Finite Group Databasebeta

← #11860339

Subgroups — #11860339

Order 1152.

1156 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×D4C211yesmaximal, characteristic, complemented
2C2×#63932C211yesmaximal, characteristic
3C4×#3795C211yesmaximal, characteristic, complemented
4#10592717C211yesmaximal, characteristic, complemented
5C3×#5014C211yesmaximal, characteristic, complemented
6Dic3×#213C211yesmaximal, characteristic, complemented
7#10591421C211yesmaximal, characteristic, complemented
8#10591401C211yesmaximal, characteristic, complemented
9#10590607C211yesmaximal, characteristic, complemented
10#10590581C211yesmaximal, characteristic, complemented
11#10590479C211yesmaximal, characteristic, complemented
12#10590452C211yesmaximal, characteristic, complemented
13#10590360C211yesmaximal, characteristic, complemented
14#10590344C211yesmaximal, characteristic, complemented
15#10590334C211yesmaximal, characteristic, complemented
16C4×#932—31nomaximal
17#79865—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C22×C3×C4×D3—21no—
20C2×#3795C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23C4×#634C2211yescharacteristic, complemented
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C3×C4×#67—21no—
27C3×#893C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic
29C3×#67⋊C4—21no—
30C3×D3×C22⋊C4—21no—
31C3×C4×D12C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic, complemented
33C3×C42×D3C2211yescharacteristic
34#63932C418yescomplemented
35C4×#625—21no—
36Dic3×D12C2211yescharacteristic, complemented
37#63879—21no—
38#63877—21no—
39C4×D3×Dic3—21no—
40#63844C2211yescharacteristic, complemented
41#63841C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C2×#3713C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46#63659C2211yescharacteristic
47#63637C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49#63630C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic
51C3×#809C2211yescharacteristic, complemented
52C3×#808C2211yescharacteristic, complemented
53C3×#803C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C2×C3×C4×D4—31no—
63C2×#932—31no—
64C2×#911—31no—
65C4×D3×D4D311yescharacteristic, complemented
66C4×#237—31no—
67C4×#235—31no—
68C3×#442—31no—
69#5215—31no—
70Dic3×D8—31no—
71#5018—31no—
72#5018—31no—
73#5018—31no—
74#5018—61no—
75C4×#214—31no—
76C4×#214—31no—
77#5014—31no—
78#5014—31no—
79#5014D311yescharacteristic, complemented
80C4×#213—31no—
81C4×#213—31no—
82#4966—31no—
83#4964—31no—
84C4×#208—31no—
85#4861—31no—
86#4852—31no—
87#4771—31no—
88#4770—31no—
89#4758—31no—
90#4756—31no—
91#4710—31no—
92#4707—31no—
93C23×C3×D3—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×D4—22no—
100C3×D3×D4C2×C414yescomplemented
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—44no—
108C2×C3×C4×D3D411yescharacteristic
109C2×C3×C4×D3D411yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×#625—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114#3795—22no—
115#3795C2×C414yescomplemented
116C32×C4⋊C4C2311yescharacteristic
117C32×C22⋊C4—21no—
118C32×C42C2311yescharacteristic
119#3754C2×C414yescomplemented
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122C4×C3⋊Dic3—21no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#217—21no—
126C3×#213C2×C414yescomplemented
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3D411yescharacteristic
134C3×C4×Dic3D411yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3724—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142Dic32—21no—
143#3716C2×C414yescomplemented
144#3713C2×C414yescomplemented
145#3711—22no—
146#3711C2×C414yescomplemented
147C4×AGL(1,ℤ/8)—91noSylow
148C22×C3×D4—31no—
149C23×C3×C4—61no—
150C2×#237—31no—
151C2×D3×D4C2×D311yescharacteristic
152C2×#235—31no—
153C22×C4×D3—21no—
154C2×C3×D8—31no—
155C3×C4×D4—21no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160C3×C4×D4—61no—
161C3×C4×D4—61no—
162C3×C4×D4C2×D311yescharacteristic
163C3×C4×D4C2×D311yescharacteristic
164C2×C3×C4⋊C4—31no—
165C2×C3×C22⋊C4—61no—
166C2×C3×C42—31no—
167D4×Dic3—31no—
168D4×Dic3C2×D311yescharacteristic
169C2×#214—31no—
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—61no—
173#932—38no—
174C2×#213—31no—
175C2×#213—31no—
176C2×#213C2×D311yescharacteristic
177C4×#67—21no—
178C4×#67—61no—
179C4×#67—61no—
180C4×#67—61no—
181#926—31no—
182C2×C4×Dic3—61no—
183C2×#208—31no—
184C2×#208—31no—
185#911—38no—
186C2×#204—31no—
187C2×ΓL(1,𝔽25)—31no—
188C2×ΓL(1,𝔽25)—31no—
189#893C2×D311yescharacteristic
190#892—31no—
191D3×C4⋊C4C2×D311yescharacteristic
192#887—31no—
193#67⋊C4—21no—
194#67⋊C4—61no—
195D3×C22⋊C4—21no—
196#877—61no—
197C4×D12—31no—
198C4×D12C2×D311yescharacteristic
199C4×D12C2×D311yescharacteristic, complemented
200#872—61no—
201C42×D3—61no—
202C42×D3C2×D311yescharacteristic
203C4×Dic6—31no—
204C4×Dic6—31no—
205C4×Dic6—31no—
206C4×Dic6—61no—
207C3×#106—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#97—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—61no—
217#832C2×D311yescharacteristic
218#821—31no—
219#818—31no—
220#816—31no—
221C8×Dic3—31no—
222C8×Dic3—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#809—31no—
228#809—31no—
229#809C2×D311yescharacteristic, complemented
230#808—31no—
231#808—31no—
232#808C2×D311yescharacteristic, complemented
233#807—31no—
234#807—31no—
235#807—31no—
236#807—61no—
237#803—31no—
238#803—31no—
239#803—61no—
240#803C2×D311yescharacteristic, complemented
241C4×C3⋊C8—31no—
242C4×C3⋊C8—31no—
243C23×C32—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—24no—
247C22×C3×D3—42no—
248C22×C3×D3—42no—
249C22×C3×D3C2×D411yescharacteristic
250C32×D4—21no—
251C32×D4C22×C412yes—
252C2×C32×C4—21no—
253C2×C32×C4—42no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259#634—21no—
260#634C22×C412yescomplemented
261C3×#67—24no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270C3×D12C22×C412yes—
271C3×D12C22×C412yescomplemented
272C3×C4×D3—22no—
273C3×C4×D3—41no—
274C3×C4×D3—42no—
275C3×C4×D3—42no—
276C3×C4×D3—42no—
277C3×C4×D3—42no—
278C3×C4×D3C22×C412yes—
279C3×C4×D3#4112yes—
280#625—24no—
281D3×Dic3—24no—
282D3×Dic3—42no—
283C3⋊(C3⋊C8)—21no—
284C3⋊(C3⋊C8)C22×C412yescomplemented
285C3×C3⋊C8—21no—
286C3×C3⋊C8C22×C412yescomplemented
287C2×AGL(1,ℤ/8)—91no—
288C4×#41—91no—
289C2×C4×D4—31no—
290#442—31no—
291#442—91no—
292#440—91no—
293#440—91no—
294C4×SD16—91no—
295C4×SD16—91no—
296C4×D8—91no—
297C4×D8—91no—
298#428—91no—
299#418—91no—
300#417—91no—
301C4×M16—91no—
302C24×C3—61no—
303C23×D3—21no—
304C2×C3×D4—21no—
305C2×C3×D4—34no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—41no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C22×C3×C4—124no—
324C2×#67—21no—
325C2×#67—61no—
326C2×#67—61no—
327C22×Dic3—21no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330#237—34no—
331#237—62no—
332D3×D4—22no—
333D3×D4C4×D314yescomplemented
334#235—34no—
335#235—62no—
336C2×D12C22×D311yescharacteristic
337C2×D12C22×D311yescharacteristic
338C2×C4×D3—21no—
339C2×C4×D3—21no—
340C2×C4×D3—21no—
341C2×C4×D3—21no—
342C2×C4×D3—44no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3#6711yescharacteristic
346C2×C4×D3#6711yescharacteristic
347C2×C4×D3C22×D311yescharacteristic
348C2×Dic6—31no—
349C2×Dic6—31no—
350C2×Dic6—61no—
351C3×D8—34no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—41no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C42—21no—
368C3×C42—31no—
369C3×C42—31no—
370C3×C42—31no—
371C3×C42C22×D311yescharacteristic
372C3×C42C22×D311yescharacteristic
373#217—21no—
374#217—61no—
375#217—61no—
376#214—34no—
377#214—34no—
378#214—34no—
379#214—64no—
380#213—34no—
381#213—34no—
382#213C4×D314yescomplemented
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393Dic3⋊C4—21no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—121no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—121no—
406C4×Dic3#6711yescharacteristic
407C4×Dic3#6711yescharacteristic
408C4×Dic3C22×D311yescharacteristic
409#208—34no—
410#208—62no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—61no—
416C2×C3⋊C8—61no—
417C2×C3⋊C8C22×D311yescharacteristic
418C2×C3⋊C8C22×D311yescharacteristic
419#204—34no—
420ΓL(1,𝔽25)—34no—
421ΓL(1,𝔽25)—62no—
422C22×C32—22no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32C22×D411yescharacteristic
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—48no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3C4×D412yes—
436C32×C4—21no—
437C32×C4—21no—
438C32×C4—41no—
439C32×C4C23×C411yescharacteristic
440C32×C4C2×#4111yescharacteristic
441C3⋊Dic3—22no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C3×Dic3C4×D412yes—
447C3×Dic3AGL(1,ℤ/8)12yescomplemented
448C2×#41—91no—
449C22×D4—31no—
450C23×C4—61no—
451AGL(1,ℤ/8)—98no—
452C2×SD16—91no—
453C2×SD16—91no—
454C2×D8—31no—
455C2×D8—91no—
456C2×M16—91no—
457C2×M16—91no—
458C4×Q8—91no—
459C4×Q8—91no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—31no—
464C4×D4—61no—
465C4×D4—61no—
466C4×D4—91no—
467C4×D4—181no—
468C4×D4—181no—
469C4×D4D3211yescharacteristic
470#117—91no—
471#117—181no—
472C2×C4⋊C4—31no—
473C2×C22⋊C4—61no—
474C2×C42—31no—
475C2×C42—181no—
476#107—91no—
477#107—91no—
478#106—31no—
479#106—91no—
480#103—91no—
481#103—91no—
482#102—31no—
483#102—31no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488#97—31no—
489#97—91no—
490C4×C8—91no—
491C4×C8—91no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—31no—
495C23×C3—41no—
496C23×C3—64no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—122no—
500C23×C3—122no—
501C22×D3—21no—
502C22×D3—21no—
503C22×D3—24no—
504C22×D3—42no—
505C22×D3—42no—
506C22×D3C2×#6711yescharacteristic
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—22no—
510C3×D4—32no—
511C3×D4—32no—
512C3×D4—41no—
513C3×D4—64no—
514C3×D4—61no—
515C3×D4—61no—
516C3×D4C2×C4×D312yes—
517C3×D4C2×C4×D312yes—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—32no—
526C2×C3×C4—32no—
527C2×C3×C4—31no—
528C2×C3×C4—41no—
529C2×C3×C4—42no—
530C2×C3×C4—42no—
531C2×C3×C4—62no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—82no—
535C2×C3×C4—121no—
536C2×C3×C4—122no—
537C2×C3×C4—122no—
538C2×C3×C4—122no—
539C2×C3×C4—122no—
540C2×C3×C4—122no—
541C2×C3×C4D3×D411yescharacteristic
542C2×C3×C4D3×D411yescharacteristic
543C2×C3×C4C2×#6711yescharacteristic
544C2×C3×C4C2×#6711yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546C2×C3×C4C23×D311yescharacteristic
547#67—24no—
548#67—64no—
549#67—64no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—42no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—64no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—121no—
559C2×Dic3—121no—
560C2×Dic3—122no—
561C2×Dic3C2×#6711yescharacteristic
562C2×Dic3C2×#6711yescharacteristic
563C2×Dic3C2×#6711yescharacteristic
564D12—21no—
565D12—21no—
566D12C2×C4×D312yes—
567D12C2×C4×D312yescomplemented
568C4×D3—22no—
569C4×D3—41no—
570C4×D3—42no—
571C4×D3—42no—
572C4×D3—42no—
573C4×D3—42no—
574C4×D3—64no—
575C4×D3—122no—
576C4×D3C2×C4×D312yes—
577C4×D3#23512yes—
578Dic6—32no—
579Dic6—32no—
580Dic6—62no—
581Dic6—61no—
582Dic6—61no—
583Dic6—121no—
584C3×C8—32no—
585C3×C8—61no—
586C3⋊C8—21no—
587C3⋊C8—32no—
588C3⋊C8—32no—
589C3⋊C8—62no—
590C3⋊C8—61no—
591C3⋊C8—61no—
592C3⋊C8—121no—
593C3⋊C8C2×C4×D312yescomplemented
594C2×C32—42no—
595C2×C32C2×C4×D411yescharacteristic
596C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
597C2×C32#57511yescharacteristic
598C3×D3—22no—
599C3×D3—42no—
600C3×D3—42no—
601C24—61no—
602#41—94no—
603#41—182no—
604C2×Q8—91no—
605C2×D4—34no—
606C2×D4—31no—
607C2×D4—31no—
608C2×D4—62no—
609C2×D4—61no—
610C2×D4—181no—
611C2×D4C2×D3211yescharacteristic
612C22×C4—21no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—124no—
622C22×C4—181no—
623C22×C4—181no—
624SD16—94no—
625SD16—94no—
626D8—34no—
627D8—94no—
628M16—94no—
629M16—182no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8—91no—
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—91no—
638C4⋊C4—181no—
639C4⋊C4—181no—
640C4⋊C4C2×D3211yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—31no—
649C42—31no—
650C42—31no—
651C42—181no—
652C42—181no—
653C42—181no—
654C42C2×D3211yescharacteristic
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—21no—
658C22×C3—32no—
659C22×C3—42no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—62no—
667C22×C3—62no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—128no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3C2×D3×D411yescharacteristic
676C22×C3C22×#6711yescharacteristic
677C2×D3—21no—
678C2×D3—21no—
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—48no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3C4×#6712yes—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—32no—
694C3×C4—32no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—61no—
700C3×C4—81no—
701C3×C4—121no—
702C3×C4—121no—
703C3×C4C22×C4×D311yescharacteristic
704C3×C4C22×C4×D311yescharacteristic
705C3×C4C2×#23511yescharacteristic
706C3×C4D3×#4111yescharacteristic
707Dic3—21no—
708Dic3—41no—
709Dic3—41no—
710Dic3—62no—
711Dic3—62no—
712Dic3—122no—
713Dic3—121no—
714Dic3—121no—
715Dic3—241no—
716Dic3C4×#6712yes—
717Dic3#93212yescomplemented
718C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
719C23—21no—
720C23—31no—
721C23—64no—
722C23—61no—
723C23—61no—
724C23—122no—
725C23—122no—
726Q8—92no—
727Q8—181no—
728D4—21no—
729D4—32no—
730D4—32no—
731D4—64no—
732D4—61no—
733D4—61no—
734D4—184no—
735D4C4×D3212yes—
736C2×C4—21no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—32no—
740C2×C4—32no—
741C2×C4—31no—
742C2×C4—42no—
743C2×C4—62no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—121no—
747C2×C4—122no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4—184no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4—362no—
756C2×C4D3×#6711yescharacteristic
757C2×C4D3×#6711yescharacteristic
758C2×C4C22×D3211yescharacteristic
759C8—32no—
760C8—61no—
761C8—92no—
762C8—181no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—42no—
767C2×C3—42no—
768C2×C3—62no—
769C2×C3—82no—
770C2×C3—122no—
771C2×C3—122no—
772C2×C3C4×D3×D411yescharacteristic
773C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
774C2×C3#577311yescharacteristic
775C2×C3C2×C4×#6711yescharacteristic
776C2×C3C2×#93211yescharacteristic
777C2×C3#582211yescharacteristic
778D3—22no—
779D3—42no—
780D3—42no—
781C22—22no—
782C22—32no—
783C22—41no—
784C22—41no—
785C22—61no—
786C22—61no—
787C22—62no—
788C22—62no—
789C22—128no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22C2×D3×#6711yescharacteristic
795C4—21no—
796C4—21no—
797C4—32no—
798C4—32no—
799C4—41no—
800C4—61no—
801C4—121no—
802C4—121no—
803C4—182no—
804C4—361no—
805C4C2×C4×D3211yescharacteristic
806C4D3×#23511yescharacteristic
807C3—21no—
808C3#7986511yescharacteristic, complemented
809C3C4×#93211yescharacteristic, complemented
810C2—42no—
811C2—62no—
812C2—122no—
813C2—122no—
814C2C4×D3×#6711yescharacteristic
815C2D3×#93211yescharacteristic
816C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#63932C2
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×C4×D3×D4C2semidirect
3. C4×#3795C2semidirect
4. #10592717C2semidirect
5. C3×#5014C2semidirect
6. Dic3×#213C2semidirect
7. #10591421C2semidirect
8. #10591401C2semidirect
9. #10590607C2semidirect
10. #10590581C2semidirect
11. #10590479C2semidirect
12. #10590452C2semidirect
13. #10590360C2semidirect
14. #10590344C2semidirect
15. #10590334C2semidirect
23. C4×#634C22semidirect
32. C3×C4×D12C22semidirect
34. #63932C4semidirect
36. Dic3×D12C22semidirect
40. #63844C22semidirect
47. #63637C22semidirect
48. #63634C22semidirect
49. #63630C22semidirect
51. C3×#809C22semidirect
52. C3×#808C22semidirect
53. C3×#803C22semidirect
54. #63575C22semidirect
55. #63574C22semidirect
56. #63567C22semidirect
59. #63562C22semidirect
60. Dic3×C3⋊C8C22semidirect
61. Dic3×C3⋊C8C22semidirect
65. C4×D3×D4D3semidirect
79. #5014D3semidirect
100. C3×D3×D4C2×C4semidirect
115. #3795C2×C4semidirect
119. #3754C2×C4semidirect
126. C3×#213C2×C4semidirect
143. #3716C2×C4semidirect
144. #3713C2×C4semidirect
146. #3711C2×C4semidirect
199. C4×D12C2×D3semidirect
229. #809C2×D3semidirect
232. #808C2×D3semidirect
240. #803C2×D3semidirect
260. #634C22×C4semidirect
271. C3×D12C22×C4semidirect
284. C3⋊(C3⋊C8)C22×C4semidirect
286. C3×C3⋊C8C22×C4semidirect
333. D3×D4C4×D3semidirect
382. #213C4×D3semidirect
447. C3×Dic3AGL(1,ℤ/8)semidirect
567. D12C2×C4×D3semidirect
593. C3⋊C8C2×C4×D3semidirect
717. Dic3#932semidirect
718. C32C4×AGL(1,ℤ/8)semidirect
808. C3#79865semidirect
809. C3C4×#932semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×D42
C2×#639322
C4×#37952
#105927172
C3×#50142
Dic3×#2132
#105914212
#105914012
#105906072
#105905812
#105904792
#105904522
#105903602
#105903442
#105903342
C4×#9323
#798653