Finite Group Databasebeta

← #11870516

Subgroups — #11870516

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×D4C211yesmaximal, characteristic
2#10593873C211yesmaximal, characteristic, complemented
3C4×#3754C211yesmaximal, characteristic, complemented
4C3×C4×#214C211yesmaximal, characteristic, complemented
5#10591489C211yesmaximal, characteristic, complemented
6#10591459C211yesmaximal, characteristic
7#10591458C211yesmaximal, characteristic
8#10591408C211yesmaximal, characteristic, complemented
9#10590559C211yesmaximal, characteristic, complemented
10#10590558C211yesmaximal, characteristic, complemented
11#10590516C211yesmaximal, characteristic, complemented
12#10590426C211yesmaximal, characteristic, complemented
13C4×#3716C211yesmaximal, characteristic, complemented
14C4×#3715C211yesmaximal, characteristic, complemented
15#10590261C211yesmaximal, characteristic, complemented
16#82314—31nomaximal
17#79651—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C22×C3×C4×D3—21no—
20C32×C4×D4C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22C4×#634C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C3×C4×#67—21no—
26C3×#893C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×#67⋊C4—21no—
29C3×D3×C22⋊C4—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C42×D3C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic, complemented
33#63918C2211yescharacteristic, complemented
34C4×#627—21no—
35#63867—21no—
36#63866C2211yescharacteristic, complemented
37#63857C2211yescharacteristic
38#63856C2211yescharacteristic
39#63855—21no—
40#63851—21no—
41C2×#3716C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43#63659C2211yescharacteristic
44#63637C2211yescharacteristic, complemented
45#63635C2211yescharacteristic, complemented
46C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#810C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50C3×C4×C3⋊C8C2211yescharacteristic, complemented
51#63574C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C2×C3×C4×D4—31no—
62#5578—31no—
63C4×D3×D4D311yescharacteristic
64#5470—31no—
65C3×C4×SD16—31no—
66#5218—31no—
67#5218—31no—
68#5169—31no—
69#5162—31no—
70C4×#215—31no—
71#5019—31no—
72#5019—31no—
73C4×#214—31no—
74C4×#214—31no—
75C4×#214—31no—
76C4×#214—31no—
77C4×#214—61no—
78C4×#214D311yescharacteristic, complemented
79#5008—31no—
80#5008—31no—
81#4971—31no—
82#4971—31no—
83#4925—31no—
84#4870—31no—
85#4862—31no—
86#4818—31no—
87#4805—31no—
88#4776—31no—
89#4761—31no—
90C4×#204—31no—
91#4685—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×D3×D4—22no—
99C3×D3×D4—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—44no—
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C42C2311yescharacteristic
113#3754—22no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#214—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3D411yescharacteristic
129C3×C4×Dic3D411yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3716—22no—
141#3715—22no—
142#3101—91noSylow
143C22×C3×D4—31no—
144C23×C3×C4—61no—
145C2×D3×D4C2×D311yescharacteristic
146C22×C4×D3—21no—
147C2×C3×SD16—31no—
148C3×C4×Q8—31no—
149C3×C4×D4—21no—
150C3×C4×D4—31no—
151C3×C4×D4—31no—
152C3×C4×D4—31no—
153C3×C4×D4—61no—
154C3×C4×D4—61no—
155C3×C4×D4C2×D311yescharacteristic
156C3×C4×D4C2×D311yescharacteristic
157C2×C3×C4⋊C4—31no—
158C2×C3×C22⋊C4—61no—
159C2×C3×C42—31no—
160#946—31no—
161#944—31no—
162C2×#215—31no—
163D4×Dic3C2×D311yescharacteristic
164C2×#214—31no—
165C2×#214—31no—
166C2×#214—31no—
167C2×#214—31no—
168C2×#214—61no—
169C2×#214C2×D311yescharacteristic
170C4×#67—21no—
171#926—61no—
172#924—31no—
173#924—31no—
174#924—61no—
175C2×#204—31no—
176#897—31no—
177#896—61no—
178#893C2×D311yescharacteristic
179D3×C4⋊C4C2×D311yescharacteristic
180#889—61no—
181#888—31no—
182#67⋊C4—21no—
183D3×C22⋊C4—21no—
184C4×D12C2×D311yescharacteristic
185#872—61no—
186C42×D3C2×D311yescharacteristic
187#870—61no—
188#869—31no—
189#869—31no—
190C4×Dic6—31no—
191C4×Dic6—31no—
192C4×Dic6—61no—
193C4×Dic6—61no—
194C4×Dic6—61no—
195C4×Dic6C2×D311yescharacteristic, complemented
196C3×#106—31no—
197C3×#103—31no—
198C3×#102—31no—
199C3×C4×C8—31no—
200#835—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—61no—
206#832C2×D311yescharacteristic
207#830—31no—
208#830—31no—
209#821—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212#817—31no—
213#816—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—61no—
221#810C2×D311yescharacteristic, complemented
222#809—31no—
223#808—31no—
224#808—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#808—61no—
229#808C2×D311yescharacteristic, complemented
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—31no—
232C4×C3⋊C8—31no—
233C4×C3⋊C8—31no—
234C4×C3⋊C8—61no—
235C4×C3⋊C8C2×D311yescharacteristic, complemented
236C23×C32—21no—
237C22×C3×D3—24no—
238C22×C3×D3—21no—
239C22×C3×D3—42no—
240C22×C3×D3—42no—
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4#4112yes—
244C2×C32×C4—21no—
245C2×C32×C4—42no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251#634—21no—
252#634—21no—
253C3×#67—24no—
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×D12—21no—
262C3×D12#4112yes—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—41no—
266C3×C4×D3—42no—
267C3×C4×D3—42no—
268C3×C4×D3—42no—
269C3×C4×D3SD1614yescomplemented
270C3×Dic6—21no—
271C3×Dic6—21no—
272#627—42no—
273C3⋊(C3⋊C8)—21no—
274C3⋊(C3⋊C8)—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#533—91no—
278C2×C4×D4—31no—
279#483—91no—
280#483—91no—
281#476—91no—
282#476—91no—
283#461—91no—
284#461—91no—
285#450—91no—
286#450—91no—
287C4×SD16—31no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291#431—91no—
292C24×C3—61no—
293C23×D3—21no—
294C2×C3×Q8—31no—
295C2×C3×D4—21no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C2×C3×D4—62no—
299C2×C3×D4—62no—
300C2×C3×D4C22×D311yescharacteristic
301C2×C3×D4C22×D311yescharacteristic
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—41no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—124no—
313C2×#67—21no—
314C22×Dic3—21no—
315D3×D4—22no—
316D3×D4—22no—
317C2×D12C22×D311yescharacteristic
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×C4×D3—44no—
322C2×C4×D3#6711yescharacteristic
323C2×C4×D3#6711yescharacteristic
324C2×C4×D3C22×D311yescharacteristic
325C2×Dic6—31no—
326C2×Dic6—31no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6C22×D311yescharacteristic
331C3×SD16—62no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C22⋊C4—21no—
342C3×C22⋊C4—21no—
343C3×C22⋊C4—41no—
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×C42C22×D311yescharacteristic
353C3×C42C22×D311yescharacteristic
354#217—21no—
355#217—61no—
356#217—61no—
357#215—62no—
358#214—22no—
359#214—62no—
360#214—62no—
361#214—64no—
362#214—62no—
363#214—62no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—121no—
388C4×Dic3—21no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—121no—
392C4×Dic3#6711yescharacteristic
393C4×Dic3#6711yescharacteristic
394C4×Dic3C22×D311yescharacteristic
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403#204—62no—
404C22×C32—22no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32C22×D411yescharacteristic
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—22no—
411C2×C3×D3—48no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3C2×SD1612yes—
415C32×C4—21no—
416C32×C4—41no—
417C32×C4C2×SD1612yes—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
420C3⋊Dic3—41no—
421C3⋊Dic3—41no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3C2×SD1612yes—
428C22×D4—31no—
429C23×C4—61no—
430C2×SD16—31no—
431C2×SD16—91no—
432C2×SD16—91no—
433C2×SD16—91no—
434C4⋊Q8—91no—
435C4⋊Q8—91no—
436#125—181no—
437C22⋊Q8—91no—
438C22⋊Q8—91no—
439C22⋊Q8—181no—
440C4×Q8—31no—
441C4×Q8—91no—
442C4×Q8—181no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4—61no—
447C4×D4—61no—
448C4×D4D3211yescharacteristic
449#117—181no—
450C2×C4⋊C4—31no—
451C2×C22⋊C4—61no—
452C2×C42—31no—
453#106—31no—
454#106—91no—
455#106—91no—
456#106—91no—
457C4⋊C8—91no—
458C4⋊C8—91no—
459#103—31no—
460#103—91no—
461#103—91no—
462#103—91no—
463#102—31no—
464#102—91no—
465#102—91no—
466#102—91no—
467C22⋊C8—91no—
468C22⋊C8—91no—
469C4×C8—31no—
470C4×C8—91no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—31no—
474C23×C3—41no—
475C23×C3—64no—
476C23×C3—61no—
477C23×C3—122no—
478C23×C3—122no—
479C22×D3—24no—
480C22×D3—21no—
481C22×D3—42no—
482C22×D3—42no—
483C22×D3C2×#6711yescharacteristic
484C3×Q8—61no—
485C3×Q8—61no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—22no—
489C3×D4—32no—
490C3×D4—41no—
491C3×D4—64no—
492C3×D4—61no—
493C3×D4#23512yes—
494C3×D4#23512yes—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—31no—
501C2×C3×C4—34no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—42no—
506C2×C3×C4—42no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—82no—
513C2×C3×C4—121no—
514C2×C3×C4—122no—
515C2×C3×C4—122no—
516C2×C3×C4—122no—
517C2×C3×C4—122no—
518C2×C3×C4D3×D411yescharacteristic
519C2×C3×C4D3×D411yescharacteristic
520C2×C3×C4C2×#6711yescharacteristic
521C2×C3×C4C2×#6711yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—24no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—42no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3C2×#6711yescharacteristic
536C2×Dic3C2×#6711yescharacteristic
537C2×Dic3C2×#6711yescharacteristic
538D12—21no—
539D12#23512yes—
540C4×D3—21no—
541C4×D3—21no—
542C4×D3—41no—
543C4×D3—42no—
544C4×D3—42no—
545C4×D3—42no—
546C4×D3#21414yescomplemented
547Dic6—21no—
548Dic6—21no—
549Dic6—62no—
550Dic6—61no—
551Dic6—61no—
552Dic6—61no—
553Dic6—61no—
554Dic6—121no—
555Dic6—122no—
556Dic6—122no—
557C3×C8—61no—
558C3×C8—61no—
559C3⋊C8—21no—
560C3⋊C8—21no—
561C3⋊C8—62no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—61no—
566C3⋊C8—121no—
567C2×C32—42no—
568C2×C32#52511yescharacteristic
569C2×C32C22×SD1611yescharacteristic
570C2×C32#57511yescharacteristic
571C3×D3—22no—
572C3×D3—42no—
573C24—61no—
574C2×Q8—31no—
575C2×Q8—91no—
576C2×Q8—181no—
577C2×D4—31no—
578C2×D4—61no—
579C2×D4—62no—
580C2×D4—62no—
581C2×D4C2×D3211yescharacteristic
582C22×C4—21no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—124no—
591SD16—62no—
592SD16—182no—
593SD16—182no—
594SD16—182no—
595C2×C8—31no—
596C2×C8—31no—
597C2×C8—91no—
598C2×C8—91no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4C2×D3211yescharacteristic
611C22⋊C4—21no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C42—31no—
618C42—31no—
619C42—31no—
620C42—61no—
621C42—181no—
622C42C2×D3211yescharacteristic
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—21no—
626C22×C3—32no—
627C22×C3—42no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—62no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—128no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C22×#6711yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—22no—
645C2×D3—48no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3C2×#21412yes—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—22no—
654C3×C4—32no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—81no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4D3×SD1612yes—
665C3×C4C2×#21412yes—
666C3×C4C2×#23511yescharacteristic
667C3×C4C2×#23511yescharacteristic
668C3×C4C2×#23511yescharacteristic
669C3×C4D3×#4111yescharacteristic
670Dic3—21no—
671Dic3—21no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3—122no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3C2×#21412yes—
682C32#310111yescharacteristic, complemented, Sylow
683C23—21no—
684C23—31no—
685C23—64no—
686C23—61no—
687C23—122no—
688C23—122no—
689Q8—61no—
690Q8—61no—
691Q8—181no—
692Q8—181no—
693Q8—362no—
694D4—21no—
695D4—32no—
696D4—64no—
697D4—61no—
698D4#379812yes—
699C2×C4—21no—
700C2×C4—31no—
701C2×C4—34no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—42no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—121no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4—181no—
716C2×C4—181no—
717C2×C4D3×#6711yescharacteristic
718C2×C4D3×#6711yescharacteristic
719C2×C4C22×D3211yescharacteristic
720C8—61no—
721C8—61no—
722C8—181no—
723C8—181no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—42no—
728C2×C3—42no—
729C2×C3—62no—
730C2×C3—82no—
731C2×C3—122no—
732C2×C3#554711yescharacteristic
733C2×C3C2×D3×SD1611yescharacteristic
734C2×C3#576811yescharacteristic
735C2×C3#579111yescharacteristic
736C2×C3C22×#21411yescharacteristic
737C2×C3#582211yescharacteristic
738D3—22no—
739D3—42no—
740C22—22no—
741C22—32no—
742C22—41no—
743C22—41no—
744C22—61no—
745C22—61no—
746C22—62no—
747C22—128no—
748C22—121no—
749C22—121no—
750C22C2×D3×#6711yescharacteristic
751C4—21no—
752C4—32no—
753C4—41no—
754C4—61no—
755C4—61no—
756C4—121no—
757C4—121no—
758C4—121no—
759C4—361no—
760C4—361no—
761C4D3×#21412yes—
762C4C2×#379811yescharacteristic
763C4D3×#23511yescharacteristic
764C3—21no—
765C3#7965111yescharacteristic, complemented
766C3#8231411yescharacteristic, complemented
767C2—42no—
768C2—62no—
769C2—122no—
770C2#1059500211yescharacteristic
771C2C2×D3×#21411yescharacteristic
772C2#1059545311yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC4×D4D32
hypocenterC32#3101
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593873C2semidirect
3. C4×#3754C2semidirect
4. C3×C4×#214C2semidirect
5. #10591489C2semidirect
8. #10591408C2semidirect
9. #10590559C2semidirect
10. #10590558C2semidirect
11. #10590516C2semidirect
12. #10590426C2semidirect
13. C4×#3716C2semidirect
14. C4×#3715C2semidirect
15. #10590261C2semidirect
22. C4×#634C22semidirect
32. C3×C4×Dic6C22semidirect
33. #63918C22semidirect
36. #63866C22semidirect
44. #63637C22semidirect
45. #63635C22semidirect
46. C4×C3⋊(C3⋊C8)C22semidirect
48. C3×#810C22semidirect
49. C3×#808C22semidirect
50. C3×C4×C3⋊C8C22semidirect
51. #63574C22semidirect
52. #63573C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
56. #63565C22semidirect
78. C4×#214D3semidirect
195. C4×Dic6C2×D3semidirect
221. #810C2×D3semidirect
229. #808C2×D3semidirect
235. C4×C3⋊C8C2×D3semidirect
269. C3×C4×D3SD16semidirect
546. C4×D3#214semidirect
682. C32#3101semidirect
765. C3#79651semidirect
766. C3#82314semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×D42
#105938732
C4×#37542
C3×C4×#2142
#105914892
#105914592
#105914582
#105914082
#105905592
#105905582
#105905162
#105904262
C4×#37162
C4×#37152
#105902612
#823143
#796513