Finite Group Databasebeta

← #11864602

Subgroups — #11864602

Order 1152.

1604 conjugacy classes of subgroups.

The subgroup lattice has 1041 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic, complemented
3C2×#63932C211yesmaximal, characteristic, complemented
4#10595004C211yesmaximal, characteristic, complemented
5#10592938C211yesmaximal, characteristic, complemented
6C3×#5238C211yesmaximal, characteristic, complemented
7#10591599C211yesmaximal, characteristic, complemented
8#10591586C211yesmaximal, characteristic, complemented
9#10591550C211yesmaximal, characteristic, complemented
10#10591459C211yesmaximal, characteristic, complemented
11#10591447C211yesmaximal, characteristic, complemented
12D3×#832C211yesmaximal, characteristic, complemented
13#10591172C211yesmaximal, characteristic, complemented
14#10591160C211yesmaximal, characteristic, complemented
15#10591145C211yesmaximal, characteristic, complemented
16#84102—31nomaximal
17#80087—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C3×#1009—24no—
20C3×#1009—24no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×#239C2211yescharacteristic
23C2×C3×D3×D4—21no—
24C2×C3×D3×D4—21no—
25C2×C3×D3×D4C2211yescharacteristic
26C2×C3×D3×D4C2211yescharacteristic
27C2×C3×#235—21no—
28C2×C3×#235C2211yescharacteristic
29C22×C3×D12—21no—
30C22×C3×D12C2211yescharacteristic
31C2×#3795C2211yescharacteristic, complemented
32C2×#3756C2211yescharacteristic, complemented
33C2×#3754C2211yescharacteristic, complemented
34#64133C2211yescharacteristic, complemented
35C2×C3×#215C2211yescharacteristic, complemented
36C2×C3×#213C2211yescharacteristic, complemented
37C3×#930C2211yescharacteristic, complemented
38#63970—21no—
39#63970—21no—
40#63947—24no—
41#63932—24no—
42#63908C2211yescharacteristic, complemented
43D3×C4⋊Dic3C2211yescharacteristic, complemented
44#63887—21no—
45#63885—21no—
46#63857C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63657C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#832C2211yescharacteristic, complemented
58C3×#830C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63562C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×C3×H(5,𝔽2)—31no—
66C2×#1009D311yescharacteristic, complemented
67#5833—31no—
68C2×#950—31no—
69C2×#932—31no—
70C2×#916—31no—
71C2×#911—31no—
72#5608—31no—
73C3×#449—31no—
74#5239—31no—
75#5239—31no—
76#5239—31no—
77#5239—61no—
78#5238—31no—
79#5238D311yescharacteristic, complemented
80#5234—31no—
81#5232—31no—
82#5218—31no—
83#5218—31no—
84#5217—31no—
85#5217—31no—
86C2×#832—31no—
87#5172—31no—
88#5156—31no—
89#5036—31no—
90#4808—31no—
91#4803—31no—
92#4776—31no—
93D3×#102—31no—
94#4731—31no—
95#4727—31no—
96C23×C3×D3—21no—
97C23×C3×D3—21no—
98C23×C3×D3—21no—
99C32×#41—22no—
100C32×#41—22no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×D4—21no—
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4—21no—
105C22×C32×C4C2311yescharacteristic
106C2×#634C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67D411yescharacteristic
111C2×C3×#67D411yescharacteristic
112C3×#239—22no—
113C3×#239—22no—
114C3×#239—22no—
115C3×#239D414yescomplemented
116C3×D3×D4—28no—
117C3×D3×D4—28no—
118C3×D3×D4—22no—
119C3×D3×D4—22no—
120C3×D3×D4—22no—
121C3×D3×D4D414yescomplemented
122C3×#235—28no—
123C3×#235—22no—
124C3×#235—22no—
125C2×C3×D12—28no—
126C2×C3×D12—21no—
127C2×C3×D12—21no—
128C2×C3×D12—21no—
129C2×C3×D12—22no—
130C2×C3×D12—22no—
131C2×C3×D12D411yescharacteristic
132C2×C3×D12C2311yescharacteristic
133C2×C3×D12C2311yescharacteristic
134C2×C3×D12C2311yescharacteristic
135C2×C3×C4×D3—21no—
136C2×C3×C4×D3—21no—
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×C4×D3C2311yescharacteristic
139C2×C3×Dic6D411yescharacteristic
140C2×#625—21no—
141C2×#625—21no—
142C2×D3×Dic3—21no—
143C2×D3×Dic3—21no—
144#3795—22no—
145#3795—22no—
146#3757—21no—
147#3756—22no—
148#3754—22no—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150#3750—21no—
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152C2×C3⋊(C3⋊C8)C2311yescharacteristic
153C3×#215—22no—
154C3×#213—22no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3C2311yescharacteristic
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159Dic3⋊Dic3—21no—
160Dic3⋊Dic3—21no—
161(C2×D3)⋊Dic3—21no—
162(C2×D3)⋊Dic3—21no—
163#3716—22no—
164#3716—22no—
165#3713—22no—
166#3713—22no—
167#3711—22no—
168D3×C3⋊C8—22no—
169#3012—91noSylow
170C3×H(5,𝔽2)—64no—
171C3×H(5,𝔽2)—64no—
172C2×C3×#41—21no—
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—31no—
176C2×C3×#41—61no—
177C2×C3×#41C2×D311yescharacteristic
178C2×C3×#41C2×D311yescharacteristic
179C22×C3×D4—31no—
180C22×C3×D4—31no—
181C22×C3×D4—31no—
182C22×C3×D4—61no—
183C22×C3×D4—61no—
184C22×C3×D4—61no—
185#1009—24no—
186#1009—24no—
187C2×#239C2×D311yescharacteristic
188C2×#239C2×D311yescharacteristic
189C2×#237—31no—
190C2×D3×D4—21no—
191C2×D3×D4—21no—
192C2×D3×D4C2×D311yescharacteristic
193C2×D3×D4C2×D311yescharacteristic
194C2×#235—21no—
195C2×#235—31no—
196C2×#235C2×D311yescharacteristic
197C22×D12—21no—
198C22×D12C2×D311yescharacteristic
199C2×C3×SD16—31no—
200C2×C3×D8—31no—
201C3×#121—31no—
202#950—64no—
203#946—61no—
204C2×#216—31no—
205C2×#216—31no—
206C2×#216—61no—
207C2×#215C2×D311yescharacteristic, complemented
208#939—61no—
209#939—61no—
210#939—61no—
211#938—31no—
212#938—61no—
213#938—61no—
214C2×#214—31no—
215C2×#214—31no—
216C2×#214—31no—
217C2×#214—31no—
218C2×#214—61no—
219#932—64no—
220C2×#213—31no—
221C2×#213—31no—
222C2×#213—31no—
223C2×#213—31no—
224C2×#213C2×D311yescharacteristic, complemented
225#930—31no—
226#930C2×D311yescharacteristic, complemented
227C2×C4⋊Dic3—31no—
228#924—31no—
229#924—31no—
230#924—31no—
231#924—61no—
232C2×#208—31no—
233C22×C3⋊C8—31no—
234#916—64no—
235#911—64no—
236C2×#204—31no—
237C2×#204—31no—
238C2×ΓL(1,𝔽25)—31no—
239C2×D3×C8—31no—
240#897—31no—
241D3×C4⋊C4—31no—
242#884—61no—
243#878—61no—
244C3×#103—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#835—31no—
249#835—61no—
250#835C2×D311yescharacteristic, complemented
251#832—31no—
252#832—31no—
253#832—31no—
254#832—31no—
255#832—31no—
256#832—31no—
257#832—61no—
258#832C2×D311yescharacteristic, complemented
259#830—31no—
260#830—31no—
261#830—31no—
262#830—31no—
263#830—61no—
264#830C2×D311yescharacteristic, complemented
265#821—31no—
266#821—31no—
267(C2×D3)⋊C8—31no—
268(C2×D3)⋊C8—31no—
269#809—31no—
270#809—31no—
271C23×C32—21no—
272C23×C32C2×D411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3—24no—
276C22×C3×D3—24no—
277C22×C3×D3—24no—
278C22×C3×D3—21no—
279C22×C3×D3—81no—
280C22×C3×D3—81no—
281C22×C3×D3—81no—
282C22×C3×D3—81no—
283C22×C3×D3—81no—
284C22×C3×D3—81no—
285C22×C3×D3C2×D411yescharacteristic
286C22×C3×D3C2×D411yescharacteristic
287C32×Q8—21no—
288C32×Q8C2×D412yes—
289C32×D4—24no—
290C32×D4—21no—
291C32×D4C2×D412yes—
292C2×C32×C4—24no—
293C2×C32×C4—21no—
294C2×C32×C4—21no—
295C2×C32×C4—21no—
296C2×C32×C4C2×D411yescharacteristic
297C2×C32×C4C2411yescharacteristic
298C2×C3⋊Dic3—21no—
299C2×C3⋊Dic3—21no—
300#634—21no—
301#634—21no—
302C3×#67—24no—
303C3×#67—22no—
304C3×#67—22no—
305C3×#67—24no—
306C3×#67—81no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3C2×D411yescharacteristic
309C2×C3×Dic3C2×D411yescharacteristic
310C3×D12—24no—
311C3×D12—24no—
312C3×D12—22no—
313C3×D12—24no—
314C3×D12—21no—
315C3×D12—21no—
316C3×D12—21no—
317C3×D12—21no—
318C3×D12C2×D412yes—
319C3×D12C2×D412yes—
320C3×C4×D3—24no—
321C3×C4×D3—21no—
322C3×C4×D3—21no—
323C3×C4×D3—24no—
324C3×C4×D3C2×D412yes—
325C3×C4×D3C2×D412yes—
326C3×Dic6—22no—
327#625—42no—
328#625—81no—
329D3×Dic3—42no—
330D3×Dic3—81no—
331C3⋊(C3⋊C8)—21no—
332C3⋊(C3⋊C8)—21no—
333C3×C3⋊C8—21no—
334C3×C3⋊C8—21no—
335C2×H(5,𝔽2)—31no—
336C2×AGL(1,ℤ/8)—91no—
337C2×#135—91no—
338#537—91no—
339#452—91no—
340#452—91no—
341#450—91no—
342#450—91no—
343#449—31no—
344#449—91no—
345#447—91no—
346#447—91no—
347#417—91no—
348C2×#102—91no—
349#408—91no—
350C24×C3—61no—
351C24×C3—61no—
352C24×C3—61no—
353C23×D3—21no—
354C23×D3—21no—
355C23×D3—21no—
356C3×#41—22no—
357C3×#41—22no—
358C3×#41—22no—
359C3×#41—22no—
360C3×#41—34no—
361C3×#41—42no—
362C3×#41—42no—
363C3×#41—62no—
364C3×#41—62no—
365C3×#41—68no—
366C3×#41—62no—
367C3×#41—62no—
368C3×#41—62no—
369C2×C3×Q8—21no—
370C2×C3×Q8—31no—
371C2×C3×Q8C22×D311yescharacteristic
372C2×C3×Q8C22×D311yescharacteristic
373C2×C3×D4—21no—
374C2×C3×D4—21no—
375C2×C3×D4—21no—
376C2×C3×D4—34no—
377C2×C3×D4—31no—
378C2×C3×D4—31no—
379C2×C3×D4—31no—
380C2×C3×D4—31no—
381C2×C3×D4—31no—
382C2×C3×D4—31no—
383C2×C3×D4—41no—
384C2×C3×D4—62no—
385C2×C3×D4—62no—
386C2×C3×D4—61no—
387C2×C3×D4—61no—
388C2×C3×D4—68no—
389C2×C3×D4—62no—
390C2×C3×D4—61no—
391C2×C3×D4—61no—
392C2×C3×D4—62no—
393C2×C3×D4—68no—
394C2×C3×D4—68no—
395C2×C3×D4—62no—
396C2×C3×D4—61no—
397C2×C3×D4—61no—
398C2×C3×D4C22×D311yescharacteristic
399C2×C3×D4C22×D311yescharacteristic
400C22×C3×C4—21no—
401C22×C3×C4—21no—
402C22×C3×C4—21no—
403C22×C3×C4—31no—
404C22×C3×C4—31no—
405C22×C3×C4—41no—
406C22×C3×C4—61no—
407C22×C3×C4—61no—
408C22×C3×C4C22×D311yescharacteristic
409C22×C3×C4C22×D311yescharacteristic
410C2×#67—21no—
411C2×#67—21no—
412C2×#67—21no—
413C2×#67—61no—
414C2×#67—61no—
415C2×#67—61no—
416C2×#67—61no—
417C2×#67#6711yescharacteristic
418C2×#67#6711yescharacteristic
419C22×Dic3—61no—
420C22×Dic3—61no—
421#239—22no—
422#239—22no—
423#239—22no—
424#239#6714yescomplemented
425#237—62no—
426#237—62no—
427D3×D4—28no—
428D3×D4—28no—
429D3×D4—22no—
430D3×D4—22no—
431D3×D4—22no—
432D3×D4#6714yescomplemented
433#235—28no—
434#235—22no—
435#235—22no—
436#235—62no—
437#235—62no—
438C2×D12—28no—
439C2×D12—21no—
440C2×D12—21no—
441C2×D12—21no—
442C2×D12—22no—
443C2×D12—22no—
444C2×D12#6711yescharacteristic
445C2×D12C22×D311yescharacteristic
446C2×D12C22×D311yescharacteristic
447C2×D12C22×D311yescharacteristic
448C2×C4×D3—21no—
449C2×C4×D3—21no—
450C2×C4×D3—61no—
451C2×C4×D3—61no—
452C2×C4×D3C22×D311yescharacteristic
453C2×C4×D3C22×D311yescharacteristic
454C2×Dic6—31no—
455C2×Dic6—31no—
456C2×Dic6—61no—
457C2×Dic6#6711yescharacteristic
458C3×SD16—62no—
459C3×D8—62no—
460C2×C3×C8—31no—
461C2×C3×C8—31no—
462C3×C4⋊C4—31no—
463C3×C22⋊C4—61no—
464#217—61no—
465#217—61no—
466#217—61no—
467#217—61no—
468#217—121no—
469#216—62no—
470#216—62no—
471#216—122no—
472#215—22no—
473#214—62no—
474#214—62no—
475#214—62no—
476#214—62no—
477#214—122no—
478#213—22no—
479#213—62no—
480#213—62no—
481#213—62no—
482#213—62no—
483(C2×D3)⋊C4—21no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—61no—
486C4⋊Dic3—31no—
487C4⋊Dic3—31no—
488C4⋊Dic3—61no—
489C4⋊Dic3—61no—
490C4⋊Dic3—61no—
491C4⋊Dic3C22×D311yescharacteristic
492Dic3⋊C4—61no—
493Dic3⋊C4—61no—
494Dic3⋊C4—61no—
495Dic3⋊C4—61no—
496Dic3⋊C4—121no—
497#208—62no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—31no—
501C2×C3⋊C8—31no—
502C2×C3⋊C8—61no—
503C2×C3⋊C8—61no—
504C2×C3⋊C8—62no—
505C2×C3⋊C8C22×D311yescharacteristic
506C2×C3⋊C8C22×D311yescharacteristic
507#204—62no—
508#204—62no—
509ΓL(1,𝔽25)—62no—
510D3×C8—62no—
511C22×C32—21no—
512C22×C32—22no—
513C22×C32—21no—
514C22×C32—21no—
515C22×C32—41no—
516C22×C32—41no—
517C22×C32C22×D411yescharacteristic
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527C2×C3×D3—41no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—84no—
533C2×C3×D3—84no—
534C2×C3×D3—84no—
535C2×C3×D3#12012yes—
536C32×C4—21no—
537C32×C4—22no—
538C32×C4C22×D411yescharacteristic
539C32×C4C22×D411yescharacteristic
540C3⋊Dic3—41no—
541C3⋊Dic3—41no—
542C3×Dic3—21no—
543C3×Dic3—41no—
544C3×Dic3#12012yes—
545H(5,𝔽2)—64no—
546H(5,𝔽2)—64no—
547C2×#41—31no—
548C2×#41—31no—
549C2×#41—31no—
550C2×#41—61no—
551C2×#41—91no—
552C2×#41D3211yescharacteristic
553C22×D4—31no—
554C22×D4—31no—
555C22×D4—31no—
556C22×D4—61no—
557C22×D4—61no—
558C22×D4—61no—
559AGL(1,ℤ/8)—184no—
560#135—184no—
561C2×Q16—91no—
562C2×SD16—31no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×D8—31no—
567C2×D8—91no—
568C2×D8—91no—
569C2×M16—91no—
570C22×C8—91no—
571C22⋊Q8—91no—
572C22⋊Q8—91no—
573C22⋊Q8—181no—
574#121—31no—
575#121—91no—
576#121—181no—
577#121—181no—
578#121—181no—
579C2×C4⋊C4—91no—
580#103—31no—
581#103—91no—
582#102—31no—
583#102—91no—
584#102—91no—
585#102—91no—
586#102—91no—
587#102—91no—
588C22⋊C8—31no—
589C22⋊C8—91no—
590C22⋊C8—91no—
591C22⋊C8—91no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—21no—
595C23×C3—31no—
596C23×C3—31no—
597C23×C3—41no—
598C23×C3—64no—
599C23×C3—64no—
600C23×C3—64no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—241no—
605C23×C3—241no—
606C23×C3—241no—
607C23×C3—241no—
608C23×C3—241no—
609C23×C3—241no—
610C23×C3D3×D411yescharacteristic
611C23×C3C2×#6711yescharacteristic
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—24no—
615C22×D3—24no—
616C22×D3—24no—
617C22×D3—21no—
618C22×D3—81no—
619C22×D3—81no—
620C22×D3—81no—
621C22×D3—81no—
622C22×D3—81no—
623C22×D3—81no—
624C22×D3C2×#6711yescharacteristic
625C22×D3C2×#6711yescharacteristic
626C3×Q8—21no—
627C3×Q8—21no—
628C3×Q8—22no—
629C3×Q8—41no—
630C3×Q8—62no—
631C3×Q8D3×D412yes—
632C3×Q8C2×#6712yes—
633C3×D4—24no—
634C3×D4—24no—
635C3×D4—21no—
636C3×D4—21no—
637C3×D4—22no—
638C3×D4—32no—
639C3×D4—32no—
640C3×D4—41no—
641C3×D4—44no—
642C3×D4—62no—
643C3×D4—64no—
644C3×D4—64no—
645C3×D4—64no—
646C3×D4—62no—
647C3×D4—64no—
648C3×D4—62no—
649C3×D4—64no—
650C3×D4—61no—
651C3×D4—61no—
652C3×D4—61no—
653C3×D4—61no—
654C3×D4—241no—
655C3×D4D3×D412yes—
656C3×D4C2×#6712yes—
657C2×C3×C4—24no—
658C2×C3×C4—24no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—31no—
668C2×C3×C4—32no—
669C2×C3×C4—32no—
670C2×C3×C4—31no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4—41no—
674C2×C3×C4—44no—
675C2×C3×C4—64no—
676C2×C3×C4—64no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4D3×D411yescharacteristic
681C2×C3×C4C2×#6711yescharacteristic
682C2×C3×C4C23×D311yescharacteristic
683C2×C3×C4C23×D311yescharacteristic
684#67—24no—
685#67—22no—
686#67—22no—
687#67—24no—
688#67—81no—
689#67—122no—
690#67—122no—
691#67—241no—
692#67—241no—
693C2×Dic3—21no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—121no—
699C2×Dic3—121no—
700C2×Dic3—122no—
701C2×Dic3—241no—
702C2×Dic3C2×#6711yescharacteristic
703C2×Dic3C2×#6711yescharacteristic
704D12—24no—
705D12—24no—
706D12—22no—
707D12—24no—
708D12—21no—
709D12—21no—
710D12—21no—
711D12—21no—
712D12C2×#6712yes—
713D12C2×#6712yes—
714C4×D3—24no—
715C4×D3—21no—
716C4×D3—21no—
717C4×D3—24no—
718C4×D3—122no—
719C4×D3—241no—
720C4×D3C2×#6712yes—
721C4×D3C2×#6712yes—
722Dic6—22no—
723Dic6—61no—
724Dic6—61no—
725Dic6—61no—
726Dic6—61no—
727Dic6—121no—
728Dic6—121no—
729C3×C8—61no—
730C3×C8—61no—
731C3⋊C8—21no—
732C3⋊C8—21no—
733C3⋊C8—61no—
734C3⋊C8—61no—
735C3⋊C8—61no—
736C3⋊C8—61no—
737C3⋊C8—121no—
738C3⋊C8—121no—
739C2×C32—41no—
740C2×C32—42no—
741C2×C32C2×#12011yescharacteristic
742C2×C32#57611yescharacteristic
743C2×C32#57711yescharacteristic
744C3×D3—22no—
745C3×D3—41no—
746C3×D3—42no—
747C3×D3—42no—
748C3×D3—81no—
749C24—61no—
750C24—61no—
751C24—61no—
752#41—22no—
753#41—22no—
754#41—34no—
755#41—62no—
756#41—62no—
757#41—68no—
758#41—62no—
759#41—62no—
760#41—62no—
761#41—182no—
762#41—182no—
763C2×Q8—31no—
764C2×Q8—91no—
765C2×Q8C2×D3211yescharacteristic
766C2×D4—21no—
767C2×D4—34no—
768C2×D4—31no—
769C2×D4—31no—
770C2×D4—31no—
771C2×D4—31no—
772C2×D4—31no—
773C2×D4—31no—
774C2×D4—62no—
775C2×D4—62no—
776C2×D4—61no—
777C2×D4—61no—
778C2×D4—68no—
779C2×D4—62no—
780C2×D4—61no—
781C2×D4—61no—
782C2×D4—62no—
783C2×D4—68no—
784C2×D4—68no—
785C2×D4—62no—
786C2×D4—61no—
787C2×D4—61no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4C2×D3211yescharacteristic
791C22×C4—21no—
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—181no—
797C22×C4—181no—
798C22×C4C2×D3211yescharacteristic
799Q16—182no—
800SD16—62no—
801SD16—182no—
802SD16—182no—
803SD16—182no—
804D8—62no—
805D8—182no—
806D8—182no—
807M16—182no—
808C2×C8—31no—
809C2×C8—31no—
810C2×C8—91no—
811C2×C8—91no—
812C2×C8—182no—
813C4⋊C4—31no—
814C4⋊C4—91no—
815C4⋊C4—181no—
816C4⋊C4—181no—
817C4⋊C4—181no—
818C22⋊C4—61no—
819C22⋊C4—181no—
820C22⋊C4—181no—
821C22⋊C4—181no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—22no—
828C22×C3—21no—
829C22×C3—22no—
830C22×C3—21no—
831C22×C3—32no—
832C22×C3—42no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—61no—
841C22×C3—61no—
842C22×C3—61no—
843C22×C3—61no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—61no—
847C22×C3—81no—
848C22×C3—81no—
849C22×C3—121no—
850C22×C3—121no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3—244no—
857C22×C3—244no—
858C22×C3—244no—
859C22×C3C2×D3×D411yescharacteristic
860C22×C3C22×#6711yescharacteristic
861C2×D3—21no—
862C2×D3—21no—
863C2×D3—21no—
864C2×D3—21no—
865C2×D3—21no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—41no—
869C2×D3—41no—
870C2×D3—41no—
871C2×D3—41no—
872C2×D3—41no—
873C2×D3—41no—
874C2×D3—41no—
875C2×D3—84no—
876C2×D3—84no—
877C2×D3—84no—
878C2×D3#95312yes—
879C3×C4—21no—
880C3×C4—22no—
881C3×C4—21no—
882C3×C4—22no—
883C3×C4—21no—
884C3×C4—21no—
885C3×C4—32no—
886C3×C4—41no—
887C3×C4—42no—
888C3×C4—61no—
889C3×C4—121no—
890C3×C4C2×D3×D411yescharacteristic
891C3×C4C2×D3×D411yescharacteristic
892C3×C4C22×#6711yescharacteristic
893C3×C4C22×#6711yescharacteristic
894Dic3—21no—
895Dic3—41no—
896Dic3—121no—
897Dic3—121no—
898Dic3—121no—
899Dic3—121no—
900Dic3—241no—
901Dic3—241no—
902Dic3#95312yes—
903C32#301211yescharacteristic, complemented, Sylow
904C23—21no—
905C23—31no—
906C23—31no—
907C23—64no—
908C23—64no—
909C23—64no—
910C23—61no—
911C23—61no—
912C23—61no—
913C23—241no—
914C23—241no—
915C23—241no—
916C23—241no—
917C23—241no—
918C23—241no—
919C23D3×#6711yescharacteristic
920Q8—21no—
921Q8—62no—
922Q8—181no—
923Q8—181no—
924Q8D3×#6712yes—
925D4—24no—
926D4—21no—
927D4—32no—
928D4—32no—
929D4—62no—
930D4—64no—
931D4—64no—
932D4—64no—
933D4—62no—
934D4—64no—
935D4—62no—
936D4—64no—
937D4—61no—
938D4—61no—
939D4—61no—
940D4—61no—
941D4—241no—
942D4—362no—
943D4—721no—
944D4D3×#6712yes—
945C2×C4—24no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—31no—
950C2×C4—32no—
951C2×C4—32no—
952C2×C4—31no—
953C2×C4—64no—
954C2×C4—64no—
955C2×C4—61no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—181no—
959C2×C4—181no—
960C2×C4—362no—
961C2×C4—721no—
962C2×C4D3×#6711yescharacteristic
963C2×C4C22×D3211yescharacteristic
964C8—61no—
965C8—61no—
966C8—181no—
967C8—181no—
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—41no—
972C2×C3—42no—
973C2×C3—41no—
974C2×C3—42no—
975C2×C3—62no—
976C2×C3—81no—
977C2×C3—82no—
978C2×C3—121no—
979C2×C3—122no—
980C2×C3—122no—
981C2×C3—241no—
982C2×C3D3×#12011yescharacteristic
983C2×C3#577011yescharacteristic
984C2×C3#577411yescharacteristic
985C2×C3#583511yescharacteristic
986C2×C3#583611yescharacteristic
987C2×C3C2×#95311yescharacteristic
988D3—22no—
989D3—41no—
990D3—42no—
991D3—42no—
992D3—81no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—22no—
997C22—32no—
998C22—41no—
999C22—41no—
1000C22—61no—
1001C22—61no—
1002C22—61no—
1003C22—61no—
1004C22—62no—
1005C22—62no—
1006C22—61no—
1007C22—121no—
1008C22—121no—
1009C22—121no—
1010C22—121no—
1011C22—121no—
1012C22—121no—
1013C22—121no—
1014C22—244no—
1015C22—244no—
1016C22—244no—
1017C22C2×D3×#6711yescharacteristic
1018C4—21no—
1019C4—22no—
1020C4—32no—
1021C4—61no—
1022C4—121no—
1023C4—361no—
1024C4—361no—
1025C4C2×D3×#6711yescharacteristic
1026C4C2×D3×#6711yescharacteristic
1027C3—21no—
1028C3#8008711yescharacteristic, complemented
1029C3#8410211yescharacteristic, complemented
1030C2—41no—
1031C2—42no—
1032C2—62no—
1033C2—121no—
1034C2—122no—
1035C2—122no—
1036C2—241no—
1037C2#1059545411yescharacteristic
1038C2#1059546611yescharacteristic
1039C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3012
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1009C2semidirect
2. C2×#63947C2semidirect
3. C2×#63932C2semidirect
4. #10595004C2semidirect
5. #10592938C2semidirect
6. C3×#5238C2semidirect
7. #10591599C2semidirect
8. #10591586C2semidirect
9. #10591550C2semidirect
10. #10591459C2semidirect
11. #10591447C2semidirect
12. D3×#832C2semidirect
13. #10591172C2semidirect
14. #10591160C2semidirect
15. #10591145C2semidirect
31. C2×#3795C22semidirect
32. C2×#3756C22semidirect
33. C2×#3754C22semidirect
34. #64133C22semidirect
35. C2×C3×#215C22semidirect
36. C2×C3×#213C22semidirect
37. C3×#930C22semidirect
42. #63908C22semidirect
43. D3×C4⋊Dic3C22semidirect
46. #63857C22semidirect
47. C2×#3716C22semidirect
48. C2×#3716C22semidirect
49. C2×#3713C22semidirect
50. C2×#3713C22semidirect
51. C2×#3711C22semidirect
52. C2×D3×C3⋊C8C22semidirect
53. #63662C22semidirect
54. #63659C22semidirect
55. #63657C22semidirect
56. C3×#835C22semidirect
57. C3×#832C22semidirect
58. C3×#830C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
66. C2×#1009D3semidirect
79. #5238D3semidirect
115. C3×#239D4semidirect
121. C3×D3×D4D4semidirect
207. C2×#215C2×D3semidirect
224. C2×#213C2×D3semidirect
226. #930C2×D3semidirect
250. #835C2×D3semidirect
258. #832C2×D3semidirect
264. #830C2×D3semidirect
424. #239#67semidirect
432. D3×D4#67semidirect
903. C32#3012semidirect
1028. C3#80087semidirect
1029. C3#84102semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C2×#639472
C2×#639322
#105950042
#105929382
C3×#52382
#105915992
#105915862
#105915502
#105914592
#105914472
D3×#8322
#105911722
#105911602
#105911452
#841023
#800873