Finite Group Databasebeta

← #11860345

Subgroups — #11860345

Order 1152.

1162 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
1C3×C4×#237C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic
3C4×D3×D12C211yesmaximal, characteristic, complemented
4#10592713C211yesmaximal, characteristic, complemented
5C3×#5014C211yesmaximal, characteristic, complemented
6Dic3×#213C211yesmaximal, characteristic, complemented
7#10591414C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10590592C211yesmaximal, characteristic, complemented
10#10590458C211yesmaximal, characteristic, complemented
11#10590453C211yesmaximal, characteristic, complemented
12#10590437C211yesmaximal, characteristic, complemented
13#10590362C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590334C211yesmaximal, characteristic, complemented
16C4×#949—31nomaximal
17#79865—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×C4×D32—21no—
21C32×C4×D4C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic
23C4×C4⋊(C3⋊D3)C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic, complemented
25C2×C3×#213C2211yescharacteristic
26C3×C4×#67—21no—
27C2×C3×C4×Dic3—21no—
28C3×#892C2211yescharacteristic
29C3×#887C2211yescharacteristic, complemented
30C3×#67⋊C4—21no—
31C3×#877—21no—
32C3×C4×D12C2211yescharacteristic
33C3×C42×D3C2211yescharacteristic
34C3×C4×Dic6C2211yescharacteristic, complemented
35#63925C418yescomplemented
36D3×(C2×D3)⋊C4—21no—
37C4×#626—21no—
38#63894C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40D3×C4⋊Dic3C2211yescharacteristic
41#63880—21no—
42C2×#3717C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46#63659C2211yescharacteristic, complemented
47#63636C2211yescharacteristic
48#63635C2211yescharacteristic, complemented
49#63630C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic, complemented
53C3×#803C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63562C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C3×C4×#41—31no—
63C2×#949—31no—
64C2×#911—31no—
65C4×D3×D4—31no—
66C4×#237D311yescharacteristic, complemented
67C2×C4×D12—31no—
68C3×#442—31no—
69#5232—31no—
70Dic3×D8—31no—
71#5026—31no—
72#5026—31no—
73C4×#215—31no—
74C4×#215—31no—
75#5018—31no—
76#5014—31no—
77#5014—31no—
78#5014—61no—
79#5014D311yescharacteristic, complemented
80C4×#213—31no—
81C4×#213—31no—
82#5001—31no—
83#4995—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—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C3×#237—22no—
102C3×#237C2×C414yescomplemented
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#626—21no—
110C2×#624—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113D3×D12—22no—
114D3×D12C2×C414yescomplemented
115C4×D32—44no—
116C32×C4⋊C4C2311yescharacteristic
117C32×C22⋊C4—21no—
118C32×C42C2311yescharacteristic
119#3753C2×C414yescomplemented
120#3752—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C3×#217—21no—
125C3×#213C2×C414yescomplemented
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3D411yescharacteristic
136C3×C4×Dic3D411yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140Dic3⋊Dic3—21no—
141#3722—21no—
142(C2×D3)⋊Dic3—21no—
143#3717C2×C414yescomplemented
144#3715C2×C414yescomplemented
145#3711—22no—
146#3711C2×C414yescomplemented
147C4×AGL(1,ℤ/8)—91noSylow
148C2×C3×#41—31no—
149C2×#237C2×D311yescharacteristic
150C2×D3×D4—31no—
151C22×D12—31no—
152C22×C4×D3—61no—
153C22×C4×D3—61no—
154C2×C3×D8—31no—
155C3×C4×Q8—31no—
156C3×C4×Q8—31no—
157C3×C4×D4—21no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160C3×C4×D4—61no—
161C3×C4×D4—61no—
162C3×C4×D4C2×D311yescharacteristic, complemented
163C3×C4×D4C2×D311yescharacteristic, complemented
164C3×#117—31no—
165C3×#117—61no—
166C2×C3×C42—31no—
167C2×C3×C42—61no—
168#949—38no—
169C2×#215—31no—
170C2×#215—31no—
171D4×Dic3—31no—
172D4×Dic3C2×D311yescharacteristic, complemented
173C2×#214—31no—
174C2×#213—31no—
175C2×#213—31no—
176C2×#213—61no—
177C2×#213C2×D311yescharacteristic
178C4×#67—21no—
179C4×#67—61no—
180C2×(C2×D3)⋊C4—61no—
181C2×C4⋊Dic3—31no—
182C2×C4×Dic3—21no—
183C2×#208—31no—
184C2×#208—31no—
185#911—38no—
186C2×#204—31no—
187C2×ΓL(1,𝔽25)—31no—
188C2×ΓL(1,𝔽25)—31no—
189#893—31no—
190#892C2×D311yescharacteristic
191D3×C4⋊C4—31no—
192#887C2×D311yescharacteristic, complemented
193#67⋊C4—21no—
194#67⋊C4—61no—
195D3×C22⋊C4—61no—
196#877—21no—
197C4×D12—31no—
198C4×D12—31no—
199C4×D12—31no—
200C4×D12—31no—
201C4×D12—61no—
202C4×D12—61no—
203C4×D12—61no—
204C4×D12C2×D311yescharacteristic
205C42×D3C2×D311yescharacteristic
206C4×Dic6C2×D311yescharacteristic, complemented
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—61no—
217#832C2×D311yescharacteristic, complemented
218#821—31no—
219#818—31no—
220#816—31no—
221C8×Dic3—31no—
222C8×Dic3—31no—
223#810—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#809C2×D311yescharacteristic
230#808—31no—
231#808—31no—
232#808—61no—
233#808C2×D311yescharacteristic, complemented
234#807—31no—
235#807—31no—
236#807—31no—
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×D3C2×D411yescharacteristic
247C2×D32—24no—
248C2×D32—42no—
249C2×D32—42no—
250C32×D4—21no—
251C32×D4C22×C412yescomplemented
252C2×C32×C4—21no—
253C2×C32×C4—42no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257C2×C3⋊Dic3—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)C22×C412yes—
260C4×C3⋊D3—42no—
261C3×#67—24no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—24no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—42no—
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12C22×C412yes—
272C3×C4×D3—22no—
273C3×C4×D3—41no—
274C3×C4×D3—42no—
275C3×C4×D3C22×C412yes—
276C3×C4×D3#4112yes—
277C3×Dic6—21no—
278C3×Dic6C22×C412yescomplemented
279#626—24no—
280#624—42no—
281D3×Dic3—42no—
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—31no—
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—
302C23×D3—61no—
303C23×D3—61no—
304C3×#41—34no—
305C3×#41—62no—
306C2×C3×Q8—31no—
307C2×C3×D4—21no—
308C2×C3×D4—31no—
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—
321C2×#67—21no—
322C2×#67—61no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327#237—22no—
328#237C4×D314yescomplemented
329D3×D4—34no—
330D3×D4—62no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—34no—
334C2×D12—61no—
335C2×D12—62no—
336C2×D12—61no—
337C2×D12C22×D311yescharacteristic
338C2×C4×D3—21no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—121no—
346C2×C4×D3—124no—
347C2×C4×D3—124no—
348C2×C4×D3#6711yescharacteristic
349C2×C4×D3#6711yescharacteristic
350C2×C4×D3C22×D311yescharacteristic
351C2×Dic6C22×D311yescharacteristic
352C3×D8—34no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C42—21no—
369C3×C42—31no—
370C3×C42—31no—
371C3×C42—31no—
372C3×C42—61no—
373C3×C42—61no—
374C3×C42—61no—
375C3×C42C22×D311yescharacteristic
376C3×C42C22×D311yescharacteristic
377#217—21no—
378#217—61no—
379#215—34no—
380#215—34no—
381#214—34no—
382#213—34no—
383#213—34no—
384#213—64no—
385#213C4×D314yescomplemented
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—121no—
394C4⋊Dic3—31no—
395C4⋊Dic3—31no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3C22×D311yescharacteristic
399C4⋊Dic3C22×D311yescharacteristic
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402Dic3⋊C4—61no—
403C4×Dic3—21no—
404C4×Dic3—21no—
405C4×Dic3—21no—
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—22no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—22no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3C4×D412yes—
435D32—48no—
436C32×C4—21no—
437C32×C4—21no—
438C32×C4—41no—
439C32×C4C23×C411yescharacteristic
440C32×C4C2×#4111yescharacteristic
441C3⋊Dic3—41no—
442C3×Dic3—22no—
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C3×Dic3C4×D412yes—
447C3×Dic3AGL(1,ℤ/8)12yescomplemented
448C2×#41—31no—
449C22×D4—91no—
450C23×C4—181no—
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—31no—
459C4×Q8—31no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—61no—
463C4×D4—61no—
464C4×D4—91no—
465C4×D4—91no—
466C4×D4—91no—
467C4×D4—181no—
468C4×D4—181no—
469C4×D4D3211yescharacteristic, complemented
470#117—31no—
471#117—61no—
472C2×C4⋊C4—91no—
473C2×C22⋊C4—181no—
474C2×C42—31no—
475C2×C42—61no—
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—61no—
497C22×D3—21no—
498C22×D3—64no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—64no—
502C22×D3—121no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3C2×#6711yescharacteristic
508C3×Q8—32no—
509C3×Q8—61no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—22no—
513C3×D4—32no—
514C3×D4—41no—
515C3×D4—64no—
516C3×D4—61no—
517C3×D4C2×C4×D312yescomplemented
518C3×D4C2×C4×D312yescomplemented
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—32no—
527C2×C3×C4—32no—
528C2×C3×C4—31no—
529C2×C3×C4—41no—
530C2×C3×C4—42no—
531C2×C3×C4—42no—
532C2×C3×C4—62no—
533C2×C3×C4—64no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—82no—
538C2×C3×C4—121no—
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—
549C2×Dic3—21no—
550C2×Dic3—24no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—42no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—121no—
557C2×Dic3—122no—
558C2×Dic3—122no—
559C2×Dic3C2×#6711yescharacteristic
560C2×Dic3C2×#6711yescharacteristic
561C2×Dic3C2×#6711yescharacteristic
562D12—21no—
563D12—32no—
564D12—32no—
565D12—62no—
566D12—64no—
567D12—61no—
568D12—61no—
569D12—121no—
570D12C2×C4×D312yes—
571C4×D3—22no—
572C4×D3—41no—
573C4×D3—42no—
574C4×D3—122no—
575C4×D3—122no—
576C4×D3—122no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3—242no—
581C4×D3C2×C4×D312yes—
582C4×D3#23512yes—
583Dic6—21no—
584Dic6C2×C4×D312yescomplemented
585C3×C8—32no—
586C3×C8—61no—
587C3⋊C8—21no—
588C3⋊C8—32no—
589C3⋊C8—32no—
590C3⋊C8—62no—
591C3⋊C8—61no—
592C3⋊C8—61no—
593C3⋊C8—121no—
594C3⋊C8C2×C4×D312yescomplemented
595C2×C32—42no—
596C2×C32C2×C4×D411yescharacteristic
597C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
598C2×C32#57511yescharacteristic
599C3⋊D3—42no—
600C3×D3—22no—
601C3×D3—42no—
602C24—181no—
603#41—34no—
604#41—62no—
605C2×Q8—31no—
606C2×D4—31no—
607C2×D4—61no—
608C2×D4—94no—
609C2×D4—91no—
610C2×D4—182no—
611C2×D4—181no—
612C2×D4C2×D3211yescharacteristic
613C22×C4—21no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—181no—
624C22×C4—364no—
625SD16—94no—
626SD16—94no—
627D8—34no—
628D8—94no—
629M16—94no—
630M16—182no—
631C2×C8—31no—
632C2×C8—31no—
633C2×C8—91no—
634C2×C8—91no—
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—91no—
640C4⋊C4—181no—
641C4⋊C4C2×D3211yescharacteristic
642C22⋊C4—21no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C42—31no—
650C42—31no—
651C42—31no—
652C42—61no—
653C42—61no—
654C42—61no—
655C42C2×D3211yescharacteristic
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—21no—
659C22×C3—32no—
660C22×C3—42no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—62no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3C2×D3×D411yescharacteristic
673C22×C3C22×#6711yescharacteristic
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—22no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—62no—
680C2×D3—62no—
681C2×D3—122no—
682C2×D3—128no—
683C2×D3—128no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—241no—
689C2×D3—241no—
690C2×D3C4×#6712yes—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—32no—
698C3×C4—32no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—61no—
704C3×C4—62no—
705C3×C4—81no—
706C3×C4—121no—
707C3×C4—121no—
708C3×C4C22×C4×D311yescharacteristic
709C3×C4C22×C4×D311yescharacteristic
710C3×C4C2×#23511yescharacteristic
711C3×C4D3×#4111yescharacteristic
712Dic3—22no—
713Dic3—21no—
714Dic3—41no—
715Dic3—41no—
716Dic3—121no—
717Dic3—121no—
718Dic3—241no—
719Dic3C4×#6712yes—
720Dic3#94912yescomplemented
721C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
722C23—21no—
723C23—31no—
724C23—61no—
725C23—184no—
726C23—181no—
727C23—362no—
728C23—362no—
729Q8—32no—
730Q8—61no—
731D4—21no—
732D4—32no—
733D4—64no—
734D4—61no—
735D4—92no—
736D4—184no—
737D4—181no—
738D4C4×D3212yescomplemented
739C2×C4—21no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—32no—
743C2×C4—32no—
744C2×C4—31no—
745C2×C4—42no—
746C2×C4—62no—
747C2×C4—64no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—121no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—181no—
755C2×C4—362no—
756C2×C4—362no—
757C2×C4—362no—
758C2×C4—362no—
759C2×C4D3×#6711yescharacteristic
760C2×C4D3×#6711yescharacteristic
761C2×C4C22×D3211yescharacteristic
762C8—32no—
763C8—61no—
764C8—92no—
765C8—181no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—42no—
770C2×C3—42no—
771C2×C3—62no—
772C2×C3—82no—
773C2×C3—122no—
774C2×C3C4×D3×D411yescharacteristic
775C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
776C2×C3#577311yescharacteristic
777C2×C3C2×C4×#6711yescharacteristic
778C2×C3C2×#94911yescharacteristic
779C2×C3#582211yescharacteristic
780D3—22no—
781D3—42no—
782D3—122no—
783D3—122no—
784D3—242no—
785C22—22no—
786C22—32no—
787C22—41no—
788C22—41no—
789C22—61no—
790C22—61no—
791C22—62no—
792C22—121no—
793C22—121no—
794C22—182no—
795C22—368no—
796C22—361no—
797C22—361no—
798C22C2×D3×#6711yescharacteristic
799C4—21no—
800C4—21no—
801C4—32no—
802C4—32no—
803C4—41no—
804C4—61no—
805C4—62no—
806C4—121no—
807C4—121no—
808C4—361no—
809C4C2×C4×D3211yescharacteristic
810C4D3×#23511yescharacteristic
811C3—21no—
812C3#7986511yescharacteristic, complemented
813C3C4×#94911yescharacteristic, complemented
814C2—42no—
815C2—62no—
816C2—122no—
817C2—362no—
818C2C4×D3×#6711yescharacteristic
819C2#1059509511yescharacteristic
820C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#63925C2
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×#237C2semidirect
3. C4×D3×D12C2semidirect
4. #10592713C2semidirect
5. C3×#5014C2semidirect
6. Dic3×#213C2semidirect
7. #10591414C2semidirect
8. #10591400C2semidirect
9. #10590592C2semidirect
10. #10590458C2semidirect
11. #10590453C2semidirect
12. #10590437C2semidirect
13. #10590362C2semidirect
14. #10590358C2semidirect
15. #10590334C2semidirect
21. C32×C4×D4C22semidirect
24. C3×D4×Dic3C22semidirect
29. C3×#887C22semidirect
34. C3×C4×Dic6C22semidirect
35. #63925C4semidirect
46. #63659C22semidirect
48. #63635C22semidirect
49. #63630C22semidirect
50. C3×#832C22semidirect
52. C3×#808C22semidirect
53. C3×#803C22semidirect
54. #63576C22semidirect
55. #63575C22semidirect
56. #63566C22semidirect
57. #63565C22semidirect
60. Dic3×C3⋊C8C22semidirect
61. Dic3×C3⋊C8C22semidirect
66. C4×#237D3semidirect
79. #5014D3semidirect
102. C3×#237C2×C4semidirect
114. D3×D12C2×C4semidirect
119. #3753C2×C4semidirect
125. C3×#213C2×C4semidirect
143. #3717C2×C4semidirect
144. #3715C2×C4semidirect
146. #3711C2×C4semidirect
162. C3×C4×D4C2×D3semidirect
163. C3×C4×D4C2×D3semidirect
172. D4×Dic3C2×D3semidirect
192. #887C2×D3semidirect
206. C4×Dic6C2×D3semidirect
217. #832C2×D3semidirect
233. #808C2×D3semidirect
240. #803C2×D3semidirect
251. C32×D4C22×C4semidirect
278. C3×Dic6C22×C4semidirect
284. C3⋊(C3⋊C8)C22×C4semidirect
286. C3×C3⋊C8C22×C4semidirect
328. #237C4×D3semidirect
385. #213C4×D3semidirect
447. C3×Dic3AGL(1,ℤ/8)semidirect
469. C4×D4D32semidirect
517. C3×D4C2×C4×D3semidirect
518. C3×D4C2×C4×D3semidirect
584. Dic6C2×C4×D3semidirect
594. C3⋊C8C2×C4×D3semidirect
720. Dic3#949semidirect
721. C32C4×AGL(1,ℤ/8)semidirect
738. D4C4×D32semidirect
812. C3#79865semidirect
813. C3C4×#949semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2372
C2×#639252
C4×D3×D122
#105927132
C3×#50142
Dic3×#2132
#105914142
#105914002
#105905922
#105904582
#105904532
#105904372
#105903622
#105903582
#105903342
C4×#9493
#798653