Finite Group Databasebeta

← #11870726

Subgroups — #11870726

Order 1152.

920 conjugacy classes of subgroups.

The subgroup lattice has 777 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×Q8×Dic3C211yesmaximal, characteristic, complemented
2#10595131C211yesmaximal, characteristic
3#10592862C211yesmaximal, characteristic, complemented
4C3×#5170C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6#10591630C211yesmaximal, characteristic, complemented
7#10591584C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10591444C211yesmaximal, characteristic, complemented
10Dic3×#214C211yesmaximal, characteristic, complemented
11#10591415C211yesmaximal, characteristic, complemented
12#10590816C211yesmaximal, characteristic, complemented
13#10590792C211yesmaximal, characteristic, complemented
14#10590677C211yesmaximal, characteristic, complemented
15#10590655C211yesmaximal, characteristic, complemented
16#80028—31nomaximal
17#79653—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3804—21no—
20C2×C32×SD16C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23#64149C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C3×#938C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28#63971—21no—
29#63953—21no—
30#63952—21no—
31#63919C2211yescharacteristic
32#63909C2211yescharacteristic
33#63894C2211yescharacteristic
34D3×C4⋊Dic3—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36C4×D3×Dic3—21no—
37C4×D3×Dic3C2211yescharacteristic
38#63843—21no—
39#63843C2211yescharacteristic
40Dic3×Dic6—21no—
41Dic3×Dic6C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43#63659C2211yescharacteristic
44#63648C2211yescharacteristic
45#63641C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×C8×Dic3C2211yescharacteristic
53#63574C2211yescharacteristic
54#63573C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C2×Q8×Dic3—31no—
62#5596—31no—
63C4×D3×Q8—31no—
64#5548—31no—
65C3×#448—31no—
66C3×C4×SD16—31no—
67#5227—31no—
68#5170D311yescharacteristic, complemented
69#5163—31no—
70#5163—31no—
71#5163—31no—
72#5163—61no—
73Dic3×SD16—31no—
74Dic3×SD16D311yescharacteristic, complemented
75#5034—31no—
76C4×#215—31no—
77C4×#214—31no—
78#4863—31no—
79#4854—31no—
80#4806—31no—
81#4791—31no—
82#4791—31no—
83#4791—31no—
84#4788—31no—
85#4788—31no—
86#4777—31no—
87#4762—31no—
88#4735—31no—
89#4718—31no—
90C4×#204—31no—
91#4685—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×D3×Q8—22no—
100C3×D3×Q8—22no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#626—21no—
107C2×#624—21no—
108#3804—44no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3D411yescharacteristic
111C2×D3×Dic3D411yescharacteristic
112C32×SD16—22no—
113C2×C32×C8C2311yescharacteristic
114#3755—22no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#217—21no—
122C3×#214—22no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137Dic32—21no—
138Dic32—21no—
139Dic32D411yescharacteristic
140Dic32D411yescharacteristic
141#3717—22no—
142#3103—91noSylow
143C22×C3×Q8—31no—
144C2×D3×Q8C2×D311yescharacteristic
145C2×#237—61no—
146C2×#235—61no—
147C2×C3×SD16—21no—
148C2×C3×SD16—31no—
149C2×C3×SD16C2×D311yescharacteristic
150C2×C3×SD16C2×D311yescharacteristic
151C3×#121—31no—
152C3×C4×Q8—31no—
153C3×C4×D4—31no—
154Q8×Dic3—31no—
155Q8×Dic3—31no—
156Q8×Dic3—31no—
157Q8×Dic3—31no—
158Q8×Dic3—61no—
159Q8×Dic3—61no—
160Q8×Dic3—61no—
161Q8×Dic3C2×D311yescharacteristic
162C2×#215—31no—
163C2×#215—31no—
164C2×#215—31no—
165C2×#215—61no—
166#940—31no—
167#940—31no—
168#940—61no—
169#939—61no—
170#938C2×D311yescharacteristic
171D4×Dic3C2×D311yescharacteristic
172C2×#214C2×D311yescharacteristic
173#930—31no—
174C4×#67—61no—
175C2×C4⋊Dic3—31no—
176C2×C4⋊Dic3—61no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—61no—
179C2×#204—31no—
180#895—31no—
181#893—31no—
182D3×C4⋊C4—31no—
183D3×C4⋊C4—61no—
184#888—31no—
185#888—31no—
186#887—31no—
187#887—61no—
188#885—61no—
189#885—61no—
190#884—61no—
191#67⋊C4—61no—
192C4×D12—31no—
193C42×D3—31no—
194C42×D3—61no—
195C4×Dic6—31no—
196C4×Dic6—61no—
197C3×#106—31no—
198C3×#103—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×C22⋊C8—31no—
203C3×C4×C8—31no—
204#835—31no—
205#835C2×D311yescharacteristic
206#835C2×D311yescharacteristic
207#832—31no—
208#832—31no—
209#832—61no—
210#832C2×D311yescharacteristic
211#830—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—61no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8C2×D311yescharacteristic
218#817—31no—
219#817—31no—
220#817C2×D311yescharacteristic
221#816C2×D311yescharacteristic
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227C8×Dic3—31no—
228C8×Dic3C2×D311yescharacteristic
229#810—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#808—31no—
234#808—31no—
235C4×C3⋊C8—31no—
236C23×C32—21no—
237C22×C3⋊D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C32×Q8—21no—
240C32×Q8#4112yescomplemented
241C32×D4—21no—
242C32×D4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245#638—42no—
246#638—42no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C3×#67—42no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×C4×D3—24no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×Dic6—24no—
265C3×Dic6—21no—
266C3×Dic6#4112yescomplemented
267#627—42no—
268#626—42no—
269#624—42no—
270D3×Dic3—41no—
271D3×Dic3—42no—
272D3×Dic3SD1614yescomplemented
273C32×C8—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#532—91no—
278C2×C4×Q8—91no—
279#481—91no—
280#481—91no—
281#475—91no—
282#475—91no—
283#460—91no—
284#460—91no—
285#448—31no—
286#448—91no—
287C4×SD16—31no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291#431—91no—
292C2×C3×Q8—21no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C2×C3×Q8—62no—
296C2×C3×Q8—62no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×D4—21no—
300C2×C3×D4—61no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C2×#67—21no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—121no—
313C2×#67—121no—
314C22×Dic3—21no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—61no—
318D3×Q8—22no—
319D3×Q8—22no—
320#237—124no—
321#235—124no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—61no—
325C2×D12—61no—
326C2×C4×D3—21no—
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—21no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6C22×D311yescharacteristic
337C3×SD16—22no—
338C3×SD16—22no—
339C3×SD16—42no—
340C3×SD16—62no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—31no—
353C3×C42—61no—
354#217—21no—
355#217—21no—
356#215—62no—
357#215—62no—
358#215—62no—
359#215—122no—
360#214—22no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365C4⋊Dic3—21no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—121no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383C4×Dic3—21no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—121no—
398C4×Dic3C22×D311yescharacteristic
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404#204—62no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32C22×D411yescharacteristic
409C2×C3⋊D3—41no—
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3C2×SD1612yes—
415C32×C4—22no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—21no—
419C3⋊Dic3—41no—
420C3⋊Dic3C2×SD1612yes—
421C3×Dic3—21no—
422C3×Dic3—22no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3C2×SD1612yes—
428C2×#41—181no—
429C22×Q8—31no—
430C2×SD16—31no—
431C2×SD16—91no—
432C2×SD16—91no—
433C2×SD16D3211yescharacteristic
434C4⋊Q8—91no—
435#127—91no—
436#124—181no—
437#121—31no—
438#121—91no—
439#121—181no—
440C4×Q8—31no—
441C4×Q8—91no—
442C4×Q8—91no—
443C4×Q8—91no—
444C4×Q8—181no—
445C4×Q8—181no—
446C4×D4—31no—
447C4×D4—91no—
448C4×D4—181no—
449C2×C4⋊C4—91no—
450C2×C4⋊C4—181no—
451C2×C42—91no—
452C2×C42—181no—
453#106—31no—
454#106—91no—
455#106—91no—
456#106—91no—
457C4⋊C8—91no—
458C4⋊C8—91no—
459#103—31no—
460#103—31no—
461#103—31no—
462#103—91no—
463#102—31no—
464#102—91no—
465#102—91no—
466#102—91no—
467C22⋊C8—31no—
468C22⋊C8—91no—
469C4×C8—31no—
470C4×C8—91no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—31no—
474C23×C3—41no—
475C22×D3—61no—
476C22×D3—61no—
477C22×D3—121no—
478C22×D3D3×D411yescharacteristic
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—22no—
482C3×Q8—32no—
483C3×Q8—41no—
484C3×Q8—64no—
485C3×Q8—61no—
486C3×Q8#23512yescomplemented
487C3×Q8#23712yescomplemented
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—41no—
493C3×D4—41no—
494C3×D4—122no—
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—61no—
509C2×C3×C4—122no—
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—42no—
513#67—122no—
514#67—122no—
515#67—122no—
516#67—122no—
517#67—122no—
518#67—242no—
519#67—242no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—34no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—42no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—122no—
537C2×Dic3D3×D411yescharacteristic
538C2×Dic3D3×D411yescharacteristic
539C2×Dic3D3×D411yescharacteristic
540D12—61no—
541D12—61no—
542D12—61no—
543D12—61no—
544D12—121no—
545D12—121no—
546D12—122no—
547C4×D3—24no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—34no—
551C4×D3—122no—
552C4×D3—121no—
553C4×D3—122no—
554C4×D3—122no—
555Dic6—24no—
556Dic6—21no—
557Dic6—122no—
558Dic6—122no—
559Dic6#23712yescomplemented
560C3×C8—21no—
561C3×C8—21no—
562C3×C8—41no—
563C3×C8—61no—
564C3×C8—61no—
565C3⋊C8—21no—
566C3⋊C8—21no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—121no—
570C2×C32—81no—
571C2×C32#52511yescharacteristic
572C2×C32C22×SD1611yescharacteristic
573C2×C32#57511yescharacteristic
574C3⋊D3—81no—
575C3×D3—22no—
576#41—364no—
577C2×Q8—31no—
578C2×Q8—61no—
579C2×Q8—62no—
580C2×Q8—62no—
581C2×Q8—181no—
582C2×Q8C2×D3211yescharacteristic
583C2×D4—61no—
584C2×D4—91no—
585C2×D4—181no—
586C2×D4—181no—
587C2×D4—181no—
588C2×D4C2×D3211yescharacteristic
589C22×C4—31no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—91no—
593C22×C4—91no—
594C22×C4—181no—
595C22×C4—181no—
596SD16—22no—
597SD16—62no—
598SD16—182no—
599SD16—182no—
600C2×C8—31no—
601C2×C8—31no—
602C2×C8—91no—
603C2×C8C2×D3211yescharacteristic
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—61no—
608C4⋊C4—91no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C42—31no—
619C42—61no—
620C42—91no—
621C42—91no—
622C42—91no—
623C42—181no—
624C42—181no—
625C42—181no—
626C22×C3—21no—
627C22×C3—32no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C2×D3×D411yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—241no—
650C2×D3—241no—
651C2×D3—241no—
652C2×D3D3×SD1612yes—
653C3×C4—22no—
654C3×C4—22no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—32no—
658C3×C4—42no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—62no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4C2×#23511yescharacteristic
666C3×C4C2×#23711yescharacteristic
667C3×C4C2×#23711yescharacteristic
668C3×C4D3×#4111yescharacteristic
669Dic3—21no—
670Dic3—21no—
671Dic3—22no—
672Dic3—32no—
673Dic3—32no—
674Dic3—41no—
675Dic3—41no—
676Dic3—41no—
677Dic3—62no—
678Dic3—61no—
679Dic3—61no—
680Dic3—121no—
681Dic3—121no—
682Dic3—121no—
683Dic3—241no—
684Dic3D3×SD1612yes—
685C32#310311yescharacteristic, complemented, Sylow
686C23—21no—
687C23—31no—
688C23—181no—
689Q8—21no—
690Q8—32no—
691Q8—64no—
692Q8—61no—
693Q8—362no—
694Q8#380412yescomplemented
695D4—21no—
696D4—21no—
697D4—122no—
698D4—181no—
699D4—181no—
700D4—362no—
701D4—362no—
702D4—362no—
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—61no—
714C2×C4—94no—
715C2×C4—91no—
716C2×C4—91no—
717C2×C4—122no—
718C2×C4—181no—
719C2×C4—362no—
720C2×C4—361no—
721C2×C4—362no—
722C2×C4C22×D3211yescharacteristic
723C8—21no—
724C8—61no—
725C8—61no—
726C8—181no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—62no—
731C2×C3—81no—
732C2×C3—81no—
733C2×C3—161no—
734C2×C3#554711yescharacteristic
735C2×C3#558611yescharacteristic
736C2×C3C2×D3×SD1611yescharacteristic
737C2×C3C2×D3×SD1611yescharacteristic
738C2×C3#576811yescharacteristic
739C2×C3#577711yescharacteristic
740D3—22no—
741D3—241no—
742D3—241no—
743D3—481no—
744C22—32no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—61no—
749C22—61no—
750C22—361no—
751C22—361no—
752C22—361no—
753C22D32×D411yescharacteristic
754C4—22no—
755C4—32no—
756C4—61no—
757C4—62no—
758C4—61no—
759C4—92no—
760C4—121no—
761C4—121no—
762C4—121no—
763C4—181no—
764C4—361no—
765C4D3×#23711yescharacteristic
766C4C2×#380411yescharacteristic
767C3—21no—
768C3#7965311yescharacteristic, complemented
769C3#8002811yescharacteristic, complemented
770C2—62no—
771C2—81no—
772C2—721no—
773C2D32×SD1611yescharacteristic
774C2#1059474611yescharacteristic
775C2#1059512911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595131C2
hypercenterC2×SD16D32
hypocenterC32#3103
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. D3×Q8×Dic3C2semidirect
3. #10592862C2semidirect
4. C3×#5170C2semidirect
5. C3×Dic3×SD16C2semidirect
6. #10591630C2semidirect
7. #10591584C2semidirect
8. #10591536C2semidirect
9. #10591444C2semidirect
10. Dic3×#214C2semidirect
11. #10591415C2semidirect
12. #10590816C2semidirect
13. #10590792C2semidirect
14. #10590677C2semidirect
15. #10590655C2semidirect
68. #5170D3semidirect
74. Dic3×SD16D3semidirect
240. C32×Q8#41semidirect
266. C3×Dic6#41semidirect
272. D3×Dic3SD16semidirect
486. C3×Q8#235semidirect
487. C3×Q8#237semidirect
559. Dic6#237semidirect
685. C32#3103semidirect
694. Q8#3804semidirect
768. C3#79653semidirect
769. C3#80028semidirect

Maximal subgroups

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

subgroupindex
D3×Q8×Dic32
#105951312
#105928622
C3×#51702
C3×Dic3×SD162
#105916302
#105915842
#105915362
#105914442
Dic3×#2142
#105914152
#105908162
#105907922
#105906772
#105906552
#800283
#796533