Finite Group Databasebeta

← #11664154

Subgroups — #11664154

Order 768.

2194 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2#85848C211yesmaximal, characteristic, complemented
3#84101C212yesmaximal, complemented
4#82568C214yesmaximal, complemented
5#82566C212yesmaximal, complemented
6#82564C212yesmaximal, complemented
7#82542C214yesmaximal, complemented
8#82538C212yesmaximal, complemented
9#82531C212yesmaximal, complemented
10#82529C212yesmaximal, complemented
11#82526C211yesmaximal, characteristic, complemented
12#82515C211yesmaximal, characteristic, complemented
13#82507C211yesmaximal, characteristic, complemented
14#82310C212yesmaximal, complemented
15#82308C212yesmaximal, complemented
16C2×#5015C211yesmaximal, characteristic, complemented
17#82296C211yesmaximal, characteristic, complemented
18#60590—31nomaximal, Sylow
19C2×C3×H(5,𝔽2)C2211yescharacteristic
20C3×#520—21no—
21C3×#520C2211yescharacteristic
22C3×#520C2211yescharacteristic
23C3×#520C2212yescomplemented
24C3×#518—22no—
25C3×#518—21no—
26C3×#518C2211yescharacteristic
27C3×#518C2212yescomplemented
28C3×C4×#41—21no—
29C3×C4×#41C2211yescharacteristic
30C3×C4×#41C2211yescharacteristic
31C3×C4×#41C2212yescomplemented
32C2×C3×C4×D4—21no—
33C2×C3×C4×D4—22no—
34C2×C3×C4×D4C2211yescharacteristic
35C2×C3×C4×D4C2212yescomplemented
36#5830C2212yes—
37C2×#949C2212yes—
38C22×#213C2212yes—
39#5585—21no—
40#5585—21no—
41#5553—21no—
42#5553—21no—
43#5550—22no—
44#5550—22no—
45#5535C2214yescomplemented
46#5521C2212yescomplemented
47#5477C2212yescomplemented
48#5477C2212yescomplemented
49C2×#874C2211yescharacteristic, complemented
50#5470C2211yescharacteristic, complemented
51#5238C2214yescomplemented
52#5238C2214yescomplemented
53#5234C2212yes—
54#5233C2212yes—
55#5217C2214yescomplemented
56#5217C2214yescomplemented
57#5215C2212yes—
58#5027C2212yescomplemented
59#5027C2212yescomplemented
60#5026C2214yescomplemented
61C4×#215C2214yescomplemented
62#5022C2212yescomplemented
63#5021C2211yescharacteristic, complemented
64#5020C2211yescharacteristic, complemented
65#5015C2212yescomplemented
66#5015C2212yescomplemented
67#5015C2212yescomplemented
68#5015C2212yescomplemented
69#5015C2214yescomplemented
70#5014C2214yescomplemented
71#5014C2214yescomplemented
72#5014C2214yescomplemented
73C4×#213C2214yescomplemented
74C4×#213C2214yescomplemented
75C4×#213C2214yescomplemented
76#5009C2212yescomplemented
77#5009C2214yescomplemented
78#5008C2211yescharacteristic, complemented
79#5008C2212yescomplemented
80#5007C2211yescharacteristic, complemented
81#5007C2212yescomplemented
82#5003C2214yescomplemented
83#5003C2214yescomplemented
84#5001C2212yescomplemented
85#5000C2214yescomplemented
86#4998C2212yescomplemented
87#4997C2212yescomplemented
88#4968C2214yescomplemented
89#4967C2214yescomplemented
90C2×#809C2212yescomplemented
91#4964C2212yescomplemented
92#4926C2212yescomplemented
93#4925C2212yescomplemented
94#4924C2211yescharacteristic, complemented
95C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
96#3508—31no—
97C4×H(5,𝔽2)D311yescharacteristic, complemented
98#3122—34no—
99#3119—34no—
100#3115—32no—
101#3109—32no—
102#3106—32no—
103#3100—32no—
104#3096—32no—
105#3077—31no—
106#3076—31no—
107#3038—31no—
108C2×#459—31no—
109#3008—32no—
110#2948—32no—
111#2946—32no—
112#2925—31no—
113C3×H(5,𝔽2)—24no—
114C3×H(5,𝔽2)—24no—
115C2×C3×#41—21no—
116C2×C3×#41C2312yes—
117C2×C3×#41C2311yescharacteristic
118C2×C3×#41C2311yescharacteristic
119C22×C3×D4—22no—
120C22×C3×D4—21no—
121C22×C3×D4C2312yes—
122C22×C3×D4C2311yescharacteristic
123C23×C3×C4—21no—
124C23×C3×C4—22no—
125C2×#235—22no—
126C2×#235—22no—
127C22×D12—21no—
128C22×D12—21no—
129C22×D12C2312yes—
130C3×C4×Q8—21no—
131C3×C4×Q8D411yescharacteristic
132C3×C4×Q8D411yescharacteristic
133C3×C4×Q8C2311yescharacteristic
134C3×C4×Q8C2311yescharacteristic
135C3×C4×Q8C2312yes—
136C3×C4×D4—22no—
137C3×C4×D4—21no—
138C3×C4×D4—21no—
139C3×C4×D4—22no—
140C3×C4×D4—21no—
141C3×C4×D4—22no—
142C3×C4×D4—21no—
143C3×C4×D4—22no—
144C3×C4×D4—21no—
145C3×C4×D4—22no—
146C3×C4×D4—22no—
147C3×C4×D4—22no—
148C3×C4×D4—22no—
149C3×C4×D4—21no—
150C3×C4×D4—22no—
151C3×C4×D4—21no—
152C3×C4×D4—22no—
153C3×C4×D4D412yes—
154C3×C4×D4D412yes—
155C3×C4×D4D411yescharacteristic
156C3×C4×D4D411yescharacteristic
157C3×C4×D4C2312yes—
158C3×C4×D4C2311yescharacteristic
159C3×C4×D4C2312yes—
160C3×C4×D4C2311yescharacteristic
161C3×C4×D4C2312yes—
162C3×C4×D4C2312yes—
163C3×C4×D4C2312yes—
164C3×#117—21no—
165C3×#117—22no—
166C3×#117—21no—
167C3×#117—22no—
168C3×#117C2311yescharacteristic
169C3×#117C2312yes—
170C3×#117C2311yescharacteristic
171C3×#117C2312yes—
172C2×C3×C4⋊C4—21no—
173C2×C3×C4⋊C4—22no—
174C2×C3×C4⋊C4C2311yescharacteristic
175C2×C3×C4⋊C4C2312yes—
176C2×C3×C22⋊C4—21no—
177C2×C3×C22⋊C4—22no—
178C2×C3×C22⋊C4—22no—
179C2×C3×C22⋊C4—22no—
180C2×C3×C22⋊C4—22no—
181C2×C3×C42—21no—
182C2×C3×C42—22no—
183C2×C3×C42C2311yescharacteristic
184C2×C3×C42C2312yes—
185#949—28no—
186#947—22no—
187C2×#215C2314yes—
188#940—22no—
189#937—24no—
190C2×#213—28no—
191C2×#213C2314yes—
192C2×#213C2314yes—
193C2×#213C2314yes—
194#930—22no—
195#930—22no—
196#930C2314yes—
197#930C2314yes—
198#926C2312yes—
199#924—21no—
200#924—21no—
201C2×#208C2312yes—
202C22×C3⋊C8C2312yes—
203#894—24no—
204#894—24no—
205#893—22no—
206#893—22no—
207#884—24no—
208#884—24no—
209D3×C22⋊C4—24no—
210#875—22no—
211#875—22no—
212#874—21no—
213#874—21no—
214#874C2312yes—
215#874C2312yes—
216C4×D12—22no—
217C4×D12—22no—
218C4×D12C2314yes—
219C4×D12C2314yes—
220#870C2312yes—
221#869C2311yescharacteristic
222#869C2311yescharacteristic
223C4×Dic6—21no—
224C4×Dic6—21no—
225#835C2312yes—
226#835C2312yes—
227#832C2314yes—
228#832C2314yes—
229#832C2312yes—
230#832C2312yes—
231#830C2314yes—
232#830C2314yes—
233#809C2314yes—
234#809C2314yes—
235#809C2314yes—
236#809C2314yes—
237#808C2314yes—
238#808C2312yes—
239#808C2312yes—
240#807C2314yes—
241#807C2312yes—
242#807C2312yes—
243C4⋊(C3⋊C8)C2311yescharacteristic
244C4⋊(C3⋊C8)C2311yescharacteristic
245C4⋊(C3⋊C8)C2312yes—
246C4⋊(C3⋊C8)C2312yes—
247C4⋊(C3⋊C8)C2312yes—
248#803C2314yes—
249C4×C3⋊C8C2314yes—
250C2×H(5,𝔽2)C2×D311yescharacteristic
251C2×AGL(1,ℤ/8)—32no—
252C22×D8—32no—
253#559—61no—
254#559—61no—
255#550—61no—
256#550—61no—
257#546—62no—
258#546—62no—
259#540—34no—
260#535—32no—
261#533—31no—
262#532—32no—
263#532—32no—
264C2×#127—31no—
265#520—21no—
266#520C2×D311yescharacteristic
267#520C2×D311yescharacteristic
268#520C2×D312yescomplemented
269#518—22no—
270#518—21no—
271#518—32no—
272#518C2×D311yescharacteristic
273#518C2×D312yescomplemented
274C4×#41—21no—
275C4×#41C2×D311yescharacteristic
276C4×#41C2×D311yescharacteristic
277C4×#41C2×D312yescomplemented
278C2×C4×D4—21no—
279C2×C4×D4—22no—
280C2×C4×D4C2×D311yescharacteristic
281C2×C4×D4C2×D312yescomplemented
282#482—34no—
283#482—34no—
284#481—34no—
285#480—34no—
286#479—32no—
287#478—32no—
288#478—34no—
289#477—31no—
290#476—31no—
291#476—32no—
292#475—31no—
293#474—31no—
294#474—32no—
295#460—32no—
296#460—32no—
297#459—32no—
298#459—32no—
299#459—32no—
300#459—34no—
301#459—32no—
302#449—34no—
303#449—34no—
304#447—34no—
305#447—34no—
306#442—34no—
307#442—34no—
308#442—34no—
309#440—34no—
310C4×SD16—34no—
311C4×D8—34no—
312C4×D8—34no—
313C4×D8—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428—32no—
318#427—32no—
319#423—31no—
320C2×C4⋊C8—31no—
321#418—32no—
322#418—32no—
323#416—32no—
324C2×#102—32no—
325#408—32no—
326#405—32no—
327C24×C3—22no—
328C24×C3—21no—
329C23×D3—22no—
330C3×#41—28no—
331C3×#41—24no—
332C3×#41—24no—
333C3×#41—22no—
334C3×#41—22no—
335C3×#41—22no—
336C3×#41#4114yescomplemented
337C2×C3×Q8C2×D411yescharacteristic
338C2×C3×Q8C2411yescharacteristic
339C2×C3×D4—216no—
340C2×C3×D4—28no—
341C2×C3×D4—22no—
342C2×C3×D4—21no—
343C2×C3×D4—24no—
344C2×C3×D4—24no—
345C2×C3×D4—22no—
346C2×C3×D4—21no—
347C2×C3×D4—22no—
348C2×C3×D4C2×D412yes—
349C2×C3×D4C2×D411yescharacteristic
350C2×C3×D4#4114yescomplemented
351C2×C3×D4C2411yescharacteristic
352C2×C3×D4C2412yes—
353C22×C3×C4—22no—
354C22×C3×C4—21no—
355C22×C3×C4—22no—
356C22×C3×C4—21no—
357C22×C3×C4—21no—
358C22×C3×C4—22no—
359C22×C3×C4—21no—
360C22×C3×C4—22no—
361C22×C3×C4—22no—
362C22×C3×C4—22no—
363C22×C3×C4—22no—
364C22×C3×C4—82no—
365C22×C3×C4—84no—
366C22×C3×C4C2×D411yescharacteristic
367C22×C3×C4C2×D412yes—
368C22×C3×C4C2×D411yescharacteristic
369C22×C3×C4C2×D412yes—
370C22×C3×C4C2412yes—
371C22×C3×C4C2411yescharacteristic
372C2×#67—24no—
373C2×#67—24no—
374#235—84no—
375#235—84no—
376C2×D12—24no—
377C2×D12—24no—
378C2×D12—22no—
379C2×D12—22no—
380C2×D12—22no—
381C2×D12—22no—
382C2×D12—22no—
383C2×D12—82no—
384C2×D12—82no—
385C2×D12C2414yes—
386C2×C4×D3—24no—
387C2×C4×D3—24no—
388C2×Dic6—21no—
389C2×Dic6—21no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4—22no—
392C3×C4⋊C4—22no—
393C3×C4⋊C4—21no—
394C3×C4⋊C4—21no—
395C3×C4⋊C4C2×D411yescharacteristic
396C3×C4⋊C4C2×D411yescharacteristic
397C3×C4⋊C4C2×D412yes—
398C3×C4⋊C4C2×D412yes—
399C3×C4⋊C4C2412yes—
400C3×C4⋊C4C2411yescharacteristic
401C3×C4⋊C4C2411yescharacteristic
402C3×C22⋊C4—22no—
403C3×C22⋊C4—21no—
404C3×C22⋊C4—21no—
405C3×C22⋊C4—22no—
406C3×C22⋊C4—22no—
407C3×C22⋊C4—22no—
408C3×C22⋊C4—21no—
409C3×C22⋊C4—22no—
410C3×C22⋊C4—22no—
411C3×C22⋊C4C2×D412yes—
412C3×C22⋊C4C2×D412yes—
413C3×C22⋊C4C2×D412yes—
414C3×C42—21no—
415C3×C42—21no—
416C3×C42—22no—
417C3×C42—22no—
418C3×C42—21no—
419C3×C42C2×D411yescharacteristic
420C3×C42C2×D411yescharacteristic
421C3×C42C2×D412yes—
422C3×C42C2×D412yes—
423C3×C42C2412yes—
424C3×C42C2411yescharacteristic
425C3×C42C2411yescharacteristic
426#217—22no—
427#215—28no—
428#213—28no—
429#213—28no—
430#213—28no—
431(C2×D3)⋊C4—24no—
432(C2×D3)⋊C4—24no—
433(C2×D3)⋊C4—24no—
434(C2×D3)⋊C4—24no—
435C4⋊Dic3—21no—
436C4⋊Dic3—21no—
437C4⋊Dic3C2412yes—
438C4⋊Dic3C2412yes—
439Dic3⋊C4—22no—
440Dic3⋊C4—22no—
441C4×Dic3—22no—
442#208—24no—
443C2×C3⋊C8—24no—
444C2×C3⋊C8C2412yes—
445C2×C3⋊C8C2414yes—
446C2×C3⋊C8C2412yes—
447H(5,𝔽2)—24no—
448H(5,𝔽2)—24no—
449C2×#41—21no—
450C2×#41—62no—
451C2×#41—62no—
452C2×#41C22×D312yes—
453C2×#41C22×D311yescharacteristic
454C2×#41C22×D311yescharacteristic
455C22×D4—22no—
456C22×D4—21no—
457C22×D4—32no—
458C22×D4—61no—
459C22×D4—61no—
460C22×D4C22×D312yes—
461C22×D4C22×D311yescharacteristic
462C23×C4—21no—
463C23×C4—22no—
464AGL(1,ℤ/8)—68no—
465C2×SD16—34no—
466C2×D8—34no—
467C2×D8—34no—
468C2×D8—34no—
469C2×D8—68no—
470C2×M16—32no—
471C22×C8—32no—
472C4⋊Q8—31no—
473C4⋊Q8—31no—
474#127—32no—
475#127—32no—
476#127—62no—
477#127—61no—
478#127—61no—
479#125—32no—
480#124—62no—
481#124—62no—
482#124—62no—
483#123—64no—
484#123—64no—
485C22⋊Q8—61no—
486C22⋊Q8—61no—
487#121—34no—
488#121—34no—
489#121—62no—
490#121—62no—
491#121—64no—
492#121—64no—
493#120—64no—
494C4×Q8—21no—
495C4×Q8—61no—
496C4×Q8—61no—
497C4×Q8#6711yescharacteristic
498C4×Q8#6711yescharacteristic
499C4×Q8C22×D311yescharacteristic
500C4×Q8C22×D311yescharacteristic
501C4×Q8C22×D312yes—
502C4×D4—22no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—22no—
506C4×D4—21no—
507C4×D4—22no—
508C4×D4—21no—
509C4×D4—22no—
510C4×D4—21no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—21no—
516C4×D4—22no—
517C4×D4—21no—
518C4×D4—22no—
519C4×D4—34no—
520C4×D4—34no—
521C4×D4—62no—
522C4×D4—62no—
523C4×D4—62no—
524C4×D4—62no—
525C4×D4#6712yes—
526C4×D4#6711yescharacteristic
527C4×D4#6712yes—
528C4×D4#6711yescharacteristic
529C4×D4C22×D312yes—
530C4×D4C22×D312yes—
531C4×D4C22×D311yescharacteristic
532C4×D4C22×D312yes—
533C4×D4C22×D312yes—
534C4×D4C22×D311yescharacteristic
535C4×D4C22×D312yes—
536#117—21no—
537#117—22no—
538#117—21no—
539#117—22no—
540#117—32no—
541#117C22×D311yescharacteristic
542#117C22×D312yes—
543#117C22×D311yescharacteristic
544#117C22×D312yes—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4C22×D311yescharacteristic
548C2×C4⋊C4C22×D312yes—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—64no—
555C2×C42—21no—
556C2×C42—22no—
557C2×C42C22×D311yescharacteristic
558C2×C42C22×D312yes—
559#107—32no—
560#107—32no—
561#107—34no—
562#106—32no—
563#106—32no—
564#106—34no—
565C4⋊C8—31no—
566C4⋊C8—31no—
567C4⋊C8—32no—
568C4⋊C8—32no—
569C4⋊C8—32no—
570#103—32no—
571#103—32no—
572#102—32no—
573#102—32no—
574#102—34no—
575#102—34no—
576#102—34no—
577#102—34no—
578#102—34no—
579#102—34no—
580C22⋊C8—34no—
581C22⋊C8—34no—
582#97—34no—
583C4×C8—34no—
584C23×C3—28no—
585C23×C3—22no—
586C23×C3—21no—
587C23×C3—24no—
588C23×C3—81no—
589C23×C3—82no—
590C23×C3—81no—
591C23×C3—82no—
592C23×C3C22×D412yes—
593C23×C3C22×D411yescharacteristic
594C22×D3—24no—
595C22×D3—44no—
596C22×D3—82no—
597C22×D3—82no—
598C3×Q8—22no—
599C3×Q8—21no—
600C3×Q8C2×#4112yes—
601C3×D4—28no—
602C3×D4—28no—
603C3×D4—24no—
604C3×D4—24no—
605C3×D4—22no—
606C3×D4—24no—
607C3×D4—22no—
608C3×D4—21no—
609C3×D4C2×#4112yes—
610C3×D4C2×#4114yes—
611C2×C3×C4—28no—
612C2×C3×C4—21no—
613C2×C3×C4—24no—
614C2×C3×C4—22no—
615C2×C3×C4—24no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—22no—
621C2×C3×C4—41no—
622C2×C3×C4—42no—
623C2×C3×C4—42no—
624C2×C3×C4—44no—
625C2×C3×C4—82no—
626C2×C3×C4—81no—
627C2×C3×C4—82no—
628C2×C3×C4—82no—
629C2×C3×C4—82no—
630C2×C3×C4—81no—
631C2×C3×C4—82no—
632C2×C3×C4C22×D411yescharacteristic
633C2×C3×C4C22×D411yescharacteristic
634C2×C3×C4C22×D411yescharacteristic
635C2×C3×C4C22×D412yes—
636C2×C3×C4C22×D412yes—
637C2×C3×C4C22×D412yes—
638C2×C3×C4C22×D411yescharacteristic
639C2×C3×C4C22×D411yescharacteristic
640C2×C3×C4C2×#4112yes—
641C2×C3×C4C2×#4112yes—
642C2×C3×C4C2511yescharacteristic
643#67—84no—
644#67—84no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647D12—24no—
648D12—24no—
649D12—44no—
650D12—44no—
651D12—44no—
652D12—82no—
653D12—82no—
654C4×D3—84no—
655C4×D3—84no—
656Dic6—42no—
657Dic6—42no—
658C3⋊C8—22no—
659C3⋊C8—22no—
660C3⋊C8—24no—
661C24—22no—
662C24—21no—
663C24—62no—
664#41—28no—
665#41—24no—
666#41—24no—
667#41—22no—
668#41—22no—
669#41—22no—
670#41—244no—
671#41—244no—
672#41#23514yescomplemented
673C2×Q8—61no—
674C2×Q8—61no—
675C2×Q8C2×#6711yescharacteristic
676C2×Q8C23×D311yescharacteristic
677C2×D4—216no—
678C2×D4—28no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—24no—
682C2×D4—24no—
683C2×D4—22no—
684C2×D4—22no—
685C2×D4—21no—
686C2×D4—34no—
687C2×D4—64no—
688C2×D4—64no—
689C2×D4—64no—
690C2×D4—64no—
691C2×D4—62no—
692C2×D4—62no—
693C2×D4—62no—
694C2×D4—62no—
695C2×D4—62no—
696C2×D4—242no—
697C2×D4—242no—
698C2×D4#23514yescomplemented
699C2×D4C2×#6712yes—
700C2×D4C2×#6711yescharacteristic
701C2×D4C23×D311yescharacteristic
702C2×D4C23×D312yes—
703C22×C4—22no—
704C22×C4—21no—
705C22×C4—22no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—21no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—64no—
715C22×C4—64no—
716C22×C4—82no—
717C22×C4—84no—
718C22×C4C2×#6712yes—
719C22×C4C2×#6711yescharacteristic
720C22×C4C2×#6712yes—
721C22×C4C2×#6711yescharacteristic
722C22×C4C23×D312yes—
723C22×C4C23×D311yescharacteristic
724SD16—68no—
725D8—68no—
726D8—68no—
727D8—68no—
728M16—64no—
729C2×C8—32no—
730C2×C8—34no—
731C2×C8—32no—
732C2×C8—64no—
733C4⋊C4—22no—
734C4⋊C4—21no—
735C4⋊C4—22no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—32no—
739C4⋊C4—32no—
740C4⋊C4—61no—
741C4⋊C4—61no—
742C4⋊C4—62no—
743C4⋊C4—62no—
744C4⋊C4C2×#6711yescharacteristic
745C4⋊C4C2×#6712yes—
746C4⋊C4C2×#6711yescharacteristic
747C4⋊C4C2×#6712yes—
748C4⋊C4C23×D312yes—
749C4⋊C4C23×D311yescharacteristic
750C4⋊C4C23×D311yescharacteristic
751C22⋊C4—22no—
752C22⋊C4—21no—
753C22⋊C4—22no—
754C22⋊C4—21no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—22no—
759C22⋊C4—21no—
760C22⋊C4—62no—
761C22⋊C4—64no—
762C22⋊C4—64no—
763C22⋊C4—64no—
764C22⋊C4—64no—
765C22⋊C4C2×#6712yes—
766C22⋊C4C2×#6712yes—
767C22⋊C4C2×#6712yes—
768C42—21no—
769C42—22no—
770C42—21no—
771C42—22no—
772C42—21no—
773C42—62no—
774C42C2×#6712yes—
775C42C2×#6711yescharacteristic
776C42C2×#6712yes—
777C42C2×#6711yescharacteristic
778C42C23×D312yes—
779C42C23×D311yescharacteristic
780C42C23×D311yescharacteristic
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—24no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—42no—
789C22×C3—41no—
790C22×C3—42no—
791C22×C3—41no—
792C22×C3—84no—
793C22×C3—88no—
794C22×C3#52512yes—
795C22×C3C23×D411yescharacteristic
796C2×D3—44no—
797C2×D3—44no—
798C2×D3—44no—
799C2×D3—164no—
800C3×C4—21no—
801C3×C4—22no—
802C3×C4—21no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—21no—
807C3×C4—41no—
808C3×C4—41no—
809C3×C4—42no—
810C3×C4#52512yes—
811C3×C4#57612yes—
812C3×C4C22×#4111yescharacteristic
813C3×C4C22×#4111yescharacteristic
814Dic3—42no—
815Dic3—42no—
816C23—28no—
817C23—22no—
818C23—21no—
819C23—24no—
820C23—64no—
821C23—81no—
822C23—82no—
823C23—81no—
824C23—82no—
825C23—124no—
826C23—242no—
827C23—242no—
828C23C22×#6712yes—
829C23C22×#6711yescharacteristic
830Q8—21no—
831Q8—22no—
832Q8—122no—
833Q8—122no—
834Q8C2×#23512yes—
835D4—28no—
836D4—28no—
837D4—24no—
838D4—24no—
839D4—22no—
840D4—21no—
841D4—24no—
842D4—22no—
843D4—64no—
844D4—64no—
845D4—124no—
846D4—124no—
847D4—124no—
848D4—242no—
849D4—242no—
850D4—244no—
851D4—244no—
852D4C2×#23512yes—
853D4C2×#23514yes—
854C2×C4—28no—
855C2×C4—21no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—24no—
859C2×C4—22no—
860C2×C4—24no—
861C2×C4—21no—
862C2×C4—22no—
863C2×C4—21no—
864C2×C4—41no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—44no—
868C2×C4—62no—
869C2×C4—62no—
870C2×C4—82no—
871C2×C4—82no—
872C2×C4—82no—
873C2×C4—82no—
874C2×C4—81no—
875C2×C4—81no—
876C2×C4—82no—
877C2×C4—244no—
878C2×C4—244no—
879C2×C4C2×#23512yes—
880C2×C4C2×#23512yes—
881C2×C4C22×#6712yes—
882C2×C4C22×#6712yes—
883C2×C4C22×#6711yescharacteristic
884C2×C4C22×#6711yescharacteristic
885C2×C4C22×#6712yes—
886C2×C4C22×#6711yescharacteristic
887C2×C4C22×#6711yescharacteristic
888C2×C4C22×#6711yescharacteristic
889C2×C4C24×D311yescharacteristic
890C8—62no—
891C8—62no—
892C8—64no—
893C2×C3—22no—
894C2×C3—42no—
895C2×C3—44no—
896C2×C3—42no—
897C2×C3C2×#52511yescharacteristic
898C2×C3C2×#57611yescharacteristic
899C2×C3#358511yescharacteristic
900D3—84no—
901C22—21no—
902C22—21no—
903C22—22no—
904C22—22no—
905C22—24no—
906C22—22no—
907C22—22no—
908C22—42no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—84no—
913C22—88no—
914C22—124no—
915C22—124no—
916C22—124no—
917C22—484no—
918C22#579112yes—
919C22C23×#6711yescharacteristic
920C4—21no—
921C4—22no—
922C4—21no—
923C4—22no—
924C4—22no—
925C4—22no—
926C4—21no—
927C4—41no—
928C4—41no—
929C4—42no—
930C4—122no—
931C4—122no—
932C4#579112yes—
933C4#583512yes—
934C4C22×#23511yescharacteristic
935C4C22×#23511yescharacteristic
936C3#6059011yescharacteristic, complemented, Sylow
937C2—22no—
938C2—42no—
939C2—44no—
940C2—42no—
941C2—244no—
942C2C2×#579111yescharacteristic
943C2C2×#583511yescharacteristic
944C2#8729811yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×C4×H(5,𝔽2)C2
socleC22×C3C23×D4
hypercenterC4×H(5,𝔽2)D3
hypocenterC3#60590
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×#41 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C3×C4×H(5,𝔽2)C2semidirect
2. #85848C2semidirect
3. #84101C2semidirect
4. #82568C2semidirect
5. #82566C2semidirect
6. #82564C2semidirect
7. #82542C2semidirect
8. #82538C2semidirect
9. #82531C2semidirect
10. #82529C2semidirect
11. #82526C2semidirect
12. #82515C2semidirect
13. #82507C2semidirect
14. #82310C2semidirect
15. #82308C2semidirect
16. C2×#5015C2semidirect
17. #82296C2semidirect
23. C3×#520C22semidirect
27. C3×#518C22semidirect
31. C3×C4×#41C22semidirect
35. C2×C3×C4×D4C22semidirect
45. #5535C22semidirect
46. #5521C22semidirect
47. #5477C22semidirect
48. #5477C22semidirect
49. C2×#874C22semidirect
50. #5470C22semidirect
51. #5238C22semidirect
52. #5238C22semidirect
55. #5217C22semidirect
56. #5217C22semidirect
58. #5027C22semidirect
59. #5027C22semidirect
60. #5026C22semidirect
61. C4×#215C22semidirect
62. #5022C22semidirect
63. #5021C22semidirect
64. #5020C22semidirect
65. #5015C22semidirect
66. #5015C22semidirect
67. #5015C22semidirect
68. #5015C22semidirect
69. #5015C22semidirect
70. #5014C22semidirect
71. #5014C22semidirect
72. #5014C22semidirect
73. C4×#213C22semidirect
74. C4×#213C22semidirect
75. C4×#213C22semidirect
76. #5009C22semidirect
77. #5009C22semidirect
78. #5008C22semidirect
79. #5008C22semidirect
80. #5007C22semidirect
81. #5007C22semidirect
82. #5003C22semidirect
83. #5003C22semidirect
84. #5001C22semidirect
85. #5000C22semidirect
86. #4998C22semidirect
87. #4997C22semidirect
88. #4968C22semidirect
89. #4967C22semidirect
90. C2×#809C22semidirect
91. #4964C22semidirect
92. #4926C22semidirect
93. #4925C22semidirect
94. #4924C22semidirect
95. C2×C4⋊(C3⋊C8)C22semidirect
97. C4×H(5,𝔽2)D3semidirect
268. #520C2×D3semidirect
273. #518C2×D3semidirect
277. C4×#41C2×D3semidirect
281. C2×C4×D4C2×D3semidirect
336. C3×#41#41semidirect
350. C2×C3×D4#41semidirect
672. #41#235semidirect
698. C2×D4#235semidirect
936. C3#60590semidirect

Maximal subgroups

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

subgroupindex
C3×C4×H(5,𝔽2)2
#858482
#841012
#825682
#825662
#825642
#825422
#825382
#825312
#825292
#825262
#825152
#825072
#823102
#823082
C2×#50152
#822962
#605903