Finite Group Databasebeta

← #11860335

Subgroups — #11860335

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 827 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595386C211yesmaximal, characteristic, complemented
2C2×#63941C211yesmaximal, characteristic
3#10594605C211yesmaximal, characteristic, complemented
4#10592502C211yesmaximal, characteristic, complemented
5C3×#4817C211yesmaximal, characteristic, complemented
6C3×#4788C211yesmaximal, characteristic, complemented
7#10591566C211yesmaximal, characteristic, complemented
8Dic3×#215C211yesmaximal, characteristic, complemented
9#10590941C211yesmaximal, characteristic, complemented
10#10590746C211yesmaximal, characteristic, complemented
11#10590745C211yesmaximal, characteristic, complemented
12#10590664C211yesmaximal, characteristic, complemented
13#10590589C211yesmaximal, characteristic, complemented
14#10590583C211yesmaximal, characteristic, complemented
15#10590456C211yesmaximal, characteristic, complemented
16#79773—31nomaximal
17C4×#914—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×#3802C2211yescharacteristic
20C2×C4×D32—21no—
21C2×#3743C2211yescharacteristic
22C4⋊C4×C3⋊D3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic, complemented
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C2×C3×#215C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×#893C2211yescharacteristic
28C3×#893C2211yescharacteristic
29#63941C418yescomplemented
30#63921—21no—
31#63894—21no—
32#63894—21no—
33#63894C2211yescharacteristic, complemented
34#63894C2211yescharacteristic, complemented
35Dic3×D12C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37C4×#624—21no—
38C4×#624C2211yescharacteristic
39#63879—21no—
40#63879—21no—
41#63849—21no—
42#63849C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45C2×#3712C2211yescharacteristic
46C32×#103C2211yescharacteristic, complemented
47#63662C2211yescharacteristic, complemented
48#63648C2211yescharacteristic, complemented
49#63636C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#815C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63573C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C2×#914—31no—
63C2×#914—31no—
64C4×#239—31no—
65C4×#239—31no—
66C4×D3×D4—31no—
67C4×D3×D4—31no—
68C3×#440—31no—
69C3×C4×SD16—31no—
70#5164—31no—
71Dic3×SD16—31no—
72#5026—31no—
73C4×#215—31no—
74#5014—31no—
75C4×#213—31no—
76#4881—31no—
77#4872—31no—
78#4869—31no—
79#4861—31no—
80#4817D311yescharacteristic, complemented
81#4803—31no—
82#4803—31no—
83#4803—61no—
84#4788D311yescharacteristic, complemented
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—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95#3832—22no—
96#3832C2×C414yescomplemented
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×#625—21no—
107C2×#624—21no—
108C2×#624—21no—
109C2×#624D411yescharacteristic
110C2×#624D411yescharacteristic
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113#3802—22no—
114#3802C2×C414yescomplemented
115C4×D32—44no—
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3743—22no—
122C3×#215C2×C414yescomplemented
123C3×#215C2×C414yescomplemented
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3722—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142Dic32D411yescharacteristic
143Dic32D411yescharacteristic
144#3714C2×C414yescomplemented
145#3714C2×C414yescomplemented
146#3712C2×C414yescomplemented
147C4×AGL(1,ℤ/8)—91noSylow
148C2×#239—31no—
149C2×#239—31no—
150C2×#239—61no—
151C2×D3×D4—31no—
152C2×D3×D4—31no—
153C22×C4×D3—61no—
154C22×C4×D3—61no—
155C2×C3×SD16—31no—
156C2×C3×SD16—31no—
157C3×C4×Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161Q8×Dic3C2×D311yescharacteristic, complemented
162Q8×Dic3C2×D311yescharacteristic, complemented
163C2×#215C2×D311yescharacteristic
164C2×#215C2×D311yescharacteristic
165D4×Dic3—31no—
166D4×Dic3—31no—
167C2×#213—31no—
168C2×#213—31no—
169C4×#67—61no—
170C4×#67—61no—
171#914—38no—
172#914—38no—
173C2×D24—31no—
174C2×D24—31no—
175C2×ΓL(1,𝔽25)—31no—
176C2×ΓL(1,𝔽25)—31no—
177C2×ΓL(1,𝔽25)—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×ΓL(1,𝔽25)—61no—
180#893—31no—
181#893—31no—
182#893—61no—
183#893—61no—
184#893C2×D311yescharacteristic
185#893C2×D311yescharacteristic
186#892—31no—
187#892—31no—
188#892—61no—
189#892—61no—
190D3×C4⋊C4—31no—
191D3×C4⋊C4—31no—
192D3×C4⋊C4—61no—
193#67⋊C4—61no—
194#67⋊C4—61no—
195D3×C22⋊C4—61no—
196D3×C22⋊C4—61no—
197C4×D12—31no—
198C4×D12—31no—
199C4×D12—31no—
200C4×D12—31no—
201C4×D12—61no—
202C4×D12—61no—
203C42×D3—31no—
204C42×D3—31no—
205C42×D3—61no—
206C42×D3—61no—
207C3×#107—31no—
208C3×#106—31no—
209C3×#103—21no—
210C3×#103C2×D311yescharacteristic, complemented
211C3×#103C2×D311yescharacteristic, complemented
212C3×#102—31no—
213C3×#102—31no—
214C3×#97—31no—
215C3×C4×C8—31no—
216#835—31no—
217#835—31no—
218#835—61no—
219#832—31no—
220#832—31no—
221#821—31no—
222#821—31no—
223#821—61no—
224#821C2×D311yescharacteristic
225#821C2×D311yescharacteristic
226#818—31no—
227#817—31no—
228#815—31no—
229#815C2×D311yescharacteristic, complemented
230C8×Dic3—31no—
231C8×Dic3C2×D311yescharacteristic, complemented
232#809—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#809—61no—
237#808—31no—
238#808C2×D311yescharacteristic, complemented
239#807—31no—
240#807C2×D311yescharacteristic, complemented
241#803—31no—
242C4×C3⋊C8—31no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C2×D32—24no—
248C2×D32—42no—
249C2×D32—42no—
250C32×Q8—21no—
251C32×Q8C22×C412yescomplemented
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4⋊(C3⋊D3)—24no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)C22×C412yescomplemented
260C4×C3⋊D3—24no—
261C4×C3⋊D3—42no—
262C4×C3⋊D3C22×C412yes—
263C4×C3⋊D3#4112yes—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12—21no—
272C3×D12C22×C412yes—
273C3×D12C22×C412yes—
274C3×C4×D3—42no—
275C3×C4×D3—42no—
276#625—24no—
277#624—22no—
278#624—41no—
279#624—42no—
280#624—42no—
281D3×Dic3—42no—
282D3×Dic3—42no—
283C32×C8—21no—
284C3⋊(C3⋊C8)—21no—
285C3×C3⋊C8C22×C412yescomplemented
286C3×C3⋊C8C22×C412yescomplemented
287C2×AGL(1,ℤ/8)—91no—
288C4×#41—91no—
289C2×C4×D4—91no—
290#442—91no—
291#442—91no—
292#440—31no—
293#440—91no—
294C4×SD16—31no—
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—
304C2×C3×Q8—21no—
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315#239—34no—
316#239—34no—
317#239—64no—
318#239—62no—
319#239—62no—
320#239—122no—
321D3×D4—34no—
322D3×D4—34no—
323D3×D4—62no—
324D3×D4—62no—
325C2×D12—31no—
326C2×D12—31no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12—121no—
331C2×D12C22×D311yescharacteristic
332C2×D12C22×D311yescharacteristic
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×C4×D3—31no—
336C2×C4×D3—31no—
337C2×C4×D3—31no—
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
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—121no—
353C2×C4×D3—121no—
354C2×C4×D3—124no—
355C2×C4×D3—124no—
356C3×SD16—34no—
357C3×SD16—34no—
358C2×C3×C8—21no—
359C2×C3×C8—31no—
360C2×C3×C8—31no—
361C2×C3×C8C22×D311yescharacteristic
362C2×C3×C8C22×D311yescharacteristic
363C3×C4⋊C4—21no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4C22×D311yescharacteristic
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C42—31no—
373C3×C42—31no—
374C3×C42—61no—
375C3×C42—61no—
376#217—61no—
377#217—61no—
378#215C4×D314yescomplemented
379#215C4×D314yescomplemented
380#213—34no—
381#213—34no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392C4⋊Dic3—21no—
393C4⋊Dic3—21no—
394C4⋊Dic3—31no—
395C4⋊Dic3—31no—
396C4⋊Dic3—61no—
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—121no—
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3—31no—
405C4×Dic3—31no—
406C4×Dic3—31no—
407C4×Dic3—31no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3C22×D311yescharacteristic
411C4×Dic3C22×D311yescharacteristic
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—61no—
415C2×C3⋊C8C22×D311yescharacteristic
416C2×C3⋊C8C22×D311yescharacteristic
417D24—34no—
418D24—34no—
419ΓL(1,𝔽25)—34no—
420ΓL(1,𝔽25)—34no—
421ΓL(1,𝔽25)—62no—
422ΓL(1,𝔽25)—62no—
423ΓL(1,𝔽25)—122no—
424C22×C32C22×D411yescharacteristic
425C2×C3⋊D3—21no—
426C2×C3⋊D3—21no—
427C2×C3⋊D3—22no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3C4×D412yes—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437D32—48no—
438C32×C4—22no—
439C32×C4—41no—
440C32×C4C23×C411yescharacteristic
441C32×C4C2×#4111yescharacteristic
442C3⋊Dic3—41no—
443C3⋊Dic3C4×D412yes—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3AGL(1,ℤ/8)12yescomplemented
450C2×#41—91no—
451C22×D4—91no—
452C23×C4—181no—
453AGL(1,ℤ/8)—98no—
454C2×SD16—31no—
455C2×SD16—31no—
456C2×D8—91no—
457C2×D8—91no—
458C2×M16—91no—
459C2×M16—91no—
460C4×Q8—31no—
461C4×Q8—31no—
462C4×D4—31no—
463C4×D4—31no—
464C4×D4—91no—
465C4×D4—91no—
466C4×D4—91no—
467C4×D4—91no—
468C4×D4—181no—
469C4×D4—181no—
470C4×D4—181no—
471C4×D4—181no—
472#117—91no—
473#117—181no—
474C2×C4⋊C4—91no—
475C2×C22⋊C4—181no—
476C2×C42—91no—
477C2×C42—181no—
478#107—31no—
479#107—91no—
480#106—31no—
481#106—91no—
482#103—91no—
483#103D3211yescharacteristic, complemented
484#102—31no—
485#102—31no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490#97—31no—
491#97—91no—
492C4×C8—31no—
493C4×C8—91no—
494C23×C3—61no—
495C23×C3—61no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—31no—
499C22×D3—31no—
500C22×D3—61no—
501C22×D3—64no—
502C22×D3—64no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—121no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C3×Q8—21no—
511C3×Q8—21no—
512C3×Q8—22no—
513C3×Q8—41no—
514C3×Q8C2×C4×D312yescomplemented
515C3×Q8C2×C4×D312yescomplemented
516C3×D4—32no—
517C3×D4—32no—
518C3×D4—61no—
519C3×D4—61no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—122no—
534C2×C3×C4—122no—
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—64no—
538#67—64no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—121no—
547C2×Dic3—122no—
548C2×Dic3—122no—
549C2×Dic3D3×D411yescharacteristic
550C2×Dic3D3×D411yescharacteristic
551C2×Dic3D3×D411yescharacteristic
552C2×Dic3D3×D411yescharacteristic
553D12—21no—
554D12—21no—
555D12—32no—
556D12—32no—
557D12—62no—
558D12—64no—
559D12—64no—
560D12—61no—
561D12—61no—
562D12—121no—
563D12—124no—
564D12C2×C4×D312yes—
565D12C2×C4×D312yes—
566C4×D3—32no—
567C4×D3—32no—
568C4×D3—32no—
569C4×D3—32no—
570C4×D3—42no—
571C4×D3—42no—
572C4×D3—62no—
573C4×D3—62no—
574C4×D3—62no—
575C4×D3—64no—
576C4×D3—64no—
577C4×D3—62no—
578C4×D3—124no—
579C4×D3—121no—
580C4×D3—121no—
581C4×D3—122no—
582C4×D3—122no—
583C4×D3—122no—
584C4×D3—122no—
585C4×D3—122no—
586C4×D3—122no—
587C4×D3—122no—
588C4×D3—122no—
589C4×D3—242no—
590C3×C8—21no—
591C3×C8—21no—
592C3×C8—32no—
593C3×C8—32no—
594C3×C8—41no—
595C3⋊C8—61no—
596C3⋊C8—61no—
597C3⋊C8—121no—
598C3⋊C8C2×C4×D312yescomplemented
599C3⋊C8C2×C4×D312yescomplemented
600C2×C32C2×C4×D411yescharacteristic
601C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
602C2×C32#57511yescharacteristic
603C3⋊D3—22no—
604C3⋊D3—42no—
605C3×D3—42no—
606C3×D3—42no—
607C24—181no—
608#41—94no—
609#41—182no—
610C2×Q8C2×D3211yescharacteristic
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—94no—
614C2×D4—91no—
615C2×D4—181no—
616C2×D4—182no—
617C2×D4—181no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—91no—
621C22×C4—91no—
622C22×C4—91no—
623C22×C4—181no—
624C22×C4—181no—
625C22×C4—181no—
626C22×C4—181no—
627C22×C4—181no—
628C22×C4—181no—
629C22×C4—364no—
630SD16—34no—
631SD16—34no—
632D8—94no—
633D8—94no—
634M16—94no—
635M16—182no—
636C2×C8—31no—
637C2×C8—31no—
638C2×C8—91no—
639C2×C8C2×D3211yescharacteristic
640C4⋊C4—31no—
641C4⋊C4—31no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—91no—
645C4⋊C4—181no—
646C4⋊C4C2×D3211yescharacteristic
647C22⋊C4—61no—
648C22⋊C4—61no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C42—31no—
655C42—31no—
656C42—61no—
657C42—61no—
658C42—91no—
659C42—91no—
660C42—181no—
661C22×C3—21no—
662C22×C3—62no—
663C22×C3—62no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3C2×D3×D411yescharacteristic
669C22×C3C2×D3×D411yescharacteristic
670C2×D3—22no—
671C2×D3—22no—
672C2×D3—32no—
673C2×D3—32no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—62no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—61no—
683C2×D3—62no—
684C2×D3—62no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—122no—
688C2×D3—128no—
689C2×D3—128no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—241no—
695C2×D3—241no—
696C3×C4—22no—
697C3×C4—22no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—32no—
701C3×C4—42no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—61no—
707C3×C4—81no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4C22×C4×D311yescharacteristic
711C3×C4C22×C4×D311yescharacteristic
712C3×C4D3×#4111yescharacteristic
713C3×C4D3×#4111yescharacteristic
714Dic3—21no—
715Dic3—21no—
716Dic3—21no—
717Dic3—32no—
718Dic3—32no—
719Dic3—41no—
720Dic3—41no—
721Dic3—62no—
722Dic3—121no—
723Dic3—121no—
724Dic3—241no—
725Dic3#91412yescomplemented
726C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
727C23—61no—
728C23—61no—
729C23—91no—
730C23—184no—
731C23—181no—
732C23—362no—
733C23—362no—
734Q8—21no—
735Q8C4×D3212yescomplemented
736D4—32no—
737D4—32no—
738D4—61no—
739D4—61no—
740D4—92no—
741D4—184no—
742D4—184no—
743D4—181no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—31no—
747C2×C4—31no—
748C2×C4—31no—
749C2×C4—31no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—91no—
753C2×C4—92no—
754C2×C4—92no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4—184no—
758C2×C4—182no—
759C2×C4—181no—
760C2×C4—362no—
761C2×C4—362no—
762C2×C4—362no—
763C2×C4—361no—
764C2×C4—362no—
765C2×C4—362no—
766C2×C4C22×D3211yescharacteristic
767C8—21no—
768C8—32no—
769C8—32no—
770C8—181no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—122no—
775C2×C3—122no—
776C2×C3C4×D3×D411yescharacteristic
777C2×C3C4×D3×D411yescharacteristic
778C2×C3C2×#91411yescharacteristic
779C2×C3#576811yescharacteristic
780C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
781C2×C3#577711yescharacteristic
782D3—42no—
783D3—42no—
784D3—62no—
785D3—62no—
786D3—122no—
787D3—122no—
788D3—122no—
789D3—242no—
790C22—62no—
791C22—62no—
792C22—92no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—181no—
798C22—181no—
799C22—182no—
800C22—368no—
801C22—361no—
802C22—361no—
803C22D32×D411yescharacteristic
804C4—22no—
805C4—32no—
806C4—41no—
807C4—61no—
808C4—61no—
809C4—61no—
810C4—92no—
811C4—121no—
812C4—121no—
813C4—361no—
814C4C2×C4×D3211yescharacteristic
815C4#6431211yescharacteristic
816C3—21no—
817C3C4×#91411yescharacteristic, complemented
818C3#7977311yescharacteristic, complemented
819C2—122no—
820C2—122no—
821C2—182no—
822C2—362no—
823C2#1059425511yescharacteristic
824C2D3×#91411yescharacteristic
825C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#63941C2
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595386C2semidirect
3. #10594605C2semidirect
4. #10592502C2semidirect
5. C3×#4817C2semidirect
6. C3×#4788C2semidirect
7. #10591566C2semidirect
8. Dic3×#215C2semidirect
9. #10590941C2semidirect
10. #10590746C2semidirect
11. #10590745C2semidirect
12. #10590664C2semidirect
13. #10590589C2semidirect
14. #10590583C2semidirect
15. #10590456C2semidirect
23. C3×Q8×Dic3C22semidirect
24. C3×Q8×Dic3C22semidirect
29. #63941C4semidirect
33. #63894C22semidirect
34. #63894C22semidirect
46. C32×#103C22semidirect
47. #63662C22semidirect
48. #63648C22semidirect
49. #63636C22semidirect
52. C3×#815C22semidirect
53. C3×C8×Dic3C22semidirect
54. C3×#808C22semidirect
55. C3×#807C22semidirect
56. #63575C22semidirect
57. #63573C22semidirect
60. #63554C22semidirect
61. Dic3×C3⋊C8C22semidirect
80. #4817D3semidirect
84. #4788D3semidirect
96. #3832C2×C4semidirect
114. #3802C2×C4semidirect
122. C3×#215C2×C4semidirect
123. C3×#215C2×C4semidirect
144. #3714C2×C4semidirect
145. #3714C2×C4semidirect
146. #3712C2×C4semidirect
161. Q8×Dic3C2×D3semidirect
162. Q8×Dic3C2×D3semidirect
210. C3×#103C2×D3semidirect
211. C3×#103C2×D3semidirect
229. #815C2×D3semidirect
231. C8×Dic3C2×D3semidirect
238. #808C2×D3semidirect
240. #807C2×D3semidirect
251. C32×Q8C22×C4semidirect
259. C4⋊(C3⋊D3)C22×C4semidirect
285. C3×C3⋊C8C22×C4semidirect
286. C3×C3⋊C8C22×C4semidirect
378. #215C4×D3semidirect
379. #215C4×D3semidirect
449. C3×Dic3AGL(1,ℤ/8)semidirect
483. #103D32semidirect
514. C3×Q8C2×C4×D3semidirect
515. C3×Q8C2×C4×D3semidirect
598. C3⋊C8C2×C4×D3semidirect
599. C3⋊C8C2×C4×D3semidirect
725. Dic3#914semidirect
726. C32C4×AGL(1,ℤ/8)semidirect
735. Q8C4×D32semidirect
817. C3C4×#914semidirect
818. C3#79773semidirect

Maximal subgroups

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

subgroupindex
#105953862
C2×#639412
#105946052
#105925022
C3×#48172
C3×#47882
#105915662
Dic3×#2152
#105909412
#105907462
#105907452
#105906642
#105905892
#105905832
#105904562
#797733
C4×#9143