Finite Group Databasebeta

← #11865768

Subgroups — #11865768

Order 1152.

1061 conjugacy classes of subgroups.

The subgroup lattice has 649 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63809C212yesmaximal, complemented
2#10593907C211yesmaximal, characteristic, complemented
3C4×#3796C211yesmaximal, characteristic, complemented
4C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
5C3×#4848C211yesmaximal, characteristic, complemented
6C3×#4841C211yesmaximal, characteristic, complemented
7#10590956C212yesmaximal, complemented
8#10590796C212yesmaximal, complemented
9#10590750C212yesmaximal, complemented
10#10590384C211yesmaximal, characteristic, complemented
11#10590347C211yesmaximal, characteristic, complemented
12#80427—31nomaximal
13#80382—31nomaximal
14C2×#3796C2212yes—
15C2×#3796C2211yescharacteristic
16C2×C8×C3⋊D3C2212yes—
17C42×C3⋊D3C2211yescharacteristic
18C2×C3×#204C2212yes—
19C2×C3×#204C2212yes—
20C3×#874C2211yescharacteristic
21C3×C4×D12C2211yescharacteristic
22C3×#869C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63916—21no—
25#63916—21no—
26C4×#626—21no—
27#63898—21no—
28#63898—21no—
29#63898C2211yescharacteristic
30#63881—21no—
31#63878—21no—
32C4×D3×Dic3—21no—
33#63863C2212yes—
34#63849C2211yescharacteristic
35#63843C2211yescharacteristic
36C2×#3718C2212yes—
37C2×#3713C2212yes—
38#63809—28no—
39C32×C4⋊C8C2211yescharacteristic
40#63641C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42C3×#821C2212yes—
43C3×#816C2212yes—
44#63565C2212yes—
45#63562C2212yes—
46C2×#916—32no—
47C2×#916—32no—
48#5725—31no—
49#5716—31no—
50C4×#239—31no—
51C4×#237—31no—
52C3×#461—31no—
53C3×#460—31no—
54#5166—32no—
55#5165—32no—
56#5090—31no—
57#5072—31no—
58#5031—31no—
59#5015—31no—
60#4848D311yescharacteristic, complemented
61#4841D311yescharacteristic, complemented
62D3×C4⋊C8—31no—
63D3×C4⋊C8—31no—
64D3×C4⋊C8—61no—
65#4804—32no—
66#4798—32no—
67#4787—32no—
68#4772—32no—
69C2×C4×C3⋊D3D411yescharacteristic
70C2×C4×C3⋊D3D411yescharacteristic
71C2×C4×C3⋊D3C2311yescharacteristic
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×D12C2311yescharacteristic
76C2×C3×C4×D3—21no—
77C2×C3×Dic6C2312yes—
78C2×C3×Dic6C2311yescharacteristic
79C2×#626—21no—
80C2×#626—22no—
81C2×D3×Dic3—21no—
82C2×D3×Dic3—22no—
83C2×D3×Dic3—21no—
84#3796—22no—
85#3796—24no—
86#3796—24no—
87#3796D414yescomplemented
88C2×C32×C8C2312yes—
89C32×C42C2311yescharacteristic
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3D411yescharacteristic
92C4×C3⋊Dic3C2311yescharacteristic
93C2×C3⋊(C3⋊C8)C2312yes—
94C8×C3⋊D3—24no—
95C3×(C2×D3)⋊C4—21no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4⋊Dic3C2311yescharacteristic
100C3×Dic3⋊C4—21no—
101C3×C4×Dic3—21no—
102C3×#204—24no—
103C3×#204—24no—
104Dic3⋊Dic3—21no—
105#3722—21no—
106(C2×D3)⋊Dic3—22no—
107(C2×D3)⋊Dic3—22no—
108(C2×D3)⋊Dic3—21no—
109Dic32—21no—
110Dic32—21no—
111#3718—24no—
112#3713—24no—
113#3035—91noSylow
114C2×#239—31no—
115C2×#239—32no—
116C2×#237—31no—
117C2×#237—32no—
118C2×C3×SD16—32no—
119C2×C3×SD16—32no—
120C3×C4⋊Q8—31no—
121C3×#127—31no—
122C3×C4×Q8—31no—
123C3×C4×D4—31no—
124#947—32no—
125Q8×Dic3—31no—
126C2×#216—32no—
127C2×#216—32no—
128#938—61no—
129#938—61no—
130#936—32no—
131D4×Dic3—31no—
132D4×Dic3—61no—
133D4×Dic3—61no—
134C2×#213—32no—
135C2×#213—32no—
136C4×#67—61no—
137C2×C4×Dic3—61no—
138#916—68no—
139#916—68no—
140C2×#204C2×D312yes—
141C2×#204C2×D312yes—
142C2×D3×C8—32no—
143C2×D3×C8—32no—
144C2×D3×C8—62no—
145#895—61no—
146#895—61no—
147#893—31no—
148#893—61no—
149#893—61no—
150#893—61no—
151#892—31no—
152#892—31no—
153#892—61no—
154#887—31no—
155#67⋊C4—61no—
156#877—61no—
157#874C2×D311yescharacteristic
158C4×D12—61no—
159C4×D12C2×D311yescharacteristic
160C42×D3—31no—
161C42×D3—31no—
162C42×D3—61no—
163C42×D3—61no—
164#869C2×D311yescharacteristic
165C4×Dic6C2×D311yescharacteristic
166C3×C4⋊C8—21no—
167C3×C4⋊C8C2×D311yescharacteristic
168C3×C4⋊C8C2×D311yescharacteristic
169C3×#103—32no—
170C3×#102—32no—
171#835—32no—
172#832—32no—
173#821C2×D312yes—
174#816C2×D312yes—
175Dic3⋊C8—32no—
176Dic3⋊C8—32no—
177Dic3⋊C8—62no—
178#810—32no—
179#809—32no—
180C4⋊(C3⋊C8)—31no—
181C4⋊(C3⋊C8)—31no—
182C4⋊(C3⋊C8)—61no—
183C22×C3⋊D3C2×D411yescharacteristic
184C22×C3×D3—21no—
185C22×C3×D3—22no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C4×C3⋊D3—22no—
193C4×C3⋊D3—41no—
194C4×C3⋊D3C2×D412yes—
195C4×C3⋊D3#4112yes—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—22no—
200C3×D12—22no—
201C3×D12—21no—
202C3×D12—22no—
203C3×D12—42no—
204C3×D12—42no—
205C3×D12C2×D412yes—
206C3×C4×D3—42no—
207C3×Dic6—21no—
208C3×Dic6—22no—
209C3×Dic6—22no—
210C3×Dic6C2×D412yes—
211#626—24no—
212#626—44no—
213D3×Dic3—24no—
214D3×Dic3—42no—
215D3×Dic3—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—91no—
224#461—31no—
225#460—31no—
226#459—91no—
227C2×C4⋊C8—91no—
228#416—92no—
229C2×C3×Q8—31no—
230C2×C3×Q8—32no—
231C2×C3×D4—31no—
232C2×C3×D4—32no—
233C2×C3×D4—61no—
234C2×C3×D4—61no—
235C22×C3×C4—61no—
236C2×#67—61no—
237C2×#67—62no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240C22×Dic3—62no—
241#239—34no—
242#239—62no—
243#239—64no—
244#239—64no—
245#237—34no—
246#237—62no—
247#237—64no—
248#237—64no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—61no—
252C2×D12—62no—
253C2×D12C22×D312yes—
254C2×D12C22×D311yescharacteristic
255C2×C4×D3—21no—
256C2×C4×D3—31no—
257C2×C4×D3—31no—
258C2×C4×D3—31no—
259C2×C4×D3—31no—
260C2×C4×D3—31no—
261C2×C4×D3—31no—
262C2×C4×D3—61no—
263C2×C4×D3—61no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×C4×D3—61no—
267C2×C4×D3—62no—
268C2×Dic6C22×D312yes—
269C2×Dic6C22×D311yescharacteristic
270C3×SD16—64no—
271C3×SD16—64no—
272C2×C3×C8—22no—
273C2×C3×C8C22×D312yes—
274C2×C3×C8C22×D312yes—
275C3×C4⋊C4—31no—
276C3×C4⋊C4—31no—
277C3×C4⋊C4—61no—
278C3×C4⋊C4—61no—
279C3×C4⋊C4—61no—
280C3×C22⋊C4—61no—
281C3×C42—21no—
282C3×C42—61no—
283C3×C42C22×D311yescharacteristic
284C3×C42C22×D311yescharacteristic
285#217—61no—
286#217—62no—
287#217—62no—
288#216—64no—
289#216—64no—
290#213—64no—
291#213—64no—
292(C2×D3)⋊C4—21no—
293(C2×D3)⋊C4—61no—
294(C2×D3)⋊C4—61no—
295(C2×D3)⋊C4—61no—
296(C2×D3)⋊C4—62no—
297(C2×D3)⋊C4—62no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3—61no—
301C4⋊Dic3C22×D311yescharacteristic
302C4⋊Dic3C22×D311yescharacteristic
303Dic3⋊C4—21no—
304Dic3⋊C4—61no—
305C4×Dic3—21no—
306C4×Dic3—31no—
307C4×Dic3—31no—
308C4×Dic3—31no—
309C4×Dic3—31no—
310C4×Dic3—31no—
311C4×Dic3—31no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314C4×Dic3—61no—
315C4×Dic3—61no—
316C4×Dic3—61no—
317C4×Dic3—61no—
318C4×Dic3—61no—
319C2×C3⋊C8—32no—
320C2×C3⋊C8—32no—
321C2×C3⋊C8—62no—
322#204—24no—
323#204—24no—
324D3×C8—64no—
325D3×C8—64no—
326D3×C8—124no—
327C22×C32C22×D411yescharacteristic
328C2×C3⋊D3—21no—
329C2×C3⋊D3—21no—
330C2×C3⋊D3#12112yes—
331C2×C3×D3—22no—
332C2×C3×D3—41no—
333C2×C3×D3—41no—
334C2×C3×D3—42no—
335C2×C3×D3—42no—
336C2×C3×D3—42no—
337C32×C4—21no—
338C32×C4#13512yescomplemented
339C32×C4C22×D411yescharacteristic
340C32×C4C2×#4111yescharacteristic
341C3⋊Dic3—21no—
342C3⋊Dic3—21no—
343C3⋊Dic3#12112yes—
344C3×Dic3—22no—
345C3×Dic3—42no—
346C3×Dic3—41no—
347C3×Dic3—41no—
348C2×#41—91no—
349C2×#41—92no—
350#135—188no—
351C2×Q16—92no—
352C2×SD16—32no—
353C2×SD16—32no—
354C2×D8—92no—
355C22×C8—92no—
356C4⋊Q8—31no—
357#127—31no—
358#124—92no—
359#121—181no—
360#121—181no—
361C4×Q8—31no—
362C4×Q8—91no—
363C4×D4—31no—
364C4×D4—91no—
365C4×D4—181no—
366C4×D4—181no—
367C4×D4—181no—
368C4×D4—181no—
369#117—91no—
370#117—181no—
371C2×C42—91no—
372C2×C42—181no—
373C4⋊C8—92no—
374C4⋊C8—91no—
375C4⋊C8D3211yescharacteristic
376#103—32no—
377#103—92no—
378#102—32no—
379#102—92no—
380C23×C3—61no—
381C23×C3—62no—
382C22×D3—21no—
383C22×D3—22no—
384C22×D3—31no—
385C22×D3—31no—
386C22×D3—61no—
387C3×Q8—32no—
388C3×Q8—61no—
389C3×Q8—62no—
390C3×Q8—62no—
391C3×D4—32no—
392C3×D4—62no—
393C3×D4—61no—
394C3×D4—62no—
395C3×D4—122no—
396C3×D4—122no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—61no—
401C2×C3×C4—61no—
402C2×C3×C4—61no—
403C2×C3×C4—62no—
404C2×C3×C4—122no—
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4D3×D411yescharacteristic
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—21no—
416C2×Dic3—22no—
417C2×Dic3—31no—
418C2×Dic3—31no—
419C2×Dic3—31no—
420C2×Dic3—31no—
421C2×Dic3—31no—
422C2×Dic3—31no—
423C2×Dic3—61no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426C2×Dic3—64no—
427C2×Dic3—124no—
428C2×Dic3—122no—
429D12—22no—
430D12—21no—
431D12—22no—
432D12—42no—
433D12—42no—
434D12—64no—
435D12—124no—
436D12D3×D412yes—
437C4×D3—32no—
438C4×D3—32no—
439C4×D3—32no—
440C4×D3—32no—
441C4×D3—42no—
442C4×D3—62no—
443C4×D3—62no—
444C4×D3—64no—
445C4×D3—64no—
446C4×D3—62no—
447C4×D3—62no—
448C4×D3—124no—
449C4×D3—121no—
450C4×D3—121no—
451C4×D3—122no—
452C4×D3—122no—
453Dic6—21no—
454Dic6—22no—
455Dic6—22no—
456Dic6D3×D412yes—
457C3×C8—22no—
458C3×C8—22no—
459C3×C8—42no—
460C3⋊C8—62no—
461C3⋊C8—62no—
462C3⋊C8—122no—
463C2×C32C2×#12111yescharacteristic
464C2×C32C2×#13511yescharacteristic
465C2×C32#57511yescharacteristic
466C3⋊D3—22no—
467C3×D3—42no—
468C3×D3—82no—
469#41—94no—
470#41—182no—
471#41—184no—
472#41—184no—
473C2×Q8—31no—
474C2×Q8—32no—
475C2×D4—31no—
476C2×D4—32no—
477C2×D4—61no—
478C2×D4—61no—
479C2×D4—181no—
480C2×D4—182no—
481C22×C4—61no—
482C22×C4—91no—
483C22×C4—91no—
484C22×C4—91no—
485C22×C4—181no—
486C22×C4—181no—
487C22×C4—182no—
488Q16—184no—
489SD16—64no—
490SD16—64no—
491D8—184no—
492C2×C8—92no—
493C2×C8—184no—
494C2×C8C2×D3212yes—
495C4⋊C4—31no—
496C4⋊C4—31no—
497C4⋊C4—61no—
498C4⋊C4—61no—
499C4⋊C4—61no—
500C4⋊C4—181no—
501C22⋊C4—61no—
502C22⋊C4—181no—
503C22⋊C4—181no—
504C22⋊C4—182no—
505C22⋊C4—182no—
506C42—61no—
507C42—91no—
508C42—91no—
509C42—91no—
510C42—181no—
511C42—181no—
512C42C2×D3211yescharacteristic
513C22×C3—21no—
514C22×C3—62no—
515C22×C3—121no—
516C22×C3—121no—
517C22×C3—122no—
518C22×C3—122no—
519C22×C3—122no—
520C22×C3C2×D3×D411yescharacteristic
521C22×C3C2×D3×D411yescharacteristic
522C2×D3—22no—
523C2×D3—32no—
524C2×D3—32no—
525C2×D3—41no—
526C2×D3—41no—
527C2×D3—42no—
528C2×D3—42no—
529C2×D3—42no—
530C2×D3—62no—
531C2×D3—62no—
532C2×D3—62no—
533C2×D3—61no—
534C2×D3—61no—
535C2×D3—61no—
536C2×D3—61no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—22no—
542C3×C4—41no—
543C3×C4—62no—
544C3×C4—121no—
545C3×C4—121no—
546C3×C4—122no—
547C3×C4#91612yescomplemented
548C3×C4#91612yescomplemented
549C3×C4C2×D3×D411yescharacteristic
550C3×C4C2×D3×D411yescharacteristic
551C3×C4D3×#4111yescharacteristic
552C3×C4D3×#4111yescharacteristic
553Dic3—22no—
554Dic3—32no—
555Dic3—32no—
556Dic3—41no—
557Dic3—41no—
558Dic3—42no—
559Dic3—62no—
560Dic3—62no—
561Dic3—61no—
562Dic3—61no—
563Dic3—61no—
564Dic3—61no—
565Dic3—121no—
566C32#303511yescharacteristic, complemented, Sylow
567C23—61no—
568C23—62no—
569C23—91no—
570Q8—32no—
571Q8—61no—
572Q8—62no—
573Q8—62no—
574D4—32no—
575D4—62no—
576D4—61no—
577D4—62no—
578D4—122no—
579D4—122no—
580D4—184no—
581D4—364no—
582C2×C4—61no—
583C2×C4—61no—
584C2×C4—61no—
585C2×C4—62no—
586C2×C4—91no—
587C2×C4—92no—
588C2×C4—92no—
589C2×C4—91no—
590C2×C4—91no—
591C2×C4—122no—
592C2×C4—184no—
593C2×C4—182no—
594C2×C4—361no—
595C2×C4—364no—
596C2×C4—362no—
597C2×C4#380211yescharacteristic
598C2×C4#380211yescharacteristic
599C2×C4C22×D3211yescharacteristic
600C8—22no—
601C8—182no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—122no—
606C2×C3—242no—
607C2×C3D3×#12111yescharacteristic
608C2×C3D3×#12111yescharacteristic
609C2×C3C2×#91611yescharacteristic
610C2×C3C2×#91611yescharacteristic
611C2×C3#577311yescharacteristic
612C2×C3#577711yescharacteristic
613D3—42no—
614D3—64no—
615D3—62no—
616D3—62no—
617D3—82no—
618C22—62no—
619C22—92no—
620C22—121no—
621C22—121no—
622C22—122no—
623C22—122no—
624C22—122no—
625C22—181no—
626C22—181no—
627C22C2×#380211yescharacteristic
628C4—21no—
629C4—62no—
630C4—92no—
631C4—122no—
632C4—121no—
633C4—121no—
634C4—181no—
635C4—181no—
636C4#6380912yescomplemented
637C4D32×D411yescharacteristic
638C4#6431911yescharacteristic
639C3—21no—
640C3#8038211yescharacteristic, complemented
641C3#8042711yescharacteristic, complemented
642C2—122no—
643C2—182no—
644C2—242no—
645C2#1059461211yescharacteristic
646C2C2×#6380911yescharacteristic
647C2#1059471811yescharacteristic
subgroupG/H
centerC22C2×#3802
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×#63809C2semidirect
2. #10593907C2semidirect
3. C4×#3796C2semidirect
4. C3⋊D3×C4⋊C8C2semidirect
5. C3×#4848C2semidirect
6. C3×#4841C2semidirect
7. #10590956C2semidirect
8. #10590796C2semidirect
9. #10590750C2semidirect
10. #10590384C2semidirect
11. #10590347C2semidirect
60. #4848D3semidirect
61. #4841D3semidirect
87. #3796D4semidirect
338. C32×C4#135semidirect
547. C3×C4#916semidirect
548. C3×C4#916semidirect
566. C32#3035semidirect
636. C4#63809semidirect
640. C3#80382semidirect
641. C3#80427semidirect

Maximal subgroups

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

subgroupindex
C2×#638092
#105939072
C4×#37962
C3⋊D3×C4⋊C82
C3×#48482
C3×#48412
#105909562
#105907962
#105907502
#105903842
#105903472
#804273
#803823