Finite Group Databasebeta

← C2×#10594768 #11918930

Subgroups — C2×#10594768 #11918930

Order 1152.

2945 conjugacy classes of subgroups.

The subgroup lattice has 775 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64315C212yesmaximal, complemented
2C2×Q16×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C3×#919C211yesmaximal, characteristic, complemented
4C2×C3×D3×Q16C211yesmaximal, characteristic, complemented
5C2×#63951C212yesmaximal, complemented
6C2×#63946C212yesmaximal, complemented
7C2×#63943C212yesmaximal, complemented
8#10594768C2116yesmaximal, direct product factor
9C2×#63810C211yesmaximal, characteristic, complemented
10C2×#63807C211yesmaximal, characteristic, complemented
11C2×#63803C211yesmaximal, characteristic, complemented
12C2×D3×Dic12C211yesmaximal, characteristic, complemented
13C2×#5771—31nomaximal
14C2×#5766—31nomaximal
15C2×Q8×C3⋊D3C2212yes—
16C2×C3×#239C2212yes—
17C2×C3×D3×Q8C2212yes—
18#64315—28no—
19#64315C22116yescomplemented
20C2×#3798—22no—
21C2×#3798C2211yescharacteristic
22C2×#3796—22no—
23C2×#3796C2212yes—
24C2×#3795—22no—
25C2×#3795C2212yes—
26C2×D3×Dic6—22no—
27C2×D3×Dic6C2212yes—
28C2×C32×Q16C2211yescharacteristic
29C2×#3756C2212yes—
30Q16×C3⋊D3C2218yescomplemented
31C2×#3746C2211yescharacteristic
32C2×C8×C3⋊D3C2211yescharacteristic
33C2×C3×#216C2212yes—
34C2×C3×#215C2212yes—
35C3×#919C2218yescomplemented
36C3×D3×Q16C2218yescomplemented
37C2×C3×Dic12C2211yescharacteristic
38C2×C3×D24C2211yescharacteristic
39C2×C3×D3×C8C2211yescharacteristic
40C2×C3×D3×C8C2211yescharacteristic
41#63951C22116yescomplemented
42#63946C22116yescomplemented
43#63943C22116yescomplemented
44C2×#3719C2212yes—
45C2×#3716C2212yes—
46C2×#3715C2212yes—
47C2×#3712C2211yescharacteristic
48C2×#3711C2211yescharacteristic
49C2×#3711C2211yescharacteristic
50#63810C2218yescomplemented
51#63807C2218yescomplemented
52#63803C2218yescomplemented
53D3×Dic12C2218yescomplemented
54C2×#1010—32no—
55C2×#1007—32no—
56C2×C3×#135—31no—
57C22×C3×Q16—31no—
58C2×#951—32no—
59C2×#942—32no—
60#5771—316no—
61#5766—316no—
62C2×#919—31no—
63C2×#919D311yescharacteristic, complemented
64C2×#918—32no—
65C2×#918—32no—
66C2×D3×Q16—31no—
67C2×D3×Q16—31no—
68C2×D3×Q16—31no—
69C2×D3×Q16—61no—
70C2×D3×Q16D311yescharacteristic, complemented
71C2×#915—32no—
72C2×#915—32no—
73C2×#912—31no—
74C2×#912—31no—
75C22×Dic12—31no—
76C2×#904—31no—
77C2×#901—31no—
78C2×#901—31no—
79C2×C32×Q8C2312yes—
80Q8×C3⋊D3—24no—
81Q8×C3⋊D3C2318yes—
82C2×C4×C3⋊D3—22no—
83C2×C4×C3⋊D3C2311yescharacteristic
84C2×#634—22no—
85C2×#634C2312yes—
86C3×#239—24no—
87C3×#239C2318yes—
88C3×D3×Q8—24no—
89C3×D3×Q8C2318yes—
90C2×C3×D12—22no—
91C2×C3×D12C2312yes—
92C2×C3×C4×D3—22no—
93C2×C3×C4×D3—22no—
94C2×C3×C4×D3C2311yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×Dic6—22no—
97C2×C3×Dic6C2312yes—
98C2×#627—22no—
99C2×#627D411yescharacteristic
100C2×#626—22no—
101C2×#626D411yescharacteristic
102C2×#626D411yescharacteristic
103C2×#625—22no—
104C2×#625D411yescharacteristic
105C2×D3×Dic3—22no—
106C2×D3×Dic3—22no—
107C2×D3×Dic3—22no—
108#3798—216no—
109#3798D414yes—
110#3798C2314yes—
111#3796—24no—
112#3796—216no—
113#3796C2318yes—
114#3795—24no—
115#3795—216no—
116#3795C2318yes—
117D3×Dic6—24no—
118D3×Dic6—216no—
119D3×Dic6C2318yes—
120C32×Q16C2314yes—
121C2×C32×C8C2311yescharacteristic
122#3756C2318yes—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3746C2314yes—
125C8×C3⋊D3C2314yes—
126C3×#216C2318yes—
127C3×#215C2318yes—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×Dic12C2314yes—
131C3×D24C2314yes—
132C3×D3×C8C2314yes—
133C3×D3×C8C2314yes—
134#3719C2318yes—
135#3716C2318yes—
136#3715C2318yes—
137#3712C2314yes—
138#3711C2314yes—
139#3711C2314yes—
140C2×#578—91noSylow
141C2×C3×#41—32no—
142C22×C3×Q8—32no—
143#1010—316no—
144#1010—68no—
145#1007—316no—
146#1007—68no—
147C2×#239—32no—
148C2×#239—62no—
149C2×#239C2×D312yes—
150C2×D3×Q8—32no—
151C2×D3×Q8—32no—
152C2×D3×Q8—32no—
153C2×D3×Q8—62no—
154C2×D3×Q8—62no—
155C2×D3×Q8C2×D312yes—
156C2×#237—32no—
157C2×#237—32no—
158C2×#237—62no—
159C2×#237—62no—
160C2×#235—31no—
161C2×#235—31no—
162C2×#235—32no—
163C2×#235—62no—
164C2×#235—62no—
165C2×#235—62no—
166C22×Dic6—32no—
167C22×Dic6—62no—
168C3×#135—38no—
169C2×C3×Q16—21no—
170C2×C3×Q16—32no—
171C2×C3×Q16—38no—
172C2×C3×Q16—31no—
173C2×C3×Q16C2×D311yescharacteristic
174C2×C3×Q16C2×D311yescharacteristic
175C2×C3×SD16—32no—
176C2×C3×D8—31no—
177C22×C3×C8—31no—
178C22×C3×C8—31no—
179#951—316no—
180C2×#216—32no—
181C2×#216—32no—
182C2×#216—32no—
183C2×#216—62no—
184C2×#216C2×D312yes—
185#942—316no—
186C2×#215—32no—
187C2×#215C2×D312yes—
188C2×#214—32no—
189C2×#214—32no—
190C2×#208—31no—
191C2×#208—31no—
192#919—38no—
193#919C2×D318yescomplemented
194#918—316no—
195#918—316no—
196D3×Q16—38no—
197D3×Q16—38no—
198D3×Q16—38no—
199D3×Q16—68no—
200D3×Q16C2×D318yescomplemented
201#915—316no—
202#915—316no—
203#912—38no—
204#912—38no—
205C2×Dic12—32no—
206C2×Dic12—31no—
207C2×Dic12—31no—
208C2×Dic12—38no—
209C2×Dic12—61no—
210C2×Dic12C2×D311yescharacteristic
211#904—38no—
212C2×D24C2×D311yescharacteristic
213C2×#204—32no—
214#901—38no—
215#901—38no—
216C2×ΓL(1,𝔽25)—31no—
217C2×ΓL(1,𝔽25)—31no—
218C2×ΓL(1,𝔽25)—31no—
219C2×ΓL(1,𝔽25)—31no—
220C2×D3×C8—31no—
221C2×D3×C8—31no—
222C2×D3×C8—61no—
223C2×D3×C8C2×D311yescharacteristic
224C2×D3×C8C2×D311yescharacteristic
225C22×C3⋊D3C2×D411yescharacteristic
226C22×C3×D3—22no—
227C22×C3×D3C2×D411yescharacteristic
228C22×C3×D3C2×D411yescharacteristic
229C32×Q8—22no—
230C32×Q8C2414yes—
231C2×C32×C4—22no—
232C2×C32×C4C2411yescharacteristic
233C2×C3⋊Dic3—22no—
234C2×C3⋊Dic3C2×D411yescharacteristic
235C4×C3⋊D3—28no—
236C4×C3⋊D3C2×D412yes—
237C4×C3⋊D3C2412yes—
238#634—22no—
239#634—28no—
240#634C2414yes—
241C2×C3×Dic3—22no—
242C2×C3×Dic3C2×D411yescharacteristic
243C2×C3×Dic3C2×D411yescharacteristic
244C3×D12—28no—
245C3×D12—22no—
246C3×D12C2414yes—
247C3×C4×D3—28no—
248C3×C4×D3—28no—
249C3×C4×D3C2×D412yes—
250C3×C4×D3C2×D412yes—
251C3×C4×D3C2412yes—
252C3×C4×D3C2412yes—
253C3×Dic6—22no—
254C3×Dic6—28no—
255C3×Dic6C2414yes—
256#627—28no—
257#627C2×D414yes—
258#626—28no—
259#626C2×D414yes—
260#626C2×D414yes—
261#625—28no—
262#625C2×D414yes—
263D3×Dic3—28no—
264D3×Dic3—28no—
265D3×Dic3—28no—
266C32×C8C2412yes—
267C3⋊(C3⋊C8)C2412yes—
268C3×C3⋊C8C2412yes—
269C3×C3⋊C8C2412yes—
270C2×2−1+4—92no—
271#578—916no—
272C2×#137—92no—
273C2×#137—92no—
274C2×#137—92no—
275C2×#135—31no—
276C2×#135—91no—
277C2×#135—91no—
278C22×Q16—31no—
279C22×Q16—91no—
280C22×Q16—91no—
281C2×#131—91no—
282C3×#41—38no—
283C3×#41—64no—
284C2×C3×Q8—22no—
285C2×C3×Q8—38no—
286C2×C3×Q8—32no—
287C2×C3×Q8—62no—
288C2×C3×Q8—64no—
289C2×C3×Q8C22×D312yes—
290C2×C3×Q8C22×D312yes—
291C2×C3×D4—32no—
292C2×C3×D4—62no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—62no—
296C22×C3×C4—62no—
297C2×#67—31no—
298C2×#67—31no—
299C2×#67—31no—
300C2×#67—31no—
301C2×#67—62no—
302C2×#67—62no—
303C2×#67—62no—
304C22×Dic3—62no—
305C22×Dic3—62no—
306C22×Dic3—62no—
307#239—24no—
308#239—38no—
309#239—64no—
310#239—616no—
311#239C22×D318yes—
312D3×Q8—24no—
313D3×Q8—38no—
314D3×Q8—38no—
315D3×Q8—38no—
316D3×Q8—68no—
317D3×Q8—616no—
318D3×Q8—64no—
319D3×Q8—64no—
320D3×Q8—64no—
321D3×Q8—124no—
322D3×Q8C22×D318yes—
323#237—38no—
324#237—38no—
325#237—64no—
326#237—616no—
327#237—616no—
328#237—64no—
329#235—34no—
330#235—34no—
331#235—34no—
332#235—34no—
333#235—38no—
334#235—616no—
335#235—616no—
336#235—616no—
337#235—64no—
338C2×D12—22no—
339C2×D12—31no—
340C2×D12—31no—
341C2×D12—62no—
342C2×D12C22×D312yes—
343C2×C4×D3—22no—
344C2×C4×D3—22no—
345C2×C4×D3—31no—
346C2×C4×D3—31no—
347C2×C4×D3—61no—
348C2×C4×D3—62no—
349C2×C4×D3—62no—
350C2×C4×D3—62no—
351C2×C4×D3—62no—
352C2×C4×D3—62no—
353C2×C4×D3—122no—
354C2×C4×D3C22×D311yescharacteristic
355C2×C4×D3C22×D311yescharacteristic
356C2×Dic6—22no—
357C2×Dic6—31no—
358C2×Dic6—31no—
359C2×Dic6—32no—
360C2×Dic6—32no—
361C2×Dic6—38no—
362C2×Dic6—62no—
363C2×Dic6—616no—
364C2×Dic6—64no—
365C2×Dic6—62no—
366C2×Dic6—62no—
367C2×Dic6—62no—
368C2×Dic6—62no—
369C2×Dic6—122no—
370C2×Dic6C22×D312yes—
371C3×Q16—24no—
372C3×Q16—38no—
373C3×Q16—34no—
374C3×Q16C22×D314yes—
375C3×Q16C22×D314yes—
376C3×SD16—38no—
377C3×D8—34no—
378C2×C3×C8—21no—
379C2×C3×C8—31no—
380C2×C3×C8—31no—
381C2×C3×C8—34no—
382C2×C3×C8—34no—
383C2×C3×C8C22×D311yescharacteristic
384C2×C3×C8C22×D311yescharacteristic
385#216—38no—
386#216—38no—
387#216—38no—
388#216—68no—
389#216C22×D318yes—
390#215—38no—
391#215C22×D318yes—
392#214—38no—
393#214—38no—
394#208—34no—
395#208—34no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8C22×D311yescharacteristic
400C2×C3⋊C8C22×D311yescharacteristic
401Dic12—38no—
402Dic12—34no—
403Dic12—34no—
404Dic12—64no—
405Dic12C22×D314yes—
406D24C22×D314yes—
407#204—38no—
408ΓL(1,𝔽25)—34no—
409ΓL(1,𝔽25)—34no—
410ΓL(1,𝔽25)—34no—
411ΓL(1,𝔽25)—34no—
412D3×C8—34no—
413D3×C8—34no—
414D3×C8—64no—
415D3×C8C22×D314yes—
416D3×C8C22×D314yes—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—22no—
419C2×C3⋊D3C22×D412yes—
420C2×C3×D3—22no—
421C2×C3×D3—22no—
422C2×C3×D3—24no—
423C2×C3×D3—44no—
424C2×C3×D3C22×D412yes—
425C2×C3×D3C22×D412yes—
426C32×C4—24no—
427C32×C4C22×D411yescharacteristic
428C32×C4C2511yescharacteristic
429C3⋊Dic3—24no—
430C3⋊Dic3C22×D412yes—
431C3×Dic3—24no—
432C3×Dic3C22×D412yes—
433C3×Dic3C22×D412yes—
4342−1+4—916no—
4352−1+4—188no—
436C2×#41—32no—
437C2×#41—91no—
438C2×#41—92no—
439C2×#41—92no—
440C2×#41—182no—
441C2×#41—182no—
442C2×#41—182no—
443C22×Q8—32no—
444C22×Q8—92no—
445C22×Q8—92no—
446C22×Q8—182no—
447#137—916no—
448#137—916no—
449#137—916no—
450#135—38no—
451#135—98no—
452#135—98no—
453C2×Q16—32no—
454C2×Q16—38no—
455C2×Q16—31no—
456C2×Q16—98no—
457C2×Q16—92no—
458C2×Q16—92no—
459C2×Q16—98no—
460C2×Q16—91no—
461C2×Q16D3211yescharacteristic
462C2×SD16—32no—
463C2×SD16—92no—
464C2×SD16—92no—
465C2×D8—31no—
466#131—98no—
467C2×M16—91no—
468C2×M16—91no—
469C2×M16—91no—
470C22×C8—31no—
471C22×C8—31no—
472C22×C8—91no—
473C23×C3—31no—
474C23×C3—31no—
475C23×C3—62no—
476C22×D3—22no—
477C22×D3—31no—
478C22×D3—31no—
479C22×D3—61no—
480C22×D3D3×D411yescharacteristic
481C22×D3D3×D411yescharacteristic
482C3×Q8—22no—
483C3×Q8—22no—
484C3×Q8—24no—
485C3×Q8—34no—
486C3×Q8—42no—
487C3×Q8—68no—
488C3×Q8—62no—
489C3×Q8C23×D314yes—
490C3×Q8C23×D314yes—
491C3×D4—34no—
492C3×D4—68no—
493C3×D4—62no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—32no—
500C2×C3×C4—32no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—42no—
504C2×C3×C4—68no—
505C2×C3×C4—68no—
506C2×C3×C4—62no—
507C2×C3×C4C23×D311yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509#67—34no—
510#67—34no—
511#67—34no—
512#67—34no—
513#67—68no—
514#67—68no—
515#67—68no—
516C2×Dic3—22no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—61no—
520C2×Dic3—68no—
521C2×Dic3—68no—
522C2×Dic3—62no—
523C2×Dic3—62no—
524C2×Dic3—68no—
525C2×Dic3—122no—
526C2×Dic3D3×D411yescharacteristic
527C2×Dic3D3×D411yescharacteristic
528D12—28no—
529D12—22no—
530D12—34no—
531D12—34no—
532D12—68no—
533D12C23×D314yes—
534C4×D3—28no—
535C4×D3—28no—
536C4×D3—32no—
537C4×D3—32no—
538C4×D3—32no—
539C4×D3—32no—
540C4×D3—62no—
541C4×D3—62no—
542C4×D3—68no—
543C4×D3—68no—
544C4×D3—68no—
545C4×D3—68no—
546C4×D3—68no—
547C4×D3—128no—
548C4×D3D3×D412yes—
549C4×D3D3×D412yes—
550C4×D3C23×D312yes—
551C4×D3C23×D312yes—
552Dic6—22no—
553Dic6—28no—
554Dic6—34no—
555Dic6—34no—
556Dic6—34no—
557Dic6—34no—
558Dic6—64no—
559Dic6—68no—
560Dic6—68no—
561Dic6—68no—
562Dic6—62no—
563Dic6—62no—
564Dic6—68no—
565Dic6—128no—
566Dic6—122no—
567Dic6C23×D314yes—
568C3×C8—22no—
569C3×C8—32no—
570C3×C8—32no—
571C3×C8C23×D312yes—
572C3×C8C23×D312yes—
573C3⋊C8—32no—
574C3⋊C8—32no—
575C3⋊C8—62no—
576C3⋊C8C23×D312yes—
577C3⋊C8C23×D312yes—
578C2×C32#57812yescomplemented
579C2×C32C23×D411yescharacteristic
580C3⋊D3—22no—
581C3×D3—22no—
582C3×D3—22no—
583C3×D3—44no—
584#41—38no—
585#41—64no—
586#41—94no—
587#41—94no—
588#41—98no—
589#41—98no—
590#41—184no—
591#41—1816no—
592#41—1816no—
593#41—184no—
594#41—1816no—
595C2×Q8—38no—
596C2×Q8—32no—
597C2×Q8—62no—
598C2×Q8—64no—
599C2×Q8—91no—
600C2×Q8—98no—
601C2×Q8—98no—
602C2×Q8—92no—
603C2×Q8—182no—
604C2×Q8—182no—
605C2×Q8—184no—
606C2×Q8—1816no—
607C2×Q8—184no—
608C2×Q8C2×D3212yes—
609C2×D4—32no—
610C2×D4—62no—
611C2×D4—91no—
612C2×D4—91no—
613C2×D4—91no—
614C2×D4—182no—
615C2×D4—182no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—62no—
619C22×C4—62no—
620C22×C4—91no—
621C22×C4—182no—
622C22×C4—182no—
623C22×C4—182no—
624C22×C4—182no—
625Q16—38no—
626Q16—34no—
627Q16—98no—
628Q16—98no—
629Q16—94no—
630Q16C2×D3214yes—
631SD16—38no—
632SD16—98no—
633SD16—98no—
634D8—34no—
635M16—94no—
636M16—94no—
637M16—94no—
638C2×C8—31no—
639C2×C8—31no—
640C2×C8—34no—
641C2×C8—34no—
642C2×C8—91no—
643C2×C8—94no—
644C2×C8C2×D3211yescharacteristic
645C22×C3—21no—
646C22×C3—32no—
647C22×C3—32no—
648C22×C3—62no—
649C22×C3—62no—
650C22×C3—64no—
651C22×C3—124no—
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C2×D3×D411yescharacteristic
654C2×D3—22no—
655C2×D3—22no—
656C2×D3—24no—
657C2×D3—32no—
658C2×D3—32no—
659C2×D3—44no—
660C2×D3—62no—
661C2×D3—64no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3C2×D3×D412yes—
665C2×D3C2×D3×D412yes—
666C3×C4—24no—
667C3×C4—24no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—32no—
671C3×C4—32no—
672C3×C4—44no—
673C3×C4—64no—
674C3×C4C2×D3×D411yescharacteristic
675C3×C4C2×D3×D411yescharacteristic
676C3×C4C24×D311yescharacteristic
677C3×C4C24×D311yescharacteristic
678Dic3—24no—
679Dic3—32no—
680Dic3—32no—
681Dic3—62no—
682Dic3—64no—
683Dic3—64no—
684Dic3—124no—
685Dic3C2×D3×D412yes—
686Dic3C2×D3×D412yes—
687C32C2×#57811yescharacteristic, complemented, Sylow
688C23—31no—
689C23—31no—
690C23—62no—
691C23—91no—
692Q8—22no—
693Q8—34no—
694Q8—68no—
695Q8—62no—
696Q8—94no—
697Q8—94no—
698Q8—188no—
699Q8—188no—
700Q8—182no—
701Q8C22×D3214yes—
702D4—34no—
703D4—68no—
704D4—62no—
705D4—94no—
706D4—94no—
707D4—94no—
708D4—188no—
709D4—188no—
710C2×C4—22no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—32no—
714C2×C4—32no—
715C2×C4—32no—
716C2×C4—32no—
717C2×C4—68no—
718C2×C4—68no—
719C2×C4—62no—
720C2×C4—91no—
721C2×C4—92no—
722C2×C4—92no—
723C2×C4—188no—
724C2×C4—188no—
725C2×C4—188no—
726C2×C4—188no—
727C2×C4—182no—
728C2×C4C22×D3211yescharacteristic
729C8—32no—
730C8—32no—
731C8—92no—
732C8C22×D3212yes—
733C2×C3—21no—
734C2×C3—22no—
735C2×C3—62no—
736C2×C3—62no—
737C2×C3—124no—
738C2×C3#576612yescomplemented
739C2×C3#577112yescomplemented
740C2×C3C22×D3×D411yescharacteristic
741C2×C3C22×D3×D411yescharacteristic
742D3—22no—
743D3—22no—
744D3—44no—
745D3—64no—
746D3—62no—
747D3—62no—
748C22—32no—
749C22—32no—
750C22—62no—
751C22—62no—
752C22—64no—
753C22—92no—
754C22—124no—
755C22—182no—
756C22D32×D411yescharacteristic
757C4—24no—
758C4—32no—
759C4—32no—
760C4—64no—
761C4—92no—
762C4—184no—
763C4D32×D411yescharacteristic
764C4C23×D3211yescharacteristic
765C3—21no—
766C3C2×#576611yescharacteristic, complemented
767C3C2×#577111yescharacteristic, complemented
768C2—62no—
769C2—62no—
770C2—124no—
771C2—182no—
772C2#1059476812yesdirect product factor
773C2C2×D32×D411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
hypercenterC2×Q16D32
hypocenterC32C2×#578
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#64315C2semidirect
2. C2×Q16×C3⋊D3C2semidirect
3. C2×C3×#919C2semidirect
4. C2×C3×D3×Q16C2semidirect
5. C2×#63951C2semidirect
6. C2×#63946C2semidirect
7. C2×#63943C2semidirect
8. #10594768C2direct (N × H)
9. C2×#63810C2semidirect
10. C2×#63807C2semidirect
11. C2×#63803C2semidirect
12. C2×D3×Dic12C2semidirect
19. #64315C22semidirect
30. Q16×C3⋊D3C22semidirect
35. C3×#919C22semidirect
36. C3×D3×Q16C22semidirect
41. #63951C22semidirect
42. #63946C22semidirect
43. #63943C22semidirect
50. #63810C22semidirect
51. #63807C22semidirect
52. #63803C22semidirect
53. D3×Dic12C22semidirect
63. C2×#919D3semidirect
70. C2×D3×Q16D3semidirect
193. #919C2×D3semidirect
200. D3×Q16C2×D3semidirect
578. C2×C32#578semidirect
687. C32C2×#578semidirect
738. C2×C3#5766semidirect
739. C2×C3#5771semidirect
766. C3C2×#5766semidirect
767. C3C2×#5771semidirect
772. C2#10594768direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643152
C2×Q16×C3⋊D32
C2×C3×#9192
C2×C3×D3×Q162
C2×#639512
C2×#639462
C2×#639432
#105947682
C2×#638102
C2×#638072
C2×#638032
C2×D3×Dic122
C2×#57713
C2×#57663