Finite Group Databasebeta

← #11872331

Subgroups — #11872331

Order 1152.

856 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595394C211yesmaximal, characteristic, complemented
2#10595125C211yesmaximal, characteristic, complemented
3#10592862C211yesmaximal, characteristic, complemented
4C3×#5172C211yesmaximal, characteristic, complemented
5C3×#5164C211yesmaximal, characteristic, complemented
6#10591615C211yesmaximal, characteristic, complemented
7#10591588C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10591433C211yesmaximal, characteristic, complemented
10Dic3×#213C211yesmaximal, characteristic, complemented
11#10591415C211yesmaximal, characteristic, complemented
12#10590780C211yesmaximal, characteristic, complemented
13#10590746C211yesmaximal, characteristic, complemented
14#10590697C211yesmaximal, characteristic, complemented
15#10590679C211yesmaximal, characteristic, complemented
16#80072—31nomaximal
17#79812—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22#64149C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×#938C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27#63978—21no—
28#63975—21no—
29#63966—21no—
30#63958—21no—
31#63909C2211yescharacteristic
32#63898—21no—
33#63898C2211yescharacteristic
34#63894C2211yescharacteristic
35Dic3×D12—21no—
36Dic3×D12C2211yescharacteristic
37D3×C4⋊Dic3—21no—
38D3×C4⋊Dic3C2211yescharacteristic
39#63872C2211yescharacteristic
40#63855—21no—
41#63855C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43#63659C2211yescharacteristic
44#63648C2211yescharacteristic
45#63641C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×#815C2211yescharacteristic
53#63575C2211yescharacteristic
54#63574C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5827—31no—
62#5619—31no—
63#5574—31no—
64#5562—31no—
65C3×#449—31no—
66C3×#440—31no—
67#5238—31no—
68#5172D311yescharacteristic, complemented
69#5164D311yescharacteristic, complemented
70#5163—31no—
71#5163—31no—
72#5163—61no—
73#5150—31no—
74Dic3×D8—31no—
75#5034—31no—
76C4×#215—31no—
77C4×#213—31no—
78#4891—31no—
79#4882—31no—
80#4810—31no—
81#4799—31no—
82#4796—31no—
83#4788—31no—
84#4786—31no—
85#4785—31no—
86#4777—31no—
87#4766—31no—
88#4736—31no—
89#4720—31no—
90#4711—31no—
91#4709—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×#239—22no—
100C3×#239—22no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×#626—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C32×SD16—22no—
111C2×C32×C8C2311yescharacteristic
112#3755—22no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#213—22no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140#3714—22no—
141#3119—91noSylow
142C2×C3×#41—31no—
143C2×#239C2×D311yescharacteristic
144C2×C3×SD16—21no—
145C2×C3×SD16C2×D311yescharacteristic
146C2×C3×SD16C2×D311yescharacteristic
147C2×C3×D8—31no—
148C3×#121—31no—
149C3×C4×Q8—31no—
150C3×C4×D4—31no—
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153Q8×Dic3—61no—
154Q8×Dic3C2×D311yescharacteristic
155C2×#215—31no—
156C2×#215—31no—
157C2×#215—61no—
158#940—31no—
159#940—31no—
160#940—61no—
161#939—61no—
162#938—61no—
163#938C2×D311yescharacteristic
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—61no—
167D4×Dic3—61no—
168D4×Dic3C2×D311yescharacteristic
169C2×#213—31no—
170C2×#213C2×D311yescharacteristic
171#930—31no—
172#930—61no—
173#929—61no—
174#926—31no—
175#926—61no—
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—61no—
178C2×D24—31no—
179#895—31no—
180#893—31no—
181#893—31no—
182#893—61no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—61no—
185#890—31no—
186#890—31no—
187#886—61no—
188#884—61no—
189#883—61no—
190#883—61no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—61no—
194#872—31no—
195#872—61no—
196C3×#107—31no—
197C3×#103—31no—
198C3×#103—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×C22⋊C8—31no—
202C3×#97—31no—
203#835C2×D311yescharacteristic
204#835C2×D311yescharacteristic
205#832—31no—
206#832—31no—
207#832—31no—
208#832—61no—
209#832C2×D311yescharacteristic
210#830—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—61no—
215#821C2×D311yescharacteristic
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8C2×D311yescharacteristic
218#818—31no—
219#818C2×D311yescharacteristic
220#817—31no—
221#815C2×D311yescharacteristic
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227C8×Dic3—31no—
228#809—31no—
229#809—31no—
230#808—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C32×Q8—21no—
240C32×Q8#4112yes—
241C32×D4—21no—
242C32×D4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245#638—81no—
246#638—81no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C3×#67—81no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—81no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—24no—
261C3×D12—21no—
262C3×D12#4112yes—
263C3×C4×D3—24no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266#626—81no—
267#624—81no—
268D3×Dic3—81no—
269D3×Dic3—81no—
270D3×Dic3—81no—
271C32×C8—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#540—91no—
276#520—91no—
277#481—91no—
278#480—91no—
279#479—91no—
280#478—91no—
281#460—91no—
282#459—91no—
283#449—31no—
284#449—91no—
285#442—91no—
286#440—31no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C3×#41—62no—
291C3×#41—62no—
292C2×C3×Q8—21no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×D4—21no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4C22×D311yescharacteristic
300C2×C3×D4C22×D311yescharacteristic
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—21no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—121no—
311C2×#67—121no—
312C22×Dic3—21no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316#239—22no—
317#239—22no—
318C2×D12—21no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C3×SD16—22no—
332C3×SD16—22no—
333C3×SD16—42no—
334C3×D8—62no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C42—31no—
347C3×C42—61no—
348#217—21no—
349#217—21no—
350#217—31no—
351#217—31no—
352#217—61no—
353#217—61no—
354#215—62no—
355#215—62no—
356#215—122no—
357#213—22no—
358#213—62no—
359(C2×D3)⋊C4—31no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367C4⋊Dic3—21no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—121no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—31no—
383Dic3⋊C4—31no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387C4×Dic3—21no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—121no—
394C4×Dic3C22×D311yescharacteristic
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8C22×D311yescharacteristic
399C2×C3⋊C8C22×D311yescharacteristic
400D24—62no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32C22×D411yescharacteristic
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3×D3—21no—
409C2×C3×D3—22no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C32×C4—22no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
417C3⋊Dic3—21no—
418C3⋊Dic3—21no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C2×#41—31no—
427C2×SD16—91no—
428C2×SD16D3211yescharacteristic
429C2×D8—31no—
430C2×D8—91no—
431#127—91no—
432#125—91no—
433#123—181no—
434#123—181no—
435#121—31no—
436#121—91no—
437#121—181no—
438#121—181no—
439C4×Q8—31no—
440C4×Q8—91no—
441C4×D4—31no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—181no—
446C4×D4—181no—
447#117—91no—
448#117—181no—
449C2×C4⋊C4—91no—
450C2×C4⋊C4—181no—
451#107—31no—
452#107—91no—
453#106—91no—
454#106—91no—
455C4⋊C8—91no—
456C4⋊C8—91no—
457#103—31no—
458#103—31no—
459#102—31no—
460#102—31no—
461#102—91no—
462#102—91no—
463#102—91no—
464#102—91no—
465C22⋊C8—31no—
466C22⋊C8—91no—
467#97—31no—
468C4×C8—91no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—31no—
472C23×C3—41no—
473C23×C3—61no—
474C22×D3—21no—
475C22×D3—61no—
476C22×D3—61no—
477C22×D3—121no—
478C22×D3D3×D411yescharacteristic
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—22no—
482C3×Q8—41no—
483C3×Q8#23512yes—
484C3×Q8#23712yes—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—32no—
490C3×D4—41no—
491C3×D4—41no—
492C3×D4—64no—
493C3×D4—61no—
494C3×D4—241no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—41no—
502C2×C3×C4—64no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—241no—
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—81no—
512#67—241no—
513#67—241no—
514#67—241no—
515#67—241no—
516#67—241no—
517#67—242no—
518#67—242no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—81no—
531C2×Dic3—121no—
532C2×Dic3—241no—
533C2×Dic3—241no—
534C2×Dic3—241no—
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537C2×Dic3D3×D411yescharacteristic
538D12—24no—
539D12—21no—
540D12—61no—
541D12—61no—
542D12—61no—
543D12—61no—
544D12—121no—
545D12—121no—
546D12—241no—
547D12#23712yes—
548C4×D3—24no—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—241no—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3—241no—
555C4×D3—241no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—121no—
566C2×C32—81no—
567C2×C32#52511yescharacteristic
568C2×C32#57611yescharacteristic
569C2×C32#57711yescharacteristic
570C3⋊D3—81no—
571C3×D3—41no—
572C3×D3—42no—
573#41—62no—
574#41—62no—
575C2×Q8C2×D3211yescharacteristic
576C2×D4—31no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4—91no—
580C2×D4—181no—
581C2×D4—181no—
582C2×D4—181no—
583C2×D4C2×D3211yescharacteristic
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—181no—
591SD16—22no—
592SD16—182no—
593D8—62no—
594D8—182no—
595C2×C8—31no—
596C2×C8—31no—
597C2×C8—91no—
598C2×C8C2×D3211yescharacteristic
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—91no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—91no—
613C22⋊C4—91no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C42—31no—
619C42—61no—
620C42—91no—
621C42—181no—
622C22×C3—21no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—62no—
632C22×C3—61no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3C2×D3×D411yescharacteristic
639C22×C3C2×D3×D411yescharacteristic
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—22no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—241no—
653C2×D3—241no—
654C2×D3—241no—
655C3×C4—22no—
656C3×C4—22no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—42no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4C2×#23511yescharacteristic
667C3×C4C2×#23711yescharacteristic
668C3×C4C2×#23711yescharacteristic
669C3×C4D3×#4111yescharacteristic
670Dic3—21no—
671Dic3—21no—
672Dic3—21no—
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676Dic3—62no—
677Dic3—61no—
678Dic3—61no—
679Dic3—61no—
680Dic3—61no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—241no—
685C32#311911yescharacteristic, complemented, Sylow
686C23—21no—
687C23—31no—
688C23—61no—
689C23—181no—
690Q8—21no—
691Q8#380412yes—
692D4—21no—
693D4—21no—
694D4—32no—
695D4—64no—
696D4—61no—
697D4—181no—
698D4—181no—
699D4—241no—
700D4—721no—
701D4—721no—
702D4—721no—
703C2×C4—21no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—64no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—91no—
714C2×C4—91no—
715C2×C4—181no—
716C2×C4—241no—
717C2×C4—721no—
718C2×C4—721no—
719C2×C4—721no—
720C2×C4—721no—
721C2×C4C22×D3211yescharacteristic
722C8—21no—
723C8—61no—
724C8—61no—
725C8—181no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—81no—
730C2×C3—81no—
731C2×C3—121no—
732C2×C3—122no—
733C2×C3—161no—
734C2×C3#554711yescharacteristic
735C2×C3#558611yescharacteristic
736C2×C3#576911yescharacteristic
737C2×C3#577411yescharacteristic
738C2×C3#577511yescharacteristic
739C2×C3#577811yescharacteristic
740D3—41no—
741D3—42no—
742D3—241no—
743D3—241no—
744D3—481no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—62no—
749C22—61no—
750C22—61no—
751C22—61no—
752C22—121no—
753C22—121no—
754C22—361no—
755C22—361no—
756C22—361no—
757C22D32×D411yescharacteristic
758C4—22no—
759C4—61no—
760C4—61no—
761C4—61no—
762C4—121no—
763C4—121no—
764C4—121no—
765C4—181no—
766C4—181no—
767C4—361no—
768C4D3×#23711yescharacteristic
769C4C2×#380411yescharacteristic
770C3—21no—
771C3#7981211yescharacteristic, complemented
772C3#8007211yescharacteristic, complemented
773C2—81no—
774C2—121no—
775C2—122no—
776C2—721no—
777C2#1059475411yescharacteristic
778C2#1059475511yescharacteristic
779C2#1059512911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10595394C2semidirect
2. #10595125C2semidirect
3. #10592862C2semidirect
4. C3×#5172C2semidirect
5. C3×#5164C2semidirect
6. #10591615C2semidirect
7. #10591588C2semidirect
8. #10591536C2semidirect
9. #10591433C2semidirect
10. Dic3×#213C2semidirect
11. #10591415C2semidirect
12. #10590780C2semidirect
13. #10590746C2semidirect
14. #10590697C2semidirect
15. #10590679C2semidirect
68. #5172D3semidirect
69. #5164D3semidirect
685. C32#3119semidirect
771. C3#79812semidirect
772. C3#80072semidirect

Maximal subgroups

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

subgroupindex
#105953942
#105951252
#105928622
C3×#51722
C3×#51642
#105916152
#105915882
#105915362
#105914332
Dic3×#2132
#105914152
#105907802
#105907462
#105906972
#105906792
#800723
#798123