Finite Group Databasebeta

← #11868666

Subgroups — #11868666

Order 1152.

934 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×D4×Dic3C211yesmaximal, characteristic
2#10594477C211yesmaximal, characteristic, complemented
3#10592458C211yesmaximal, characteristic, complemented
4C3×#4770C211yesmaximal, characteristic
5C3×#4763C211yesmaximal, characteristic, complemented
6#10591495C211yesmaximal, characteristic, complemented
7#10591421C211yesmaximal, characteristic
8#10591411C211yesmaximal, characteristic, complemented
9#10590776C211yesmaximal, characteristic, complemented
10#10590767C211yesmaximal, characteristic, complemented
11#10590681C211yesmaximal, characteristic, complemented
12#10590663C211yesmaximal, characteristic, complemented
13#10590471C211yesmaximal, characteristic, complemented
14#10590467C211yesmaximal, characteristic, complemented
15#10590436C211yesmaximal, characteristic, complemented
16#81166—31nomaximal
17#78917—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C22×D3×Dic3—21no—
20D4×C3⋊Dic3C2211yescharacteristic
21#64097C2211yescharacteristic, complemented
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×#890C2211yescharacteristic, complemented
26#67⋊Dic3—21no—
27Dic3×#67—21no—
28D3×#217—21no—
29#63919C2211yescharacteristic, complemented
30#63899—21no—
31#63898C2211yescharacteristic
32#63896—21no—
33Dic3×D12C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic
35C4×D3×Dic3C2211yescharacteristic
36#63869C2211yescharacteristic, complemented
37#63844—21no—
38#63841C2211yescharacteristic
39#63837—21no—
40C2×#3711C2211yescharacteristic
41C32×#102C2211yescharacteristic
42#63659C2211yescharacteristic
43#63645C2211yescharacteristic, complemented
44#63641C2211yescharacteristic, complemented
45#63634C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#817C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#807C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63572C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61C2×D4×Dic3—31no—
62#5688—31no—
63C4×D3×D4—31no—
64#5517—31no—
65C3×#478—31no—
66C3×#418—31no—
67#5215—31no—
68#5121—31no—
69#5118—31no—
70#5066—31no—
71#5009—31no—
72#4995—31no—
73#4890—31no—
74#4881—31no—
75#4870—31no—
76#4861—31no—
77#4847—31no—
78#4837—31no—
79#4770—31no—
80#4770D311yescharacteristic
81#4766—31no—
82#4766—31no—
83#4763—31no—
84#4763D311yescharacteristic, complemented
85#4761—31no—
86#4761—31no—
87#4761—31no—
88#4759—31no—
89#4759—31no—
90#4759—31no—
91#4759—61no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×D3×D4—22no—
99C3×D3×D4Q814yescomplemented
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×#627—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—44no—
107C2×D3×Dic3D411yescharacteristic
108C2×D3×Dic3D411yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111#3757—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115C4×C3⋊Dic3C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×ΓL(1,𝔽25)—22no—
129#3724—21no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137Dic32D411yescharacteristic
138Dic32D411yescharacteristic
139#3711—22no—
140#3077—91noSylow
141C22×C3×D4—31no—
142C23×Dic3—61no—
143C2×D3×D4C2×D311yescharacteristic
144C22×C4×D3—61no—
145C2×C3×M16—31no—
146C3×#125—31no—
147C3×C4×D4—31no—
148C3×#117—31no—
149C2×#217—61no—
150D4×Dic3—31no—
151D4×Dic3—31no—
152D4×Dic3—31no—
153D4×Dic3—31no—
154D4×Dic3—61no—
155D4×Dic3—61no—
156D4×Dic3—61no—
157D4×Dic3C2×D311yescharacteristic
158C4×#67—61no—
159#926—31no—
160C2×C4⋊Dic3—31no—
161C2×C4×Dic3—31no—
162C2×#208—31no—
163C2×ΓL(1,𝔽25)—31no—
164C2×ΓL(1,𝔽25)C2×D311yescharacteristic
165#896—61no—
166#896—61no—
167#893—31no—
168#892—31no—
169#892C2×D311yescharacteristic
170D3×C4⋊C4—31no—
171#890—31no—
172#890C2×D311yescharacteristic, complemented
173#888—31no—
174#888—31no—
175#888—31no—
176#888—31no—
177#888—61no—
178#887—61no—
179#887—61no—
180#67⋊C4—61no—
181D3×C22⋊C4—61no—
182#878—61no—
183#878—61no—
184C4×D12—31no—
185C42×D3—31no—
186#870—31no—
187C4×Dic6—61no—
188C4×Dic6—61no—
189C3×#107—31no—
190C3×#106—31no—
191C3×C4⋊C8—31no—
192C3×#102—21no—
193C3×#102—31no—
194C3×#102—31no—
195C3×#102—31no—
196C3×#102—31no—
197C3×#102C2×D311yescharacteristic
198C3×#102C2×D311yescharacteristic
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—61no—
204#832C2×D311yescharacteristic
205#832C2×D311yescharacteristic
206#821—31no—
207#821C2×D311yescharacteristic
208#818—31no—
209#818—31no—
210#818—31no—
211#818—61no—
212#817—31no—
213#817—31no—
214#817C2×D311yescharacteristic, complemented
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—61no—
221Dic3⋊C8C2×D311yescharacteristic, complemented
222#809—31no—
223#809C2×D311yescharacteristic
224#808—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231#807—61no—
232#807C2×D311yescharacteristic, complemented
233C4⋊(C3⋊C8)—31no—
234C23×C32—21no—
235C22×C3×D3—21no—
236C22×C3×D3—24no—
237C22×C3×D3—42no—
238C22×C3×D3—42no—
239C22×C3×D3C2×D411yescharacteristic
240C32×D4—21no—
241C32×D4C2×Q812yes—
242C2×C32×C4—21no—
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—42no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249#634—42no—
250C3×#67—24no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—42no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12C2×Q812yes—
260C3×C4×D3C2×Q812yes—
261C3×C4×D3#4112yes—
262#627—42no—
263D3×Dic3—22no—
264D3×Dic3—41no—
265D3×Dic3—42no—
266D3×Dic3—42no—
267D3×Dic3—42no—
268C32×C8—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#533—91no—
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—31no—
286#418—91no—
287C24×C3—61no—
288C23×D3—21no—
289C2×C3×D4—21no—
290C2×C3×D4—34no—
291C2×C3×D4—31no—
292C2×C3×D4—62no—
293C2×C3×D4—61no—
294C2×C3×D4C22×D311yescharacteristic
295C2×C3×D4C22×D311yescharacteristic
296C22×C3×C4—31no—
297C22×C3×C4—61no—
298C2×#67—21no—
299C22×Dic3—21no—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—121no—
308C22×Dic3—124no—
309D3×D4—22no—
310D3×D4Dic614yescomplemented
311C2×D12C22×D311yescharacteristic
312C2×C4×D3—31no—
313C2×C4×D3—31no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—124no—
318C2×C4×D3C22×D311yescharacteristic
319C2×Dic6—61no—
320C2×Dic6—61no—
321C2×Dic6—61no—
322C2×Dic6—61no—
323C2×Dic6—121no—
324C3×M16—62no—
325C2×C3×C8—21no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C2×C3×C8C22×D311yescharacteristic
329C2×C3×C8C22×D311yescharacteristic
330C3×C4⋊C4—21no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C42—31no—
341C3×C42—61no—
342#217—21no—
343#217—61no—
344#217—61no—
345#217—61no—
346#217—61no—
347#217—61no—
348#217—121no—
349(C2×D3)⋊C4—21no—
350(C2×D3)⋊C4—61no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353C4⋊Dic3—21no—
354C4⋊Dic3—31no—
355C4⋊Dic3—31no—
356C4⋊Dic3—31no—
357C4⋊Dic3—31no—
358C4⋊Dic3—61no—
359C4⋊Dic3—61no—
360C4⋊Dic3—61no—
361C4⋊Dic3—61no—
362C4⋊Dic3C22×D311yescharacteristic
363C4⋊Dic3C22×D311yescharacteristic
364C4⋊Dic3C22×D311yescharacteristic
365Dic3⋊C4—21no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—121no—
375C4×Dic3—21no—
376C4×Dic3—31no—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C4×Dic3—31no—
380C4×Dic3—31no—
381C4×Dic3—31no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3C22×D311yescharacteristic
386#208—62no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—61no—
390C2×C3⋊C8C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392ΓL(1,𝔽25)—22no—
393ΓL(1,𝔽25)—62no—
394C22×C32—22no—
395C22×C32—41no—
396C22×C32—41no—
397C22×C32C22×D411yescharacteristic
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—22no—
401C2×C3×D3—48no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3C22⋊Q812yes—
405C32×C4—41no—
406C32×C4C22×Q811yescharacteristic
407C32×C4C2×#4111yescharacteristic
408C3⋊Dic3—21no—
409C3⋊Dic3—41no—
410C3⋊Dic3—41no—
411C3⋊Dic3AGL(1,ℤ/8)12yes—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C3×Dic3—41no—
417C3×Dic3C22⋊Q812yes—
418C22×D4—31no—
419C23×C4—181no—
420C2×M16—31no—
421C2×M16—91no—
422C4⋊Q8—91no—
423C4⋊Q8—91no—
424#125—31no—
425#125—91no—
426C22⋊Q8—181no—
427C22⋊Q8—181no—
428C4×Q8—181no—
429C4×Q8—181no—
430C4×D4—31no—
431C4×D4—91no—
432C4×D4—91no—
433C4×D4—91no—
434C4×D4—181no—
435C4×D4—181no—
436#117—31no—
437#117—91no—
438C2×C4⋊C4—91no—
439C2×C22⋊C4—181no—
440C2×C42—91no—
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—31no—
456#102—31no—
457#102—91no—
458#102—91no—
459#102—91no—
460#102D3211yescharacteristic
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—31no—
464C23×C3—41no—
465C23×C3—64no—
466C23×C3—61no—
467C23×C3—122no—
468C23×C3—122no—
469C22×D3—21no—
470C22×D3—24no—
471C22×D3—42no—
472C22×D3—42no—
473C22×D3D3×D411yescharacteristic
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—22no—
477C3×D4—32no—
478C3×D4—41no—
479C3×D4—64no—
480C3×D4—61no—
481C3×D4C2×Dic612yes—
482C3×D4D3×Q812yes—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—31no—
487C2×C3×C4—32no—
488C2×C3×C4—32no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—41no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—122no—
496C2×C3×C4C23×D311yescharacteristic
497C2×C3×C4C23×D311yescharacteristic
498#67—24no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—31no—
503C2×Dic3—31no—
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—42no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—62no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—121no—
515C2×Dic3—121no—
516C2×Dic3—121no—
517C2×Dic3—122no—
518C2×Dic3—122no—
519C2×Dic3—122no—
520C2×Dic3—122no—
521C2×Dic3—122no—
522C2×Dic3—242no—
523C2×Dic3D3×D411yescharacteristic
524C2×Dic3D3×D411yescharacteristic
525C2×Dic3D3×D411yescharacteristic
526D12—21no—
527D12C2×Dic612yes—
528C4×D3—62no—
529C4×D3—122no—
530C4×D3—121no—
531C4×D3—122no—
532C4×D3—122no—
533C4×D3C2×Dic612yes—
534C4×D3#23712yes—
535Dic6—122no—
536Dic6—122no—
537Dic6—122no—
538Dic6—122no—
539Dic6—242no—
540C3×C8—21no—
541C3×C8—21no—
542C3×C8—41no—
543C3×C8—61no—
544C3×C8—61no—
545C3⋊C8—21no—
546C3⋊C8—21no—
547C3⋊C8—61no—
548C3⋊C8—61no—
549C3⋊C8—121no—
550C2×C32—42no—
551C2×C32C2×C22⋊Q811yescharacteristic
552C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
553C2×C32#57511yescharacteristic
554C3×D3—22no—
555C3×D3—42no—
556C24—61no—
557C2×Q8—181no—
558C2×Q8—181no—
559C2×D4—34no—
560C2×D4—31no—
561C2×D4—62no—
562C2×D4—61no—
563C2×D4C2×D3211yescharacteristic
564C22×C4—31no—
565C22×C4—61no—
566C22×C4—91no—
567C22×C4—91no—
568C22×C4—181no—
569C22×C4—181no—
570C22×C4—181no—
571C22×C4—181no—
572C22×C4—364no—
573M16—62no—
574M16—182no—
575C2×C8—31no—
576C2×C8—31no—
577C2×C8—91no—
578C2×C8C2×D3211yescharacteristic
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—31no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—91no—
585C4⋊C4—91no—
586C4⋊C4—181no—
587C4⋊C4—181no—
588C4⋊C4—181no—
589C4⋊C4—181no—
590C4⋊C4—181no—
591C4⋊C4C2×D3211yescharacteristic
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—181no—
595C22⋊C4—181no—
596C22⋊C4—181no—
597C22⋊C4—181no—
598C42—31no—
599C42—61no—
600C42—91no—
601C42—91no—
602C42—91no—
603C42—181no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—21no—
607C22×C3—32no—
608C22×C3—42no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—61no—
614C22×C3—61no—
615C22×C3—62no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3—128no—
619C22×C3—121no—
620C22×C3—121no—
621C22×C3C2×D3×D411yescharacteristic
622C22×C3C2×D3×D411yescharacteristic
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—22no—
626C2×D3—48no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3#87812yes—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—32no—
633C3×C4—41no—
634C3×C4—41no—
635C3×C4—61no—
636C3×C4—61no—
637C3×C4—81no—
638C3×C4—121no—
639C3×C4—121no—
640C3×C4—121no—
641C3×C4C22×Dic611yescharacteristic
642C3×C4C2×#23711yescharacteristic
643C3×C4C2×D3×Q811yescharacteristic
644C3×C4D3×#4111yescharacteristic
645Dic3—21no—
646Dic3—21no—
647Dic3—32no—
648Dic3—32no—
649Dic3—41no—
650Dic3—41no—
651Dic3—41no—
652Dic3—62no—
653Dic3—61no—
654Dic3—61no—
655Dic3—121no—
656Dic3—121no—
657Dic3—121no—
658Dic3—121no—
659Dic3—121no—
660Dic3—241no—
661Dic3—241no—
662Dic3#87812yes—
663C32#307711yescharacteristic, complemented, Sylow
664C23—21no—
665C23—31no—
666C23—64no—
667C23—61no—
668C23—122no—
669C23—122no—
670Q8—362no—
671Q8—362no—
672D4—21no—
673D4—32no—
674D4—64no—
675D4—61no—
676D4D3×Dic612yes—
677C2×C4—21no—
678C2×C4—31no—
679C2×C4—32no—
680C2×C4—32no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—91no—
687C2×C4—91no—
688C2×C4—122no—
689C2×C4—182no—
690C2×C4—181no—
691C2×C4—181no—
692C2×C4—361no—
693C2×C4—362no—
694C2×C4—362no—
695C2×C4—362no—
696C2×C4—362no—
697C2×C4C22×D3211yescharacteristic
698C8—21no—
699C8—61no—
700C8—61no—
701C8—181no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—42no—
706C2×C3—42no—
707C2×C3—62no—
708C2×C3—82no—
709C2×C3—122no—
710C2×C3C2×#87811yescharacteristic
711C2×C3D3×C22⋊Q811yescharacteristic
712C2×C3#576811yescharacteristic
713C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
714C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
715C2×C3#577311yescharacteristic
716D3—22no—
717D3—42no—
718C22—22no—
719C22—32no—
720C22—41no—
721C22—41no—
722C22—61no—
723C22—61no—
724C22—62no—
725C22—128no—
726C22—121no—
727C22—121no—
728C22D32×D411yescharacteristic
729C4—32no—
730C4—41no—
731C4—61no—
732C4—61no—
733C4—92no—
734C4—121no—
735C4—121no—
736C4—121no—
737C4—181no—
738C4—361no—
739C4—361no—
740C4C2×D3×Dic611yescharacteristic
741C4D3×#23711yescharacteristic
742C3—21no—
743C3#7891711yescharacteristic, complemented
744C3#8116611yescharacteristic, complemented
745C2—42no—
746C2—62no—
747C2—122no—
748C2D3×#87811yescharacteristic
749C2#1059472611yescharacteristic
750C2#1059474511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenter#102D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594477C2semidirect
3. #10592458C2semidirect
5. C3×#4763C2semidirect
6. #10591495C2semidirect
8. #10591411C2semidirect
9. #10590776C2semidirect
10. #10590767C2semidirect
11. #10590681C2semidirect
12. #10590663C2semidirect
13. #10590471C2semidirect
14. #10590467C2semidirect
15. #10590436C2semidirect
21. #64097C22semidirect
25. C3×#890C22semidirect
29. #63919C22semidirect
36. #63869C22semidirect
43. #63645C22semidirect
44. #63641C22semidirect
45. #63634C22semidirect
49. C3×#817C22semidirect
50. C3×Dic3⋊C8C22semidirect
52. C3×#807C22semidirect
53. #63575C22semidirect
54. #63574C22semidirect
55. #63573C22semidirect
56. #63573C22semidirect
57. #63572C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
84. #4763D3semidirect
99. C3×D3×D4Q8semidirect
172. #890C2×D3semidirect
214. #817C2×D3semidirect
221. Dic3⋊C8C2×D3semidirect
232. #807C2×D3semidirect
310. D3×D4Dic6semidirect
663. C32#3077semidirect
743. C3#78917semidirect
744. C3#81166semidirect

Maximal subgroups

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

subgroupindex
D3×D4×Dic32
#105944772
#105924582
C3×#47702
C3×#47632
#105914952
#105914212
#105914112
#105907762
#105907672
#105906812
#105906632
#105904712
#105904672
#105904362
#811663
#789173