Finite Group Databasebeta

← C2×#10595322 #11918705

Subgroups — C2×#10595322 #11918705

Order 1152.

3353 conjugacy classes of subgroups.

The subgroup lattice has 677 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#64306C211yesmaximal, characteristic
3C2×C3×#942C212yesmaximal, complemented
4C2×#63951C214yesmaximal, complemented
5C2×#63944C212yesmaximal, complemented
6#10595322C2116yesmaximal, direct product factor
7C2×#63940C212yesmaximal, complemented
8C2×#63831C212yesmaximal, complemented
9C2×#63818C211yesmaximal, characteristic, complemented
10C2×D3×#137—32nomaximal
11C22×C32×Q8C2211yescharacteristic, complemented
12C2×Q8×C3⋊D3—21no—
13C2×Q8×C3⋊D3—21no—
14C2×Q8×C3⋊D3—24no—
15C2×Q8×C3⋊D3C2212yes—
16C2×Q8×C3⋊D3C2212yescomplemented
17C2×Q8×C3⋊D3C2218yescomplemented
18C22×C4×C3⋊D3—21no—
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#634—21no—
21C22×#634C2211yescharacteristic, complemented
22C2×C3×#235C2212yes—
23C2×#3811—21no—
24C2×#3805—21no—
25#64306—24no—
26#64306C2218yes—
27C2×#3802C2211yescharacteristic
28C2×C4×D32—21no—
29C2×#3798—21no—
30C2×#3797C2211yescharacteristic
31C2×#3796C2212yes—
32C2×C3×#216C2214yescomplemented
33C3×#942C22116yescomplemented
34C2×C3×#215C2214yescomplemented
35C2×C3×#208C2212yescomplemented
36#63951C22132yescomplemented
37#63944C22116yescomplemented
38#63940C22116yescomplemented
39C2×#3719C2214yescomplemented
40#63831C22116yescomplemented
41C2×#3716C2214yescomplemented
42C2×#3712C2212yescomplemented
43#63818C2218yescomplemented
44C2×#3710C2212yes—
45C2×D3×#41—32no—
46C22×D3×Q8—32no—
47C22×D3×Q8—61no—
48C2×C3×#137—32no—
49C2×#951—32no—
50C2×#942D312yescomplemented
51D3×#137—332no—
52C2×#918—34no—
53C2×D3×Q16—34no—
54C2×#915—34no—
55C2×D3×SD16—34no—
56C2×#909—32no—
57C2×D3×M16—32no—
58C23×C3⋊D3D411yescharacteristic
59C22×D32—21no—
60C2×C32×Q8—21no—
61C2×C32×Q8—22no—
62C2×C32×Q8C2312yes—
63C2×C32×Q8C2314yescomplemented
64C22×C32×C4—21no—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3—21no—
67C22×C3⋊Dic3D411yescharacteristic
68Q8×C3⋊D3—24no—
69Q8×C3⋊D3—24no—
70Q8×C3⋊D3—28no—
71Q8×C3⋊D3—28no—
72Q8×C3⋊D3C2318yes—
73Q8×C3⋊D3C2318yescomplemented
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—28no—
76C2×C4×C3⋊D3—22no—
77C2×C4×C3⋊D3D411yescharacteristic
78C2×C4×C3⋊D3D411yescharacteristic
79C2×C4×C3⋊D3D414yes—
80C2×C4×C3⋊D3C2311yescharacteristic
81C2×C4×C3⋊D3C2311yescharacteristic
82C2×C4×C3⋊D3C2314yes—
83C2×#634—22no—
84C2×#634—21no—
85C2×#634—22no—
86C2×#634—28no—
87C2×#634—22no—
88C2×#634C2312yes—
89C2×#634C2314yescomplemented
90C2×C3×#67—22no—
91C3×#235—24no—
92C3×#235C2318yes—
93C2×C3×D12C2312yes—
94C2×C3×C4×D3—22no—
95C2×C3×Dic6C2312yes—
96#3811—28no—
97C2×#627—21no—
98C2×#626—22no—
99C2×#625—21no—
100C2×#624—21no—
101#3805—28no—
102C2×D3×Dic3—22no—
103#3802—22no—
104#3802C2314yes—
105C4×D32—28no—
106#3798—28no—
107#3797—22no—
108#3797C2314yes—
109#3796—24no—
110#3796C2318yes—
111C3×#216C23116yescomplemented
112C3×#215C23116yescomplemented
113C3×#208C2318yescomplemented
114C2×C3×C3⋊C8C2314yes—
115#3719C23116yescomplemented
116#3716C23116yescomplemented
117#3712C2318yescomplemented
118#3710C2318yes—
119C22×#137—91noSylow
120C2×C3×#41—32no—
121C22×C3×Q8—21no—
122C22×C3×Q8C2×D312yescomplemented
123D3×#41—316no—
124D3×#41—68no—
125C2×#239—32no—
126C2×D3×Q8—34no—
127C2×D3×Q8—34no—
128C2×D3×Q8—316no—
129C2×D3×Q8—32no—
130C2×D3×Q8—62no—
131C2×D3×Q8—62no—
132C2×D3×Q8—68no—
133C2×D3×Q8—62no—
134C2×D3×Q8—62no—
135C2×D3×Q8—68no—
136C2×D3×Q8—62no—
137C2×D3×Q8—62no—
138C2×D3×Q8—68no—
139C2×#237—32no—
140C2×#237—62no—
141C2×D3×D4—32no—
142C2×D3×D4—62no—
143C2×#235—62no—
144C2×#235C2×D312yes—
145C22×C4×D3—32no—
146C22×C4×D3—61no—
147C22×C4×D3—62no—
148C22×C4×D3—62no—
149C22×C4×D3—62no—
150C22×Dic6—32no—
151C22×Dic6—61no—
152C22×Dic6—62no—
153C22×Dic6—62no—
154C3×#137—316no—
155C2×C3×Q16—34no—
156C2×C3×SD16—34no—
157C2×C3×M16—32no—
158#951—316no—
159C2×#216—34no—
160C2×#216C2×D314yescomplemented
161#942C2×D3116yescomplemented
162C2×#215C2×D314yescomplemented
163C2×#214—34no—
164C2×#208C2×D312yescomplemented
165#918—332no—
166D3×Q16—332no—
167#915—332no—
168D3×SD16—332no—
169#909—316no—
170D3×M16—316no—
171C2×Dic12—34no—
172C2×#204—34no—
173C2×ΓL(1,𝔽25)—34no—
174C2×D3×C8—34no—
175C23×C32C2×D411yescharacteristic
176C22×C3⋊D3—24no—
177C22×C3⋊D3C2×D411yescharacteristic
178C22×C3⋊D3C2×D414yes—
179C22×C3⋊D3C2×D411yescharacteristic
180C22×C3×D3—22no—
181C2×D32—24no—
182C2×D32—44no—
183C32×Q8—22no—
184C32×Q8—24no—
185C32×Q8C2414yes—
186C2×C32×C4—22no—
187C2×C32×C4—24no—
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D412yes—
190C2×C32×C4C2411yescharacteristic
191C2×C32×C4C2412yes—
192C2×C3⋊Dic3—22no—
193C2×C3⋊Dic3—24no—
194C2×C3⋊Dic3C2×D411yescharacteristic
195C2×C3⋊Dic3C2×D414yes—
196C2×C3⋊Dic3C2×D411yescharacteristic
197C4×C3⋊D3—28no—
198C4×C3⋊D3—28no—
199C4×C3⋊D3C2×D412yes—
200C4×C3⋊D3C2×D412yes—
201C4×C3⋊D3C2×D414yes—
202C4×C3⋊D3C2×D414yes—
203C4×C3⋊D3C2412yes—
204C4×C3⋊D3C2412yes—
205#634—22no—
206#634—24no—
207#634—28no—
208#634—28no—
209#634C2414yes—
210C3×#67—28no—
211C2×C3×Dic3—22no—
212C3×D12—22no—
213C3×D12C2414yes—
214C3×C4×D3—28no—
215C3×Dic6—22no—
216C3×Dic6C2414yes—
217#627—24no—
218#626—28no—
219#625—24no—
220#624—24no—
221D3×Dic3—28no—
222C3×C3⋊C8C2418yes—
223C22×#41—91no—
224C23×Q8—91no—
225C2×#137—32no—
226C2×#137—92no—
227C2×#137—94no—
228C2×#137—916no—
229C22×Q16—92no—
230C22×SD16—92no—
231C22×M16—91no—
232C23×D3—32no—
233C23×D3—61no—
234C23×D3—62no—
235C3×#41—38no—
236C3×#41—64no—
237C2×C3×Q8—24no—
238C2×C3×Q8—22no—
239C2×C3×Q8—22no—
240C2×C3×Q8—24no—
241C2×C3×Q8—22no—
242C2×C3×Q8—24no—
243C2×C3×Q8—32no—
244C2×C3×Q8C22×D314yes—
245C2×C3×Q8C22×D318yescomplemented
246C2×C3×D4—32no—
247C2×C3×D4—62no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—21no—
251C22×C3×C4—62no—
252C22×C3×C4C22×D312yes—
253C2×#67—22no—
254C2×#67—62no—
255C2×#67—62no—
256C22×Dic3—32no—
257C22×Dic3—61no—
258C22×Dic3—62no—
259C22×Dic3—62no—
260C22×Dic3—62no—
261#239—38no—
262#239—64no—
263D3×Q8—316no—
264D3×Q8—316no—
265D3×Q8—38no—
266D3×Q8—68no—
267D3×Q8—68no—
268D3×Q8—64no—
269D3×Q8—616no—
270D3×Q8—616no—
271D3×Q8—68no—
272D3×Q8—68no—
273D3×Q8—68no—
274D3×Q8—616no—
275D3×Q8—68no—
276D3×Q8—616no—
277#237—38no—
278#237—64no—
279#237—616no—
280D3×D4—38no—
281D3×D4—64no—
282D3×D4—616no—
283#235—24no—
284#235—616no—
285#235C22×D318yes—
286C2×D12—62no—
287C2×D12C22×D312yes—
288C2×C4×D3—22no—
289C2×C4×D3—32no—
290C2×C4×D3—32no—
291C2×C4×D3—38no—
292C2×C4×D3—32no—
293C2×C4×D3—32no—
294C2×C4×D3—38no—
295C2×C4×D3—61no—
296C2×C4×D3—61no—
297C2×C4×D3—64no—
298C2×C4×D3—61no—
299C2×C4×D3—61no—
300C2×C4×D3—64no—
301C2×C4×D3—616no—
302C2×C4×D3—62no—
303C2×C4×D3—62no—
304C2×C4×D3—64no—
305C2×C4×D3—64no—
306C2×C4×D3—616no—
307C2×C4×D3—64no—
308C2×C4×D3—616no—
309C2×C4×D3—64no—
310C2×Dic6—34no—
311C2×Dic6—38no—
312C2×Dic6—62no—
313C2×Dic6—64no—
314C2×Dic6—62no—
315C2×Dic6—64no—
316C2×Dic6—64no—
317C2×Dic6—616no—
318C2×Dic6—64no—
319C2×Dic6—616no—
320C2×Dic6—64no—
321C2×Dic6—64no—
322C2×Dic6—62no—
323C2×Dic6—62no—
324C2×Dic6—64no—
325C2×Dic6C22×D312yes—
326C3×Q16—316no—
327C3×SD16—316no—
328C3×M16—38no—
329C2×C3×C8—34no—
330#216—316no—
331#216C22×D3116yescomplemented
332#215C22×D3116yescomplemented
333#214—316no—
334#208C22×D318yescomplemented
335C2×C3⋊C8C22×D314yes—
336Dic12—316no—
337#204—316no—
338ΓL(1,𝔽25)—316no—
339D3×C8—316no—
340C22×C32—22no—
341C22×C32C22×D412yes—
342C22×C32C22×D411yescharacteristic
343C2×C3⋊D3—22no—
344C2×C3⋊D3—28no—
345C2×C3⋊D3#13714yescomplemented
346C2×C3⋊D3C22×D412yes—
347C2×C3⋊D3C22×D412yes—
348C2×C3×D3—24no—
349C2×C3×D3—44no—
350D32—48no—
351C32×C4—24no—
352C32×C4C22×D411yescharacteristic
353C32×C4C22×D412yes—
354C32×C4C2511yescharacteristic
355C3⋊Dic3—24no—
356C3⋊Dic3C22×D412yes—
357C3⋊Dic3C22×D412yes—
358C3×Dic3—24no—
359C2×#41—32no—
360C2×#41—92no—
361C2×#41—98no—
362C2×#41—181no—
363C2×#41—181no—
364C2×#41—184no—
365C22×Q8—91no—
366C22×Q8—92no—
367C22×Q8—92no—
368C22×Q8—98no—
369C22×Q8—91no—
370C22×Q8—181no—
371C22×Q8—181no—
372C22×Q8—184no—
373C22×Q8—181no—
374C22×Q8D3211yescharacteristic, complemented
375C22×D4—91no—
376C22×D4—181no—
377C23×C4—91no—
378C23×C4—181no—
379C23×C4—181no—
380#137—316no—
381#137—916no—
382#137—932no—
383C2×Q16—34no—
384C2×Q16—94no—
385C2×Q16—916no—
386C2×SD16—34no—
387C2×SD16—94no—
388C2×SD16—916no—
389C2×M16—32no—
390C2×M16—92no—
391C2×M16—98no—
392C22×C8—92no—
393C23×C3—21no—
394C23×C3—62no—
395C23×C3D3×D412yes—
396C22×D3—22no—
397C22×D3—32no—
398C22×D3—32no—
399C22×D3—38no—
400C22×D3—61no—
401C22×D3—64no—
402C22×D3—61no—
403C22×D3—68no—
404C22×D3—68no—
405C22×D3—68no—
406C22×D3—128no—
407C3×Q8—24no—
408C3×Q8—28no—
409C3×Q8—24no—
410C3×Q8—28no—
411C3×Q8—24no—
412C3×Q8—34no—
413C3×Q8—62no—
414C3×Q8C23×D318yes—
415C3×D4—34no—
416C3×D4—68no—
417C3×D4—62no—
418C2×C3×C4—28no—
419C2×C3×C4—24no—
420C2×C3×C4—24no—
421C2×C3×C4—28no—
422C2×C3×C4—22no—
423C2×C3×C4—21no—
424C2×C3×C4—22no—
425C2×C3×C4—21no—
426C2×C3×C4—62no—
427C2×C3×C4—68no—
428C2×C3×C4D3×D412yes—
429C2×C3×C4D3×D414yes—
430C2×C3×C4C23×D312yes—
431C2×C3×C4C23×D314yes—
432#67—28no—
433#67—68no—
434#67—68no—
435C2×Dic3—22no—
436C2×Dic3—32no—
437C2×Dic3—32no—
438C2×Dic3—38no—
439C2×Dic3—64no—
440C2×Dic3—61no—
441C2×Dic3—61no—
442C2×Dic3—68no—
443C2×Dic3—68no—
444C2×Dic3—64no—
445C2×Dic3—68no—
446C2×Dic3—64no—
447D12—22no—
448D12—68no—
449D12C23×D314yes—
450C4×D3—28no—
451C4×D3—38no—
452C4×D3—38no—
453C4×D3—34no—
454C4×D3—34no—
455C4×D3—34no—
456C4×D3—34no—
457C4×D3—64no—
458C4×D3—62no—
459C4×D3—62no—
460C4×D3—64no—
461C4×D3—62no—
462C4×D3—62no—
463C4×D3—68no—
464C4×D3—68no—
465C4×D3—616no—
466C4×D3—616no—
467C4×D3—616no—
468C4×D3—616no—
469Dic6—22no—
470Dic6—38no—
471Dic6—64no—
472Dic6—68no—
473Dic6—616no—
474Dic6—616no—
475Dic6—616no—
476Dic6—616no—
477Dic6—64no—
478Dic6—68no—
479Dic6—64no—
480Dic6—68no—
481Dic6C23×D314yes—
482C3×C8—38no—
483C3⋊C8C23×D318yes—
484C2×C32—22no—
485C2×C32C2×#13712yescomplemented
486C2×C32C23×D411yescharacteristic
487C3⋊D3—22no—
488C3⋊D3C2×#13714yescomplemented
489C3×D3—44no—
490C24—91no—
491C24—181no—
492#41—38no—
493#41—64no—
494#41—98no—
495#41—188no—
496#41—188no—
497#41—184no—
498C2×Q8—22no—
499C2×Q8—21no—
500C2×Q8—32no—
501C2×Q8—94no—
502C2×Q8—98no—
503C2×Q8—98no—
504C2×Q8—92no—
505C2×Q8—94no—
506C2×Q8—188no—
507C2×Q8—182no—
508C2×Q8—182no—
509C2×Q8—181no—
510C2×Q8—188no—
511C2×Q8—184no—
512C2×Q8—184no—
513C2×Q8—188no—
514C2×Q8—182no—
515C2×Q8—182no—
516C2×Q8—181no—
517C2×Q8C2×D3212yes—
518C2×Q8C2×D3214yescomplemented
519C2×D4—32no—
520C2×D4—62no—
521C2×D4—94no—
522C2×D4—182no—
523C2×D4—182no—
524C2×D4—181no—
525C2×D4—188no—
526C22×C4—21no—
527C22×C4—62no—
528C22×C4—91no—
529C22×C4—91no—
530C22×C4—94no—
531C22×C4—91no—
532C22×C4—91no—
533C22×C4—94no—
534C22×C4—91no—
535C22×C4—188no—
536C22×C4—182no—
537C22×C4—182no—
538C22×C4—188no—
539C22×C4—181no—
540C22×C4—182no—
541C22×C4—181no—
542C22×C4C2×D3211yescharacteristic
543Q16—316no—
544Q16—916no—
545SD16—316no—
546SD16—916no—
547M16—38no—
548M16—98no—
549C2×C8—34no—
550C2×C8—98no—
551C22×C3—24no—
552C22×C3—24no—
553C22×C3—22no—
554C22×C3—21no—
555C22×C3—64no—
556C22×C3—124no—
557C22×C3C2×D3×D414yes—
558C22×C3C2×D3×D412yes—
559C2×D3—24no—
560C2×D3—34no—
561C2×D3—38no—
562C2×D3—34no—
563C2×D3—44no—
564C2×D3—62no—
565C2×D3—62no—
566C2×D3—64no—
567C2×D3—616no—
568C2×D3—616no—
569C2×D3—64no—
570C2×D3—64no—
571C2×D3—1216no—
572C3×C4—28no—
573C3×C4—28no—
574C3×C4—22no—
575C3×C4—21no—
576C3×C4—21no—
577C3×C4—64no—
578C3×C4C2×D3×D412yes—
579C3×C4C2×D3×D414yes—
580C3×C4C24×D312yes—
581Dic3—24no—
582Dic3—34no—
583Dic3—34no—
584Dic3—62no—
585Dic3—62no—
586Dic3—68no—
587Dic3—68no—
588C32C22×#13711yescharacteristic, complemented, Sylow
589C23—62no—
590C23—91no—
591C23—94no—
592C23—91no—
593C23—184no—
594C23—184no—
595C23—364no—
596C23#381111yescharacteristic
597Q8—22no—
598Q8—24no—
599Q8—34no—
600Q8—62no—
601Q8—94no—
602Q8—188no—
603Q8—188no—
604Q8—184no—
605Q8—184no—
606Q8—182no—
607Q8C22×D3214yes—
608D4—34no—
609D4—68no—
610D4—62no—
611D4—188no—
612D4—184no—
613C2×C4—24no—
614C2×C4—22no—
615C2×C4—62no—
616C2×C4—68no—
617C2×C4—94no—
618C2×C4—91no—
619C2×C4—91no—
620C2×C4—94no—
621C2×C4—92no—
622C2×C4—92no—
623C2×C4—94no—
624C2×C4—92no—
625C2×C4—92no—
626C2×C4—188no—
627C2×C4—188no—
628C2×C4—184no—
629C2×C4—188no—
630C2×C4—184no—
631C2×C4—182no—
632C2×C4#381112yes—
633C2×C4#381111yescharacteristic
634C2×C4C22×D3212yes—
635C2×C4C22×D3211yescharacteristic
636C8—38no—
637C2×C3—24no—
638C2×C3—24no—
639C2×C3—21no—
640C2×C3—22no—
641C2×C3—124no—
642C2×C3D3×#13714yescomplemented
643C2×C3C22×D3×D412yes—
644D3—38no—
645D3—44no—
646D3—64no—
647D3—64no—
648D3—64no—
649C22—22no—
650C22—64no—
651C22—92no—
652C22—94no—
653C22—92no—
654C22—124no—
655C22—188no—
656C22—182no—
657C22—368no—
658C22C2×#381112yes—
659C22C2×#381111yescharacteristic
660C4—24no—
661C4—64no—
662C4—92no—
663C4—92no—
664C4—184no—
665C4C2×#381112yes—
666C4C2×#381111yescharacteristic
667C4C23×D3211yescharacteristic
668C3—21no—
669C3C2×D3×#13712yescomplemented
670C2—22no—
671C2—94no—
672C2—124no—
673C2—182no—
674C2#1059532212yesdirect product factor
675C2C22×#381111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×#64306C2
hypercenterC22×Q8D32
hypocenterC32C22×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×Q8×C3⋊D3C2semidirect
3. C2×C3×#942C2semidirect
4. C2×#63951C2semidirect
5. C2×#63944C2semidirect
6. #10595322C2direct (N × H)
7. C2×#63940C2semidirect
8. C2×#63831C2semidirect
9. C2×#63818C2semidirect
11. C22×C32×Q8C22semidirect
16. C2×Q8×C3⋊D3C22semidirect
17. C2×Q8×C3⋊D3C22semidirect
21. C22×#634C22semidirect
32. C2×C3×#216C22semidirect
33. C3×#942C22semidirect
34. C2×C3×#215C22semidirect
35. C2×C3×#208C22semidirect
36. #63951C22semidirect
37. #63944C22semidirect
38. #63940C22semidirect
39. C2×#3719C22semidirect
40. #63831C22semidirect
41. C2×#3716C22semidirect
42. C2×#3712C22semidirect
43. #63818C22semidirect
50. C2×#942D3semidirect
63. C2×C32×Q8C23semidirect
73. Q8×C3⋊D3C23semidirect
89. C2×#634C23semidirect
111. C3×#216C23semidirect
112. C3×#215C23semidirect
113. C3×#208C23semidirect
115. #3719C23semidirect
116. #3716C23semidirect
117. #3712C23semidirect
122. C22×C3×Q8C2×D3semidirect
160. C2×#216C2×D3semidirect
161. #942C2×D3semidirect
162. C2×#215C2×D3semidirect
164. C2×#208C2×D3semidirect
245. C2×C3×Q8C22×D3semidirect
331. #216C22×D3semidirect
332. #215C22×D3semidirect
334. #208C22×D3semidirect
345. C2×C3⋊D3#137semidirect
374. C22×Q8D32semidirect
485. C2×C32C2×#137semidirect
488. C3⋊D3C2×#137semidirect
518. C2×Q8C2×D32semidirect
588. C32C22×#137semidirect
642. C2×C3D3×#137semidirect
669. C3C2×D3×#137semidirect
674. C2#10595322direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C2×#643062
C2×C3×#9422
C2×#639512
C2×#639442
#105953222
C2×#639402
C2×#638312
C2×#638182
C2×D3×#1373