Finite Group Databasebeta

← #11868696

Subgroups — #11868696

Order 1152.

931 conjugacy classes of subgroups.

The subgroup lattice has 751 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5688C211yesmaximal, characteristic, complemented
2C4×D3×D12C211yesmaximal, characteristic
3#10592765C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5#10590592C211yesmaximal, characteristic
6#10590592C211yesmaximal, characteristic
7#10590466C211yesmaximal, characteristic, complemented
8#10590465C211yesmaximal, characteristic, complemented
9#10590464C211yesmaximal, characteristic, complemented
10#10590463C211yesmaximal, characteristic, complemented
11#10590437C211yesmaximal, characteristic, complemented
12#10590436C211yesmaximal, characteristic, complemented
13#10590336C211yesmaximal, characteristic, complemented
14#10590308C211yesmaximal, characteristic, complemented
15#10590270C211yesmaximal, characteristic, complemented
16#83350—31nomaximal
17#81166—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×C4×D32—21no—
20C32×#125C2211yescharacteristic, complemented
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C3×#896—21no—
23C3×#896—21no—
24C3×#892C2211yescharacteristic
25C3×#892C2211yescharacteristic
26C3×#888C2211yescharacteristic, complemented
27C3×#888C2211yescharacteristic, complemented
28C3×#887—21no—
29C3×#887—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C42×D3C2211yescharacteristic
32C3×#870C2211yescharacteristic, complemented
33D3×(C2×D3)⋊C4—21no—
34C4×#626—21no—
35#63894C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37D3×C4⋊Dic3C2211yescharacteristic
38#63880—21no—
39C2×#3711C2211yescharacteristic
40C2×#3711C2211yescharacteristic
41#63636C2211yescharacteristic
42#63636C2211yescharacteristic
43#63635C2211yescharacteristic, complemented
44#63634C2211yescharacteristic, complemented
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
46C3×#809C2211yescharacteristic
47C3×#809C2211yescharacteristic
48C3×#808C2211yescharacteristic, complemented
49C3×#807C2211yescharacteristic, complemented
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61C3×#533—31no—
62#5688D311yescharacteristic, complemented
63C4×D3×D4—31no—
64C2×C4×D12—31no—
65C3×#478—31no—
66#5087—31no—
67#5087—31no—
68#5084—31no—
69#5084—31no—
70#5066—31no—
71#5066—31no—
72#5066—31no—
73#5066—31no—
74#5066—61no—
75#5066D311yescharacteristic, complemented
76#5009—31no—
77#5001—31no—
78#5001—31no—
79#4995—31no—
80#4995—31no—
81#4924—31no—
82#4890—31no—
83#4881—31no—
84#4870—31no—
85#4861—31no—
86#4847—31no—
87#4837—31no—
88#4770—31no—
89#4770—31no—
90#4761—31no—
91#4759—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3D411yescharacteristic
98C2×C3×C4×D3D411yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—21no—
101C2×C3×Dic6—21no—
102C2×#626—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12Q814yescomplemented
108C4×D32—44no—
109C32×C4⋊C4—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C42C2311yescharacteristic
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3D411yescharacteristic
131C3×C4×Dic3D411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138#3711—22no—
139#3711—22no—
140#3077—91noSylow
141C2×D3×D4—31no—
142C22×D12—31no—
143C22×C4×D3—61no—
144C22×C4×D3—61no—
145C3×C4⋊Q8—31no—
146C3×C4⋊Q8—31no—
147C3×#125—21no—
148C3×#125—31no—
149C3×#125C2×D311yescharacteristic, complemented
150C3×#125C2×D311yescharacteristic, complemented
151C3×C22⋊Q8—61no—
152C3×C22⋊Q8—61no—
153C3×C4×Q8—61no—
154C3×C4×Q8—61no—
155C3×C4×D4—31no—
156C3×#117—31no—
157C3×#117—31no—
158C2×C3×C42—31no—
159D4×Dic3—31no—
160C4×#67—61no—
161C2×(C2×D3)⋊C4—61no—
162C2×C4⋊Dic3—31no—
163C2×#208—31no—
164C2×#208—31no—
165C2×ΓL(1,𝔽25)—31no—
166C2×ΓL(1,𝔽25)—31no—
167#896—21no—
168#896—21no—
169#893—31no—
170#892C2×D311yescharacteristic
171#892C2×D311yescharacteristic
172D3×C4⋊C4—31no—
173#888C2×D311yescharacteristic, complemented
174#888C2×D311yescharacteristic, complemented
175#887—21no—
176#887—21no—
177#67⋊C4—61no—
178D3×C22⋊C4—61no—
179C4×D12—31no—
180C4×D12—31no—
181C4×D12—31no—
182C4×D12—31no—
183C4×D12—61no—
184C4×D12—61no—
185C4×D12—61no—
186C4×D12C2×D311yescharacteristic
187C42×D3C2×D311yescharacteristic
188#870C2×D311yescharacteristic, complemented
189C3×#107—31no—
190C3×#106—31no—
191C3×C4⋊C8—31no—
192C3×#102—31no—
193C3×#102—31no—
194#832—31no—
195#832—31no—
196#821—31no—
197#821—31no—
198#818—31no—
199#817—31no—
200Dic3⋊C8—31no—
201Dic3⋊C8—31no—
202#809—31no—
203#809—31no—
204#809—31no—
205#809—31no—
206#809—31no—
207#809—31no—
208#809—31no—
209#809—31no—
210#809—61no—
211#809—61no—
212#809C2×D311yescharacteristic
213#809C2×D311yescharacteristic
214#808—31no—
215#808—31no—
216#808—31no—
217#808—31no—
218#808—31no—
219#808—61no—
220#808C2×D311yescharacteristic, complemented
221#807—31no—
222#807—31no—
223#807—31no—
224#807—31no—
225#807—31no—
226#807—61no—
227#807C2×D311yescharacteristic, complemented
228C4⋊(C3⋊C8)—31no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—61no—
233C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
234C22×C3⋊D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3C2×D411yescharacteristic
237C2×D32—24no—
238C2×D32—42no—
239C2×D32—42no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C4⋊(C3⋊D3)—21no—
247C4⋊(C3⋊D3)C2×Q812yes—
248C4×C3⋊D3—42no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—21no—
256C3×D12C2×Q812yes—
257C3×C4×D3—22no—
258C3×C4×D3—41no—
259C3×C4×D3—42no—
260C3×C4×D3C2×Q812yes—
261C3×C4×D3#4112yes—
262C3×Dic6—42no—
263C3×Dic6—42no—
264#626—24no—
265#624—42no—
266D3×Dic3—42no—
267D3×Dic3—42no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#533—31no—
273C2×C4×D4—91no—
274#478—31no—
275#478—91no—
276#478—91no—
277#478—91no—
278#476—91no—
279#476—91no—
280#474—91no—
281#474—91no—
282#428—91no—
283#428—91no—
284#423—91no—
285#418—91no—
286#418—91no—
287C23×D3—61no—
288C23×D3—61no—
289C2×C3×Q8—61no—
290C2×C3×Q8—61no—
291C2×C3×D4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—61no—
296C2×#67—61no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299D3×D4—34no—
300D3×D4—62no—
301C2×D12—31no—
302C2×D12—31no—
303C2×D12—34no—
304C2×D12—61no—
305C2×D12—62no—
306C2×D12—61no—
307C2×D12C22×D311yescharacteristic
308C2×C4×D3—21no—
309C2×C4×D3—61no—
310C2×C4×D3—61no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—121no—
316C2×C4×D3—124no—
317C2×C4×D3—124no—
318C2×C4×D3#6711yescharacteristic
319C2×C4×D3#6711yescharacteristic
320C2×C4×D3C22×D311yescharacteristic
321C2×Dic6—21no—
322C2×Dic6—21no—
323C2×C3×C8—31no—
324C2×C3×C8—31no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—41no—
335C3×C4⋊C4—41no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C42—21no—
348C3×C42—31no—
349C3×C42—31no—
350C3×C42—31no—
351C3×C42—61no—
352C3×C42—61no—
353C3×C42C22×D311yescharacteristic
354C3×C42C22×D311yescharacteristic
355#217—61no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—121no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3C22×D311yescharacteristic
370C4⋊Dic3C22×D311yescharacteristic
371C4⋊Dic3C22×D311yescharacteristic
372Dic3⋊C4—21no—
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4—61no—
377C4×Dic3—21no—
378C4×Dic3—21no—
379C4×Dic3#6711yescharacteristic
380C4×Dic3#6711yescharacteristic
381C4×Dic3C22×D311yescharacteristic
382#208—62no—
383#208—62no—
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—61no—
389C2×C3⋊C8—61no—
390C2×C3⋊C8C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392ΓL(1,𝔽25)—62no—
393ΓL(1,𝔽25)—62no—
394C22×C32C22×D411yescharacteristic
395C2×C3⋊D3—22no—
396C2×C3⋊D3—41no—
397C2×C3⋊D3—41no—
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—22no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3C22⋊Q812yes—
404D32—48no—
405C32×C4—21no—
406C32×C4—21no—
407C32×C4—41no—
408C32×C4—41no—
409C32×C4C22×Q811yescharacteristic
410C32×C4C2×#4111yescharacteristic
411C3⋊Dic3—41no—
412C3×Dic3—21no—
413C3×Dic3—41no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C3×Dic3C22⋊Q812yes—
417C3×Dic3AGL(1,ℤ/8)12yes—
418C22×D4—91no—
419C23×C4—181no—
420C2×M16—91no—
421C2×M16—91no—
422C4⋊Q8—31no—
423C4⋊Q8—31no—
424#125—31no—
425#125D3211yescharacteristic, complemented
426C22⋊Q8—61no—
427C22⋊Q8—61no—
428C4×Q8—61no—
429C4×Q8—61no—
430C4×D4—31no—
431C4×D4—91no—
432C4×D4—91no—
433C4×D4—91no—
434C4×D4—181no—
435C4×D4—181no—
436#117—31no—
437#117—31no—
438C2×C4⋊C4—91no—
439C2×C22⋊C4—181no—
440C2×C42—31no—
441#107—31no—
442#107—91no—
443#107—91no—
444#107—91no—
445#106—31no—
446#106—91no—
447#106—91no—
448#106—91no—
449C4⋊C8—31no—
450C4⋊C8—91no—
451C4⋊C8—91no—
452C4⋊C8—91no—
453#102—31no—
454#102—31no—
455#102—91no—
456#102—91no—
457#102—91no—
458#102—91no—
459#102—91no—
460#102—91no—
461C23×C3—31no—
462C23×C3—61no—
463C22×D3—21no—
464C22×D3—64no—
465C22×D3—61no—
466C22×D3—61no—
467C22×D3—64no—
468C22×D3—121no—
469C22×D3—122no—
470C22×D3—122no—
471C22×D3—122no—
472C22×D3—122no—
473C22×D3C2×#6711yescharacteristic
474C3×Q8—122no—
475C3×Q8—122no—
476C3×D4—32no—
477C3×D4—61no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—32no—
488C2×C3×C4—32no—
489C2×C3×C4—31no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—62no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—121no—
497C2×C3×C4—122no—
498C2×C3×C4D3×D411yescharacteristic
499C2×C3×C4D3×D411yescharacteristic
500C2×C3×C4C2×#6711yescharacteristic
501C2×C3×C4C2×#6711yescharacteristic
502C2×C3×C4C23×D311yescharacteristic
503C2×C3×C4C23×D311yescharacteristic
504#67—64no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—121no—
511C2×Dic3—122no—
512C2×Dic3—122no—
513C2×Dic3C2×#6711yescharacteristic
514C2×Dic3C2×#6711yescharacteristic
515C2×Dic3C2×#6711yescharacteristic
516D12—21no—
517D12—32no—
518D12—32no—
519D12—62no—
520D12—64no—
521D12—61no—
522D12—61no—
523D12—121no—
524D12D3×Q812yes—
525C4×D3—22no—
526C4×D3—41no—
527C4×D3—42no—
528C4×D3—122no—
529C4×D3—122no—
530C4×D3—122no—
531C4×D3—122no—
532C4×D3—122no—
533C4×D3—122no—
534C4×D3—242no—
535C4×D3D3×Q812yes—
536C4×D3#23912yes—
537Dic6—42no—
538Dic6—42no—
539C3×C8—61no—
540C3×C8—61no—
541C3⋊C8—21no—
542C3⋊C8—21no—
543C3⋊C8—61no—
544C3⋊C8—61no—
545C3⋊C8—61no—
546C3⋊C8—61no—
547C3⋊C8—121no—
548C3⋊C8—121no—
549C2×C32C2×C22⋊Q811yescharacteristic
550C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
551C2×C32#57511yescharacteristic
552C3⋊D3—42no—
553C3×D3—22no—
554C3×D3—42no—
555C24—181no—
556C2×Q8—61no—
557C2×Q8—61no—
558C2×D4—31no—
559C2×D4—94no—
560C2×D4—91no—
561C2×D4—182no—
562C2×D4—181no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—61no—
567C22×C4—181no—
568C22×C4—181no—
569C22×C4—181no—
570C22×C4—181no—
571C22×C4—364no—
572M16—182no—
573M16—182no—
574C2×C8—31no—
575C2×C8—31no—
576C2×C8—91no—
577C2×C8—91no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—31no—
581C4⋊C4—31no—
582C4⋊C4—31no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—91no—
588C4⋊C4—181no—
589C4⋊C4C2×D3211yescharacteristic
590C4⋊C4C2×D3211yescharacteristic
591C22⋊C4—61no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—181no—
595C22⋊C4—181no—
596C22⋊C4—181no—
597C42—31no—
598C42—31no—
599C42—31no—
600C42—61no—
601C42—61no—
602C42C2×D3211yescharacteristic
603C22×C3—21no—
604C22×C3—32no—
605C22×C3—61no—
606C22×C3—61no—
607C22×C3—62no—
608C22×C3—121no—
609C22×C3—121no—
610C22×C3C2×D3×D411yescharacteristic
611C22×C3C22×#6711yescharacteristic
612C2×D3—21no—
613C2×D3—21no—
614C2×D3—22no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—62no—
618C2×D3—62no—
619C2×D3—122no—
620C2×D3—128no—
621C2×D3—128no—
622C2×D3—121no—
623C2×D3—121no—
624C2×D3—121no—
625C2×D3—121no—
626C2×D3—241no—
627C2×D3—241no—
628C2×D3#94612yes—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—32no—
636C3×C4—32no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—61no—
644C3×C4—81no—
645C3×C4—81no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4C2×D3×Q811yescharacteristic
650C3×C4C2×D3×Q811yescharacteristic
651C3×C4C2×#23911yescharacteristic
652C3×C4D3×#4111yescharacteristic
653Dic3—21no—
654Dic3—41no—
655Dic3—41no—
656Dic3—41no—
657Dic3—121no—
658Dic3—121no—
659Dic3—241no—
660Dic3#94612yes—
661Dic3#94912yes—
662C32#307711yescharacteristic, complemented, Sylow
663C23—31no—
664C23—61no—
665C23—184no—
666C23—181no—
667C23—362no—
668C23—362no—
669Q8—122no—
670Q8—122no—
671D4—32no—
672D4—61no—
673D4—92no—
674D4—184no—
675D4—181no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—32no—
681C2×C4—32no—
682C2×C4—31no—
683C2×C4—62no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—121no—
688C2×C4—122no—
689C2×C4—181no—
690C2×C4—362no—
691C2×C4—362no—
692C2×C4—362no—
693C2×C4—362no—
694C2×C4D3×#6711yescharacteristic
695C2×C4D3×#6711yescharacteristic
696C2×C4C22×D3211yescharacteristic
697C8—61no—
698C8—61no—
699C8—181no—
700C8—181no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—62no—
705C2×C3—122no—
706C2×C3D3×C22⋊Q811yescharacteristic
707C2×C3#576811yescharacteristic
708C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
709C2×C3C2×#94611yescharacteristic
710C2×C3C2×#94911yescharacteristic
711C2×C3#582211yescharacteristic
712D3—22no—
713D3—42no—
714D3—122no—
715D3—122no—
716D3—242no—
717C22—32no—
718C22—61no—
719C22—61no—
720C22—62no—
721C22—121no—
722C22—121no—
723C22—182no—
724C22—368no—
725C22—361no—
726C22—361no—
727C22C2×D3×#6711yescharacteristic
728C4—21no—
729C4—21no—
730C4—32no—
731C4—32no—
732C4—41no—
733C4—41no—
734C4—61no—
735C4—121no—
736C4—121no—
737C4—121no—
738C4—361no—
739C4D32×Q811yescharacteristic
740C4D3×#23911yescharacteristic
741C3—21no—
742C3#8116611yescharacteristic, complemented
743C3#8335011yescharacteristic, complemented
744C2—62no—
745C2—122no—
746C2—362no—
747C2D3×#94611yescharacteristic
748C2D3×#94911yescharacteristic
749C2#1059545311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenter#125D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C3×#5688C2semidirect
3. #10592765C2semidirect
4. C3×#5066C2semidirect
7. #10590466C2semidirect
8. #10590465C2semidirect
9. #10590464C2semidirect
10. #10590463C2semidirect
11. #10590437C2semidirect
12. #10590436C2semidirect
13. #10590336C2semidirect
14. #10590308C2semidirect
15. #10590270C2semidirect
20. C32×#125C22semidirect
26. C3×#888C22semidirect
27. C3×#888C22semidirect
32. C3×#870C22semidirect
43. #63635C22semidirect
44. #63634C22semidirect
45. C4⋊(C3⋊(C3⋊C8))C22semidirect
48. C3×#808C22semidirect
49. C3×#807C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. #63576C22semidirect
52. #63575C22semidirect
53. #63574C22semidirect
54. #63573C22semidirect
55. Dic3⋊(C3⋊C8)C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
62. #5688D3semidirect
75. #5066D3semidirect
107. D3×D12Q8semidirect
149. C3×#125C2×D3semidirect
150. C3×#125C2×D3semidirect
173. #888C2×D3semidirect
174. #888C2×D3semidirect
188. #870C2×D3semidirect
220. #808C2×D3semidirect
227. #807C2×D3semidirect
233. C4⋊(C3⋊C8)C2×D3semidirect
425. #125D32semidirect
662. C32#3077semidirect
742. C3#81166semidirect
743. C3#83350semidirect

Maximal subgroups

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

subgroupindex
C3×#56882
C4×D3×D122
#105927652
C3×#50662
#105905922
#105904662
#105904652
#105904642
#105904632
#105904372
#105904362
#105903362
#105903082
#105902702
#833503
#811663