Finite Group Databasebeta

← #11865761

Subgroups — #11865761

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63808C212yesmaximal, complemented
2#10593970C211yesmaximal, characteristic, complemented
3C4×#3799C211yesmaximal, characteristic, complemented
4#10592542C211yesmaximal, characteristic, complemented
5C3×#4849C211yesmaximal, characteristic, complemented
6C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
7#10590801C212yesmaximal, complemented
8#10590770C212yesmaximal, complemented
9#10590690C212yesmaximal, complemented
10#10590379C211yesmaximal, characteristic, complemented
11#10590367C211yesmaximal, characteristic, complemented
12#80475—31nomaximal
13#79021—31nomaximal
14C2×#3799C2212yes—
15C2×#3799C2211yescharacteristic
16C2×#3745C2212yes—
17#64083C2211yescharacteristic
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×Dic12C2212yes—
20C2×C3×D3×C8C2212yes—
21C3×C42×D3C2211yescharacteristic
22C3×#869C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63909—21no—
25#63909—21no—
26#63904—21no—
27C4×#626—21no—
28#63894—21no—
29#63894—21no—
30#63894C2211yescharacteristic
31C4×#624—21no—
32#63864C2212yes—
33Dic3×Dic6C2211yescharacteristic
34#63841C2211yescharacteristic
35#63836—21no—
36C2×#3717C2212yes—
37C2×#3717C2212yes—
38#63808—28no—
39C32×C4⋊C8C2211yescharacteristic
40#63648C2212yes—
41C3×#816C2212yes—
42C3×Dic3⋊C8C2212yes—
43C3×C4⋊(C3⋊C8)C2211yescharacteristic
44#63566C2212yes—
45#63564C2212yes—
46C2×#919—32no—
47C2×#904—32no—
48#5725—31no—
49C4×#239—31no—
50#5477—31no—
51C4×#235—31no—
52C3×#462—31no—
53C2×C3×C4⋊C8—31no—
54#5185—32no—
55#5113—32no—
56#5083—31no—
57#5027—31no—
58#4849D311yescharacteristic, complemented
59#4848—31no—
60#4845—32no—
61#4844—32no—
62#4843—31no—
63#4843—31no—
64#4843—61no—
65#4841—31no—
66D3×C4⋊C8D311yescharacteristic, complemented
67#4819—32no—
68#4804—32no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)C2312yes—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×Dic6C2312yes—
78C2×C3×Dic6C2311yescharacteristic
79C2×#626—21no—
80C2×#626—22no—
81C2×#624—21no—
82C2×#624—22no—
83C2×#624—21no—
84#3799—22no—
85#3799—24no—
86#3799—24no—
87#3799D414yescomplemented
88C2×C32×C8C2312yes—
89C32×C42C2311yescharacteristic
90#3752—21no—
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92#3745—24no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×Dic3⋊C4—21no—
97C3×C4×Dic3—21no—
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102C3×Dic12—24no—
103C3×D3×C8—24no—
104Dic3⋊Dic3—21no—
105#3722—21no—
106#3722—22no—
107#3722—22no—
108(C2×D3)⋊Dic3—21no—
109Dic32—21no—
110Dic32—21no—
111#3717—24no—
112#3717—24no—
113#3035—91noSylow
114C2×#239—31no—
115C2×#239—32no—
116C2×#235—31no—
117C2×#235—32no—
118C2×C3×Q16—32no—
119C22×C3×C8—32no—
120C3×C4⋊Q8—31no—
121C3×C4×Q8—31no—
122C2×C3×C42—31no—
123#947—32no—
124Q8×Dic3—31no—
125C2×#215—32no—
126C2×#215—32no—
127#930—61no—
128#930—61no—
129C4×#67—61no—
130C4×#67—61no—
131#926—31no—
132#919—68no—
133C2×Dic12C2×D312yes—
134#904—68no—
135C2×D24—32no—
136C2×D24—32no—
137C2×D24—62no—
138C2×#204—32no—
139C2×#204—32no—
140C2×D3×C8C2×D312yes—
141#895—61no—
142#895—61no—
143#893—31no—
144#893—61no—
145#893—61no—
146#893—61no—
147#892—31no—
148#892—61no—
149#875—32no—
150#874—31no—
151#874—31no—
152#874—61no—
153C4×D12—31no—
154C4×D12—31no—
155C4×D12—31no—
156C4×D12—61no—
157C4×D12—61no—
158C4×D12—61no—
159C4×D12—61no—
160#872—61no—
161C42×D3—61no—
162C42×D3—61no—
163C42×D3C2×D311yescharacteristic
164#869C2×D311yescharacteristic
165C4×Dic6—31no—
166C4×Dic6C2×D311yescharacteristic
167C3×C4⋊C8—21no—
168C3×C4⋊C8—32no—
169C3×C4⋊C8—31no—
170C3×C4⋊C8C2×D311yescharacteristic
171C3×C4⋊C8C2×D311yescharacteristic
172C3×#103—32no—
173#835—32no—
174#821—32no—
175#821—32no—
176#821—32no—
177#821—62no—
178#816—32no—
179#816C2×D312yes—
180Dic3⋊C8C2×D312yes—
181#809—32no—
182C4⋊(C3⋊C8)C2×D311yescharacteristic
183C22×C3⋊D3—21no—
184C22×C3⋊D3—22no—
185C22×C3×D3C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189C2×C3⋊Dic3—21no—
190C4⋊(C3⋊D3)—22no—
191C4⋊(C3⋊D3)—21no—
192C4⋊(C3⋊D3)—22no—
193C4⋊(C3⋊D3)—42no—
194C4⋊(C3⋊D3)—42no—
195C4⋊(C3⋊D3)C2×D412yes—
196C4×C3⋊D3—42no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203C3×C4×D3—22no—
204C3×C4×D3—41no—
205C3×C4×D3C2×D412yes—
206C3×C4×D3#4112yes—
207C3×Dic6—21no—
208C3×Dic6—22no—
209C3×Dic6—22no—
210C3×Dic6C2×D412yes—
211#626—24no—
212#626—44no—
213#624—24no—
214#624—42no—
215#624—44no—
216C32×C8—22no—
217C3×C3⋊C8—22no—
218C2×#135—92no—
219#532—91no—
220C4×#41—91no—
221#464—92no—
222#463—92no—
223#462—31no—
224#461—91no—
225#460—91no—
226#459—91no—
227C2×C4⋊C8—31no—
228#416—92no—
229C2×C3×Q8—31no—
230C2×C3×Q8—32no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C2×#67—61no—
235C2×#67—62no—
236#239—34no—
237#239—62no—
238#239—64no—
239#239—64no—
240#235—34no—
241#235—62no—
242#235—64no—
243#235—64no—
244C2×D12—31no—
245C2×D12—31no—
246C2×D12—32no—
247C2×D12—32no—
248C2×D12—61no—
249C2×D12—62no—
250C2×D12—61no—
251C2×D12—62no—
252C2×D12—61no—
253C2×D12—61no—
254C2×D12—61no—
255C2×D12—61no—
256C2×D12—121no—
257C2×D12—121no—
258C2×C4×D3—61no—
259C2×C4×D3—61no—
260C2×C4×D3—61no—
261C2×C4×D3—62no—
262C2×C4×D3—61no—
263C2×C4×D3—61no—
264C2×C4×D3—61no—
265C2×C4×D3—62no—
266C2×C4×D3—121no—
267C2×C4×D3D1211yescharacteristic
268C2×C4×D3D1211yescharacteristic
269C2×C4×D3C22×D311yescharacteristic
270C2×Dic6C22×D312yes—
271C2×Dic6C22×D311yescharacteristic
272C3×Q16—64no—
273C2×C3×C8—22no—
274C2×C3×C8—32no—
275C2×C3×C8—64no—
276C2×C3×C8C22×D312yes—
277C2×C3×C8C22×D312yes—
278C3×C4⋊C4—31no—
279C3×C4⋊C4—61no—
280C3×C4⋊C4—61no—
281C3×C4⋊C4—61no—
282C3×C42—21no—
283C3×C42—31no—
284C3×C42—31no—
285C3×C42—31no—
286C3×C42—61no—
287C3×C42C22×D311yescharacteristic
288C3×C42C22×D311yescharacteristic
289#217—61no—
290#215—64no—
291#215—64no—
292(C2×D3)⋊C4—61no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—61no—
296(C2×D3)⋊C4—61no—
297(C2×D3)⋊C4—61no—
298(C2×D3)⋊C4—61no—
299(C2×D3)⋊C4—62no—
300(C2×D3)⋊C4—62no—
301(C2×D3)⋊C4—121no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—31no—
305C4⋊Dic3—31no—
306C4⋊Dic3—61no—
307C4⋊Dic3—61no—
308C4⋊Dic3C22×D311yescharacteristic
309Dic3⋊C4—21no—
310Dic3⋊C4—61no—
311C4×Dic3—21no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314C4×Dic3—61no—
315C4×Dic3—61no—
316C4×Dic3D1211yescharacteristic
317C4×Dic3D1211yescharacteristic
318C4×Dic3C22×D311yescharacteristic
319C2×C3⋊C8C22×D312yes—
320Dic12—24no—
321D24—64no—
322D24—64no—
323D24—124no—
324#204—64no—
325#204—64no—
326D3×C8—24no—
327C22×C32C22×D411yescharacteristic
328C2×C3⋊D3—22no—
329C2×C3⋊D3—41no—
330C2×C3⋊D3—41no—
331C2×C3⋊D3—42no—
332C2×C3⋊D3—42no—
333C2×C3⋊D3—42no—
334C2×C3×D3—21no—
335C2×C3×D3—21no—
336C2×C3×D3#12112yes—
337C32×C4—21no—
338C32×C4#13512yescomplemented
339C32×C4C22×D411yescharacteristic
340C32×C4C2×#4111yescharacteristic
341C3⋊Dic3—41no—
342C3×Dic3—22no—
343C3×Dic3—21no—
344C3×Dic3—21no—
345C3×Dic3—42no—
346C3×Dic3—41no—
347C3×Dic3#12112yes—
348C2×#41—91no—
349C2×#41—92no—
350#135—188no—
351C2×Q16—32no—
352C2×SD16—92no—
353C2×SD16—92no—
354C2×D8—92no—
355C22×C8—32no—
356C4⋊Q8—31no—
357#127—91no—
358#124—92no—
359#121—181no—
360#121—181no—
361C4×Q8—31no—
362C4×Q8—91no—
363C4×D4—91no—
364C4×D4—91no—
365C4×D4—181no—
366C4×D4—181no—
367C4×D4—181no—
368C4×D4—181no—
369#117—91no—
370#117—181no—
371C2×C42—31no—
372C2×C42—181no—
373C4⋊C8—32no—
374C4⋊C8—31no—
375C4⋊C8D3211yescharacteristic
376#103—32no—
377#103—92no—
378#102—92no—
379#102—92no—
380C23×C3—31no—
381C22×D3—61no—
382C22×D3—61no—
383C22×D3—62no—
384C22×D3—62no—
385C22×D3—121no—
386C22×D3—122no—
387C22×D3C2×D1211yescharacteristic
388C3×Q8—32no—
389C3×Q8—61no—
390C3×Q8—62no—
391C3×Q8—62no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—31no—
396C2×C3×C4—32no—
397C2×C3×C4—32no—
398C2×C3×C4—31no—
399C2×C3×C4—31no—
400C2×C3×C4—61no—
401C2×C3×C4—62no—
402C2×C3×C4—61no—
403C2×C3×C4—62no—
404C2×C3×C4—121no—
405C2×C3×C4C2×D1211yescharacteristic
406C2×C3×C4C2×D1211yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411#67—64no—
412#67—124no—
413C2×Dic3—21no—
414C2×Dic3—21no—
415C2×Dic3—22no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—121no—
419C2×Dic3C2×D1211yescharacteristic
420C2×Dic3C2×D1211yescharacteristic
421C2×Dic3C2×D1211yescharacteristic
422D12—32no—
423D12—32no—
424D12—62no—
425D12—64no—
426D12—62no—
427D12—62no—
428D12—61no—
429D12—62no—
430D12—61no—
431D12—62no—
432D12—121no—
433D12—122no—
434D12—122no—
435D12—122no—
436D12—122no—
437D12—124no—
438D12—122no—
439D12—122no—
440D12—242no—
441D12—242no—
442C4×D3—22no—
443C4×D3—41no—
444C4×D3—64no—
445C4×D3—64no—
446C4×D3—122no—
447C4×D3—124no—
448C4×D3—122no—
449C4×D3—122no—
450C4×D3—122no—
451C4×D3—124no—
452C4×D3—242no—
453C4×D3D3×D412yes—
454C4×D3#23912yes—
455Dic6—21no—
456Dic6—22no—
457Dic6—22no—
458Dic6D3×D412yes—
459C3×C8—22no—
460C3×C8—22no—
461C3×C8—42no—
462C3×C8—62no—
463C3⋊C8—22no—
464C2×C32C2×#12111yescharacteristic
465C2×C32C2×#13511yescharacteristic
466C2×C32#57511yescharacteristic
467C3⋊D3—42no—
468C3⋊D3—82no—
469C3×D3—22no—
470#41—94no—
471#41—182no—
472#41—184no—
473#41—184no—
474C2×Q8—31no—
475C2×Q8—32no—
476C2×D4—91no—
477C2×D4—92no—
478C2×D4—181no—
479C2×D4—182no—
480C2×D4—181no—
481C2×D4—181no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—31no—
485C22×C4—181no—
486C22×C4—181no—
487C22×C4—182no—
488C22×C4—181no—
489Q16—64no—
490SD16—184no—
491SD16—184no—
492D8—184no—
493C2×C8—32no—
494C2×C8—64no—
495C2×C8C2×D3212yes—
496C4⋊C4—31no—
497C4⋊C4—61no—
498C4⋊C4—61no—
499C4⋊C4—61no—
500C4⋊C4—91no—
501C4⋊C4—181no—
502C22⋊C4—181no—
503C22⋊C4—182no—
504C22⋊C4—182no—
505C22⋊C4—181no—
506C22⋊C4—181no—
507C42—31no—
508C42—31no—
509C42—31no—
510C42—61no—
511C42—181no—
512C42—181no—
513C42C2×D3211yescharacteristic
514C22×C3—21no—
515C22×C3—32no—
516C22×C3—61no—
517C22×C3—61no—
518C22×C3C22×D1211yescharacteristic
519C22×C3C2×D3×D411yescharacteristic
520C2×D3—21no—
521C2×D3—21no—
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—122no—
525C2×D3—121no—
526C2×D3—121no—
527C2×D3—121no—
528C2×D3—121no—
529C2×D3—122no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—122no—
534C2×D3—122no—
535C2×D3—241no—
536C2×D3—241no—
537C2×D3—242no—
538C2×D3—242no—
539C2×D3—242no—
540C2×D3#89512yes—
541C3×C4—21no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—21no—
545C3×C4—22no—
546C3×C4—32no—
547C3×C4—41no—
548C3×C4—62no—
549C3×C4—61no—
550C3×C4—61no—
551C3×C4—121no—
552C3×C4—122no—
553C3×C4#90412yescomplemented
554C3×C4#91912yescomplemented
555C3×C4C2×D3×D411yescharacteristic
556C3×C4C2×D3×D411yescharacteristic
557C3×C4C2×#23911yescharacteristic
558C3×C4D3×#4111yescharacteristic
559Dic3—21no—
560Dic3—21no—
561Dic3—22no—
562Dic3—41no—
563Dic3—42no—
564Dic3—121no—
565Dic3—121no—
566Dic3—241no—
567Dic3#89512yes—
568C32#303511yescharacteristic, complemented, Sylow
569C23—31no—
570C23—181no—
571C23—182no—
572Q8—32no—
573Q8—61no—
574Q8—62no—
575Q8—62no—
576D4—92no—
577D4—184no—
578D4—182no—
579D4—181no—
580D4—182no—
581D4—362no—
582D4—364no—
583D4—362no—
584C2×C4—31no—
585C2×C4—32no—
586C2×C4—32no—
587C2×C4—31no—
588C2×C4—31no—
589C2×C4—61no—
590C2×C4—62no—
591C2×C4—61no—
592C2×C4—62no—
593C2×C4—121no—
594C2×C4—184no—
595C2×C4—181no—
596C2×C4—364no—
597C2×C4—362no—
598C2×C4—362no—
599C2×C4D3×D1211yescharacteristic
600C2×C4D3×D1211yescharacteristic
601C2×C4C22×D3211yescharacteristic
602C8—22no—
603C8—62no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—62no—
608C2×C3C2×#89511yescharacteristic
609C2×C3D3×#12111yescharacteristic
610C2×C3C2×#90411yescharacteristic
611C2×C3#574811yescharacteristic
612C2×C3C2×#91911yescharacteristic
613C2×C3#577711yescharacteristic
614D3—22no—
615D3—122no—
616D3—122no—
617D3—242no—
618D3—242no—
619D3—242no—
620D3—482no—
621C22—32no—
622C22—61no—
623C22—61no—
624C22—182no—
625C22—361no—
626C22—361no—
627C22—362no—
628C22—362no—
629C22—362no—
630C22C2×D3×D1211yescharacteristic
631C4—21no—
632C4—32no—
633C4—62no—
634C4—61no—
635C4—61no—
636C4—122no—
637C4—121no—
638C4—361no—
639C4#6380812yescomplemented
640C4D32×D411yescharacteristic
641C4D3×#23911yescharacteristic
642C3—21no—
643C3#7902111yescharacteristic, complemented
644C3#8047511yescharacteristic, complemented
645C2—62no—
646C2—362no—
647C2—722no—
648C2D3×#89511yescharacteristic
649C2C2×#6380811yescharacteristic
650C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63808C2semidirect
2. #10593970C2semidirect
3. C4×#3799C2semidirect
4. #10592542C2semidirect
5. C3×#4849C2semidirect
6. C3×D3×C4⋊C8C2semidirect
7. #10590801C2semidirect
8. #10590770C2semidirect
9. #10590690C2semidirect
10. #10590379C2semidirect
11. #10590367C2semidirect
58. #4849D3semidirect
66. D3×C4⋊C8D3semidirect
87. #3799D4semidirect
338. C32×C4#135semidirect
553. C3×C4#904semidirect
554. C3×C4#919semidirect
568. C32#3035semidirect
639. C4#63808semidirect
643. C3#79021semidirect
644. C3#80475semidirect

Maximal subgroups

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

subgroupindex
C2×#638082
#105939702
C4×#37992
#105925422
C3×#48492
C3×D3×C4⋊C82
#105908012
#105907702
#105906902
#105903792
#105903672
#804753
#790213