Finite Group Databasebeta

← #11860331

Subgroups — #11860331

Order 1152.

1157 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
1C2×#63795C211yesmaximal, characteristic
2D3×#893C211yesmaximal, characteristic, complemented
3#10594358C211yesmaximal, characteristic, complemented
4#10592551C211yesmaximal, characteristic, complemented
5C3×#4869C211yesmaximal, characteristic, complemented
6C3×#4861C211yesmaximal, characteristic, complemented
7#10590777C211yesmaximal, characteristic, complemented
8#10590773C211yesmaximal, characteristic, complemented
9#10590667C211yesmaximal, characteristic, complemented
10#10590607C211yesmaximal, characteristic, complemented
11#10590592C211yesmaximal, characteristic, complemented
12#10590590C211yesmaximal, characteristic, complemented
13#10590589C211yesmaximal, characteristic, complemented
14#10590460C211yesmaximal, characteristic, complemented
15#10590459C211yesmaximal, characteristic, complemented
16#79865—31nomaximal
17#79199—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×C4×D32—21no—
20C2×#3795C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22#64102C2211yescharacteristic
23#64096C2211yescharacteristic, complemented
24C2×C3×D24C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#893C2211yescharacteristic, complemented
28C3×#892C2211yescharacteristic
29C3×D3×C4⋊C4C2211yescharacteristic
30D3×(C2×D3)⋊C4—21no—
31#63904—21no—
32#63902—21no—
33#63898C2211yescharacteristic
34#63898C2211yescharacteristic, complemented
35#63894C2211yescharacteristic
36#63881—21no—
37#63879—21no—
38#63877—21no—
39C4×D3×Dic3—21no—
40C4×D3×Dic3C2211yescharacteristic
41#63844C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45#63795C418yescomplemented
46C32×#106C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48#63637C2211yescharacteristic, complemented
49#63636C2211yescharacteristic
50C3×#818C2211yescharacteristic, complemented
51C3×#815C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#809C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61#63553C2211yescharacteristic, complemented
62C2×#911—31no—
63C2×#908—31no—
64C4×D3×D4—31no—
65C4×#237—31no—
66#5522—31no—
67C2×#893—31no—
68C3×#442—31no—
69C3×#428—31no—
70Dic3×D8—31no—
71Dic3×M16—31no—
72#5018—31no—
73#5014—31no—
74#5001—31no—
75#4966—31no—
76#4889—31no—
77#4889—31no—
78#4872—31no—
79#4872—31no—
80#4869—31no—
81#4869D311yescharacteristic, complemented
82#4861D311yescharacteristic, complemented
83#4852—31no—
84#4852—31no—
85#4852—31no—
86#4852—61no—
87#4771—31no—
88#4770—31no—
89#4758—31no—
90#4756—31no—
91#4710—31no—
92#4707—31no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×#626—21no—
104C2×#625—21no—
105C2×#624—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3D411yescharacteristic
110C2×D3×Dic3D411yescharacteristic
111D3×D12—22no—
112D3×D12C2×C414yescomplemented
113C4×D32—44no—
114#3795—22no—
115#3795C2×C414yescomplemented
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3752—21no—
120#3750—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3744C2×C414yescomplemented
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×D24C2×C414yescomplemented
136C3×ΓL(1,𝔽25)C2×C414yescomplemented
137#3724—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142Dic32D411yescharacteristic
143Dic32D411yescharacteristic
144#3716C2×C414yescomplemented
145#3714C2×C414yescomplemented
146#3711—22no—
147C4×AGL(1,ℤ/8)—91noSylow
148C2×#237—31no—
149C2×D3×D4—31no—
150C2×#235—31no—
151C22×D12—31no—
152C22×C4×D3—61no—
153C22×C4×D3—61no—
154C2×C3×D8—31no—
155C2×C3×M16—31no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×#117—31no—
159C2×C3×C4⋊C4—31no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162C2×#214—31no—
163C2×#213—31no—
164C4×#67—61no—
165C4×#67—61no—
166C2×(C2×D3)⋊C4—61no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—61no—
169C2×#208—31no—
170#911—38no—
171#908—38no—
172C2×D24—31no—
173C2×D24C2×D311yescharacteristic
174C2×#204—31no—
175C2×#204—31no—
176C2×#204—31no—
177C2×#204—61no—
178C2×ΓL(1,𝔽25)—31no—
179C2×ΓL(1,𝔽25)C2×D311yescharacteristic
180#893—31no—
181#893—31no—
182#893—31no—
183#893—31no—
184#893—31no—
185#893—61no—
186#893—61no—
187#893—61no—
188#893C2×D311yescharacteristic
189#893C2×D311yescharacteristic, complemented
190#892C2×D311yescharacteristic
191D3×C4⋊C4C2×D311yescharacteristic
192#887—31no—
193#887—31no—
194#887—31no—
195#887—61no—
196#67⋊C4—61no—
197#67⋊C4—61no—
198#67⋊C4—61no—
199#67⋊C4—61no—
200D3×C22⋊C4—61no—
201#877—61no—
202C4×D12—31no—
203#872—61no—
204C42×D3—31no—
205C42×D3—61no—
206C4×Dic6—31no—
207C3×#107—31no—
208C3×#107—31no—
209C3×#106—21no—
210C3×#106—31no—
211C3×#106C2×D311yescharacteristic, complemented
212C3×#106C2×D311yescharacteristic, complemented
213C3×#102—31no—
214C3×#102—31no—
215C3×#97—31no—
216#832—31no—
217#832—31no—
218#821—31no—
219#818C2×D311yescharacteristic, complemented
220#816—31no—
221#815—31no—
222#815C2×D311yescharacteristic, complemented
223C8×Dic3—31no—
224C8×Dic3—31no—
225C8×Dic3—31no—
226C8×Dic3—31no—
227C8×Dic3—61no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—61no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#809—61no—
238#809C2×D311yescharacteristic
239#809C2×D311yescharacteristic, complemented
240#808C2×D311yescharacteristic, complemented
241#807C2×D311yescharacteristic, complemented
242#803—31no—
243C22×C3⋊D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—24no—
248C2×D32—42no—
249C2×D32—42no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D411yescharacteristic
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)C22×C412yes—
258C4×C3⋊D3—42no—
259#634—21no—
260#634C22×C412yescomplemented
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×D12C22×C412yes—
269C3×D12C22×C412yescomplemented
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272C3×C4×D3—42no—
273C3×C4×D3C22×C412yes—
274C3×C4×D3#4112yes—
275#626—24no—
276#625—24no—
277#624—42no—
278D3×Dic3—22no—
279D3×Dic3—24no—
280D3×Dic3—41no—
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)—91no—
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—31no—
299#418—91no—
300#417—91no—
301C4×M16—91no—
302C23×D3—61no—
303C23×D3—61no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318#237—34no—
319#237—62no—
320D3×D4—34no—
321D3×D4—62no—
322#235—34no—
323#235—62no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—34no—
327C2×D12—61no—
328C2×D12—62no—
329C2×D12—61no—
330C2×D12C22×D311yescharacteristic
331C2×D12C22×D311yescharacteristic
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×C4×D3—31no—
336C2×C4×D3—31no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—121no—
345C2×C4×D3—124no—
346C2×C4×D3—124no—
347C2×C4×D3C22×D311yescharacteristic
348C2×Dic6—31no—
349C2×Dic6—31no—
350C2×Dic6—61no—
351C3×D8—34no—
352C3×M16—34no—
353C2×C3×C8—21no—
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C42—31no—
371C3×C42—61no—
372#217—61no—
373#217—61no—
374#214—34no—
375#213—34no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—121no—
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—121no—
394C4×Dic3—21no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—121no—
407C4×Dic3C22×D311yescharacteristic
408#208—62no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414D24—34no—
415D24C4×D314yescomplemented
416#204—34no—
417#204—34no—
418#204—34no—
419#204—64no—
420ΓL(1,𝔽25)—62no—
421ΓL(1,𝔽25)C4×D314yescomplemented
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—22no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3C4×D412yes—
435D32—48no—
436C32×C4—41no—
437C32×C4—41no—
438C32×C4C23×C411yescharacteristic
439C32×C4C2×#4111yescharacteristic
440C3⋊Dic3—22no—
441C3⋊Dic3—21no—
442C3⋊Dic3AGL(1,ℤ/8)12yescomplemented
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3C4×D412yes—
448C2×#41—91no—
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—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—31no—
471#117—181no—
472C2×C4⋊C4—31no—
473C2×C22⋊C4—181no—
474C2×C42—91no—
475C2×C42—181no—
476#107—31no—
477#107—31no—
478#106—31no—
479#106D3211yescharacteristic, complemented
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—31no—
493C23×C3—61no—
494C23×C3—61no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—64no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—64no—
501C22×D3—121no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3D3×D411yescharacteristic
507C3×D4—32no—
508C3×D4—32no—
509C3×D4—61no—
510C3×D4—61no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—32no—
518C2×C3×C4—32no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—122no—
526C2×C3×C4—122no—
527C2×C3×C4—122no—
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530#67—64no—
531#67—64no—
532#67—64no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—62no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—64no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—122no—
548C2×Dic3—122no—
549C2×Dic3D3×D411yescharacteristic
550C2×Dic3D3×D411yescharacteristic
551C2×Dic3D3×D411yescharacteristic
552D12—21no—
553D12—21no—
554D12—32no—
555D12—32no—
556D12—62no—
557D12—64no—
558D12—61no—
559D12—61no—
560D12—121no—
561D12C2×C4×D312yes—
562D12C2×C4×D312yescomplemented
563C4×D3—42no—
564C4×D3—42no—
565C4×D3—42no—
566C4×D3—62no—
567C4×D3—64no—
568C4×D3—122no—
569C4×D3—122no—
570C4×D3—122no—
571C4×D3—122no—
572C4×D3—122no—
573C4×D3—122no—
574C4×D3—121no—
575C4×D3—242no—
576C4×D3C2×C4×D312yes—
577C4×D3#23912yes—
578Dic6—32no—
579Dic6—32no—
580Dic6—62no—
581Dic6—61no—
582Dic6—61no—
583Dic6—121no—
584C3×C8—22no—
585C3×C8—32no—
586C3×C8—61no—
587C3×C8C2×C4×D312yescomplemented
588C3×C8C2×C4×D312yescomplemented
589C3⋊C8—21no—
590C3⋊C8—61no—
591C3⋊C8—61no—
592C3⋊C8—121no—
593C3⋊C8C2×C4×D312yescomplemented
594C2×C32C2×C4×D411yescharacteristic
595C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
596C2×C32#57511yescharacteristic
597C3⋊D3—42no—
598C3×D3—22no—
599C3×D3—42no—
600C3×D3—42no—
601C24—181no—
602#41—94no—
603#41—182no—
604C2×Q8—91no—
605C2×D4—31no—
606C2×D4—31no—
607C2×D4—94no—
608C2×D4—91no—
609C2×D4—182no—
610C2×D4—181no—
611C2×D4—181no—
612C22×C4—31no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4—181no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—364no—
624SD16—94no—
625SD16—94no—
626D8—34no—
627D8—94no—
628M16—34no—
629M16—182no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8C2×D3211yescharacteristic
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—181no—
638C4⋊C4—181no—
639C4⋊C4C2×D3211yescharacteristic
640C4⋊C4C2×D3211yescharacteristic
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—31no—
649C42—61no—
650C42—91no—
651C42—91no—
652C42—91no—
653C42—181no—
654C42—181no—
655C22×C3—21no—
656C22×C3—32no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—62no—
660C22×C3—62no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3C2×D3×D411yescharacteristic
666C22×C3C2×D3×D411yescharacteristic
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—22no—
670C2×D3—22no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—62no—
676C2×D3—62no—
677C2×D3—122no—
678C2×D3—128no—
679C2×D3—128no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—241no—
685C2×D3—241no—
686C2×D3#89312yes—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—32no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—61no—
695C3×C4—61no—
696C3×C4—81no—
697C3×C4—81no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4C22×C4×D311yescharacteristic
701C3×C4C22×C4×D311yescharacteristic
702C3×C4C2×#23911yescharacteristic
703C3×C4D3×#4111yescharacteristic
704Dic3—21no—
705Dic3—21no—
706Dic3—32no—
707Dic3—32no—
708Dic3—41no—
709Dic3—41no—
710Dic3—62no—
711Dic3—62no—
712Dic3—61no—
713Dic3—61no—
714Dic3—62no—
715Dic3—122no—
716Dic3—121no—
717Dic3#89312yes—
718C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
719C23—31no—
720C23—61no—
721C23—61no—
722C23—184no—
723C23—181no—
724C23—362no—
725C23—362no—
726Q8—92no—
727Q8—181no—
728D4—32no—
729D4—32no—
730D4—61no—
731D4—61no—
732D4—92no—
733D4—184no—
734D4—184no—
735D4—181no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—31no—
739C2×C4—32no—
740C2×C4—32no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—91no—
746C2×C4—91no—
747C2×C4—122no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—184no—
751C2×C4—182no—
752C2×C4—181no—
753C2×C4—362no—
754C2×C4—362no—
755C2×C4—361no—
756C2×C4—362no—
757C2×C4—362no—
758C2×C4C22×D3211yescharacteristic
759C8—32no—
760C8—61no—
761C8—181no—
762C8C4×D3212yescomplemented
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—62no—
767C2×C3—122no—
768C2×C3—122no—
769C2×C3C2×#89311yescharacteristic
770C2×C3C4×D3×D411yescharacteristic
771C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
772C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
773C2×C3#577311yescharacteristic
774C2×C3#577711yescharacteristic
775D3—22no—
776D3—42no—
777D3—42no—
778D3—122no—
779D3—122no—
780D3—242no—
781C22—32no—
782C22—61no—
783C22—61no—
784C22—62no—
785C22—62no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—182no—
791C22—368no—
792C22—361no—
793C22—361no—
794C22D32×D411yescharacteristic
795C4—32no—
796C4—41no—
797C4—41no—
798C4—61no—
799C4—61no—
800C4—92no—
801C4—121no—
802C4—121no—
803C4—182no—
804C4—181no—
805C4C2×C4×D3211yescharacteristic
806C4D3×#23911yescharacteristic
807C3—21no—
808C3#7919911yescharacteristic, complemented
809C3#7986511yescharacteristic, complemented
810C2—62no—
811C2—122no—
812C2—122no—
813C2—362no—
814C2D3×#89311yescharacteristic
815C2#1059474011yescharacteristic
816C2#1059474411yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#63795C2
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. D3×#893C2semidirect
3. #10594358C2semidirect
4. #10592551C2semidirect
5. C3×#4869C2semidirect
6. C3×#4861C2semidirect
7. #10590777C2semidirect
8. #10590773C2semidirect
9. #10590667C2semidirect
10. #10590607C2semidirect
11. #10590592C2semidirect
12. #10590590C2semidirect
13. #10590589C2semidirect
14. #10590460C2semidirect
15. #10590459C2semidirect
23. #64096C22semidirect
27. C3×#893C22semidirect
34. #63898C22semidirect
41. #63844C22semidirect
45. #63795C4semidirect
46. C32×#106C22semidirect
47. C8×C3⋊Dic3C22semidirect
48. #63637C22semidirect
50. C3×#818C22semidirect
51. C3×#815C22semidirect
53. C3×#809C22semidirect
54. C3×#808C22semidirect
55. C3×#807C22semidirect
56. #63567C22semidirect
59. #63562C22semidirect
60. #63554C22semidirect
61. #63553C22semidirect
81. #4869D3semidirect
82. #4861D3semidirect
112. D3×D12C2×C4semidirect
115. #3795C2×C4semidirect
124. #3744C2×C4semidirect
135. C3×D24C2×C4semidirect
136. C3×ΓL(1,𝔽25)C2×C4semidirect
144. #3716C2×C4semidirect
145. #3714C2×C4semidirect
189. #893C2×D3semidirect
211. C3×#106C2×D3semidirect
212. C3×#106C2×D3semidirect
219. #818C2×D3semidirect
222. #815C2×D3semidirect
239. #809C2×D3semidirect
240. #808C2×D3semidirect
241. #807C2×D3semidirect
260. #634C22×C4semidirect
269. C3×D12C22×C4semidirect
283. C32×C8C22×C4semidirect
286. C3×C3⋊C8C22×C4semidirect
415. D24C4×D3semidirect
421. ΓL(1,𝔽25)C4×D3semidirect
442. C3⋊Dic3AGL(1,ℤ/8)semidirect
479. #106D32semidirect
562. D12C2×C4×D3semidirect
587. C3×C8C2×C4×D3semidirect
588. C3×C8C2×C4×D3semidirect
593. C3⋊C8C2×C4×D3semidirect
718. C32C4×AGL(1,ℤ/8)semidirect
762. C8C4×D32semidirect
808. C3#79199semidirect
809. C3#79865semidirect

Maximal subgroups

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

subgroupindex
C2×#637952
D3×#8932
#105943582
#105925512
C3×#48692
C3×#48612
#105907772
#105907732
#105906672
#105906072
#105905922
#105905902
#105905892
#105904602
#105904592
#798653
#791993