Finite Group Databasebeta

← #11864600

Subgroups — #11864600

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 1045 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic, complemented
3C2×#63934C211yesmaximal, characteristic, complemented
4#10594894C211yesmaximal, characteristic, complemented
5#10592937C211yesmaximal, characteristic, complemented
6C3×#5239C211yesmaximal, characteristic, complemented
7#10591597C211yesmaximal, characteristic, complemented
8#10591588C211yesmaximal, characteristic, complemented
9#10591550C211yesmaximal, characteristic, complemented
10#10591458C211yesmaximal, characteristic, complemented
11#10591448C211yesmaximal, characteristic, complemented
12D3×#832C211yesmaximal, characteristic, complemented
13#10591169C211yesmaximal, characteristic, complemented
14#10591162C211yesmaximal, characteristic, complemented
15#10591145C211yesmaximal, characteristic, complemented
16#84102—31nomaximal
17#80231—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×#3799C2211yescharacteristic, complemented
32C2×#3755C2211yescharacteristic, complemented
33C2×#3753C2211yescharacteristic, complemented
34#64139C2211yescharacteristic, complemented
35C2×C3×#216C2211yescharacteristic, complemented
36C2×C3×#214C2211yescharacteristic, complemented
37C3×#924C2211yescharacteristic, complemented
38#63971—21no—
39#63958—21no—
40#63949—24no—
41#63934—24no—
42#63909C2211yescharacteristic, complemented
43D3×C4⋊Dic3C2211yescharacteristic, complemented
44#63888—21no—
45#63886—21no—
46#63856C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, 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×#919—31no—
71C2×#914—31no—
72#5629—31no—
73C3×#452—31no—
74#5239—31no—
75#5239D311yescharacteristic, complemented
76#5238—31no—
77#5238—31no—
78#5238—31no—
79#5238—61no—
80#5234—31no—
81#5232—31no—
82#5218—31no—
83#5218—31no—
84#5217—31no—
85#5217—31no—
86C2×#832—31no—
87#5187—31no—
88#5169—31no—
89#5046—31no—
90#4810—31no—
91#4803—31no—
92#4773—31no—
93D3×#102—31no—
94#4732—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×#638—21no—
107C2×C4⋊(C3⋊D3)C2311yescharacteristic
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×C4×D3—21no—
135C2×C3×C4×D3—21no—
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×Dic6D411yescharacteristic
139C2×C3×Dic6C2311yescharacteristic
140C2×#626—21no—
141C2×#626—21no—
142C2×#624—21no—
143C2×D3×Dic3—21no—
144#3799—22no—
145#3799—22no—
146#3755—22no—
147#3753—22no—
148#3752—21no—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152C3×#217—21no—
153C3×#216—22no—
154C3×#214—22no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×Dic3⋊C4—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159#3724—21no—
160Dic3⋊Dic3—21no—
161#3722—21no—
162(C2×D3)⋊Dic3—21no—
163#3715—22no—
164#3715—22no—
165#3714—22no—
166#3714—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×#239—31no—
188C2×#239C2×D311yescharacteristic
189C2×#239C2×D311yescharacteristic
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×Q16—31no—
200C2×C3×SD16—31no—
201C3×C22⋊Q8—31no—
202#950—64no—
203#946—31no—
204#946—61no—
205C2×#216C2×D311yescharacteristic, complemented
206C2×#215—31no—
207C2×#215—31no—
208C2×#215—31no—
209C2×#215—31no—
210C2×#215—61no—
211#939—61no—
212#939—61no—
213#938—61no—
214C2×#214—31no—
215C2×#214—31no—
216C2×#214C2×D311yescharacteristic, complemented
217#932—64no—
218C2×#213—31no—
219C2×#213—31no—
220C2×#213—31no—
221C2×#213—31no—
222C2×#213—61no—
223#930—31no—
224#930—31no—
225#930—31no—
226#930—61no—
227C2×C4⋊Dic3—31no—
228#924—31no—
229#924C2×D311yescharacteristic, complemented
230C2×#208—31no—
231C22×C3⋊C8—31no—
232#919—64no—
233#914—64no—
234C2×D24—31no—
235C2×D24—31no—
236C2×ΓL(1,𝔽25)—31no—
237C2×D3×C8—31no—
238#896—61no—
239#895—31no—
240#895—61no—
241D3×C4⋊C4—31no—
242#884—61no—
243#884—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—21no—
276C22×C3×D3—24no—
277C22×C3×D3—24no—
278C22×C3×D3—24no—
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
298#638—81no—
299C2×C3⋊Dic3—21no—
300C4⋊(C3⋊D3)—21no—
301C4⋊(C3⋊D3)—21no—
302C3×#67—24no—
303C3×#67—22no—
304C3×#67—22no—
305C3×#67—24no—
306C2×C3×Dic3—21no—
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×D12C2×D412yes—
317C3×D12C2×D412yes—
318C3×C4×D3—24no—
319C3×C4×D3—21no—
320C3×C4×D3—21no—
321C3×C4×D3—24no—
322C3×C4×D3C2×D412yes—
323C3×C4×D3C2×D412yes—
324C3×Dic6—22no—
325C3×Dic6—21no—
326C3×Dic6—21no—
327#626—42no—
328#626—81no—
329#624—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—31no—
340#452—91no—
341#450—91no—
342#450—91no—
343#449—91no—
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×Q8—31no—
372C2×C3×Q8C22×D311yescharacteristic
373C2×C3×Q8C22×D311yescharacteristic
374C2×C3×D4—21no—
375C2×C3×D4—21no—
376C2×C3×D4—21no—
377C2×C3×D4—34no—
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×D4C22×D311yescharacteristic
398C2×C3×D4C22×D311yescharacteristic
399C22×C3×C4—21no—
400C22×C3×C4—21no—
401C22×C3×C4—21no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4—41no—
405C22×C3×C4—61no—
406C22×C3×C4—61no—
407C22×C3×C4C22×D311yescharacteristic
408C22×C3×C4C22×D311yescharacteristic
409C2×#67—21no—
410C2×#67—21no—
411C2×#67—61no—
412C2×#67—61no—
413C2×#67—61no—
414C2×#67—61no—
415C2×#67—121no—
416C2×#67#6711yescharacteristic
417C2×#67#6711yescharacteristic
418C22×Dic3—61no—
419#239—22no—
420#239—22no—
421#239—22no—
422#239—62no—
423#239—62no—
424#239#6714yescomplemented
425D3×D4—28no—
426D3×D4—28no—
427D3×D4—22no—
428D3×D4—22no—
429D3×D4—22no—
430D3×D4#6714yescomplemented
431#235—28no—
432#235—22no—
433#235—22no—
434#235—62no—
435#235—62no—
436C2×D12—28no—
437C2×D12—21no—
438C2×D12—21no—
439C2×D12—21no—
440C2×D12—22no—
441C2×D12—22no—
442C2×D12—31no—
443C2×D12—31no—
444C2×D12—61no—
445C2×D12—61no—
446C2×D12—61no—
447C2×D12#6711yescharacteristic
448C2×D12C22×D311yescharacteristic
449C2×D12C22×D311yescharacteristic
450C2×C4×D3—21no—
451C2×C4×D3—21no—
452C2×C4×D3—61no—
453C2×C4×D3—61no—
454C2×C4×D3—61no—
455C2×C4×D3C22×D311yescharacteristic
456C2×C4×D3C22×D311yescharacteristic
457C2×Dic6#6711yescharacteristic
458C2×Dic6C22×D311yescharacteristic
459C3×Q16—62no—
460C3×SD16—62no—
461C2×C3×C8—31no—
462C2×C3×C8—31no—
463C3×C4⋊C4—31no—
464C3×C4⋊C4—61no—
465C3×C22⋊C4—61no—
466#217—21no—
467#217—61no—
468#216—22no—
469#215—62no—
470#215—62no—
471#215—62no—
472#215—62no—
473#215—122no—
474#214—22no—
475#214—62no—
476#214—62no—
477#213—62no—
478#213—62no—
479#213—62no—
480#213—62no—
481#213—122no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—61no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—61no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—121no—
488C4⋊Dic3—31no—
489C4⋊Dic3—31no—
490C4⋊Dic3—61no—
491C4⋊Dic3—61no—
492C4⋊Dic3C22×D311yescharacteristic
493Dic3⋊C4—21no—
494Dic3⋊C4—61no—
495Dic3⋊C4—61no—
496Dic3⋊C4—61no—
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
507D24—62no—
508D24—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—41no—
519C2×C3⋊D3—41no—
520C2×C3⋊D3—41no—
521C2×C3×D3—21no—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—22no—
525C2×C3×D3—22no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
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—21no—
542C3×Dic3—41no—
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—31no—
562C2×SD16—31no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×D8—91no—
567C2×D8—91no—
568C2×D8—91no—
569C2×M16—91no—
570C22×C8—91no—
571C22⋊Q8—31no—
572C22⋊Q8—91no—
573C22⋊Q8—181no—
574#121—91no—
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—241no—
604C23×C3—241no—
605C23×C3—241no—
606C23×C3—241no—
607C23×C3—241no—
608C23×C3—241no—
609C23×C3D3×D411yescharacteristic
610C23×C3C2×#6711yescharacteristic
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—24no—
614C22×D3—24no—
615C22×D3—24no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—81no—
619C22×D3—81no—
620C22×D3—81no—
621C22×D3—81no—
622C22×D3—81no—
623C22×D3—81no—
624C22×D3—121no—
625C22×D3C2×#6711yescharacteristic
626C22×D3C2×#6711yescharacteristic
627C3×Q8—21no—
628C3×Q8—21no—
629C3×Q8—22no—
630C3×Q8—41no—
631C3×Q8—62no—
632C3×Q8—61no—
633C3×Q8—61no—
634C3×Q8D3×D412yes—
635C3×Q8C2×#6712yes—
636C3×D4—24no—
637C3×D4—24no—
638C3×D4—21no—
639C3×D4—21no—
640C3×D4—22no—
641C3×D4—32no—
642C3×D4—32no—
643C3×D4—41no—
644C3×D4—44no—
645C3×D4—62no—
646C3×D4—64no—
647C3×D4—64no—
648C3×D4—64no—
649C3×D4—62no—
650C3×D4—64no—
651C3×D4—62no—
652C3×D4—64no—
653C3×D4—61no—
654C3×D4—61no—
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×C4—61no—
681C2×C3×C4D3×D411yescharacteristic
682C2×C3×C4C2×#6711yescharacteristic
683C2×C3×C4C23×D311yescharacteristic
684C2×C3×C4C23×D311yescharacteristic
685#67—24no—
686#67—22no—
687#67—22no—
688#67—24no—
689#67—122no—
690#67—241no—
691#67—241no—
692#67—241no—
693#67—242no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—121no—
699C2×Dic3—241no—
700C2×Dic3C2×#6711yescharacteristic
701C2×Dic3C2×#6711yescharacteristic
702D12—24no—
703D12—24no—
704D12—22no—
705D12—24no—
706D12—21no—
707D12—21no—
708D12—61no—
709D12—61no—
710D12—61no—
711D12—61no—
712D12—121no—
713D12—121no—
714D12—122no—
715D12—241no—
716D12C2×#6712yes—
717D12C2×#6712yes—
718C4×D3—24no—
719C4×D3—21no—
720C4×D3—21no—
721C4×D3—24no—
722C4×D3—122no—
723C4×D3—122no—
724C4×D3—241no—
725C4×D3C2×#6712yes—
726C4×D3C2×#6712yes—
727Dic6—22no—
728Dic6—21no—
729Dic6—21no—
730C3×C8—61no—
731C3×C8—61no—
732C3⋊C8—21no—
733C3⋊C8—21no—
734C3⋊C8—61no—
735C3⋊C8—61no—
736C3⋊C8—61no—
737C3⋊C8—61no—
738C3⋊C8—121no—
739C3⋊C8—121no—
740C2×C32—41no—
741C2×C32—42no—
742C2×C32C2×#12011yescharacteristic
743C2×C32#57611yescharacteristic
744C2×C32#57711yescharacteristic
745C3⋊D3—81no—
746C3×D3—22no—
747C3×D3—41no—
748C3×D3—42no—
749C3×D3—42no—
750C24—61no—
751C24—61no—
752C24—61no—
753#41—22no—
754#41—22no—
755#41—34no—
756#41—62no—
757#41—62no—
758#41—68no—
759#41—62no—
760#41—62no—
761#41—62no—
762#41—182no—
763#41—182no—
764C2×Q8—31no—
765C2×Q8—31no—
766C2×Q8C2×D3211yescharacteristic
767C2×D4—21no—
768C2×D4—34no—
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—91no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4—181no—
791C2×D4C2×D3211yescharacteristic
792C22×C4—21no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—181no—
798C22×C4—181no—
799C22×C4C2×D3211yescharacteristic
800Q16—62no—
801SD16—62no—
802SD16—182no—
803SD16—182no—
804SD16—182no—
805D8—182no—
806D8—182no—
807D8—182no—
808M16—182no—
809C2×C8—31no—
810C2×C8—31no—
811C2×C8—91no—
812C2×C8—91no—
813C2×C8—182no—
814C4⋊C4—31no—
815C4⋊C4—61no—
816C4⋊C4—91no—
817C4⋊C4—181no—
818C4⋊C4—181no—
819C22⋊C4—61no—
820C22⋊C4—181no—
821C22⋊C4—181no—
822C22⋊C4—181no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—22no—
829C22×C3—21no—
830C22×C3—22no—
831C22×C3—21no—
832C22×C3—32no—
833C22×C3—41no—
834C22×C3—42no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—61no—
842C22×C3—61no—
843C22×C3—61no—
844C22×C3—61no—
845C22×C3—62no—
846C22×C3—62no—
847C22×C3—61no—
848C22×C3—81no—
849C22×C3—81no—
850C22×C3—121no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—244no—
855C22×C3—244no—
856C22×C3—244no—
857C22×C3C2×D3×D411yescharacteristic
858C22×C3C22×#6711yescharacteristic
859C2×D3—21no—
860C2×D3—21no—
861C2×D3—21no—
862C2×D3—21no—
863C2×D3—21no—
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—41no—
867C2×D3—41no—
868C2×D3—41no—
869C2×D3—41no—
870C2×D3—84no—
871C2×D3—84no—
872C2×D3—84no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—241no—
880C2×D3—241no—
881C2×D3—241no—
882C2×D3#95312yes—
883C3×C4—21no—
884C3×C4—22no—
885C3×C4—21no—
886C3×C4—22no—
887C3×C4—21no—
888C3×C4—21no—
889C3×C4—32no—
890C3×C4—41no—
891C3×C4—42no—
892C3×C4—61no—
893C3×C4—121no—
894C3×C4—121no—
895C3×C4C2×D3×D411yescharacteristic
896C3×C4C2×D3×D411yescharacteristic
897C3×C4C22×#6711yescharacteristic
898C3×C4C22×#6711yescharacteristic
899Dic3—21no—
900Dic3—41no—
901Dic3—41no—
902Dic3—121no—
903Dic3—121no—
904Dic3—241no—
905Dic3#95312yes—
906C32#301211yescharacteristic, complemented, Sylow
907C23—21no—
908C23—31no—
909C23—31no—
910C23—64no—
911C23—64no—
912C23—64no—
913C23—61no—
914C23—61no—
915C23—181no—
916C23—241no—
917C23—241no—
918C23—241no—
919C23—241no—
920C23—241no—
921C23—241no—
922C23D3×#6711yescharacteristic
923Q8—21no—
924Q8—62no—
925Q8—61no—
926Q8—61no—
927Q8D3×#6712yes—
928D4—24no—
929D4—21no—
930D4—32no—
931D4—32no—
932D4—62no—
933D4—64no—
934D4—64no—
935D4—64no—
936D4—62no—
937D4—64no—
938D4—62no—
939D4—64no—
940D4—61no—
941D4—61no—
942D4—181no—
943D4—181no—
944D4—362no—
945D4—721no—
946D4—721no—
947D4D3×#6712yes—
948C2×C4—24no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—31no—
953C2×C4—32no—
954C2×C4—32no—
955C2×C4—31no—
956C2×C4—64no—
957C2×C4—64no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—181no—
963C2×C4—362no—
964C2×C4—721no—
965C2×C4D3×#6711yescharacteristic
966C2×C4C22×D3211yescharacteristic
967C8—61no—
968C8—61no—
969C8—181no—
970C8—181no—
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—21no—
974C2×C3—41no—
975C2×C3—42no—
976C2×C3—41no—
977C2×C3—42no—
978C2×C3—62no—
979C2×C3—81no—
980C2×C3—82no—
981C2×C3—121no—
982C2×C3—122no—
983C2×C3—122no—
984C2×C3D3×#12011yescharacteristic
985C2×C3#576911yescharacteristic
986C2×C3#577811yescharacteristic
987C2×C3#583511yescharacteristic
988C2×C3#583611yescharacteristic
989C2×C3C2×#95311yescharacteristic
990D3—22no—
991D3—41no—
992D3—42no—
993D3—42no—
994D3—241no—
995D3—241no—
996D3—481no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—22no—
1001C22—32no—
1002C22—41no—
1003C22—41no—
1004C22—61no—
1005C22—61no—
1006C22—61no—
1007C22—61no—
1008C22—62no—
1009C22—62no—
1010C22—61no—
1011C22—121no—
1012C22—121no—
1013C22—121no—
1014C22—121no—
1015C22—244no—
1016C22—244no—
1017C22—244no—
1018C22—361no—
1019C22—361no—
1020C22—361no—
1021C22C2×D3×#6711yescharacteristic
1022C4—21no—
1023C4—22no—
1024C4—32no—
1025C4—61no—
1026C4—121no—
1027C4—121no—
1028C4—361no—
1029C4C2×D3×#6711yescharacteristic
1030C4C2×D3×#6711yescharacteristic
1031C3—21no—
1032C3#8023111yescharacteristic, complemented
1033C3#8410211yescharacteristic, complemented
1034C2—41no—
1035C2—42no—
1036C2—62no—
1037C2—121no—
1038C2—122no—
1039C2—122no—
1040C2—721no—
1041C2#1059545611yescharacteristic
1042C2#1059546411yescharacteristic
1043C2D3×#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×#63949C2semidirect
3. C2×#63934C2semidirect
4. #10594894C2semidirect
5. #10592937C2semidirect
6. C3×#5239C2semidirect
7. #10591597C2semidirect
8. #10591588C2semidirect
9. #10591550C2semidirect
10. #10591458C2semidirect
11. #10591448C2semidirect
12. D3×#832C2semidirect
13. #10591169C2semidirect
14. #10591162C2semidirect
15. #10591145C2semidirect
31. C2×#3799C22semidirect
32. C2×#3755C22semidirect
33. C2×#3753C22semidirect
34. #64139C22semidirect
35. C2×C3×#216C22semidirect
36. C2×C3×#214C22semidirect
37. C3×#924C22semidirect
42. #63909C22semidirect
43. D3×C4⋊Dic3C22semidirect
46. #63856C22semidirect
47. C2×#3715C22semidirect
48. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3714C22semidirect
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
75. #5239D3semidirect
115. C3×#239D4semidirect
121. C3×D3×D4D4semidirect
205. C2×#216C2×D3semidirect
216. C2×#214C2×D3semidirect
229. #924C2×D3semidirect
250. #835C2×D3semidirect
258. #832C2×D3semidirect
264. #830C2×D3semidirect
424. #239#67semidirect
430. D3×D4#67semidirect
906. C32#3012semidirect
1032. C3#80231semidirect
1033. 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×#639492
C2×#639342
#105948942
#105929372
C3×#52392
#105915972
#105915882
#105915502
#105914582
#105914482
D3×#8322
#105911692
#105911622
#105911452
#841023
#802313