×D3—42no—
556C22×D3—42no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—61no—
560C22×D3—81no—
561C22×D3—121no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—122no—
565C22×D3—122no—
566C22×D3—241no—
567C22×D3—241no—
568C22×D3D3×D411yescharacteristic
569C3×Q8—22no—
570C3×Q8—21no—
571C3×Q8—21no—
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—41no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4—22no—
578C3×D4—41no—
579C3×D4—61no—
580C3×D4—61no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—122no—
584C3×D4D3×D412yes—
585C3×D4D3×D412yes—
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—241no—
598C2×C3×C4C23×D311yescharacteristic
599C2×C3×C4C23×D311yescharacteristic
600#67—42no—
601#67—62no—
602#67—122no—
603#67—122no—
604#67—122no—
605#67—124no—
606#67—241no—
607#67—241no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—81no—
616C2×Dic3—121no—
617C2×Dic3—122no—
618C2×Dic3—122no—
619C2×Dic3—124no—
620C2×Dic3D3×D411yescharacteristic
621C2×Dic3D3×D411yescharacteristic
622C2×Dic3D3×D411yescharacteristic
623D12—21no—
624D12—21no—
625D12—21no—
626D12—21no—
627D12—32no—
628D12—32no—
629D12—62no—
630D12—62no—
631D12—61no—
632D12—61no—
633D12—121no—
634D12—122no—
635D12—122no—
636D12—124no—
637D12—122no—
638D12—241no—
639D12—241no—
640C4×D3—21no—
641C4×D3—21no—
642C4×D3—62no—
643C4×D3—62no—
644C4×D3—61no—
645C4×D3—61no—
646C4×D3—61no—
647C4×D3—61no—
648C4×D3—122no—
649C4×D3—122no—
650C4×D3—124no—
651C4×D3—241no—
652C4×D3—241no—
653Dic6—62no—
654Dic6—61no—
655Dic6—61no—
656Dic6—61no—
657Dic6—61no—
658Dic6—121no—
659C3×C8—22no—
660C3×C8—21no—
661C3×C8—21no—
662C3×C8—61no—
663C3×C8—61no—
664C3⋊C8—21no—
665C3⋊C8—21no—
666C3⋊C8—32no—
667C3⋊C8—32no—
668C3⋊C8—62no—
669C2×C32—42no—
670C2×C32D4211yescharacteristic
671C2×C32C2×#13511yescharacteristic
672C2×C32#57611yescharacteristic
673C3⋊D3—41no—
674C3⋊D3—42no—
675C3×D3—22no—
676C3×D3—81no—
677C3×D3—81no—
678C24—61no—
679C24—181no—
680#41—182no—
681#41—182no—
682#41—361no—
683#41—361no—
684C2×Q8—91no—
685C2×Q8C2×D3211yescharacteristic
686C2×D4—31no—
687C2×D4—31no—
688C2×D4—61no—
689C2×D4—62no—
690C2×D4—91no—
691C2×D4—91no—
692C2×D4—121no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—182no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—361no—
700C2×D4C2×D3211yescharacteristic
701C22×C4—31no—
702C22×C4—61no—
703C22×C4—91no—
704C22×C4—181no—
705C22×C4—181no—
706C22×C4—181no—
707Q16—182no—
708SD16—22no—
709SD16—121no—
710SD16—182no—
711SD16—361no—
712D8—62no—
713D8—94no—
714D8—182no—
715D8—182no—
716C2×C8—31no—
717C2×C8—31no—
718C2×C8—91no—
719C2×C8—182no—
720C2×C8—182no—
721C2×C8C2×D3211yescharacteristic
722C4⋊C4—31no—
723C4⋊C4—31no—
724C4⋊C4—61no—
725C4⋊C4—91no—
726C4⋊C4—181no—
727C22⋊C4—61no—
728C22⋊C4—61no—
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—
738C22⋊C4—181no—
739C42—31no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—21no—
743C22×C3—32no—
744C22×C3—42no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—61no—
750C22×C3—61no—
751C22×C3—81no—
752C22×C3—81no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
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—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—62no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—62no—
777C2×D3—61no—
778C2×D3—62no—
779C2×D3—84no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—122no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—241no—
788C2×D3—241no—
789C2×D3—244no—
790C2×D3—244no—
791C2×D3#91612yescomplemented
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—42no—
795C3×C4—41no—
796C3×C4—41no—
797C3×C4—61no—
798C3×C4—61no—
799C3×C4—61no—
800C3×C4—121no—
801C3×C4—121no—
802C3×C4C2×D3×D411yescharacteristic
803C3×C4C2×D3×D411yescharacteristic
804C3×C4#100411yescharacteristic
805C3×C4#100911yescharacteristic
806Dic3—21no—
807Dic3—21no—
808Dic3—21no—
809Dic3—41no—
810Dic3—41no—
811Dic3—62no—
812Dic3—61no—
813Dic3—61no—
814Dic3—122no—
815Dic3—121no—
816Dic3—121no—
817C32#328011yescharacteristic, complemented, Sylow
818C23—21no—
819C23—31no—
820C23—61no—
821C23—61no—
822C23—91no—
823C23—122no—
824C23—122no—
825C23—181no—
826C23—241no—
827C23—362no—
828C23—362no—
829C23—721no—
830Q8—21no—
831Q8—21no—
832Q8—181no—
833Q8—181no—
834D4—21no—
835D4—61no—
836D4—61no—
837D4—61no—
838D4—61no—
839D4—92no—
840D4—122no—
841D4—182no—
842D4—181no—
843D4—362no—
844D4—362no—
845D4—362no—
846D4—721no—
847D4—721no—
848D4#381112yes—
849C2×C4—21no—
850C2×C4—31no—
851C2×C4—31no—
852C2×C4—31no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—91no—
858C2×C4—181no—
859C2×C4—181no—
860C2×C4—181no—
861C2×C4—241no—
862C2×C4—362no—
863C2×C4—362no—
864C2×C4—721no—
865C2×C4C22×D3211yescharacteristic
866C8—21no—
867C8—61no—
868C8—61no—
869C8—92no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—42no—
874C2×C3—42no—
875C2×C3—62no—
876C2×C3—82no—
877C2×C3—241no—
878C2×C3—241no—
879C2×C3#559011yescharacteristic
880C2×C3#560911yescharacteristic
881C2×C3C2×#91611yescharacteristic
882C2×C3D3×#13511yescharacteristic
883C2×C3#577411yescharacteristic
884C2×C3#577411yescharacteristic
885D3—22no—
886D3—81no—
887D3—81no—
888D3—122no—
889D3—121no—
890D3—122no—
891D3—121no—
892D3—122no—
893D3—242no—
894C22—22no—
895C22—32no—
896C22—41no—
897C22—41no—
898C22—61no—
899C22—61no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—181no—
907C22—181no—
908C22—181no—
909C22—182no—
910C22—244no—
911C22—361no—
912C22—361no—
913C22—724no—
914C22D32×D411yescharacteristic
915C4—41no—
916C4—61no—
917C4—61no—
918C4—61no—
919C4—121no—
920C4—121no—
921C4—181no—
922C4—361no—
923C4#6431411yescharacteristic
924C4C2×#381111yescharacteristic
925C3—21no—
926C3#8016811yescharacteristic, complemented
927C3#8055711yescharacteristic, complemented
928C2—42no—
929C2—62no—
930C2—241no—
931C2—241no—
932C2—361no—
933C2—362no—
934C2D3×#91611yescharacteristic
935C2#1059475011yescharacteristic
936C2#1059529211yescharacteristic
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×#64125C2semidirect
2. #10595431C2semidirect
3. #10595246C2semidirect
4. C2×D3×#213C2semidirect
5. C3×#5169C2semidirect
6. C3×#5165C2semidirect
7. #10591606C2semidirect
8. #10591596C2semidirect
9. #10591593C2semidirect
10. #10591457C2semidirect
11. #10591400C2semidirect
12. #10590946C2semidirect
13. #10590906C2semidirect
14. #10590860C2semidirect
15. #10590839C2semidirect
18. C2×#3832C22semidirect
19. C2×#3830C22semidirect
22. C2×C32×SD16C22semidirect
23. C2×#3756C22semidirect
26. C2×#3744C22semidirect
27. C2×C8×C3⋊D3C22semidirect
28. C3×#947C22semidirect
30. C2×C3×#215C22semidirect
31. C3×D4×Dic3C22semidirect
40. #63916C22semidirect
41. #63916C22semidirect
44. #63894C22semidirect
45. #63860C22semidirect
48. C2×#3716C22semidirect
52. C3×#835C22semidirect
53. C3×#832C22semidirect
54. C3×#821C22semidirect
55. C3×#821C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. #63576C22semidirect
59. #63567C22semidirect
60. #63564C22semidirect
61. #63557C22semidirect
62. Dic3×C3⋊C8C22semidirect
75. #5169D3semidirect
77. #5165D3semidirect
126. #3753D4semidirect
169. C2×C3×SD16C2×D3semidirect
170. C2×C3×SD16C2×D3semidirect
177. #947C2×D3semidirect
182. C2×#215C2×D3semidirect
188. D4×Dic3C2×D3semidirect
239. #835C2×D3semidirect
240. #832C2×D3semidirect
242. #821C2×D3semidirect
243. #821C2×D3semidirect
248. Dic3⋊C8C2×D3semidirect
485. C2×C3×D3#135semidirect
506. C2×SD16D32semidirect
791. C2×D3#916semidirect
817. C32#3280semidirect
926. C3#80168semidirect
927. C3#80557semidirect

Maximal subgroups

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

subgroupindex
C2×#641252
#105954312
#105952462
C2×D3×#2132
C3×#51692
C3×#51652
#105916062
#105915962
#105915932
#105914572
#105914002
#105909462
#105909062
#105908602
#105908392
#805573
#801683