Finite Group Databasebeta

← Q8×#3811 #11902661

Subgroups — Q8×#3811 #11902661

Order 1152.

3561 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×D32×Q8C211yesmaximal, characteristic, complemented
3C3×Q8×#67C212yesmaximal, complemented
4#10595429C213yesmaximal, complemented
5Q8×#626C212yesmaximal, complemented
6Q8×#624C211yesmaximal, characteristic, complemented
7#10595365C213yesmaximal, complemented
8#10595361C216yesmaximal, complemented
9C4×#3811C213yesmaximal
10#10594925C213yesmaximal, complemented
11#10594915C216yesmaximal, complemented
12D3×D4×Q8—32nomaximal
13C22×C32×Q8C2211yescharacteristic, complemented
14C2×Q8×C3⋊D3—28no—
15C2×Q8×C3⋊D3C2213yes—
16C2×Q8×C3⋊D3C2211yescharacteristic
17C2×Q8×C3⋊D3C2213yescomplemented
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C22×C4×C3⋊D3C2213yes—
20C22×#634C2213yescomplemented
21C2×C3×D3×Q8C2212yescomplemented
22C2×#3811C2211yescharacteristic
23D32×Q8—28no—
24C2×C4×D32C2213yes—
25C2×#3797C2213yes—
26C2×D3×Dic6C2216yescomplemented
27C3×#946C2216yescomplemented
28C3×Q8×Dic3C2212yescomplemented
29C3×#944C2216yescomplemented
30C3×C4×#67C2216yes—
31C3×#924C2216yescomplemented
32#63982C2216yescomplemented
33#63974C2213yes—
34#67⋊Dic3C2216yes—
35#63921C2213yes—
36C4×#626C2216yes—
37#63900C2213yes—
38#63896C22112yescomplemented
39#63883C2213yes—
40#63883C2216yes—
41C4×#624C2213yes—
42#63881C2216yes—
43#63871C2216yescomplemented
44#63866C2216yescomplemented
45#63865C2216yescomplemented
46#63857C2216yescomplemented
47#63844C2216yescomplemented
48#63840C22112yescomplemented
49C22×D3×Q8—32no—
50C22×D3×Q8—32no—
51C22×D3×Q8—61no—
52C3×D4×Q8—32no—
53Q8×#67—32no—
54Q8×#67D312yescomplemented
55#5727—36no—
56D3×C4⋊Q8—36no—
57#5632—36no—
58#5632—36no—
59D3×C22⋊Q8—36no—
60D3×C22⋊Q8—36no—
61Q8×D12—32no—
62C4×D3×Q8—32no—
63C4×D3×D4—36no—
64D4×Dic6—36no—
65C23×C3⋊D3C2311yescharacteristic
66C22×D32C2311yescharacteristic
67C2×C32×Q8—24no—
68C2×C32×Q8C2313yes—
69C2×C32×Q8C2311yescharacteristic
70C22×C32×C4C2313yes—
71C22×C3⋊Dic3C2313yes—
72Q8×C3⋊D3—24no—
73Q8×C3⋊D3—212no—
74Q8×C3⋊D3—212no—
75Q8×C3⋊D3D418yescomplemented
76C2×C4×C3⋊D3—212no—
77C2×C4×C3⋊D3C2313yes—
78C2×C4×C3⋊D3C2313yes—
79C2×C4×C3⋊D3C2313yes—
80C2×C4×C3⋊D3C2313yes—
81C2×#634—212no—
82C2×#634C2316yes—
83C2×#634C2313yes—
84C2×#634C2313yes—
85C2×C3×#67C2312yes—
86C3×D3×Q8—28no—
87C2×C3×C4×D3C2316yes—
88C2×C3×Dic6C2316yes—
89#3811Q818yesdirect product factor
90C2×#627C2316yes—
91C2×#626C2312yes—
92C2×#624C2313yes—
93C2×#624C2313yes—
94C2×#624C2311yescharacteristic
95C2×D3×Dic3C2316yes—
96C4×D32—212no—
97#3797—212no—
98D3×Dic6—224no—
99C3×#217C2316yes—
100C3×(C2×D3)⋊C4C2316yes—
101C3×C4⋊Dic3C2316yes—
102C3×Dic3⋊C4C23112yes—
103C3×Dic3⋊C4C2316yes—
104C3×C4×Dic3C2316yes—
105#3724C2316yes—
106Dic3⋊Dic3C2316yes—
107Dic3⋊Dic3C23112yes—
108#3722C2316yes—
109(C2×D3)⋊Dic3C2316yes—
110Dic32C2316yes—
111C2×D4×Q8—91noSylow
112C22×C3×Q8—21no—
113C22×C3×Q8—32no—
114C22×C3×Q8C2×D312yescomplemented
115C2×D3×Q8—32no—
116C2×D3×Q8—36no—
117C2×D3×Q8—36no—
118C2×D3×Q8—32no—
119C2×D3×Q8—36no—
120C2×D3×Q8—36no—
121C2×D3×Q8—61no—
122C2×D3×Q8—63no—
123C2×D3×Q8—63no—
124C2×D3×Q8—61no—
125C2×D3×Q8—616no—
126C2×D3×Q8—616no—
127C2×D3×Q8—616no—
128C2×D3×Q8C2×D312yescomplemented
129C2×D3×D4—32no—
130C22×C4×D3—36no—
131C22×C4×D3—36no—
132C22×C4×D3—63no—
133C22×Dic6—36no—
134C22×Dic6—36no—
135C22×Dic6—63no—
136C3×C4⋊Q8—36no—
137C3×C22⋊Q8—36no—
138C3×C22⋊Q8—36no—
139C3×C4×Q8—32no—
140C3×C4×D4—36no—
141#946—36no—
142#946C2×D316yescomplemented
143Q8×Dic3C2×D312yescomplemented
144#944—36no—
145#944C2×D316yescomplemented
146D4×Dic3—36no—
147C4×#67—36no—
148C4×#67C2×D316yes—
149#924—36no—
150#924C2×D316yescomplemented
151#897—36no—
152#897—36no—
153#896—312no—
154#896—312no—
155#893—36no—
156D3×C4⋊C4—36no—
157D3×C4⋊C4—36no—
158D3×C4⋊C4—312no—
159#888—312no—
160#888—312no—
161#887—36no—
162#67⋊C4—36no—
163#67⋊C4—36no—
164D3×C22⋊C4—36no—
165D3×C22⋊C4—36no—
166#878—312no—
167#878—312no—
168C4×D12—36no—
169C42×D3—36no—
170#869—36no—
171C4×Dic6—36no—
172C23×C32C2411yescharacteristic
173C22×C3⋊D3—22no—
174C22×C3⋊D3—22no—
175C22×C3⋊D3C2×Q814yescomplemented
176C22×C3⋊D3C2411yescharacteristic
177C22×C3⋊D3C2411yescharacteristic
178C22×C3×D3C2412yes—
179C2×D32—22no—
180C2×D32—22no—
181C2×D32C2×Q814yescomplemented
182C32×Q8—26no—
183C32×Q8C2×D414yescomplemented
184C2×C32×C4—26no—
185C2×C32×C4C2413yes—
186C2×C32×C4C2413yes—
187C2×C3⋊Dic3—26no—
188C2×C3⋊Dic3C2413yes—
189C2×C3⋊Dic3C2413yes—
190C4×C3⋊D3—26no—
191C4×C3⋊D3—26no—
192C4×C3⋊D3—26no—
193C4×C3⋊D3C2×D4112yes—
194#634—26no—
195#634—212no—
196#634C2×D4112yescomplemented
197C3×#67C2×Q818yescomplemented
198C2×C3×Dic3C2416yes—
199C2×C3×Dic3C2416yes—
200C2×C3×Dic3C2412yes—
201C3×C4×D3—212no—
202C3×Dic6—212no—
203#627—212no—
204#626C2×Q818yescomplemented
205#624—26no—
206#624—26no—
207#624C2×Q814yescomplemented
208D3×Dic3—212no—
209C23×Q8—91no—
210C23×Q8—91no—
211D4×Q8—32no—
212D4×Q8—96no—
213D4×Q8—92no—
214D4×Q8—96no—
215C2×C4⋊Q8—93no—
216C2×C22⋊Q8—93no—
217C2×C22⋊Q8—93no—
218C2×C4×Q8—91no—
219C2×C4×D4—93no—
220C23×D3—32no—
221C23×D3—32no—
222C23×D3—61no—
223C2×C3×Q8—28no—
224C2×C3×Q8—28no—
225C2×C3×Q8—23no—
226C2×C3×Q8—21no—
227C2×C3×Q8—36no—
228C2×C3×Q8—68no—
229C2×C3×Q8C22×D316yes—
230C2×C3×Q8C22×D312yes—
231C2×C3×D4—32no—
232C22×C3×C4—23no—
233C22×C3×C4—36no—
234C22×C3×C4C22×D316yes—
235C2×#67—32no—
236C2×#67C22×D312yes—
237C22×Dic3—36no—
238C22×Dic3—36no—
239C22×Dic3—63no—
240D3×Q8—28no—
241D3×Q8—316no—
242D3×Q8—68no—
243D3×Q8—624no—
244D3×Q8—624no—
245D3×Q8—624no—
246D3×Q8—624no—
247D3×Q8—624no—
248D3×Q8—624no—
249D3×Q8—68no—
250D3×Q8—68no—
251D3×D4—316no—
252C2×D12—32no—
253C2×C4×D3—36no—
254C2×C4×D3—32no—
255C2×C4×D3—36no—
256C2×C4×D3—36no—
257C2×C4×D3—36no—
258C2×C4×D3—36no—
259C2×C4×D3—36no—
260C2×C4×D3—36no—
261C2×C4×D3—63no—
262C2×C4×D3—63no—
263C2×C4×D3—63no—
264C2×C4×D3—63no—
265C2×C4×D3—624no—
266C2×C4×D3—624no—
267C2×C4×D3—624no—
268C2×C4×D3C22×D316yes—
269C2×Dic6—36no—
270C2×Dic6—36no—
271C2×Dic6—312no—
272C2×Dic6—312no—
273C2×Dic6—63no—
274C2×Dic6—66no—
275C2×Dic6—63no—
276C2×Dic6—624no—
277C2×Dic6—624no—
278C2×Dic6—624no—
279C2×Dic6C22×D316yes—
280C3×C4⋊C4—36no—
281C3×C4⋊C4—36no—
282C3×C4⋊C4—312no—
283C3×C22⋊C4—36no—
284C3×C22⋊C4—36no—
285C3×C42—36no—
286#217—36no—
287#217C22×D316yes—
288(C2×D3)⋊C4—36no—
289(C2×D3)⋊C4—36no—
290(C2×D3)⋊C4—36no—
291(C2×D3)⋊C4C22×D316yes—
292C4⋊Dic3—36no—
293C4⋊Dic3—312no—
294C4⋊Dic3C22×D316yes—
295Dic3⋊C4—312no—
296Dic3⋊C4—312no—
297Dic3⋊C4—36no—
298Dic3⋊C4C22×D3112yes—
299Dic3⋊C4C22×D316yes—
300C4×Dic3—36no—
301C4×Dic3—36no—
302C4×Dic3C22×D316yes—
303C22×C32—21no—
304C22×C32—21no—
305C22×C32C22×Q812yescomplemented
306C22×C32C2511yescharacteristic
307C2×C3⋊D3—21no—
308C2×C3⋊D3—21no—
309C2×C3⋊D3—28no—
310C2×C3⋊D3C22×D412yes—
311C2×C3⋊D3C22×Q812yes—
312C2×C3⋊D3C22×Q812yescomplemented
313C2×C3⋊D32−1+412yes—
314C2×C3×D3—22no—
315C2×C3×D3—22no—
316C2×C3×D3C22×Q814yescomplemented
317D32—28no—
318C32×C4—23no—
319C32×C4C22×D416yes—
320C3⋊Dic3—23no—
321C3⋊Dic3C22×D416yes—
322C3×Dic3—26no—
323C3×Dic3—26no—
324C3×Dic3C22×Q814yescomplemented
325C22×Q8—32no—
326C22×Q8—96no—
327C22×Q8—93no—
328C22×Q8—91no—
329C22×Q8—93no—
330C22×Q8—93no—
331C22×Q8—91no—
332C22×Q8—93no—
333C22×Q8—188no—
334C22×Q8—188no—
335C22×Q8D3211yescharacteristic, complemented
336C22×D4—91no—
337C23×C4—93no—
338C23×C4—93no—
339C4⋊Q8—36no—
340C4⋊Q8—96no—
341C4⋊Q8—912no—
342C22⋊Q8—36no—
343C22⋊Q8—36no—
344C22⋊Q8—96no—
345C22⋊Q8—912no—
346C22⋊Q8—96no—
347C22⋊Q8—96no—
348C22⋊Q8—96no—
349C4×Q8—32no—
350C4×Q8—96no—
351C4×D4—36no—
352C4×D4—96no—
353C4×D4—96no—
354C4×D4—96no—
355C2×C4⋊C4—93no—
356C2×C4⋊C4—93no—
357C2×C4⋊C4—96no—
358C2×C22⋊C4—93no—
359C2×C22⋊C4—93no—
360C2×C42—93no—
361C23×C3—21no—
362C23×C3—32no—
363C23×C3C23×D312yes—
364C22×D3—32no—
365C22×D3—38no—
366C22×D3—32no—
367C22×D3—38no—
368C22×D3—64no—
369C22×D3—61no—
370C22×D3—61no—
371C22×D3—64no—
372C22×D3—64no—
373C22×D3—64no—
374C22×D3—64no—
375C22×D3—64no—
376C22×D3—64no—
377C22×D3C23×D312yes—
378C3×Q8—212no—
379C3×Q8—212no—
380C3×Q8—24no—
381C3×Q8—612no—
382C3×Q8D3×D418yescomplemented
383C3×D4—38no—
384C2×C3×C4—212no—
385C2×C3×C4—212no—
386C2×C3×C4—23no—
387C2×C3×C4—23no—
388C2×C3×C4—32no—
389C2×C3×C4—36no—
390C2×C3×C4—36no—
391C2×C3×C4—612no—
392C2×C3×C4C23×D316yes—
393C2×C3×C4C23×D316yes—
394#67—38no—
395#67D3×Q818yescomplemented
396C2×Dic3—36no—
397C2×Dic3—36no—
398C2×Dic3—63no—
399C2×Dic3—63no—
400C2×Dic3—612no—
401C2×Dic3—612no—
402C2×Dic3—612no—
403C2×Dic3C23×D316yes—
404C2×Dic3C23×D316yes—
405C2×Dic3C23×D312yes—
406D12—38no—
407C4×D3—212no—
408C4×D3—324no—
409C4×D3—38no—
410C4×D3—612no—
411C4×D3—612no—
412C4×D3—612no—
413C4×D3—612no—
414C4×D3—612no—
415C4×D3—612no—
416C4×D3—612no—
417C4×D3—612no—
418C4×D3—612no—
419C4×D3—612no—
420Dic6—212no—
421Dic6—324no—
422Dic6—612no—
423Dic6—624no—
424Dic6—624no—
425Dic6—624no—
426Dic6—612no—
427Dic6—612no—
428C2×C32—22no—
429C2×C32C23×D411yescharacteristic
430C2×C32C23×Q811yescharacteristic
431C2×C32C2×2−1+411yescharacteristic
432C3⋊D3—22no—
433C3⋊D3D4×Q814yescomplemented
434C3×D3—24no—
435C24—91no—
436C24—91no—
437C2×Q8—24no—
438C2×Q8—36no—
439C2×Q8—68no—
440C2×Q8—96no—
441C2×Q8—98no—
442C2×Q8—93no—
443C2×Q8—96no—
444C2×Q8—93no—
445C2×Q8—1812no—
446C2×Q8—1824no—
447C2×Q8—1812no—
448C2×Q8—1812no—
449C2×Q8—1812no—
450C2×Q8—184no—
451C2×Q8C2×D3213yes—
452C2×Q8C2×D3211yescharacteristic
453C2×D4—32no—
454C2×D4—92no—
455C2×D4—98no—
456C22×C4—36no—
457C22×C4—91no—
458C22×C4—93no—
459C22×C4—93no—
460C22×C4—96no—
461C22×C4—93no—
462C22×C4—93no—
463C22×C4—93no—
464C22×C4—93no—
465C22×C4—93no—
466C22×C4—1812no—
467C22×C4—1812no—
468C22×C4C2×D3213yes—
469C4⋊C4—36no—
470C4⋊C4—36no—
471C4⋊C4—312no—
472C4⋊C4—96no—
473C4⋊C4—96no—
474C4⋊C4—912no—
475C22⋊C4—36no—
476C22⋊C4—36no—
477C22⋊C4—96no—
478C22⋊C4—96no—
479C42—36no—
480C42—96no—
481C22×C3—22no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—21no—
487C22×C3—34no—
488C22×C3—62no—
489C22×C3—62no—
490C22×C3C2×D3×Q814yescomplemented
491C22×C3C24×D312yes—
492C2×D3—22no—
493C2×D3—22no—
494C2×D3—34no—
495C2×D3—34no—
496C2×D3—34no—
497C2×D3—34no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—62no—
501C2×D3—62no—
502C2×D3—616no—
503C2×D3—616no—
504C2×D3—62no—
505C2×D3—616no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—62no—
509C2×D3C2×D3×Q814yescomplemented
510C3×C4—26no—
511C3×C4—26no—
512C3×C4—26no—
513C3×C4—34no—
514C3×C4—66no—
515C3×C4—66no—
516C3×C4C2×D3×D4112yes—
517Dic3—26no—
518Dic3—26no—
519Dic3—312no—
520Dic3—66no—
521Dic3—66no—
522Dic3—66no—
523Dic3C2×D3×Q814yescomplemented
524C32C2×D4×Q811yescharacteristic, complemented, Sylow
525C23—32no—
526C23—94no—
527C23—91no—
528C23—94no—
529C23—91no—
530C23—182no—
531C23—182no—
532C23—182no—
533C23—182no—
534C23C22×D3211yescharacteristic
535Q8—26no—
536Q8—612no—
537Q8—912no—
538Q8—1812no—
539Q8—1812no—
540Q8—186no—
541Q8#381114yesdirect product factor
542D4—38no—
543D4—98no—
544C2×C4—26no—
545C2×C4—32no—
546C2×C4—36no—
547C2×C4—36no—
548C2×C4—612no—
549C2×C4—94no—
550C2×C4—93no—
551C2×C4—912no—
552C2×C4—93no—
553C2×C4—186no—
554C2×C4—186no—
555C2×C4—186no—
556C2×C4—186no—
557C2×C4—1812no—
558C2×C4—186no—
559C2×C4—186no—
560C2×C4C22×D3213yes—
561C2×C4C22×D3213yes—
562C2×C3—24no—
563C2×C3—24no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—64no—
568C2×C3C22×D3×D412yes—
569C2×C3C22×D3×Q812yes—
570C2×C3D3×2−1+412yes—
571D3—24no—
572D3—38no—
573D3—64no—
574D3—64no—
575D3—64no—
576C22—21no—
577C22—21no—
578C22—34no—
579C22—62no—
580C22—62no—
581C22—92no—
582C22—92no—
583C22—92no—
584C22—92no—
585C22—188no—
586C22—188no—
587C22—181no—
588C22—181no—
589C22D32×Q812yescomplemented
590C22C23×D3211yescharacteristic
591C4—23no—
592C4—34no—
593C4—66no—
594C4—66no—
595C4—96no—
596C4—183no—
597C4C2×#381116yes—
598C3—21no—
599C3D3×D4×Q812yescomplemented
600C2—22no—
601C2—64no—
602C2—94no—
603C2—182no—
604C2C2×D32×Q811yescharacteristic
605C2#1059668711yescharacteristic
606C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
prime radicalC2×#3811C22
hypercenterC22×Q8D32
hypocenterC32C2×D4×Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×Q8×C3⋊D3C2semidirect
2. C2×D32×Q8C2semidirect
3. C3×Q8×#67C2semidirect
4. #10595429C2semidirect
5. Q8×#626C2semidirect
6. Q8×#624C2semidirect
7. #10595365C2semidirect
8. #10595361C2semidirect
10. #10594925C2semidirect
11. #10594915C2semidirect
13. C22×C32×Q8C22semidirect
17. C2×Q8×C3⋊D3C22semidirect
18. C2×Q8×C3⋊D3C22semidirect
20. C22×#634C22semidirect
21. C2×C3×D3×Q8C22semidirect
26. C2×D3×Dic6C22semidirect
27. C3×#946C22semidirect
28. C3×Q8×Dic3C22semidirect
29. C3×#944C22semidirect
31. C3×#924C22semidirect
32. #63982C22semidirect
38. #63896C22semidirect
43. #63871C22semidirect
44. #63866C22semidirect
45. #63865C22semidirect
46. #63857C22semidirect
47. #63844C22semidirect
48. #63840C22semidirect
54. Q8×#67D3semidirect
75. Q8×C3⋊D3D4semidirect
89. #3811Q8direct (N × H)
114. C22×C3×Q8C2×D3semidirect
128. C2×D3×Q8C2×D3semidirect
142. #946C2×D3semidirect
143. Q8×Dic3C2×D3semidirect
145. #944C2×D3semidirect
150. #924C2×D3semidirect
175. C22×C3⋊D3C2×Q8semidirect
181. C2×D32C2×Q8semidirect
183. C32×Q8C2×D4semidirect
196. #634C2×D4semidirect
197. C3×#67C2×Q8semidirect
204. #626C2×Q8semidirect
207. #624C2×Q8semidirect
305. C22×C32C22×Q8semidirect
312. C2×C3⋊D3C22×Q8semidirect
316. C2×C3×D3C22×Q8semidirect
324. C3×Dic3C22×Q8semidirect
335. C22×Q8D32semidirect
382. C3×Q8D3×D4semidirect
395. #67D3×Q8semidirect
433. C3⋊D3D4×Q8semidirect
490. C22×C3C2×D3×Q8semidirect
509. C2×D3C2×D3×Q8semidirect
523. Dic3C2×D3×Q8semidirect
524. C32C2×D4×Q8semidirect
541. Q8#3811direct (N × H)
589. C22D32×Q8semidirect
599. C3D3×D4×Q8semidirect

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×D32×Q82
C3×Q8×#672
#105954292
Q8×#6262
Q8×#6242
#105953652
#105953612
C4×#38112
#105949252
#105949152
D3×D4×Q83