Finite Group Databasebeta

← #11866790

Subgroups — #11866790

Order 1152.

1185 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C22⋊Q8C211yesmaximal, characteristic
2C2×#63944C211yesmaximal, characteristic, complemented
3#10594925C211yesmaximal, characteristic
4C22×#3710C211yesmaximal, characteristic
5C3×#5051C212yesmaximal, complemented
6#10591601C212yesmaximal, complemented
7#10591552C211yesmaximal, characteristic, complemented
8#10591187C212yesmaximal, complemented
9#10590601C211yesmaximal, characteristic, complemented
10#10590573C211yesmaximal, characteristic, complemented
11#10590525C212yesmaximal, complemented
12D3×#467—32nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C2×#3797C2211yescharacteristic
16C32×C22⋊Q8C2211yescharacteristic
17#64155C2211yescharacteristic
18#64133C2211yescharacteristic
19#64106C2211yescharacteristic
20#64105—21no—
21C4⋊C4×C3⋊D3—21no—
22C4⋊C4×C3⋊D3C2211yescharacteristic
23C22⋊C4×C3⋊D3—21no—
24#64087—21no—
25C2×C3×#216C2212yescomplemented
26C3×#924C2212yes—
27C22×C3×C3⋊C8C2212yes—
28#63982—21no—
29#63974—21no—
30#63944—24no—
31#63900C2211yescharacteristic
32#63883—21no—
33#63871C2212yes—
34#63865—21no—
35C2×#3719C2212yescomplemented
36C2×#3710—24no—
37C2×#3710C2212yes—
38C2×#3710C2211yescharacteristic
39C2×#3710C2211yescharacteristic
40C3×#835C2212yescomplemented
41C3×#810C2212yescomplemented
42C3×#807C2212yescomplemented
43#63575C2212yescomplemented
44#63567C2212yescomplemented
45#63566C2212yescomplemented
46C2×D3×Q16—32no—
47C22×D3×C8—32no—
48D3×C22⋊Q8—32no—
49D3×C22⋊Q8—32no—
50D3×C22⋊Q8—61no—
51C3×#467—32no—
52#5188—32no—
53#5116—32no—
54#5051—32no—
55#5051D312yescomplemented
56#4887—32no—
57D3×#107—32no—
58#4813—32no—
59#4813—32no—
60D3×#103—32no—
61D3×#103—32no—
62C23×C3⋊D3D411yescharacteristic
63C2×C32×Q8C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3D411yescharacteristic
66Q8×C3⋊D3—22no—
67Q8×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3—21no—
71C2×C4×C3⋊D3—21no—
72C2×C4×C3⋊D3D411yescharacteristic
73C2×C4×C3⋊D3D411yescharacteristic
74C2×C4×C3⋊D3C2311yescharacteristic
75C2×C4×C3⋊D3C2311yescharacteristic
76C2×#634—21no—
77C2×#634C2311yescharacteristic
78C2×C3×Dic6C2312yes—
79C2×#627—21no—
80C2×#624—21no—
81C2×#624—21no—
82#3797—22no—
83#3797—22no—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87#3757—21no—
88#3752—21no—
89#3752—21no—
90C4⋊(C3⋊Dic3)—21no—
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92#3750—21no—
93#3750—21no—
94#3750—21no—
95C3×#217—22no—
96C3×#216—24no—
97C3×C4⋊Dic3C2312yes—
98C3×Dic3⋊C4—22no—
99C2×C3×C3⋊C8—24no—
100C2×C3×C3⋊C8C2312yes—
101C2×C3×C3⋊C8C2312yes—
102#3724—21no—
103Dic3⋊Dic3—22no—
104#3722—22no—
105#3719—24no—
106#3710—22no—
107#3710—24no—
108#3710D414yes—
109C2×#467—91noSylow
110C2×D3×Q8—32no—
111C2×D3×Q8—32no—
112C2×D3×Q8—61no—
113C22×C4×D3—32no—
114C22×C4×D3—61no—
115C2×C3×Q16—32no—
116C22×C3×C8—32no—
117C3×C22⋊Q8—21no—
118C3×C22⋊Q8—32no—
119C3×C22⋊Q8C2×D312yes—
120#946—32no—
121#946—32no—
122#946—61no—
123C2×#216—32no—
124C2×#216C2×D312yescomplemented
125#924—32no—
126#924—61no—
127#924C2×D312yes—
128C22×C3⋊C8C2×D312yes—
129D3×Q16—68no—
130C2×Dic12—32no—
131C2×D3×C8—32no—
132C2×D3×C8—32no—
133C2×D3×C8—32no—
134C2×D3×C8—32no—
135C2×D3×C8—68no—
136#897—32no—
137#897—32no—
138#897—61no—
139#896—62no—
140#896—62no—
141#896—62no—
142D3×C4⋊C4—32no—
143D3×C4⋊C4—32no—
144D3×C4⋊C4—61no—
145D3×C4⋊C4—62no—
146D3×C4⋊C4—62no—
147D3×C4⋊C4—62no—
148D3×C22⋊C4—62no—
149D3×C22⋊C4—62no—
150D3×C22⋊C4—62no—
151#878—62no—
152#878—62no—
153#878—62no—
154C3×#107—32no—
155C3×#103—32no—
156C3×#103—32no—
157#835—32no—
158#835C2×D312yescomplemented
159#818—32no—
160#816—32no—
161#816—32no—
162#810—32no—
163#810C2×D312yescomplemented
164#807—32no—
165#807C2×D312yescomplemented
166C23×C32C2×D411yescharacteristic
167C22×C3⋊D3—22no—
168C22×C3⋊D3—22no—
169C22×C3⋊D3Q1614yescomplemented
170C22×C3⋊D3C2×D411yescharacteristic
171C22×C3⋊D3C2×D411yescharacteristic
172C32×Q8—21no—
173C32×Q8—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3C2×D411yescharacteristic
184C2×C3⋊Dic3C2×D411yescharacteristic
185C4×C3⋊D3—22no—
186C4×C3⋊D3—21no—
187C4×C3⋊D3—21no—
188C4×C3⋊D3—22no—
189C4×C3⋊D3—42no—
190C4×C3⋊D3—42no—
191C4×C3⋊D3C2×D412yes—
192C4×C3⋊D3#4112yes—
193#634—21no—
194#634—21no—
195#634—42no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C3×Dic6—22no—
199C3×Dic6—22no—
200#627—42no—
201#624—42no—
202#624—42no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8C2×D414yes—
205C22×Q16—91no—
206C23×C8—91no—
207C2×C22⋊Q8—91no—
208C2×C22⋊Q8—91no—
209#467—32no—
210#467—92no—
211#467—92no—
212#467—92no—
213C2×#107—91no—
214C2×#103—91no—
215C2×#103—91no—
216C23×D3—32no—
217C23×D3—61no—
218C2×C3×Q8—21no—
219C2×C3×Q8—32no—
220C2×C3×Q8C22×D312yes—
221C22×C3×C4—21no—
222C22×C3×C4C22×D312yes—
223C22×Dic3—32no—
224C22×Dic3—61no—
225D3×Q8—64no—
226D3×Q8—64no—
227D3×Q8—64no—
228D3×Q8—64no—
229D3×Q8—122no—
230D3×Q8—122no—
231C2×C4×D3—32no—
232C2×C4×D3—32no—
233C2×C4×D3—32no—
234C2×C4×D3—32no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×C4×D3—61no—
238C2×C4×D3—61no—
239C2×C4×D3—64no—
240C2×C4×D3—64no—
241C2×C4×D3—62no—
242C2×C4×D3—62no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C2×C4×D3—62no—
246C2×C4×D3—62no—
247C2×C4×D3—122no—
248C2×C4×D3—122no—
249C2×Dic6—32no—
250C2×Dic6—61no—
251C2×Dic6—62no—
252C2×Dic6—62no—
253C2×Dic6—62no—
254C2×Dic6C22×D312yes—
255C3×Q16—64no—
256C2×C3×C8—32no—
257C2×C3×C8—32no—
258C2×C3×C8—64no—
259C3×C4⋊C4—22no—
260C3×C4⋊C4—22no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—32no—
263C3×C4⋊C4—62no—
264C3×C4⋊C4C22×D312yes—
265C3×C22⋊C4—22no—
266C3×C22⋊C4—22no—
267C3×C22⋊C4—62no—
268#217—22no—
269#217—62no—
270#217—62no—
271#216—24no—
272#216—64no—
273(C2×D3)⋊C4—62no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—62no—
277(C2×D3)⋊C4—62no—
278(C2×D3)⋊C4—62no—
279C4⋊Dic3—32no—
280C4⋊Dic3—61no—
281C4⋊Dic3—62no—
282C4⋊Dic3—62no—
283C4⋊Dic3—62no—
284C4⋊Dic3C22×D312yes—
285Dic3⋊C4—22no—
286Dic3⋊C4—62no—
287Dic3⋊C4—62no—
288Dic3⋊C4—62no—
289Dic3⋊C4—62no—
290Dic3⋊C4—62no—
291Dic3⋊C4—62no—
292Dic3⋊C4—62no—
293Dic3⋊C4—62no—
294C2×C3⋊C8—24no—
295C2×C3⋊C8C22×D312yes—
296C2×C3⋊C8C22×D312yes—
297Dic12—64no—
298D3×C8—38no—
299D3×C8—64no—
300D3×C8—64no—
301D3×C8—64no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32C2×Q1612yescomplemented
305C22×C32C22×D411yescharacteristic
306C2×C3⋊D3—21no—
307C2×C3⋊D3—21no—
308C2×C3⋊D3—28no—
309C2×C3⋊D3#12112yes—
310C2×C3⋊D3C2×Q1612yes—
311C2×C3⋊D3C2×Q1612yescomplemented
312C2×C3⋊D3#13512yes—
313C32×C4—21no—
314C32×C4—41no—
315C32×C4—41no—
316C32×C4C22×D411yescharacteristic
317C32×C4C2×#4111yescharacteristic
318C3⋊Dic3—21no—
319C3⋊Dic3—41no—
320C3⋊Dic3—41no—
321C3⋊Dic3#12112yes—
322C3×Dic3—42no—
323C3×Dic3—42no—
324C22×Q8—91no—
325C22×Q8—91no—
326C23×C4—91no—
327C2×Q16—32no—
328C2×Q16—92no—
329C2×Q16—184no—
330C22×C8—32no—
331C22×C8—91no—
332C22×C8—91no—
333C22×C8—92no—
334C22×C8—184no—
335C22⋊Q8—32no—
336C22⋊Q8—92no—
337C22⋊Q8—91no—
338C22⋊Q8—91no—
339C22⋊Q8—91no—
340C22⋊Q8—181no—
341C22⋊Q8—181no—
342C22⋊Q8—181no—
343C22⋊Q8—181no—
344C22⋊Q8D3211yescharacteristic
345C2×C4⋊C4—91no—
346C2×C4⋊C4—91no—
347C2×C4⋊C4—181no—
348C2×C4⋊C4—181no—
349C2×C22⋊C4—181no—
350C2×C22⋊C4—181no—
351#107—32no—
352#107—92no—
353#103—32no—
354#103—32no—
355#103—92no—
356#103—92no—
357C23×C3—21no—
358C23×C3D3×D412yes—
359C22×D3—32no—
360C22×D3—38no—
361C22×D3—32no—
362C22×D3—61no—
363C22×D3—64no—
364C22×D3—61no—
365C22×D3—64no—
366C22×D3—64no—
367C22×D3—122no—
368C22×D3—122no—
369C3×Q8—22no—
370C3×Q8—22no—
371C3×Q8—41no—
372C3×Q8—41no—
373C3×Q8—62no—
374C3×Q8—62no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4D3×D412yes—
388C2×C3×C4C23×D312yes—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—32no—
392C2×Dic3—32no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—64no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—122no—
401C4×D3—34no—
402C4×D3—34no—
403C4×D3—62no—
404C4×D3—62no—
405C4×D3—64no—
406C4×D3—64no—
407C4×D3—62no—
408C4×D3—62no—
409C4×D3—122no—
410C4×D3—121no—
411C4×D3—121no—
412C4×D3—122no—
413C4×D3—124no—
414C4×D3—124no—
415C4×D3—124no—
416C4×D3—124no—
417C4×D3—124no—
418C4×D3—124no—
419Dic6—22no—
420Dic6—22no—
421Dic6—62no—
422Dic6—62no—
423Dic6—121no—
424Dic6—121no—
425Dic6—124no—
426Dic6—124no—
427Dic6—124no—
428C3×C8—34no—
429C3×C8—62no—
430C3⋊C8—22no—
431C3⋊C8D3×D414yes—
432C2×C32—22no—
433C2×C32C2×#12111yescharacteristic
434C2×C32C22×Q1611yescharacteristic
435C2×C32C2×#13511yescharacteristic
436C3⋊D3—22no—
437C3⋊D3#46714yescomplemented
438C24—91no—
439C2×Q8—32no—
440C2×Q8—91no—
441C2×Q8—181no—
442C2×Q8—181no—
443C2×Q8—182no—
444C2×Q8—182no—
445C2×Q8—182no—
446C2×Q8—182no—
447C2×Q8C2×D3211yescharacteristic
448C22×C4—91no—
449C22×C4—91no—
450C22×C4—91no—
451C22×C4—91no—
452C22×C4—91no—
453C22×C4—182no—
454C22×C4—182no—
455C22×C4—181no—
456C22×C4—181no—
457C22×C4—181no—
458C22×C4—181no—
459C22×C4C2×D3211yescharacteristic
460Q16—64no—
461Q16—184no—
462C2×C8—32no—
463C2×C8—32no—
464C2×C8—64no—
465C2×C8—94no—
466C2×C8—184no—
467C2×C8—182no—
468C4⋊C4—21no—
469C4⋊C4—32no—
470C4⋊C4—62no—
471C4⋊C4—91no—
472C4⋊C4—181no—
473C4⋊C4—181no—
474C4⋊C4—181no—
475C4⋊C4—181no—
476C4⋊C4—182no—
477C4⋊C4—181no—
478C4⋊C4C2×D3211yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—62no—
481C22⋊C4—181no—
482C22⋊C4—181no—
483C22⋊C4—182no—
484C22⋊C4—181no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—21no—
488C22×C3—22no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3D3×Q1614yescomplemented
492C22×C3C2×D3×D412yes—
493C2×D3—34no—
494C2×D3—34no—
495C2×D3—34no—
496C2×D3—34no—
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—62no—
501C2×D3—616no—
502C2×D3—62no—
503C2×D3—62no—
504C2×D3—128no—
505C2×D3—121no—
506C2×D3—121no—
507C3×C4—22no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—41no—
511C3×C4—42no—
512C3×C4—42no—
513C3×C4—42no—
514C3×C4—42no—
515C3×C4—122no—
516C3×C4—122no—
517C3×C4C2×D3×D412yes—
518C3×C4D3×#4112yes—
519Dic3—34no—
520Dic3—42no—
521Dic3—42no—
522Dic3—62no—
523Dic3—62no—
524Dic3—121no—
525Dic3—122no—
526Dic3—122no—
527Dic3—122no—
528Dic3—122no—
529C32C2×#46711yescharacteristic, complemented, Sylow
530C23—91no—
531C23—91no—
532C23—94no—
533C23—182no—
534C23—182no—
535C23#381111yescharacteristic
536Q8—21no—
537Q8—21no—
538Q8—62no—
539Q8—62no—
540Q8—181no—
541Q8—181no—
542Q8—362no—
543Q8—362no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—91no—
551C2×C4—92no—
552C2×C4—92no—
553C2×C4—91no—
554C2×C4—182no—
555C2×C4—182no—
556C2×C4—182no—
557C2×C4—181no—
558C2×C4—181no—
559C2×C4—181no—
560C2×C4—181no—
561C2×C4—362no—
562C2×C4—362no—
563C2×C4—362no—
564C2×C4—362no—
565C2×C4#381111yescharacteristic
566C2×C4C22×D3211yescharacteristic
567C8—34no—
568C8—62no—
569C2×C3—24no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—42no—
574C2×C3D3×#12112yes—
575C2×C3C2×D3×Q1612yes—
576C2×C3D3×#13512yes—
577D3—38no—
578D3—64no—
579D3—64no—
580D3—122no—
581C22—21no—
582C22—21no—
583C22—92no—
584C22—92no—
585C22—92no—
586C22—92no—
587C22—188no—
588C22—181no—
589C22—181no—
590C22#6394412yescomplemented
591C22C2×#381111yescharacteristic
592C4—21no—
593C4—41no—
594C4—41no—
595C4—92no—
596C4—122no—
597C4—122no—
598C4—181no—
599C4—361no—
600C4—361no—
601C4D32×D411yescharacteristic
602C4#6431211yescharacteristic
603C3—21no—
604C3D3×#46712yescomplemented
605C2—22no—
606C2—94no—
607C2—182no—
608C2#1059529811yescharacteristic
609C2C2×#6394411yescharacteristic
610C2#1059545911yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
hypercenterC22⋊Q8D32
hypocenterC32C2×#467
LCSG ▷ C2×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
2. C2×#63944C2semidirect
5. C3×#5051C2semidirect
6. #10591601C2semidirect
7. #10591552C2semidirect
8. #10591187C2semidirect
9. #10590601C2semidirect
10. #10590573C2semidirect
11. #10590525C2semidirect
25. C2×C3×#216C22semidirect
35. C2×#3719C22semidirect
40. C3×#835C22semidirect
41. C3×#810C22semidirect
42. C3×#807C22semidirect
43. #63575C22semidirect
44. #63567C22semidirect
45. #63566C22semidirect
55. #5051D3semidirect
124. C2×#216C2×D3semidirect
158. #835C2×D3semidirect
163. #810C2×D3semidirect
165. #807C2×D3semidirect
169. C22×C3⋊D3Q16semidirect
304. C22×C32C2×Q16semidirect
311. C2×C3⋊D3C2×Q16semidirect
437. C3⋊D3#467semidirect
491. C22×C3D3×Q16semidirect
529. C32C2×#467semidirect
590. C22#63944semidirect
604. C3D3×#467semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C22⋊Q82
C2×#639442
#105949252
C22×#37102
C3×#50512
#105916012
#105915522
#105911872
#105906012
#105905732
#105905252
D3×#4673