Finite Group Databasebeta

← #11870725

Subgroups — #11870725

Order 1152.

917 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×Q8×Dic3C211yesmaximal, characteristic, complemented
2#10595133C211yesmaximal, characteristic
3SD16×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#5170C211yesmaximal, characteristic, complemented
5C3×#5163C211yesmaximal, characteristic, complemented
6#10591583C211yesmaximal, characteristic, complemented
7#10591571C211yesmaximal, characteristic, complemented
8#10591544C211yesmaximal, characteristic, complemented
9#10591445C211yesmaximal, characteristic, complemented
10#10591438C211yesmaximal, characteristic, complemented
11#10591415C211yesmaximal, characteristic, complemented
12#10590803C211yesmaximal, characteristic, complemented
13#10590742C211yesmaximal, characteristic, complemented
14#10590676C211yesmaximal, characteristic, complemented
15#10590656C211yesmaximal, characteristic, complemented
16#80360—31nomaximal
17#80028—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3805—21no—
20C2×C32×SD16C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22D4×C3⋊Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#940C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28#67⋊Dic3—21no—
29#63970—21no—
30#63959—21no—
31#63918C2211yescharacteristic
32#63908C2211yescharacteristic
33#63898C2211yescharacteristic
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×#3715C2211yescharacteristic
43#63662C2211yescharacteristic
44#63659C2211yescharacteristic
45#63644C2211yescharacteristic
46C8×C3⋊Dic3C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53#63574C2211yescharacteristic
54#63573C2211yescharacteristic
55#63573C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63566C2211yescharacteristic
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic
61C2×Q8×Dic3—31no—
62#5716—31no—
63#5596—31no—
64C4×D3×Q8—31no—
65C3×#460—31no—
66C3×#448—31no—
67#5227—31no—
68#5170—31no—
69#5170D311yescharacteristic, complemented
70#5163—31no—
71#5163D311yescharacteristic, complemented
72Dic3×SD16—31no—
73Dic3×SD16—31no—
74Dic3×SD16—31no—
75Dic3×SD16—31no—
76Dic3×SD16—61no—
77#5075—31no—
78#5034—31no—
79#5020—31no—
80#4851—31no—
81#4833—31no—
82#4791—31no—
83#4791—31no—
84#4788—31no—
85#4788—31no—
86#4777—31no—
87#4777—31no—
88#4758—31no—
89#4758—31no—
90#4735—31no—
91#4718—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×D3×Q8—22no—
99C3×D3×Q8—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#625—21no—
107#3805—44no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3D411yescharacteristic
111C2×D3×Dic3D411yescharacteristic
112C32×SD16—22no—
113C2×C32×C8C2311yescharacteristic
114#3757—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×#215—22no—
123C3×#214—22no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139Dic32D411yescharacteristic
140Dic32D411yescharacteristic
141#3715—22no—
142#3103—91noSylow
143C22×C3×Q8—31no—
144C2×D3×Q8C2×D311yescharacteristic
145C2×#237—61no—
146C2×#237—61no—
147C2×C3×SD16—21no—
148C2×C3×SD16—31no—
149C2×C3×SD16—31no—
150C2×C3×SD16C2×D311yescharacteristic
151C2×C3×SD16C2×D311yescharacteristic
152C3×#127—31no—
153C3×#121—31no—
154C3×C4×Q8—31no—
155Q8×Dic3—31no—
156Q8×Dic3—31no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159Q8×Dic3—61no—
160Q8×Dic3—61no—
161Q8×Dic3—61no—
162Q8×Dic3C2×D311yescharacteristic
163C2×#215—31no—
164C2×#215C2×D311yescharacteristic
165#940C2×D311yescharacteristic
166#939—61no—
167#938—31no—
168#938—61no—
169#938C2×D311yescharacteristic
170#936—61no—
171D4×Dic3—31no—
172D4×Dic3—31no—
173D4×Dic3—31no—
174D4×Dic3—61no—
175D4×Dic3—61no—
176C2×#214—31no—
177C2×#214C2×D311yescharacteristic
178#930—31no—
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3—61no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3—61no—
183#893—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—61no—
186#888—31no—
187#887—31no—
188#887—61no—
189#885—61no—
190#67⋊C4—61no—
191C42×D3—31no—
192C42×D3—61no—
193#869—31no—
194C4×Dic6—31no—
195C4×Dic6—61no—
196C3×C4⋊C8—31no—
197C3×#103—31no—
198C3×#103—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×C22⋊C8—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—61no—
206#835C2×D311yescharacteristic
207#832—31no—
208#832—31no—
209#832—31no—
210#832—61no—
211#832C2×D311yescharacteristic
212#830—31no—
213#821—31no—
214#821C2×D311yescharacteristic
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8C2×D311yescharacteristic
217#817—31no—
218#817—31no—
219#817—31no—
220#817—31no—
221#817—61no—
222#816—31no—
223#816C2×D311yescharacteristic
224Dic3⋊C8—31no—
225Dic3⋊C8C2×D311yescharacteristic
226C8×Dic3—31no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229C8×Dic3—31no—
230C8×Dic3—61no—
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
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—42no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C3×#67—42no—
251C3×#67—42no—
252C3×#67—42no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
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#625—42no—
269D3×Dic3—41no—
270D3×Dic3—42no—
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—31no—
284#460—91no—
285#448—31no—
286#448—91no—
287C4×SD16—91no—
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—31no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C2×#67—21no—
309C2×#67—21no—
310C2×#67—21no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—121no—
320D3×Q8—22no—
321D3×Q8—22no—
322#237—124no—
323#237—124no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—31no—
327C2×C4×D3—31no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—21no—
332C2×Dic6—61no—
333C2×Dic6—61no—
334C2×Dic6C22×D311yescharacteristic
335C3×SD16—24no—
336C3×SD16—22no—
337C3×SD16—22no—
338C3×SD16—62no—
339C3×SD16—62no—
340C2×C3×C8—21no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—31no—
350C3×C42—61no—
351#217—21no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—121no—
357#215—22no—
358#215—62no—
359#214—22no—
360#214—62no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363C4⋊Dic3—21no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
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—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—121no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
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
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32C22×D411yescharacteristic
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3C2×SD1612yes—
414C32×C4—22no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
417C3⋊Dic3—21no—
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3⋊Dic3C2×SD1612yes—
421C3×Dic3—21no—
422C3×Dic3—22no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3C2×SD1612yes—
427C2×#41—181no—
428C22×Q8—31no—
429C2×SD16—31no—
430C2×SD16—31no—
431C2×SD16—91no—
432C2×SD16D3211yescharacteristic
433C4⋊Q8—91no—
434#127—31no—
435#124—181no—
436#121—31no—
437#121—91no—
438#121—181no—
439C4×Q8—31no—
440C4×Q8—91no—
441C4×Q8—91no—
442C4×Q8—91no—
443C4×Q8—181no—
444C4×Q8—181no—
445C4×D4—91no—
446C4×D4—91no—
447C4×D4—181no—
448C2×C4⋊C4—91no—
449C2×C4⋊C4—181no—
450C2×C42—91no—
451C2×C42—181no—
452#106—91no—
453#106—91no—
454#106—91no—
455#106—91no—
456C4⋊C8—31no—
457C4⋊C8—91no—
458#103—31no—
459#103—31no—
460#103—91no—
461#103—91no—
462#102—31no—
463#102—31no—
464#102—91no—
465#102—91no—
466C22⋊C8—31no—
467C22⋊C8—91no—
468C4×C8—91no—
469C4×C8—91no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—31no—
473C23×C3—41no—
474C23×C3—61no—
475C22×D3—21no—
476C22×D3D3×D411yescharacteristic
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—22no—
480C3×Q8—32no—
481C3×Q8—41no—
482C3×Q8—64no—
483C3×Q8—61no—
484C3×Q8#23712yescomplemented
485C3×Q8#23712yescomplemented
486C3×D4—22no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—41no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—122no—
495C3×D4—122no—
496C3×D4—122no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—41no—
504C2×C3×C4—64no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512#67—42no—
513#67—42no—
514#67—42no—
515#67—122no—
516#67—122no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—34no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—122no—
535C2×Dic3—122no—
536C2×Dic3—122no—
537C2×Dic3—122no—
538C2×Dic3—242no—
539C2×Dic3D3×D411yescharacteristic
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542D12—21no—
543D12—21no—
544C4×D3—24no—
545C4×D3—21no—
546C4×D3—21no—
547C4×D3—34no—
548C4×D3—122no—
549C4×D3—121no—
550C4×D3—122no—
551Dic6—24no—
552Dic6—21no—
553Dic6—122no—
554Dic6—122no—
555Dic6#23712yescomplemented
556C3×C8—22no—
557C3×C8—21no—
558C3×C8—21no—
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×C32C22×SD1611yescharacteristic
569C2×C32#57511yescharacteristic
570C3×D3—22no—
571C3×D3—81no—
572#41—364no—
573C2×Q8—31no—
574C2×Q8—61no—
575C2×Q8—62no—
576C2×Q8—62no—
577C2×Q8—181no—
578C2×Q8C2×D3211yescharacteristic
579C2×D4—31no—
580C2×D4—61no—
581C2×D4—61no—
582C2×D4—61no—
583C2×D4—181no—
584C2×D4C2×D3211yescharacteristic
585C22×C4—31no—
586C22×C4—61no—
587C22×C4—91no—
588C22×C4—91no—
589C22×C4—181no—
590C22×C4—181no—
591C22×C4—181no—
592SD16—22no—
593SD16—62no—
594SD16—62no—
595SD16—182no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—91no—
599C2×C8C2×D3211yescharacteristic
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—91no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C22⋊C4—61no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C42—31no—
615C42—61no—
616C42—91no—
617C42—91no—
618C42—91no—
619C42—181no—
620C42—181no—
621C42—181no—
622C22×C3—21no—
623C22×C3—32no—
624C22×C3—42no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3C2×D3×D411yescharacteristic
639C22×C3C2×D3×D411yescharacteristic
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3D3×SD1612yes—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—32no—
651C3×C4—42no—
652C3×C4—61no—
653C3×C4—61no—
654C3×C4—62no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4C2×#23711yescharacteristic
658C3×C4C2×#23711yescharacteristic
659C3×C4C2×#23711yescharacteristic
660C3×C4D3×#4111yescharacteristic
661Dic3—21no—
662Dic3—21no—
663Dic3—22no—
664Dic3—32no—
665Dic3—32no—
666Dic3—41no—
667Dic3—41no—
668Dic3—62no—
669Dic3—61no—
670Dic3—61no—
671Dic3—121no—
672Dic3—121no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—241no—
677Dic3—241no—
678Dic3D3×SD1612yes—
679C32#310311yescharacteristic, complemented, Sylow
680C23—21no—
681C23—31no—
682C23—61no—
683Q8—21no—
684Q8—32no—
685Q8—64no—
686Q8—61no—
687Q8—362no—
688Q8#380512yescomplemented
689D4—21no—
690D4—21no—
691D4—61no—
692D4—61no—
693D4—122no—
694D4—122no—
695D4—122no—
696D4—362no—
697C2×C4—21no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—64no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—94no—
708C2×C4—91no—
709C2×C4—91no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—361no—
713C2×C4—362no—
714C2×C4—362no—
715C2×C4—362no—
716C2×C4C22×D3211yescharacteristic
717C8—21no—
718C8—61no—
719C8—61no—
720C8—181no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—62no—
725C2×C3—82no—
726C2×C3—81no—
727C2×C3—81no—
728C2×C3—241no—
729C2×C3#558611yescharacteristic
730C2×C3#560611yescharacteristic
731C2×C3C2×D3×SD1611yescharacteristic
732C2×C3C2×D3×SD1611yescharacteristic
733C2×C3#577311yescharacteristic
734C2×C3#577711yescharacteristic
735D3—22no—
736D3—81no—
737C22—32no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—61no—
742C22—61no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22D32×D411yescharacteristic
747C4—22no—
748C4—32no—
749C4—61no—
750C4—62no—
751C4—61no—
752C4—92no—
753C4—121no—
754C4—121no—
755C4—181no—
756C4—361no—
757C4—361no—
758C4D3×#23711yescharacteristic
759C4C2×#380511yescharacteristic
760C3—21no—
761C3#8002811yescharacteristic, complemented
762C3#8036011yescharacteristic, complemented
763C2—62no—
764C2—81no—
765C2—241no—
766C2D32×SD1611yescharacteristic
767C2#1059474411yescharacteristic
768C2#1059513011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595133C2
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. SD16×C3⋊Dic3C2semidirect
4. C3×#5170C2semidirect
5. C3×#5163C2semidirect
6. #10591583C2semidirect
7. #10591571C2semidirect
8. #10591544C2semidirect
9. #10591445C2semidirect
10. #10591438C2semidirect
11. #10591415C2semidirect
12. #10590803C2semidirect
13. #10590742C2semidirect
14. #10590676C2semidirect
15. #10590656C2semidirect
69. #5170D3semidirect
71. #5163D3semidirect
240. C32×Q8#41semidirect
266. C3×Dic6#41semidirect
272. D3×Dic3SD16semidirect
484. C3×Q8#237semidirect
485. C3×Q8#237semidirect
555. Dic6#237semidirect
679. C32#3103semidirect
688. Q8#3805semidirect
761. C3#80028semidirect
762. C3#80360semidirect

Maximal subgroups

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

subgroupindex
D3×Q8×Dic32
#105951332
SD16×C3⋊Dic32
C3×#51702
C3×#51632
#105915832
#105915712
#105915442
#105914452
#105914382
#105914152
#105908032
#105907422
#105906762
#105906562
#803603
#800283