Finite Group Databasebeta

← #11860292

Subgroups — #11860292

Order 1152.

1245 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64123C211yesmaximal, characteristic
2#10595386C211yesmaximal, characteristic, complemented
3D4×#624C211yesmaximal, characteristic, complemented
4C3×#5164C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6#10591554C211yesmaximal, characteristic, complemented
7#10591540C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10591426C211yesmaximal, characteristic, complemented
10#10591404C211yesmaximal, characteristic, complemented
11#10591400C211yesmaximal, characteristic, complemented
12#10590768C211yesmaximal, characteristic, complemented
13#10590763C211yesmaximal, characteristic, complemented
14#10590688C211yesmaximal, characteristic, complemented
15#10590664C211yesmaximal, characteristic, complemented
16#79773—31nomaximal
17C4×#914—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C22×#624—21no—
21C2×C32×SD16C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C2×#3753C2211yescharacteristic
24#64123C418yescomplemented
25C2×#3745C2211yescharacteristic
26C2×#3743C2211yescharacteristic
27C3×Q8×Dic3C2211yescharacteristic, complemented
28C3×Q8×Dic3C2211yescharacteristic, complemented
29C3×D4×Dic3C2211yescharacteristic
30C3×D4×Dic3C2211yescharacteristic
31#63974—21no—
32#63952—21no—
33#63952—21no—
34#63900C2211yescharacteristic
35#63894—21no—
36#63894—21no—
37#63894C2211yescharacteristic
38#63894C2211yescharacteristic
39#63894C2211yescharacteristic, complemented
40#63894C2211yescharacteristic, complemented
41C4×#624—21no—
42C4×#624C2211yescharacteristic
43#63849—21no—
44#63849C2211yescharacteristic
45C2×#3712C2211yescharacteristic
46C3×#835C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#818C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C2×#914—31no—
63C2×#914—31no—
64C2×#914—61no—
65C4×#239—31no—
66C4×#239—31no—
67C4×D3×D4—31no—
68C4×D3×D4—31no—
69C3×#440—31no—
70C3×C4×SD16—31no—
71#5164D311yescharacteristic, complemented
72Dic3×SD16D311yescharacteristic, complemented
73#5026—31no—
74C4×#215—31no—
75#5014—31no—
76C4×#213—31no—
77#4881—31no—
78#4872—31no—
79#4869—31no—
80#4861—31no—
81#4817—31no—
82#4803—31no—
83#4803—31no—
84#4788—31no—
85#4785—31no—
86#4770—31no—
87#4770—31no—
88#4756—31no—
89#4711—31no—
90#4707—31no—
91C4×D24—31no—
92C4×ΓL(1,𝔽25)—31no—
93C23×C3⋊D3—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97#3832—22no—
98#3832C2×C414yescomplemented
99D4×C3⋊D3—22no—
100D4×C3⋊D3C2×C414yescomplemented
101C2×C4⋊(C3⋊D3)—21no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3C2311yescharacteristic
106C22×C3×Dic3—21no—
107C22×C3×Dic3—21no—
108C2×#624—21no—
109C2×#624—21no—
110C2×#624—21no—
111C2×#624—21no—
112C2×#624—21no—
113C2×#624—44no—
114C2×#624D411yescharacteristic
115C2×#624D411yescharacteristic
116C32×SD16C2×C414yescomplemented
117C2×C32×C8C2311yescharacteristic
118#3755C2×C414yescomplemented
119#3753C2×C414yescomplemented
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3745C2×C414yescomplemented
122#3743C2×C414yescomplemented
123C3×#217—21no—
124C3×#217—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138#3722—21no—
139#3722—21no—
140#3722—21no—
141#3722—21no—
142#3722—21no—
143Dic32—21no—
144Dic32D411yescharacteristic
145Dic32D411yescharacteristic
146#3712—22no—
147C4×AGL(1,ℤ/8)—91noSylow
148C2×#239—31no—
149C2×#239—31no—
150C2×#239—61no—
151C2×D3×D4—31no—
152C2×D3×D4—31no—
153C2×D3×D4—61no—
154C22×C4×D3—61no—
155C22×C4×D3—61no—
156C2×C3×SD16—21no—
157C2×C3×SD16C2×D311yescharacteristic
158C2×C3×SD16C2×D311yescharacteristic
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163Q8×Dic3C2×D311yescharacteristic, complemented
164Q8×Dic3C2×D311yescharacteristic, complemented
165C2×#215—31no—
166C2×#215—31no—
167C2×#215—61no—
168D4×Dic3C2×D311yescharacteristic
169D4×Dic3C2×D311yescharacteristic
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—61no—
173C4×#67—61no—
174C4×#67—61no—
175#914—38no—
176#914—38no—
177#914—68no—
178C2×D24—31no—
179C2×D24—31no—
180C2×D24—61no—
181C2×ΓL(1,𝔽25)—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—31no—
184C2×ΓL(1,𝔽25)—31no—
185C2×ΓL(1,𝔽25)—61no—
186#893—31no—
187#893—31no—
188#893—31no—
189#893—31no—
190#893—61no—
191#893—61no—
192#892—31no—
193#892—31no—
194#892—61no—
195#892—61no—
196D3×C4⋊C4—31no—
197D3×C4⋊C4—31no—
198#67⋊C4—61no—
199#67⋊C4—61no—
200D3×C22⋊C4—61no—
201D3×C22⋊C4—61no—
202C4×D12—31no—
203C4×D12—31no—
204C4×D12—31no—
205C4×D12—31no—
206C4×D12—61no—
207C4×D12—61no—
208C42×D3—31no—
209C42×D3—31no—
210C42×D3—61no—
211C42×D3—61no—
212C3×#107—31no—
213C3×#106—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#97—31no—
219C3×C4×C8—31no—
220#835C2×D311yescharacteristic, complemented
221#835C2×D311yescharacteristic, complemented
222#832C2×D311yescharacteristic
223#832C2×D311yescharacteristic
224#821—31no—
225#821—31no—
226#821—31no—
227#821—31no—
228#818C2×D311yescharacteristic, complemented
229#817C2×D311yescharacteristic, complemented
230#815—31no—
231#815C2×D311yescharacteristic, complemented
232C8×Dic3—31no—
233C8×Dic3C2×D311yescharacteristic, complemented
234#809—31no—
235#809—31no—
236#809—31no—
237#809—31no—
238#808—31no—
239#808—31no—
240#807—31no—
241#807—31no—
242#803—31no—
243C4×C3⋊C8—31no—
244C23×C32—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—24no—
248C22×C3⋊D3—42no—
249C22×C3⋊D3—42no—
250C22×C3⋊D3C2×D411yescharacteristic
251C32×Q8—21no—
252C32×Q8C22×C412yescomplemented
253C32×D4—21no—
254C32×D4C22×C412yes—
255C2×C32×C4—21no—
256C2×C32×C4C2411yescharacteristic
257#638—24no—
258C2×C3⋊Dic3C2×D411yescharacteristic
259C4⋊(C3⋊D3)—24no—
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)C22×C412yes—
263C4⋊(C3⋊D3)C22×C412yescomplemented
264C4×C3⋊D3—24no—
265C4×C3⋊D3C22×C412yes—
266C4×C3⋊D3#4112yes—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—42no—
272C2×C3×Dic3—42no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277#624—22no—
278#624—41no—
279#624—42no—
280#624—42no—
281#624—42no—
282#624—42no—
283#624—42no—
284C32×C8C22×C412yescomplemented
285C3⋊(C3⋊C8)C22×C412yescomplemented
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288C2×AGL(1,ℤ/8)—91no—
289C4×#41—91no—
290C2×C4×D4—91no—
291#442—91no—
292#442—91no—
293#440—31no—
294#440—91no—
295C4×SD16—31no—
296C4×SD16—91no—
297C4×D8—91no—
298C4×D8—91no—
299#428—91no—
300#418—91no—
301#417—91no—
302C4×M16—91no—
303C23×D3—61no—
304C23×D3—61no—
305C23×D3—121no—
306C2×C3×Q8—21no—
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×D4—21no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—121no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319#239—34no—
320#239—34no—
321#239—64no—
322#239—62no—
323#239—62no—
324#239—122no—
325D3×D4—34no—
326D3×D4—34no—
327D3×D4—64no—
328D3×D4—62no—
329D3×D4—62no—
330D3×D4—122no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—31no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12—121no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3—61no—
358C2×C4×D3—61no—
359C2×C4×D3—121no—
360C2×C4×D3—124no—
361C2×C4×D3—124no—
362C3×SD16—24no—
363C3×SD16C4×D314yescomplemented
364C3×SD16C4×D314yescomplemented
365C2×C3×C8—21no—
366C2×C3×C8—31no—
367C2×C3×C8—31no—
368C2×C3×C8C22×D311yescharacteristic
369C2×C3×C8C22×D311yescharacteristic
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—31no—
373C3×C4⋊C4—31no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C42—31no—
379C3×C42—31no—
380C3×C42—61no—
381C3×C42—61no—
382#217—21no—
383#217—21no—
384#215—34no—
385#215—34no—
386#215—64no—
387#213—34no—
388#213—34no—
389#213—64no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400C4⋊Dic3—21no—
401C4⋊Dic3—21no—
402C4⋊Dic3C22×D311yescharacteristic
403C4⋊Dic3C22×D311yescharacteristic
404C4⋊Dic3C22×D311yescharacteristic
405C4⋊Dic3C22×D311yescharacteristic
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408C4×Dic3—21no—
409C4×Dic3—21no—
410C4×Dic3—31no—
411C4×Dic3—31no—
412C4×Dic3—31no—
413C4×Dic3—31no—
414C4×Dic3—61no—
415C4×Dic3—61no—
416C4×Dic3C22×D311yescharacteristic
417C4×Dic3C22×D311yescharacteristic
418C2×C3⋊C8—31no—
419C2×C3⋊C8—31no—
420C2×C3⋊C8—61no—
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423D24—34no—
424D24—34no—
425D24—64no—
426ΓL(1,𝔽25)—34no—
427ΓL(1,𝔽25)—34no—
428ΓL(1,𝔽25)—64no—
429ΓL(1,𝔽25)—62no—
430ΓL(1,𝔽25)—62no—
431C22×C32—22no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32C22×D411yescharacteristic
435C2×C3⋊D3—21no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3—22no—
438C2×C3⋊D3—22no—
439C2×C3⋊D3—48no—
440C2×C3⋊D3—41no—
441C2×C3⋊D3—41no—
442C2×C3⋊D3—41no—
443C2×C3⋊D3—41no—
444C2×C3⋊D3C4×D412yes—
445C32×C4—22no—
446C32×C4C23×C411yescharacteristic
447C32×C4C2×#4111yescharacteristic
448C3⋊Dic3C4×D412yes—
449C3×Dic3—21no—
450C3×Dic3—21no—
451C3×Dic3—21no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3AGL(1,ℤ/8)12yescomplemented
457C2×#41—91no—
458C22×D4—91no—
459C23×C4—181no—
460AGL(1,ℤ/8)—98no—
461C2×SD16—91no—
462C2×SD16D3211yescharacteristic
463C2×D8—91no—
464C2×D8—91no—
465C2×M16—91no—
466C2×M16—91no—
467C4×Q8—31no—
468C4×Q8—31no—
469C4×D4—31no—
470C4×D4—31no—
471C4×D4—91no—
472C4×D4—91no—
473C4×D4—91no—
474C4×D4—91no—
475C4×D4—181no—
476C4×D4—181no—
477C4×D4—181no—
478C4×D4—181no—
479#117—91no—
480#117—181no—
481C2×C4⋊C4—91no—
482C2×C22⋊C4—181no—
483C2×C42—91no—
484C2×C42—181no—
485#107—31no—
486#107—91no—
487#106—31no—
488#106—91no—
489#103—31no—
490#103—31no—
491#102—31no—
492#102—31no—
493#102—91no—
494#102—91no—
495#102—91no—
496#102—91no—
497#97—31no—
498#97—91no—
499C4×C8—31no—
500C4×C8—91no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—41no—
504C22×D3—31no—
505C22×D3—31no—
506C22×D3—61no—
507C22×D3—64no—
508C22×D3—64no—
509C22×D3—61no—
510C22×D3—61no—
511C22×D3—61no—
512C22×D3—61no—
513C22×D3—124no—
514C22×D3—121no—
515C22×D3—121no—
516C22×D3—122no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—242no—
521C22×D3—242no—
522C3×Q8—21no—
523C3×Q8—21no—
524C3×Q8—22no—
525C3×Q8—41no—
526C3×Q8C2×C4×D312yescomplemented
527C3×Q8C2×C4×D312yescomplemented
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—22no—
531C3×D4—41no—
532C3×D4C2×C4×D312yes—
533C3×D4C2×C4×D312yes—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—41no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—122no—
547C2×C3×C4—122no—
548C2×C3×C4C23×D311yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550#67—64no—
551#67—64no—
552#67—124no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—42no—
560C2×Dic3—42no—
561C2×Dic3—61no—
562C2×Dic3D3×D411yescharacteristic
563C2×Dic3D3×D411yescharacteristic
564C2×Dic3D3×D411yescharacteristic
565C2×Dic3D3×D411yescharacteristic
566D12—32no—
567D12—32no—
568D12—32no—
569D12—32no—
570D12—62no—
571D12—62no—
572D12—64no—
573D12—64no—
574D12—61no—
575D12—61no—
576D12—61no—
577D12—61no—
578D12—121no—
579D12—121no—
580D12—124no—
581C4×D3—32no—
582C4×D3—32no—
583C4×D3—32no—
584C4×D3—32no—
585C4×D3—62no—
586C4×D3—62no—
587C4×D3—62no—
588C4×D3—64no—
589C4×D3—64no—
590C4×D3—62no—
591C4×D3—124no—
592C4×D3—121no—
593C4×D3—121no—
594C4×D3—122no—
595C4×D3—122no—
596C4×D3—122no—
597C4×D3—122no—
598C4×D3—122no—
599C4×D3—122no—
600C4×D3—122no—
601C4×D3—122no—
602C4×D3—122no—
603C4×D3—122no—
604C3×C8—22no—
605C3×C8—61no—
606C3×C8—61no—
607C3×C8C2×C4×D312yescomplemented
608C3×C8C2×C4×D312yescomplemented
609C3⋊C8—21no—
610C3⋊C8—21no—
611C3⋊C8—32no—
612C3⋊C8—32no—
613C3⋊C8—62no—
614C2×C32—42no—
615C2×C32C2×C4×D411yescharacteristic
616C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
617C2×C32#57511yescharacteristic
618C3⋊D3—22no—
619C3⋊D3—42no—
620C3⋊D3—42no—
621C24—181no—
622#41—94no—
623#41—182no—
624C2×Q8C2×D3211yescharacteristic
625C2×D4—94no—
626C2×D4—91no—
627C2×D4—91no—
628C2×D4—181no—
629C2×D4—182no—
630C2×D4—181no—
631C2×D4C2×D3211yescharacteristic
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—91no—
635C22×C4—91no—
636C22×C4—91no—
637C22×C4—181no—
638C22×C4—181no—
639C22×C4—181no—
640C22×C4—181no—
641C22×C4—181no—
642C22×C4—181no—
643C22×C4—364no—
644SD16—94no—
645SD16#62414yescomplemented
646D8—94no—
647D8—94no—
648M16—94no—
649M16—182no—
650C2×C8—31no—
651C2×C8—31no—
652C2×C8—91no—
653C2×C8C2×D3211yescharacteristic
654C4⋊C4—31no—
655C4⋊C4—31no—
656C4⋊C4—31no—
657C4⋊C4—31no—
658C4⋊C4—61no—
659C4⋊C4—61no—
660C4⋊C4—181no—
661C22⋊C4—61no—
662C22⋊C4—61no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C22⋊C4—181no—
667C22⋊C4—181no—
668C42—31no—
669C42—31no—
670C42—61no—
671C42—61no—
672C42—91no—
673C42—91no—
674C42—181no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—21no—
678C22×C3—42no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—81no—
684C22×C3—81no—
685C22×C3C2×D3×D411yescharacteristic
686C22×C3C2×D3×D411yescharacteristic
687C2×D3—32no—
688C2×D3—32no—
689C2×D3—62no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—62no—
695C2×D3—62no—
696C2×D3—62no—
697C2×D3—62no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—122no—
701C2×D3—122no—
702C2×D3—128no—
703C2×D3—128no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—248no—
713C2×D3—241no—
714C2×D3—241no—
715C2×D3—241no—
716C2×D3—241no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—32no—
722C3×C4—42no—
723C3×C4—61no—
724C3×C4—61no—
725C3×C4—61no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4—121no—
729C3×C4—121no—
730C3×C4C22×C4×D311yescharacteristic
731C3×C4C22×C4×D311yescharacteristic
732C3×C4D3×#4111yescharacteristic
733C3×C4D3×#4111yescharacteristic
734Dic3—21no—
735Dic3—21no—
736Dic3—21no—
737Dic3—32no—
738Dic3—32no—
739Dic3—41no—
740Dic3—41no—
741Dic3—41no—
742Dic3—41no—
743Dic3—62no—
744Dic3#91412yescomplemented
745C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
746C23—21no—
747C23—91no—
748C23—184no—
749C23—181no—
750C23—181no—
751C23—362no—
752C23—362no—
753Q8—21no—
754Q8C2×#62412yescomplemented
755D4—21no—
756D4—92no—
757D4—92no—
758D4—184no—
759D4—184no—
760D4—181no—
761D4—181no—
762D4C2×#62412yes—
763C2×C4—21no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—31no—
767C2×C4—31no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—91no—
773C2×C4—92no—
774C2×C4—92no—
775C2×C4—122no—
776C2×C4—122no—
777C2×C4—184no—
778C2×C4—182no—
779C2×C4—362no—
780C2×C4—362no—
781C2×C4—361no—
782C2×C4—362no—
783C2×C4—362no—
784C2×C4—362no—
785C2×C4C22×D3211yescharacteristic
786C8—61no—
787C8—61no—
788C8—92no—
789C8C2×#62412yescomplemented
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—42no—
794C2×C3—42no—
795C2×C3—82no—
796C2×C3C4×D3×D411yescharacteristic
797C2×C3C4×D3×D411yescharacteristic
798C2×C3C2×#91411yescharacteristic
799C2×C3#576811yescharacteristic
800C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
801C2×C3#577711yescharacteristic
802D3—62no—
803D3—62no—
804D3—122no—
805D3—122no—
806D3—122no—
807D3—122no—
808D3—122no—
809D3—242no—
810D3—242no—
811C22—22no—
812C22—41no—
813C22—41no—
814C22—92no—
815C22—181no—
816C22—181no—
817C22—182no—
818C22—182no—
819C22—368no—
820C22—361no—
821C22—361no—
822C22—361no—
823C22—361no—
824C22D32×D411yescharacteristic
825C4—22no—
826C4—32no—
827C4—61no—
828C4—61no—
829C4—61no—
830C4—92no—
831C4—121no—
832C4—121no—
833C4—121no—
834C4—121no—
835C4#6431211yescharacteristic
836C4C22×#62411yescharacteristic
837C3—21no—
838C3C4×#91411yescharacteristic, complemented
839C3#7977311yescharacteristic, complemented
840C2—42no—
841C2—182no—
842C2—362no—
843C2—362no—
844C2D3×#91411yescharacteristic
845C2#1059474611yescharacteristic
846C2D4×#62411yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×#64123C2
cosocleC2×C32×C4C24
hypercenterC2×SD16D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. #10595386C2semidirect
3. D4×#624C2semidirect
4. C3×#5164C2semidirect
5. C3×Dic3×SD16C2semidirect
6. #10591554C2semidirect
7. #10591540C2semidirect
8. #10591536C2semidirect
9. #10591426C2semidirect
10. #10591404C2semidirect
11. #10591400C2semidirect
12. #10590768C2semidirect
13. #10590763C2semidirect
14. #10590688C2semidirect
15. #10590664C2semidirect
24. #64123C4semidirect
27. C3×Q8×Dic3C22semidirect
28. C3×Q8×Dic3C22semidirect
39. #63894C22semidirect
40. #63894C22semidirect
46. C3×#835C22semidirect
47. C3×#835C22semidirect
50. C3×#818C22semidirect
51. C3×#817C22semidirect
52. C3×#815C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63576C22semidirect
55. #63574C22semidirect
58. #63564C22semidirect
59. #63564C22semidirect
60. #63554C22semidirect
61. Dic3×C3⋊C8C22semidirect
71. #5164D3semidirect
72. Dic3×SD16D3semidirect
98. #3832C2×C4semidirect
100. D4×C3⋊D3C2×C4semidirect
116. C32×SD16C2×C4semidirect
118. #3755C2×C4semidirect
119. #3753C2×C4semidirect
121. #3745C2×C4semidirect
122. #3743C2×C4semidirect
163. Q8×Dic3C2×D3semidirect
164. Q8×Dic3C2×D3semidirect
220. #835C2×D3semidirect
221. #835C2×D3semidirect
228. #818C2×D3semidirect
229. #817C2×D3semidirect
231. #815C2×D3semidirect
233. C8×Dic3C2×D3semidirect
252. C32×Q8C22×C4semidirect
263. C4⋊(C3⋊D3)C22×C4semidirect
284. C32×C8C22×C4semidirect
285. C3⋊(C3⋊C8)C22×C4semidirect
363. C3×SD16C4×D3semidirect
364. C3×SD16C4×D3semidirect
456. C3×Dic3AGL(1,ℤ/8)semidirect
526. C3×Q8C2×C4×D3semidirect
527. C3×Q8C2×C4×D3semidirect
607. C3×C8C2×C4×D3semidirect
608. C3×C8C2×C4×D3semidirect
645. SD16#624semidirect
744. Dic3#914semidirect
745. C32C4×AGL(1,ℤ/8)semidirect
754. Q8C2×#624semidirect
789. C8C2×#624semidirect
838. C3C4×#914semidirect
839. C3#79773semidirect

Maximal subgroups

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

subgroupindex
C2×#641232
#105953862
D4×#6242
C3×#51642
C3×Dic3×SD162
#105915542
#105915402
#105915362
#105914262
#105914042
#105914002
#105907682
#105907632
#105906882
#105906642
#797733
C4×#9143