Finite Group Databasebeta

← #11860285

Subgroups — #11860285

Order 1152.

1163 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#911C211yesmaximal, characteristic
2Dic3×#237C211yesmaximal, characteristic, complemented
3D3×D4×Dic3C211yesmaximal, characteristic, complemented
4D8×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#5152C211yesmaximal, characteristic, complemented
6#10591445C211yesmaximal, characteristic, complemented
7#10591440C211yesmaximal, characteristic, complemented
8#10591435C211yesmaximal, characteristic, complemented
9#10591430C211yesmaximal, characteristic, complemented
10#10591421C211yesmaximal, characteristic, complemented
11#10591414C211yesmaximal, characteristic, complemented
12#10590775C211yesmaximal, characteristic, complemented
13#10590766C211yesmaximal, characteristic, complemented
14#10590681C211yesmaximal, characteristic, complemented
15#10590667C211yesmaximal, characteristic, complemented
16Dic3×AGL(1,ℤ/8)—31nomaximal
17#79865—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×D3×Dic3—21no—
21C2×C32×D8C2211yescharacteristic
22D4×C3⋊Dic3C2211yescharacteristic
23D4×C3⋊Dic3C2211yescharacteristic, complemented
24C3×D4×Dic3C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic, complemented
26C2×C3×#214C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C3×#911C418yescomplemented
29C2×C3×#204C2211yescharacteristic
30C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
31#67⋊Dic3—21no—
32#67⋊Dic3—21no—
33Dic3×#67—21no—
34Dic3×#67—21no—
35D3×#217—21no—
36#63955—21no—
37C2×Dic32—21no—
38#63898C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40D3×C4⋊Dic3C2211yescharacteristic
41C4×D3×Dic3C2211yescharacteristic
42#63843C2211yescharacteristic, complemented
43Dic3×Dic6C2211yescharacteristic, complemented
44#63841C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic, complemented
48#63645C2211yescharacteristic, complemented
49C8×C3⋊Dic3C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic
51C3×#832C2211yescharacteristic, complemented
52C3×#817C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#63553C2211yescharacteristic, complemented
62C2×C3×AGL(1,ℤ/8)—31no—
63Dic3×#41—31no—
64C2×D4×Dic3—31no—
65C2×#911D311yescharacteristic
66C4×D3×D4—31no—
67C4×#237—31no—
68C3×#442—31no—
69#5232—31no—
70#5215—31no—
71#5164—31no—
72#5164—31no—
73Dic3×SD16—31no—
74Dic3×SD16—31no—
75#5152—31no—
76#5152D311yescharacteristic, complemented
77Dic3×D8—31no—
78Dic3×D8—31no—
79Dic3×D8—31no—
80Dic3×D8—61no—
81#5121—31no—
82Dic3×M16—31no—
83#5018—31no—
84#5014—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
95C2×C32×D4C2311yescharacteristic
96C22×C3⋊Dic3—21no—
97C22×C3⋊Dic3—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C3×#237—22no—
104C3×#237C2×C414yescomplemented
105C3×D3×D4—22no—
106C3×D3×D4C2×C414yescomplemented
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—44no—
114C2×D3×Dic3D411yescharacteristic
115C2×D3×Dic3D411yescharacteristic
116C32×D8C2×C414yescomplemented
117C2×C32×C8C2311yescharacteristic
118#3757—21no—
119#3757—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C3×#217—21no—
125C3×#217—21no—
126C3×#214C2×C414yescomplemented
127C3×#213C2×C414yescomplemented
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×#204C2×C414yescomplemented
134C3×ΓL(1,𝔽25)C2×C414yescomplemented
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142Dic32—21no—
143Dic32—21no—
144Dic32D411yescharacteristic
145Dic32D411yescharacteristic
146#3711—22no—
147C4×AGL(1,ℤ/8)—91noSylow
148C2×C3×#41—31no—
149C22×C3×D4—31no—
150C23×Dic3—61no—
151C2×#237C2×D311yescharacteristic
152C2×D3×D4C2×D311yescharacteristic
153C22×C4×D3—61no—
154C3×AGL(1,ℤ/8)—38no—
155C2×C3×SD16—31no—
156C2×C3×SD16—31no—
157C2×C3×D8—21no—
158C2×C3×D8—31no—
159C2×C3×D8C2×D311yescharacteristic
160C2×C3×D8C2×D311yescharacteristic
161C2×C3×M16—31no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C2×#217—61no—
165Q8×Dic3—31no—
166Q8×Dic3—31no—
167D4×Dic3—31no—
168D4×Dic3—31no—
169D4×Dic3—31no—
170D4×Dic3—31no—
171D4×Dic3—31no—
172D4×Dic3—31no—
173D4×Dic3—61no—
174D4×Dic3—61no—
175D4×Dic3—61no—
176D4×Dic3—61no—
177D4×Dic3—61no—
178D4×Dic3—61no—
179D4×Dic3C2×D311yescharacteristic
180D4×Dic3C2×D311yescharacteristic, complemented
181C2×#214C2×D311yescharacteristic
182C2×#213C2×D311yescharacteristic
183C4×#67—61no—
184C4×#67—61no—
185#926—31no—
186#926—61no—
187C2×C4⋊Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—61no—
190C2×C4×Dic3—61no—
191C2×#208—31no—
192#911Dic318yescomplemented
193C2×#204C2×D311yescharacteristic
194C2×ΓL(1,𝔽25)—31no—
195C2×ΓL(1,𝔽25)C2×D311yescharacteristic
196#893—31no—
197#892—31no—
198D3×C4⋊C4—31no—
199#887—31no—
200#67⋊C4—61no—
201#67⋊C4—61no—
202D3×C22⋊C4—61no—
203#877—61no—
204C4×D12—31no—
205C42×D3—31no—
206C4×Dic6—31no—
207C3×#106—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#97—31no—
211#835—31no—
212#835—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—31no—
217#832—31no—
218#832—31no—
219#832—61no—
220#832—61no—
221#832C2×D311yescharacteristic
222#832C2×D311yescharacteristic, complemented
223#821—31no—
224#818—31no—
225#818—31no—
226#818—31no—
227#818—61no—
228#817—31no—
229#817C2×D311yescharacteristic, complemented
230#816—31no—
231#815—31no—
232#815C2×D311yescharacteristic, complemented
233C8×Dic3—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236C8×Dic3—31no—
237C8×Dic3—61no—
238#810—31no—
239#809—31no—
240#808—31no—
241#807—31no—
242#803—31no—
243C23×C32—21no—
244C23×C32—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×D4—21no—
252C32×D4C22×C412yes—
253C32×D4C22×C412yescomplemented
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—42no—
258C2×C3⋊Dic3—42no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261C3×#67—24no—
262C3×#67—24no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—24no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—42no—
268C2×C3×Dic3—42no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12C22×C412yes—
274C3×C4×D3C22×C412yes—
275C3×C4×D3#4112yes—
276C3×Dic6—21no—
277C3×Dic6C22×C412yescomplemented
278D3×Dic3—22no—
279D3×Dic3—41no—
280D3×Dic3—42no—
281D3×Dic3—42no—
282D3×Dic3—42no—
283C32×C8C22×C412yescomplemented
284C3⋊(C3⋊C8)—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8C22×C412yescomplemented
287C2×AGL(1,ℤ/8)—31no—
288C4×#41—91no—
289C2×C4×D4—91no—
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—
304C3×#41—34no—
305C3×#41—62no—
306C2×C3×Q8—31no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—34no—
310C2×C3×D4—31no—
311C2×C3×D4—62no—
312C2×C3×D4—61no—
313C2×C3×D4—61no—
314C2×C3×D4C22×D311yescharacteristic
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C2×C3×D4C22×D311yescharacteristic
318C22×C3×C4—31no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C2×#67—21no—
323C2×#67—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3—61no—
336C22×Dic3—121no—
337C22×Dic3—121no—
338C22×Dic3—124no—
339#237—22no—
340#237C2×Dic314yescomplemented
341D3×D4—22no—
342D3×D4C2×Dic314yescomplemented
343C2×D12C22×D311yescharacteristic
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—124no—
350C2×C4×D3C22×D311yescharacteristic
351C2×Dic6C22×D311yescharacteristic
352C3×SD16—34no—
353C3×SD16—34no—
354C3×D8—24no—
355C3×D8—34no—
356C3×D8C4×D314yescomplemented
357C3×D8C2×Dic314yescomplemented
358C3×M16—34no—
359C2×C3×C8—21no—
360C2×C3×C8—31no—
361C2×C3×C8—31no—
362C2×C3×C8C22×D311yescharacteristic
363C2×C3×C8C22×D311yescharacteristic
364C3×C4⋊C4—31no—
365C3×C4⋊C4—31no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C42—31no—
369#217—21no—
370#217—21no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—61no—
376#217—61no—
377#217—61no—
378#217—121no—
379#217—121no—
380#214C2×Dic314yescomplemented
381#213C2×Dic314yescomplemented
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412C4×Dic3C22×D311yescharacteristic
413#208—62no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—61no—
417C2×C3⋊C8C22×D311yescharacteristic
418C2×C3⋊C8C22×D311yescharacteristic
419#204C2×Dic314yescomplemented
420ΓL(1,𝔽25)—62no—
421ΓL(1,𝔽25)C2×Dic314yescomplemented
422C22×C32—22no—
423C22×C32—22no—
424C22×C32—41no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32C22×D411yescharacteristic
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—22no—
432C2×C3×D3—48no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3C4×D412yes—
436C32×C4C23×C411yescharacteristic
437C32×C4C2×#4111yescharacteristic
438C3⋊Dic3—21no—
439C3⋊Dic3—41no—
440C3⋊Dic3—41no—
441C3⋊Dic3AGL(1,ℤ/8)12yescomplemented
442C3×Dic3—22no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3C4×D412yes—
448C2×#41—31no—
449C22×D4—31no—
450C23×C4—181no—
451AGL(1,ℤ/8)—38no—
452C2×SD16—31no—
453C2×SD16—31no—
454C2×D8—31no—
455C2×D8D3211yescharacteristic
456C2×M16—31no—
457C2×M16—91no—
458C4×Q8—91no—
459C4×Q8—91no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—91no—
465C4×D4—91no—
466C4×D4—181no—
467C4×D4—181no—
468C4×D4—181no—
469C4×D4—181no—
470#117—91no—
471#117—181no—
472C2×C4⋊C4—91no—
473C2×C22⋊C4—181no—
474C2×C42—91no—
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—21no—
495C23×C3—21no—
496C23×C3—31no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—64no—
500C23×C3—61no—
501C23×C3—122no—
502C23×C3—122no—
503C22×D3—21no—
504C22×D3—24no—
505C22×D3—42no—
506C22×D3—42no—
507C22×D3D3×D411yescharacteristic
508C3×Q8—32no—
509C3×Q8—61no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—22no—
515C3×D4—22no—
516C3×D4—32no—
517C3×D4—41no—
518C3×D4—41no—
519C3×D4—64no—
520C3×D4—64no—
521C3×D4—61no—
522C3×D4C2×C4×D312yes—
523C3×D4C2×C4×D312yescomplemented
524C3×D4C22×Dic312yes—
525C3×D4C22×Dic312yescomplemented
526C2×C3×C4—21no—
527C2×C3×C4—31no—
528C2×C3×C4—32no—
529C2×C3×C4—32no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—64no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—122no—
537C2×C3×C4—122no—
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—24no—
541#67—24no—
542C2×Dic3—21no—
543C2×Dic3—24no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—42no—
551C2×Dic3—42no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—62no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3—122no—
563C2×Dic3—122no—
564C2×Dic3—122no—
565C2×Dic3—122no—
566C2×Dic3—122no—
567C2×Dic3—122no—
568C2×Dic3—122no—
569C2×Dic3—242no—
570C2×Dic3—242no—
571C2×Dic3D3×D411yescharacteristic
572C2×Dic3D3×D411yescharacteristic
573C2×Dic3D3×D411yescharacteristic
574D12—21no—
575D12C22×Dic312yes—
576C4×D3—62no—
577C4×D3—122no—
578C4×D3—121no—
579C4×D3—122no—
580C4×D3—122no—
581C4×D3#23712yes—
582C4×D3C22×Dic312yes—
583Dic6—21no—
584Dic6C22×Dic312yescomplemented
585C3×C8—22no—
586C3×C8—32no—
587C3×C8—61no—
588C3×C8C2×C4×D312yescomplemented
589C3×C8C22×Dic312yescomplemented
590C3⋊C8—21no—
591C3⋊C8—61no—
592C3⋊C8—61no—
593C3⋊C8—121no—
594C3⋊C8C22×Dic312yescomplemented
595C2×C32—42no—
596C2×C32—42no—
597C2×C32C2×C4×D411yescharacteristic
598C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
599C2×C32#57511yescharacteristic
600C3×D3—22no—
601C3×D3—42no—
602C24—61no—
603#41—34no—
604#41—62no—
605C2×Q8—31no—
606C2×D4—34no—
607C2×D4—31no—
608C2×D4—62no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4C2×D3211yescharacteristic
612C2×D4C2×D3211yescharacteristic
613C22×C4—31no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—181no—
624C22×C4—364no—
625SD16—34no—
626SD16—34no—
627D8—34no—
628D8D3×Dic314yescomplemented
629M16—34no—
630M16—182no—
631C2×C8—31no—
632C2×C8—31no—
633C2×C8—91no—
634C2×C8C2×D3211yescharacteristic
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—91no—
638C4⋊C4—91no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C4⋊C4—181no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C42—31no—
650C42—91no—
651C42—91no—
652C42—91no—
653C42—181no—
654C42—181no—
655C42—181no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—21no—
661C22×C3—32no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—62no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—128no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3C2×D3×D411yescharacteristic
683C22×C3C2×D3×D411yescharacteristic
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—22no—
687C2×D3—48no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3D4×Dic312yes—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—32no—
694C3×C4—61no—
695C3×C4—61no—
696C3×C4—62no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4C22×C4×D311yescharacteristic
700C3×C4C2×#23711yescharacteristic
701C3×C4D3×#4111yescharacteristic
702C3×C4C23×Dic311yescharacteristic
703Dic3—21no—
704Dic3—21no—
705Dic3—22no—
706Dic3—32no—
707Dic3—32no—
708Dic3—41no—
709Dic3—41no—
710Dic3—62no—
711Dic3—61no—
712Dic3—61no—
713Dic3—121no—
714Dic3—121no—
715Dic3—121no—
716Dic3—121no—
717Dic3—121no—
718Dic3—241no—
719Dic3—241no—
720Dic3D4×Dic312yes—
721C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
722C23—21no—
723C23—21no—
724C23—31no—
725C23—64no—
726C23—61no—
727C23—122no—
728C23—122no—
729Q8—32no—
730Q8—61no—
731D4—21no—
732D4—21no—
733D4—32no—
734D4—64no—
735D4—64no—
736D4—61no—
737D4C2×D3×Dic312yes—
738D4C2×D3×Dic312yescomplemented
739C2×C4—31no—
740C2×C4—32no—
741C2×C4—32no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—64no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—91no—
749C2×C4—91no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4—182no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4—361no—
756C2×C4—362no—
757C2×C4—362no—
758C2×C4—362no—
759C2×C4—362no—
760C2×C4—362no—
761C2×C4C22×D3211yescharacteristic
762C8—32no—
763C8—61no—
764C8—181no—
765C8C2×D3×Dic312yescomplemented
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—42no—
770C2×C3—42no—
771C2×C3—42no—
772C2×C3—42no—
773C2×C3—62no—
774C2×C3—82no—
775C2×C3—82no—
776C2×C3—122no—
777C2×C3C4×D3×D411yescharacteristic
778C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
779C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
780C2×C3#577311yescharacteristic
781C2×C3#577311yescharacteristic
782C2×C3C2×D4×Dic311yescharacteristic
783D3—22no—
784D3—42no—
785C22—22no—
786C22—22no—
787C22—32no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—61no—
793C22—61no—
794C22—62no—
795C22—128no—
796C22—121no—
797C22—121no—
798C22D32×D411yescharacteristic
799C4—32no—
800C4—62no—
801C4—61no—
802C4—61no—
803C4—92no—
804C4—121no—
805C4—121no—
806C4—181no—
807C4—361no—
808C4—361no—
809C4D3×#23711yescharacteristic
810C4C22×D3×Dic311yescharacteristic
811C3—21no—
812C3#7986511yescharacteristic, complemented
813C3Dic3×AGL(1,ℤ/8)11yescharacteristic, complemented
814C2—42no—
815C2—42no—
816C2—62no—
817C2—122no—
818C2#1059472611yescharacteristic
819C2#1059472811yescharacteristic
820C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radicalC2×C3×#911C2
cosocleC2×C32×C4C24
hypercenterC2×D8D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. Dic3×#237C2semidirect
3. D3×D4×Dic3C2semidirect
4. D8×C3⋊Dic3C2semidirect
5. C3×#5152C2semidirect
6. #10591445C2semidirect
7. #10591440C2semidirect
8. #10591435C2semidirect
9. #10591430C2semidirect
10. #10591421C2semidirect
11. #10591414C2semidirect
12. #10590775C2semidirect
13. #10590766C2semidirect
14. #10590681C2semidirect
15. #10590667C2semidirect
23. D4×C3⋊Dic3C22semidirect
25. C3×D4×Dic3C22semidirect
28. C3×#911C4semidirect
42. #63843C22semidirect
43. Dic3×Dic6C22semidirect
47. #63659C22semidirect
48. #63645C22semidirect
49. C8×C3⋊Dic3C22semidirect
51. C3×#832C22semidirect
52. C3×#817C22semidirect
53. C3×#815C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. #63566C22semidirect
57. #63565C22semidirect
60. #63554C22semidirect
61. #63553C22semidirect
76. #5152D3semidirect
104. C3×#237C2×C4semidirect
106. C3×D3×D4C2×C4semidirect
116. C32×D8C2×C4semidirect
126. C3×#214C2×C4semidirect
127. C3×#213C2×C4semidirect
133. C3×#204C2×C4semidirect
134. C3×ΓL(1,𝔽25)C2×C4semidirect
180. D4×Dic3C2×D3semidirect
192. #911Dic3semidirect
222. #832C2×D3semidirect
229. #817C2×D3semidirect
232. #815C2×D3semidirect
253. C32×D4C22×C4semidirect
277. C3×Dic6C22×C4semidirect
283. C32×C8C22×C4semidirect
286. C3×C3⋊C8C22×C4semidirect
340. #237C2×Dic3semidirect
342. D3×D4C2×Dic3semidirect
356. C3×D8C4×D3semidirect
357. C3×D8C2×Dic3semidirect
380. #214C2×Dic3semidirect
381. #213C2×Dic3semidirect
419. #204C2×Dic3semidirect
421. ΓL(1,𝔽25)C2×Dic3semidirect
441. C3⋊Dic3AGL(1,ℤ/8)semidirect
523. C3×D4C2×C4×D3semidirect
525. C3×D4C22×Dic3semidirect
584. Dic6C22×Dic3semidirect
588. C3×C8C2×C4×D3semidirect
589. C3×C8C22×Dic3semidirect
594. C3⋊C8C22×Dic3semidirect
628. D8D3×Dic3semidirect
721. C32C4×AGL(1,ℤ/8)semidirect
738. D4C2×D3×Dic3semidirect
765. C8C2×D3×Dic3semidirect
812. C3#79865semidirect
813. C3Dic3×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9112
Dic3×#2372
D3×D4×Dic32
D8×C3⋊Dic32
C3×#51522
#105914452
#105914402
#105914352
#105914302
#105914212
#105914142
#105907752
#105907662
#105906812
#105906672
Dic3×AGL(1,ℤ/8)3
#798653