Finite Group Databasebeta

← #72271296

Subgroups — #72271296

Order 1536.

16800 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#87284C212yesmaximal, complemented
2C2×#84107C212yesmaximal, complemented
3#10955196C211yesmaximal, characteristic, complemented
4#10822443C214yesmaximal, complemented
5#10822436C218yesmaximal, complemented
6#10822429C214yesmaximal, complemented
7C2×#71851C218yesmaximal, complemented
8#10792623C211yesmaximal, characteristic, complemented
9C3×#62842C211yesmaximal, characteristic, complemented
10#6431795—31nomaximal, Sylow
11C22×C3×H(5,𝔽2)C2212yes—
12C23×D3×D4C2211yescharacteristic
13C3×#3496—28no—
14C3×#3485—28no—
15C3×#3484—28no—
16C3×#3449C2214yescomplemented
17C2×C3×#534C2218yescomplemented
18C2×C3×#518C2211yescharacteristic
19#87284—216no—
20#87284—216no—
21C2×#5829—28no—
22C2×#5830C2214yescomplemented
23C2×#5828C2214yescomplemented
24C2×D4×#67—28no—
25C2×#5804C2218yescomplemented
26C22×#937C2218yescomplemented
27C2×#5798C2211yescharacteristic
28C2×#5798C2212yes—
29#84107—216no—
30C2×#5240C2218yescomplemented
31C22×#834C22116yescomplemented
32D4×(C2×D3)⋊C4—28no—
33#82269C2212yescomplemented
34#82267C2212yescomplemented
35#82121C2214yescomplemented
36C2×#4955C2214yescomplemented
37#71851C22116yescomplemented
38#71851C22132yescomplemented
39#71849C22116yescomplemented
40#71592C2214yescomplemented
41C2×#4526C2218yescomplemented
42#62842D311yescharacteristic, complemented
43C2×#3484—32no—
44C2×#2883—32no—
45#34171—31no—
46#23445—34no—
47#23444—38no—
48#23443—34no—
49C2×#2021—38no—
50#20354—31no—
51C25×D3C2312yes—
52C2×C3×H(5,𝔽2)—28no—
53C2×C3×H(5,𝔽2)—28no—
54C2×C3×H(5,𝔽2)—28no—
55C2×C3×H(5,𝔽2)—28no—
56C2×C3×H(5,𝔽2)—28no—
57C2×C3×H(5,𝔽2)—28no—
58C22×C3×#41D418yescomplemented
59C22×C3×#41C2314yes—
60C23×C3×D4D418yescomplemented
61C23×C3×D4C2318yes—
62C23×C3×D4C2311yescharacteristic
63C23×#67—28no—
64C23×#67C2312yes—
65C22×D3×D4—28no—
66C22×D3×D4—24no—
67C22×D3×D4—28no—
68C22×D3×D4—24no—
69C22×D3×D4D418yescomplemented
70C23×D12C2311yescharacteristic
71C23×C4×D3C2311yescharacteristic
72C3×#547—232no—
73C3×#546—264no—
74C3×D42—232no—
75C3×#537—28no—
76C3×#536—28no—
77C3×#535—28no—
78C3×#534—232no—
79C3×#534—216no—
80C3×#534C23116yes—
81C3×#532—28no—
82C3×#525—216no—
83C2×C3×#123—216no—
84C2×C3×#121—216no—
85C2×C3×#120—216no—
86C3×#518—28no—
87C2×C3×C4×D4D418yescomplemented
88C2×C3×#117C2312yes—
89C22×C3×C22⋊C4C2314yes—
90C2×#953—28no—
91C22×#217C2314yes—
92C22×#217C2318yes—
93#5830—216no—
94#5830—216no—
95#5829—2128no—
96#5828—216no—
97#5828—216no—
98C2×#947—24no—
99C2×#946—24no—
100#5804—232no—
101#5804—232no—
102C2×#940—24no—
103C2×#939—216no—
104D4×#67—2128no—
105C2×#938—24no—
106C2×#937—232no—
107C2×#937—216no—
108C2×#937—232no—
109C2×#937C2318yes—
110C2×#937C23116yes—
111#5798—28no—
112#5798—28no—
113#5798D4116yescomplemented
114C2×#935C2318yes—
115C2×D4×Dic3—28no—
116C2×D4×Dic3—24no—
117C2×#930—28no—
118C2×#929—28no—
119C2×C4×#67—28no—
120C22×(C2×D3)⋊C4—28no—
121C22×(C2×D3)⋊C4—28no—
122C2×#926C2312yes—
123C2×#926C2314yes—
124#5240—232no—
125C2×#834—264no—
126C2×#834C23132yes—
127#5213—28no—
128#4988—24no—
129#4987—24no—
130#4958—28no—
131#4955—28no—
132#4955C2314yes—
133#4955C2318yes—
134#4943C2314yes—
135#4939—24no—
136C4×(C2×D3)⋊C4—24no—
137#4526C23116yes—
138C22×H(5,𝔽2)C2×D312yes—
139C24×D4—31no—
140#3496—28no—
141#3485—28no—
142#3484—28no—
143#3484—616no—
144#3484—616no—
145C2×#546—68no—
146C2×D42—68no—
147#3449C2×D314yescomplemented
148C2×#535—34no—
149C2×#534—38no—
150C2×#534C2×D318yescomplemented
151C2×#525—34no—
152C22×#120—38no—
153C2×#518—32no—
154C2×#518—31no—
155C2×#518C2×D311yescharacteristic
156#2883—616no—
157C2×#410—38no—
158C22×#99—316no—
159D4×C22⋊C4—68no—
160#2309—32no—
161#2308—34no—
162#2280—32no—
163C2×#379—34no—
164#2022—316no—
165#2021—316no—
166#2021—332no—
167#1740—34no—
168C2×#342—38no—
169C25×C3C2×D418yescomplemented
170C25×C3C2412yes—
171C24×D3—28no—
172C24×D3—24no—
173C24×D3—28no—
174C24×D3—24no—
175C24×D3—88no—
176C24×D3C2×D418yescomplemented
177C24×D3C2411yescharacteristic
178C24×D3C2412yes—
179C3×H(5,𝔽2)—432no—
180C3×H(5,𝔽2)—432no—
181C3×H(5,𝔽2)—432no—
182C3×H(5,𝔽2)—432no—
183C2×C3×#41—232no—
184C2×C3×#41—232no—
185C2×C3×#41—232no—
186C2×C3×#41—28no—
187C2×C3×#41—28no—
188C2×C3×#41—28no—
189C2×C3×#41—28no—
190C2×C3×#41—28no—
191C2×C3×#41—28no—
192C22×C3×Q8C2×D414yescomplemented
193C22×C3×D4—216no—
194C22×C3×D4—216no—
195C22×C3×D4—216no—
196C22×C3×D4—216no—
197C22×C3×D4—216no—
198C22×C3×D4—216no—
199C22×C3×D4—216no—
200C22×C3×D4—232no—
201C22×C3×D4—232no—
202C22×C3×D4—232no—
203C22×C3×D4C2×D414yes—
204C22×C3×D4C2×D418yes—
205C22×C3×D4C2×D418yes—
206C22×C3×D4C2×D414yes—
207C22×C3×D4C2×D414yescomplemented
208C22×C3×D4C2×D4116yescomplemented
209C22×C3×D4#4114yes—
210C22×C3×D4C2418yes—
211C23×C3×C4C2×D418yescomplemented
212C23×C3×C4C2×D418yescomplemented
213C23×C3×C4C2×D418yescomplemented
214C23×C3×C4C2411yescharacteristic
215C22×#67—24no—
216C22×#67—28no—
217C22×#67—28no—
218C22×#67—28no—
219C22×#67—24no—
220C22×#67—264no—
221C22×#67—216no—
222C22×#67—832no—
223C22×#67C2×D418yescomplemented
224C23×Dic3—28no—
225C23×Dic3—24no—
226C23×Dic3C2411yescharacteristic
227C2×D3×D4—264no—
228C2×D3×D4—232no—
229C2×D3×D4—416no—
230C2×D3×D4—432no—
231C2×D3×D4—416no—
232C22×D12—22no—
233C22×D12—24no—
234C22×D12—24no—
235C22×D12—22no—
236C22×D12C2×D414yescomplemented
237C22×C4×D3—22no—
238C22×C4×D3—24no—
239C22×C4×D3—24no—
240C22×C4×D3—22no—
241C22×C4×D3C2×D414yescomplemented
242C3×C4⋊Q8—28no—
243C3×#127—28no—
244C3×#124—216no—
245C3×#123—264no—
246C3×#123—232no—
247C3×C22⋊Q8—232no—
248C3×#121—264no—
249C3×#121—232no—
250C3×#121—232no—
251C3×#120—264no—
252C3×#120—232no—
253C3×C4×D4—232no—
254C3×C4×D4—232no—
255C3×#117—28no—
256C2×C3×C4⋊C4—216no—
257C2×C3×C4⋊C4C2×D414yescomplemented
258C2×C3×C22⋊C4—232no—
259C2×C3×C22⋊C4—216no—
260C2×C3×C22⋊C4C2×D418yescomplemented
261C2×C3×C22⋊C4C2414yes—
262C2×C3×C42C2×D414yescomplemented
263#953—264no—
264C2×#217—28no—
265C2×#217—28no—
266C2×#217—216no—
267C2×#217—216no—
268C2×#217—24no—
269C2×#217C2×D4132yescomplemented
270C2×#217C2414yes—
271C2×#217C2418yes—
272#947—232no—
273#946—232no—
274#940—232no—
275#939—2128no—
276#938—232no—
277#937—2128no—
278#937—216no—
279#937—232no—
280#937—216no—
281#937—232no—
282#935—216no—
283#935—216no—
284D4×Dic3—264no—
285D4×Dic3—416no—
286#930—264no—
287#929—264no—
288C4×#67—264no—
289C2×(C2×D3)⋊C4—264no—
290C2×(C2×D3)⋊C4—28no—
291C2×(C2×D3)⋊C4—216no—
292C2×(C2×D3)⋊C4—28no—
293C2×(C2×D3)⋊C4—216no—
294C2×(C2×D3)⋊C4—816no—
295#926—28no—
296#926—28no—
297#926C2×D4116yescomplemented
298C2×C4⋊Dic3—24no—
299C2×C4⋊Dic3—22no—
300C2×Dic3⋊C4—28no—
301C2×C4×Dic3—24no—
302C2×C4×Dic3—22no—
303#834—264no—
304C3⋊#95—28no—
305C26—32no—
306C2×H(5,𝔽2)—28no—
307C2×H(5,𝔽2)—28no—
308C2×H(5,𝔽2)—28no—
309C2×H(5,𝔽2)—28no—
310C2×H(5,𝔽2)—28no—
311C2×H(5,𝔽2)—28no—
312C22×#41#6718yescomplemented
313C22×#41C22×D314yes—
314C23×D4—32no—
315C23×D4—38no—
316C23×D4—31no—
317C23×D4—68no—
318C23×D4—68no—
319C23×D4—64no—
320C23×D4—64no—
321C23×D4—68no—
322C23×D4#6718yescomplemented
323C23×D4C22×D318yes—
324C23×D4C22×D311yescharacteristic
325C24×C4—31no—
326#547—232no—
327#546—264no—
328#546—6128no—
329D42—232no—
330D42—6128no—
331#537—28no—
332#536—28no—
333#535—28no—
334#535—616no—
335#535—616no—
336#534—232no—
337#534—216no—
338#534—632no—
339#534—632no—
340#534C22×D3116yes—
341#532—28no—
342C2×#127—64no—
343C2×#124—64no—
344#525—216no—
345#525—616no—
346#525—616no—
347C2×#123—216no—
348C2×#123—38no—
349C2×#123—68no—
350C2×C22⋊Q8—64no—
351C2×#121—216no—
352C2×#121—64no—
353C2×#121—616no—
354C2×#121—68no—
355C2×#120—216no—
356C2×#120—38no—
357C2×#120—316no—
358C2×#120—632no—
359C2×#120—632no—
360C2×#120—68no—
361C2×#120—616no—
362#518—28no—
363#518—316no—
364#518—68no—
365#518—68no—
366C2×C4×D4—68no—
367C2×C4×D4—68no—
368C2×C4×D4—64no—
369C2×C4×D4#6718yescomplemented
370C2×#117—34no—
371C2×#117—32no—
372C2×#117C22×D312yes—
373C22×C22⋊C4—38no—
374C22×C22⋊C4—34no—
375C22×C22⋊C4—68no—
376C22×C22⋊C4—68no—
377C22×C22⋊C4C22×D314yes—
378#410—632no—
379C2×#99—332no—
380C2×#99—664no—
381#390—64no—
382#390—64no—
383#386—68no—
384#386—68no—
385#381—34no—
386#380—64no—
387#379—38no—
388#379—34no—
389#379—68no—
390C4×C22⋊C4—64no—
391#342—316no—
392C24×C3—216no—
393C24×C3—216no—
394C24×C3—216no—
395C24×C3—84no—
396C24×C3—816no—
397C24×C3C22×D414yes—
398C24×C3C22×D418yes—
399C24×C3C22×D418yes—
400C24×C3C22×D418yes—
401C24×C3C22×D414yes—
402C24×C3C2×#4114yes—
403C24×C3C2511yescharacteristic
404C23×D3—21no—
405C23×D3—22no—
406C23×D3—22no—
407C23×D3—24no—
408C23×D3—22no—
409C23×D3—21no—
410C23×D3—232no—
411C23×D3—216no—
412C23×D3—24no—
413C23×D3—22no—
414C23×D3—44no—
415C23×D3—416no—
416C23×D3—432no—
417C23×D3—48no—
418C23×D3—416no—
419C23×D3—48no—
420C23×D3—816no—
421C23×D3—84no—
422C23×D3—832no—
423C23×D3—816no—
424C23×D3—88no—
425C23×D3—816no—
426C23×D3C22×D412yes—
427C23×D3C22×D414yes—
428C3×#41—4128no—
429C3×#41—416no—
430C3×#41—416no—
431C3×#41—416no—
432C3×#41—416no—
433C2×C3×Q8—28no—
434C2×C3×Q8—28no—
435C2×C3×Q8—28no—
436C2×C3×D4—232no—
437C2×C3×D4—232no—
438C2×C3×D4—232no—
439C2×C3×D4—28no—
440C2×C3×D4—28no—
441C2×C3×D4—28no—
442C2×C3×D4—28no—
443C2×C3×D4—28no—
444C2×C3×D4—28no—
445C2×C3×D4—232no—
446C2×C3×D4—28no—
447C2×C3×D4—28no—
448C2×C3×D4—28no—
449C2×C3×D4—432no—
450C2×C3×D4—432no—
451C2×C3×D4—432no—
452C2×C3×D4—432no—
453C2×C3×D4—4128no—
454C2×C3×D4—1616no—
455C2×C3×D4#120132yes—
456C2×C3×D4#120116yes—
457C2×C3×D4#121116yes—
458C2×C3×D4#121132yes—
459C2×C3×D4#127116yes—
460C22×C3×C4—216no—
461C22×C3×C4—216no—
462C22×C3×C4—216no—
463C22×C3×C4—216no—
464C22×C3×C4—216no—
465C22×C3×C4—216no—
466C22×C3×C4—216no—
467C22×C3×C4—88no—
468C22×C3×C4C22×D412yes—
469C22×C3×C4C22×D414yes—
470C22×C3×C4C22×D418yes—
471C22×C3×C4C22×D418yes—
472C22×C3×C4C22×D414yes—
473C22×C3×C4C22×D412yes—
474C22×C3×C4C2×#4112yes—
475C2×#67—232no—
476C2×#67—232no—
477C2×#67—216no—
478C2×#67—264no—
479C2×#67—432no—
480C2×#67—48no—
481C2×#67—416no—
482C2×#67—48no—
483C2×#67—832no—
484C2×#67—8128no—
485C22×Dic3—21no—
486C22×Dic3—28no—
487C22×Dic3—22no—
488C22×Dic3—22no—
489C22×Dic3—21no—
490C22×Dic3—232no—
491C22×Dic3—24no—
492C22×Dic3—48no—
493C22×Dic3—816no—
494C22×Dic3—88no—
495C22×Dic3C22×D412yes—
496D3×D4—4128no—
497C2×D12—216no—
498C2×D12—28no—
499C2×D12—44no—
500C2×D12—48no—
501C2×D12—44no—
502C2×C4×D3—216no—
503C2×C4×D3—28no—
504C2×C4×D3—44no—
505C2×C4×D3—48no—
506C2×C4×D3—44no—
507C3×C4⋊C4—232no—
508C3×C4⋊C4—28no—
509C3×C22⋊C4—264no—
510C3×C22⋊C4—216no—
511C3×C22⋊C4—28no—
512C3×C42—28no—
513#217—232no—
514#217—232no—
515#217—28no—
516#217—28no—
517#217—48no—
518#217C22×D4116yes—
519(C2×D3)⋊C4—232no—
520(C2×D3)⋊C4—264no—
521(C2×D3)⋊C4—416no—
522(C2×D3)⋊C4—816no—
523C4⋊Dic3—216no—
524C4⋊Dic3—44no—
525Dic3⋊C4—232no—
526C4×Dic3—216no—
527C4×Dic3—44no—
528C25—31no—
529C25—38no—
530C25—32no—
531C25—64no—
532C25—68no—
533C25—68no—
534C25—64no—
535C25—248no—
536C25C2×#6718yescomplemented
537C25C23×D312yes—
538H(5,𝔽2)—432no—
539H(5,𝔽2)—432no—
540H(5,𝔽2)—432no—
541H(5,𝔽2)—432no—
542C2×#41—232no—
543C2×#41—232no—
544C2×#41—232no—
545C2×#41—28no—
546C2×#41—28no—
547C2×#41—28no—
548C2×#41—28no—
549C2×#41—28no—
550C2×#41—28no—
551C22×Q8C2×#6714yescomplemented
552C22×D4—216no—
553C22×D4—216no—
554C22×D4—216no—
555C22×D4—216no—
556C22×D4—216no—
557C22×D4—216no—
558C22×D4—216no—
559C22×D4—232no—
560C22×D4—232no—
561C22×D4—232no—
562C22×D4—38no—
563C22×D4—34no—
564C22×D4—68no—
565C22×D4—64no—
566C22×D4—68no—
567C22×D4—68no—
568C22×D4—64no—
569C22×D4—664no—
570C22×D4—616no—
571C22×D4—664no—
572C22×D4—632no—
573C22×D4—64no—
574C22×D4—62no—
575C22×D4—64no—
576C22×D4—62no—
577C22×D4—1232no—
578C22×D4—1216no—
579C22×D4—1216no—
580C22×D4—2432no—
581C22×D4D3×D414yes—
582C22×D4D3×D418yes—
583C22×D4#23714yes—
584C22×D4C2×#6718yes—
585C22×D4C2×#6714yes—
586C22×D4C2×#67116yescomplemented
587C22×D4C2×#6714yescomplemented
588C22×D4C23×D318yes—
589C23×C4—31no—
590C23×C4—34no—
591C23×C4—68no—
592C23×C4—64no—
593C23×C4—62no—
594C23×C4—64no—
595C23×C4—62no—
596C23×C4—64no—
597C23×C4C2×#6718yescomplemented
598C23×C4C2×#6718yescomplemented
599C23×C4C2×#6718yescomplemented
600C23×C4C23×D311yescharacteristic
601C4⋊Q8—28no—
602#127—28no—
603#127—632no—
604#124—216no—
605#124—632no—
606#123—264no—
607#123—232no—
608#123—616no—
609#123—664no—
610#123—616no—
611C22⋊Q8—232no—
612C22⋊Q8—632no—
613#121—264no—
614#121—232no—
615#121—232no—
616#121—664no—
617#121—632no—
618#121—6128no—
619#120—264no—
620#120—232no—
621#120—616no—
622#120—632no—
623#120—616no—
624#120—632no—
625#120—6128no—
626#120—664no—
627C4×D4—232no—
628C4×D4—232no—
629C4×D4—664no—
630C4×D4—664no—
631C4×D4—1216no—
632#117—28no—
633#117—316no—
634#117—68no—
635#117—68no—
636C2×C4⋊C4—216no—
637C2×C4⋊C4—64no—
638C2×C4⋊C4—68no—
639C2×C4⋊C4—62no—
640C2×C4⋊C4C2×#6714yescomplemented
641C2×C22⋊C4—232no—
642C2×C22⋊C4—216no—
643C2×C22⋊C4—332no—
644C2×C22⋊C4—38no—
645C2×C22⋊C4—34no—
646C2×C22⋊C4—664no—
647C2×C22⋊C4—616no—
648C2×C22⋊C4—68no—
649C2×C22⋊C4—68no—
650C2×C22⋊C4—68no—
651C2×C22⋊C4—616no—
652C2×C22⋊C4—616no—
653C2×C22⋊C4—64no—
654C2×C22⋊C4—68no—
655C2×C22⋊C4—616no—
656C2×C22⋊C4—2416no—
657C2×C22⋊C4C2×#6718yescomplemented
658C2×C22⋊C4C23×D314yes—
659C2×C42—64no—
660C2×C42—62no—
661C2×C42C2×#6714yescomplemented
662#99—664no—
663#95—68no—
664C23×C3—28no—
665C23×C3—28no—
666C23×C3—28no—
667C23×C3—48no—
668C23×C3—416no—
669C23×C3—42no—
670C23×C3—416no—
671C23×C3—432no—
672C23×C3—832no—
673C23×C3—84no—
674C23×C3—88no—
675C23×C3—84no—
676C23×C3—832no—
677C23×C3—1616no—
678C23×C3C2×#120116yes—
679C23×C3C2×#12018yes—
680C23×C3C2×#12118yes—
681C23×C3C2×#121116yes—
682C23×C3C2×#12718yes—
683C23×C3C23×D411yescharacteristic
684C23×C3C23×D412yes—
685C23×C3C23×D412yes—
686C23×C3C23×D411yescharacteristic
687C23×C3C22×#4111yescharacteristic
688C22×D3—24no—
689C22×D3—28no—
690C22×D3—24no—
691C22×D3—22no—
692C22×D3—28no—
693C22×D3—24no—
694C22×D3—44no—
695C22×D3—48no—
696C22×D3—44no—
697C22×D3—464no—
698C22×D3—432no—
699C22×D3—42no—
700C22×D3—44no—
701C22×D3—41no—
702C22×D3—42no—
703C22×D3—41no—
704C22×D3—48no—
705C22×D3—416no—
706C22×D3—432no—
707C22×D3—42no—
708C22×D3—44no—
709C22×D3—42no—
710C22×D3—84no—
711C22×D3—832no—
712C22×D3—816no—
713C22×D3—88no—
714C22×D3—84no—
715C22×D3—832no—
716C22×D3—832no—
717C22×D3—864no—
718C3×Q8—416no—
719C3×D4—464no—
720C3×D4—48no—
721C3×D4—48no—
722C3×D4—48no—
723C3×D4—48no—
724C3×D4—416no—
725C3×D4—832no—
726C3×D4#392164yes—
727C2×C3×C4—28no—
728C2×C3×C4—28no—
729C2×C3×C4—28no—
730C2×C3×C4—28no—
731C2×C3×C4—432no—
732C2×C3×C4—432no—
733C2×C3×C4—48no—
734C2×C3×C4—816no—
735C2×C3×C4C2×#12018yes—
736C2×C3×C4C2×#12014yes—
737C2×C3×C4C2×#12114yes—
738C2×C3×C4C2×#12118yes—
739C2×C3×C4C2×#12714yes—
740#67—464no—
741#67—432no—
742#67—864no—
743C2×Dic3—216no—
744C2×Dic3—24no—
745C2×Dic3—22no—
746C2×Dic3—416no—
747C2×Dic3—41no—
748C2×Dic3—42no—
749C2×Dic3—41no—
750C2×Dic3—48no—
751C2×Dic3—44no—
752C2×Dic3—832no—
753C2×Dic3—168no—
754D12—416no—
755C4×D3—416no—
756C24—216no—
757C24—216no—
758C24—216no—
759C24—32no—
760C24—34no—
761C24—61no—
762C24—62no—
763C24—62no—
764C24—61no—
765C24—62no—
766C24—64no—
767C24—632no—
768C24—616no—
769C24—64no—
770C24—62no—
771C24—84no—
772C24—816no—
773C24—124no—
774C24—1216no—
775C24—1232no—
776C24—1216no—
777C24—128no—
778C24—128no—
779C24—244no—
780C24—248no—
781C24—2416no—
782C24—2416no—
783C24—2432no—
784C24—2416no—
785C24C2×D3×D414yes—
786C24C2×D3×D418yes—
787C24C2×#23714yes—
788C24C22×#6718yes—
789C24C22×#6718yes—
790C24C22×#6714yes—
791C24C24×D311yescharacteristic
792#41—4128no—
793#41—416no—
794#41—416no—
795#41—416no—
796#41—416no—
797C2×Q8—28no—
798C2×Q8—28no—
799C2×Q8—28no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—232no—
807C2×D4—232no—
808C2×D4—232no—
809C2×D4—232no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—28no—
813C2×D4—432no—
814C2×D4—432no—
815C2×D4—432no—
816C2×D4—432no—
817C2×D4—4128no—
818C2×D4—632no—
819C2×D4—632no—
820C2×D4—616no—
821C2×D4—664no—
822C2×D4—616no—
823C2×D4—68no—
824C2×D4—1232no—
825C2×D4—1216no—
826C2×D4—128no—
827C2×D4—128no—
828C2×D4—12128no—
829C2×D4—128no—
830C2×D4—124no—
831C2×D4—124no—
832C2×D4—1616no—
833C2×D4—2432no—
834C2×D4—24128no—
835C2×D4#937132yes—
836C2×D4#938116yes—
837C2×D4#939132yes—
838C2×D4#940116yes—
839C2×D4#953116yes—
840C22×C4—216no—
841C22×C4—216no—
842C22×C4—216no—
843C22×C4—216no—
844C22×C4—216no—
845C22×C4—216no—
846C22×C4—216no—
847C22×C4—32no—
848C22×C4—62no—
849C22×C4—61no—
850C22×C4—61no—
851C22×C4—68no—
852C22×C4—62no—
853C22×C4—632no—
854C22×C4—616no—
855C22×C4—68no—
856C22×C4—64no—
857C22×C4—88no—
858C22×C4—128no—
859C22×C4—124no—
860C22×C4—124no—
861C22×C4—128no—
862C22×C4—2416no—
863C22×C4—248no—
864C22×C4C2×D3×D412yes—
865C22×C4C2×D3×D414yes—
866C22×C4C2×#23712yes—
867C22×C4C22×#6718yes—
868C22×C4C22×#6718yes—
869C22×C4C22×#6714yes—
870C22×C4C22×#6712yes—
871C4⋊C4—232no—
872C4⋊C4—28no—
873C4⋊C4—632no—
874C4⋊C4—616no—
875C4⋊C4—124no—
876C22⋊C4—264no—
877C22⋊C4—28no—
878C22⋊C4—216no—
879C22⋊C4—316no—
880C22⋊C4—632no—
881C22⋊C4—664no—
882C22⋊C4—632no—
883C22⋊C4—68no—
884C22⋊C4—632no—
885C22⋊C4—68no—
886C22⋊C4—1216no—
887C22⋊C4—128no—
888C22⋊C4—2416no—
889C42—28no—
890C42—616no—
891C42—124no—
892C22×C3—22no—
893C22×C3—24no—
894C22×C3—216no—
895C22×C3—416no—
896C22×C3—48no—
897C22×C3—41no—
898C22×C3—42no—
899C22×C3—41no—
900C22×C3—48no—
901C22×C3—416no—
902C22×C3—416no—
903C22×C3—48no—
904C22×C3—416no—
905C22×C3—88no—
906C22×C3—1632no—
907C22×C3C2×#392116yes—
908C22×C3C22×#12011yescharacteristic
909C22×C3C22×#12012yes—
910C22×C3C22×#12112yes—
911C22×C3C22×#12111yescharacteristic
912C22×C3C22×#12711yescharacteristic
913C2×D3—28no—
914C2×D3—24no—
915C2×D3—44no—
916C2×D3—44no—
917C2×D3—42no—
918C2×D3—48no—
919C2×D3—42no—
920C2×D3—44no—
921C2×D3—416no—
922C2×D3—48no—
923C2×D3—44no—
924C2×D3—864no—
925C2×D3—84no—
926C2×D3—88no—
927C2×D3—84no—
928C3×C4—48no—
929C3×C4—48no—
930C3×C4C2×#39218yes—
931Dic3—416no—
932Dic3—42no—
933Dic3—84no—
934C23—28no—
935C23—28no—
936C23—28no—
937C23—48no—
938C23—416no—
939C23—42no—
940C23—416no—
941C23—432no—
942C23—64no—
943C23—68no—
944C23—64no—
945C23—62no—
946C23—68no—
947C23—64no—
948C23—832no—
949C23—84no—
950C23—88no—
951C23—84no—
952C23—832no—
953C23—122no—
954C23—124no—
955C23—128no—
956C23—1216no—
957C23—124no—
958C23—128no—
959C23—124no—
960C23—1264no—
961C23—1232no—
962C23—121no—
963C23—122no—
964C23—121no—
965C23—122no—
966C23—1232no—
967C23—124no—
968C23—122no—
969C23—1616no—
970C23—2432no—
971C23—244no—
972C23—2432no—
973C23—248no—
974C23—244no—
975C23—2416no—
976C23—2432no—
977C23—2464no—
978C23C2×#937116yes—
979C23C2×#93818yes—
980C23C2×#939116yes—
981C23C2×#94018yes—
982C23C2×#95318yes—
983C23C22×D3×D412yes—
984C23C22×D3×D411yescharacteristic
985C23C22×#23711yescharacteristic
986C23C23×#6712yes—
987C23C23×#6711yescharacteristic
988Q8—416no—
989D4—464no—
990D4—48no—
991D4—48no—
992D4—48no—
993D4—48no—
994D4—416no—
995D4—832no—
996D4—1264no—
997D4—1232no—
998D4—1216no—
999D4—2464no—
1000D4#5223164yes—
1001C2×C4—28no—
1002C2×C4—28no—
1003C2×C4—28no—
1004C2×C4—28no—
1005C2×C4—432no—
1006C2×C4—432no—
1007C2×C4—48no—
1008C2×C4—616no—
1009C2×C4—64no—
1010C2×C4—62no—
1011C2×C4—816no—
1012C2×C4—1216no—
1013C2×C4—121no—
1014C2×C4—122no—
1015C2×C4—121no—
1016C2×C4—1216no—
1017C2×C4—128no—
1018C2×C4—124no—
1019C2×C4—2432no—
1020C2×C4—488no—
1021C2×C4C2×#93718yes—
1022C2×C4C2×#93814yes—
1023C2×C4C2×#93918yes—
1024C2×C4C2×#94014yes—
1025C2×C4C2×#95314yes—
1026C2×C3—22no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—22no—
1030C2×C3—216no—
1031C2×C3—88no—
1032C2×C3C22×#39211yescharacteristic
1033C2×C3#6039912yes—
1034D3—44no—
1035D3—84no—
1036C22—22no—
1037C22—216no—
1038C22—24no—
1039C22—416no—
1040C22—48no—
1041C22—41no—
1042C22—42no—
1043C22—41no—
1044C22—48no—
1045C22—416no—
1046C22—416no—
1047C22—416no—
1048C22—48no—
1049C22—68no—
1050C22—64no—
1051C22—88no—
1052C22—124no—
1053C22—124no—
1054C22—122no—
1055C22—128no—
1056C22—1216no—
1057C22—128no—
1058C22—124no—
1059C22—122no—
1060C22—124no—
1061C22—1632no—
1062C22—2464no—
1063C22—244no—
1064C22—248no—
1065C22—244no—
1066C22C2×#5223116yes—
1067C22C22×#93912yes—
1068C22C22×#94011yescharacteristic
1069C22C22×#93712yes—
1070C22C22×#93811yescharacteristic
1071C22C22×#95311yescharacteristic
1072C4—48no—
1073C4—48no—
1074C4—1216no—
1075C4—122no—
1076C4—244no—
1077C4C2×#522318yes—
1078C3#643179511yescharacteristic, complemented, Sylow
1079C2—22no—
1080C2—21no—
1081C2—21no—
1082C2—22no—
1083C2—216no—
1084C2—88no—
1085C2—124no—
1086C2—244no—
1087C2C22×#522311yescharacteristic
1088C2#1166193812yes—
subgroupG/H
centerC22C22×#953
commutator, cosocleC24×C3C25
FrattiniC24C24×D3
FittingC3×#62842C2
socleC22×C3C22×#120
hypercenter#62842D3
hypocenterC3#6431795
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×D4 ◁ #62842

Complements

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

NH ≅ G/Ntype
1. C2×#87284C2semidirect
2. C2×#84107C2semidirect
3. #10955196C2semidirect
4. #10822443C2semidirect
5. #10822436C2semidirect
6. #10822429C2semidirect
7. C2×#71851C2semidirect
8. #10792623C2semidirect
9. C3×#62842C2semidirect
16. C3×#3449C22semidirect
17. C2×C3×#534C22semidirect
22. C2×#5830C22semidirect
23. C2×#5828C22semidirect
25. C2×#5804C22semidirect
26. C22×#937C22semidirect
30. C2×#5240C22semidirect
31. C22×#834C22semidirect
33. #82269C22semidirect
34. #82267C22semidirect
35. #82121C22semidirect
36. C2×#4955C22semidirect
37. #71851C22semidirect
38. #71851C22semidirect
39. #71849C22semidirect
40. #71592C22semidirect
41. C2×#4526C22semidirect
42. #62842D3semidirect
58. C22×C3×#41D4semidirect
60. C23×C3×D4D4semidirect
69. C22×D3×D4D4semidirect
87. C2×C3×C4×D4D4semidirect
113. #5798D4semidirect
147. #3449C2×D3semidirect
150. C2×#534C2×D3semidirect
169. C25×C3C2×D4semidirect
176. C24×D3C2×D4semidirect
192. C22×C3×Q8C2×D4semidirect
207. C22×C3×D4C2×D4semidirect
208. C22×C3×D4C2×D4semidirect
211. C23×C3×C4C2×D4semidirect
212. C23×C3×C4C2×D4semidirect
213. C23×C3×C4C2×D4semidirect
223. C22×#67C2×D4semidirect
236. C22×D12C2×D4semidirect
241. C22×C4×D3C2×D4semidirect
257. C2×C3×C4⋊C4C2×D4semidirect
260. C2×C3×C22⋊C4C2×D4semidirect
262. C2×C3×C42C2×D4semidirect
269. C2×#217C2×D4semidirect
297. #926C2×D4semidirect
312. C22×#41#67semidirect
322. C23×D4#67semidirect
369. C2×C4×D4#67semidirect
536. C25C2×#67semidirect
551. C22×Q8C2×#67semidirect
586. C22×D4C2×#67semidirect
587. C22×D4C2×#67semidirect
597. C23×C4C2×#67semidirect
598. C23×C4C2×#67semidirect
599. C23×C4C2×#67semidirect
640. C2×C4⋊C4C2×#67semidirect
657. C2×C22⋊C4C2×#67semidirect
661. C2×C42C2×#67semidirect
1078. C3#6431795semidirect

Maximal subgroups

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

subgroupindex
C2×#872842
C2×#841072
#109551962
#108224432
#108224362
#108224292
C2×#718512
#107926232
C3×#628422
#64317953