Finite Group Databasebeta

← #11870428

Subgroups — #11870428

Order 1152.

1083 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63894C211yesmaximal, characteristic, complemented
2#10594910C211yesmaximal, characteristic, complemented
3#10592431C211yesmaximal, characteristic, complemented
4C3×#4736C211yesmaximal, characteristic, complemented
5C3×#4718C211yesmaximal, characteristic, complemented
6#10591168C211yesmaximal, characteristic, complemented
7#10591133C211yesmaximal, characteristic, complemented
8#10590765C212yesmaximal, complemented
9#10590764C212yesmaximal, complemented
10#10590763C212yesmaximal, complemented
11#10590745C212yesmaximal, complemented
12#81268—31nomaximal
13#79297—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×#624—21no—
16C2×#3804—21no—
17#64139C2211yescharacteristic
18C2×#3745C2212yes—
19C3×#930C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22#63978—21no—
23C2×#3722—21no—
24#63918C2211yescharacteristic, complemented
25#63911C2211yescharacteristic, complemented
26#63894—21no—
27#63894—21no—
28#63894C2212yes—
29#63894C2212yes—
30#63894C2211yescharacteristic, complemented
31Dic3×D12C2211yescharacteristic, complemented
32#63880—21no—
33#63852—21no—
34C2×#3714C2212yes—
35C32×C22⋊C8C2211yescharacteristic
36#63648C2212yes—
37C3×#830C2211yescharacteristic
38C3×#821C2212yescomplemented
39C3×#818C2212yescomplemented
40C3×Dic3⋊C8C2212yescomplemented
41C3×C8×Dic3C2212yescomplemented
42#63575C2212yescomplemented
43#63564C2212yes—
44#63564C2212yescomplemented
45#5596—31no—
46C2×#893—31no—
47#5477—31no—
48C2×C4×D12—31no—
49C3×#480—31no—
50C3×#431—31no—
51#5036—31no—
52#4967—31no—
53#4890—32no—
54#4872—32no—
55#4846—32no—
56#4843—32no—
57#4786—32no—
58#4756—32no—
59#4736—31no—
60#4736D311yescharacteristic, complemented
61#4732—31no—
62#4732—31no—
63#4732—31no—
64#4732—61no—
65#4718D311yescharacteristic, complemented
66C4×D24—32no—
67C4×D24—32no—
68C23×C3⋊D3—21no—
69C22×C32×C4C2311yescharacteristic
70C2×#638—21no—
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)—24no—
73C2×C4⋊(C3⋊D3)C2311yescharacteristic
74C2×C4⋊(C3⋊D3)C2312yes—
75C2×C3×#67—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3D411yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C2×C3×D12C2311yescharacteristic
80C2×#627—21no—
81C2×#626—21no—
82C2×#626—21no—
83C2×#624—21no—
84C2×#624—22no—
85C2×#624—22no—
86C2×#624—44no—
87#3804—44no—
88C2×D3×Dic3—21no—
89C2×C32×C8C2312yes—
90#3752—21no—
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92#3745—24no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2312yes—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3C2311yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102Dic3⋊Dic3—21no—
103#3722—21no—
104#3722—22no—
105#3722—22no—
106(C2×D3)⋊Dic3—21no—
107#3714—24no—
108#3100—91noSylow
109C2×#237—61no—
110C2×#235—61no—
111C22×D12—31no—
112C22×D12—31no—
113C22×D12—61no—
114C22×C4×D3—61no—
115C22×C4×D3—61no—
116C3×#121—31no—
117C2×C3×C4⋊C4—31no—
118C2×C3×C42—31no—
119#940—31no—
120#939—61no—
121D4×Dic3—31no—
122C2×#213—32no—
123#930—31no—
124#930—31no—
125#930—61no—
126#930—61no—
127#930C2×D311yescharacteristic
128C2×(C2×D3)⋊C4—61no—
129C2×(C2×D3)⋊C4—61no—
130C2×C4⋊Dic3C2×D311yescharacteristic
131C2×C4×Dic3C2×D311yescharacteristic
132C2×D24—32no—
133C2×D24—32no—
134C2×D24—32no—
135C2×D24—62no—
136#893—31no—
137#893—32no—
138#893—32no—
139#893—61no—
140#893—61no—
141#888—31no—
142#885—61no—
143#67⋊C4—61no—
144#875—61no—
145#874—31no—
146C4×D12—31no—
147C4×D12—32no—
148C4×D12—31no—
149C4×D12—32no—
150C4×D12—61no—
151C4×D12—61no—
152C4×D12—61no—
153#869—31no—
154C3×#107—32no—
155C3×C4⋊C8—32no—
156C3×#102—32no—
157C3×C22⋊C8—21no—
158C3×C22⋊C8—31no—
159C3×C22⋊C8C2×D311yescharacteristic
160C3×C22⋊C8C2×D311yescharacteristic
161C3×C4×C8—32no—
162#830C2×D311yescharacteristic
163#821—32no—
164#821—32no—
165#821—32no—
166#821—32no—
167#821—62no—
168#821C2×D312yescomplemented
169#818—32no—
170#818C2×D312yescomplemented
171Dic3⋊C8C2×D312yescomplemented
172C8×Dic3C2×D312yescomplemented
173#809—32no—
174#809—32no—
175#807—32no—
176C23×C32C2×D411yescharacteristic
177C22×C3⋊D3—24no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3—21no—
180C22×C3⋊D3—42no—
181C22×C3⋊D3—42no—
182C22×C3×D3—21no—
183C2×C32×C4—22no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186#638—42no—
187C2×C3⋊Dic3—21no—
188C4⋊(C3⋊D3)—24no—
189C4⋊(C3⋊D3)—22no—
190C4⋊(C3⋊D3)—22no—
191C4⋊(C3⋊D3)#4114yescomplemented
192C3×#67—42no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—41no—
196C2×C3×Dic3—42no—
197C2×C3×Dic3D814yescomplemented
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C3×D12—22no—
203#627—42no—
204#626—42no—
205#626—42no—
206#624—42no—
207#624—44no—
208#624—44no—
209D3×Dic3—42no—
210C32×C8—22no—
211C3×C3⋊C8—22no—
212#532—91no—
213C2×C4×D4—91no—
214#480—31no—
215#480—91no—
216#474—92no—
217#459—92no—
218#447—91no—
219#447—91no—
220C4×D8—92no—
221C4×D8—92no—
222#431—31no—
223C23×D3—61no—
224C23×D3—61no—
225C23×D3—121no—
226C2×C3×D4—31no—
227C2×C3×D4—61no—
228C22×C3×C4—21no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—61no—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C2×#67—21no—
235C2×#67—61no—
236C2×#67—61no—
237C2×#67—61no—
238C2×#67—61no—
239C2×#67—121no—
240C22×Dic3—21no—
241C22×Dic3—61no—
242C22×Dic3D1211yescharacteristic
243C22×Dic3D1211yescharacteristic
244#237—124no—
245#235—124no—
246C2×D12—32no—
247C2×D12—32no—
248C2×D12—31no—
249C2×D12—31no—
250C2×D12—62no—
251C2×D12—61no—
252C2×D12—64no—
253C2×D12—64no—
254C2×D12—61no—
255C2×D12—61no—
256C2×D12—61no—
257C2×D12—61no—
258C2×D12—124no—
259C2×D12—121no—
260C2×D12C22×D311yescharacteristic
261C2×C4×D3—62no—
262C2×C4×D3—62no—
263C2×C4×D3—61no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×C4×D3—62no—
267C2×C4×D3—62no—
268C2×C4×D3—124no—
269C2×C4×D3—124no—
270C2×Dic6—61no—
271C2×Dic6—61no—
272C2×C3×C8—22no—
273C2×C3×C8—32no—
274C2×C3×C8C22×D312yes—
275C2×C3×C8C22×D312yes—
276C3×C4⋊C4—32no—
277C3×C4⋊C4—31no—
278C3×C4⋊C4—61no—
279C3×C22⋊C4—61no—
280C3×C42—31no—
281C3×C42—31no—
282C3×C42—31no—
283C3×C42—31no—
284#217—61no—
285#213—64no—
286(C2×D3)⋊C4—21no—
287(C2×D3)⋊C4—62no—
288(C2×D3)⋊C4—62no—
289(C2×D3)⋊C4—61no—
290(C2×D3)⋊C4—61no—
291(C2×D3)⋊C4—61no—
292(C2×D3)⋊C4—61no—
293(C2×D3)⋊C4—61no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—62no—
296(C2×D3)⋊C4—121no—
297C4⋊Dic3—21no—
298C4⋊Dic3—31no—
299C4⋊Dic3—31no—
300C4⋊Dic3—61no—
301C4⋊Dic3—61no—
302C4⋊Dic3C22×D312yes—
303C4⋊Dic3C22×D311yescharacteristic
304Dic3⋊C4—61no—
305C4×Dic3D1211yescharacteristic
306C4×Dic3D1211yescharacteristic
307C4×Dic3C22×D311yescharacteristic
308C4×Dic3C22×D311yescharacteristic
309C2×C3⋊C8C22×D312yes—
310D24—64no—
311D24—64no—
312D24—64no—
313D24—124no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32C2×D812yes—
317C22×C32C22×D411yescharacteristic
318C2×C3⋊D3—24no—
319C2×C3⋊D3—48no—
320C2×C3⋊D3—42no—
321C2×C3⋊D3—42no—
322C2×C3⋊D3—41no—
323C2×C3⋊D3—41no—
324C2×C3⋊D3—41no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C32×C4—21no—
329C32×C4C2×#4112yes—
330C3⋊Dic3—41no—
331C3×Dic3—21no—
332C3×Dic3—21no—
333C3×Dic3—42no—
334C3×Dic3—41no—
335C3×Dic3C2×D812yes—
336C3×Dic3C2×D812yes—
337C2×#41—181no—
338C22×D4—91no—
339C23×C4—181no—
340C2×D8—92no—
341C2×D8—92no—
342C4⋊Q8—91no—
343#127—91no—
344#124—181no—
345#121—31no—
346#121—91no—
347#121—181no—
348C4×D4—92no—
349C4×D4—92no—
350C4×D4—91no—
351C4×D4—91no—
352C4×D4—181no—
353C4×D4—181no—
354C4×D4—181no—
355C2×C4⋊C4—31no—
356C2×C22⋊C4—181no—
357C2×C42—31no—
358#107—32no—
359#107—92no—
360C4⋊C8—32no—
361#102—32no—
362#102—92no—
363#102—92no—
364#102—92no—
365C22⋊C8—31no—
366C22⋊C8D3211yescharacteristic
367C4×C8—32no—
368C23×C3—21no—
369C23×C3—61no—
370C23×C3C2×D1211yescharacteristic
371C23×C3D3×D411yescharacteristic
372C22×D3—21no—
373C22×D3—64no—
374C22×D3—64no—
375C22×D3—62no—
376C22×D3—62no—
377C22×D3—61no—
378C22×D3—61no—
379C22×D3—122no—
380C22×D3—124no—
381C22×D3—121no—
382C22×D3—122no—
383C22×D3—122no—
384C22×D3—122no—
385C22×D3—122no—
386C22×D3—242no—
387C22×D3—242no—
388C3×D4—62no—
389C3×D4—122no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—34no—
395C2×C3×C4—31no—
396C2×C3×C4—31no—
397C2×C3×C4—31no—
398C2×C3×C4—31no—
399C2×C3×C4—42no—
400C2×C3×C4—61no—
401C2×C3×C4—62no—
402C2×C3×C4—121no—
403C2×C3×C4—122no—
404C2×C3×C4C2×D1211yescharacteristic
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4C23×D311yescharacteristic
407C2×C3×C4C23×D311yescharacteristic
408#67—42no—
409#67—122no—
410#67—122no—
411#67—122no—
412#67—122no—
413#67—242no—
414C2×Dic3—22no—
415C2×Dic3—21no—
416C2×Dic3—41no—
417C2×Dic3—42no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—121no—
421C2×Dic3—122no—
422C2×Dic3D2414yescomplemented
423C2×Dic3C2×D1211yescharacteristic
424C2×Dic3C2×D1211yescharacteristic
425C2×Dic3C2×D1211yescharacteristic
426C2×Dic3C2×D1211yescharacteristic
427D12—22no—
428D12—34no—
429D12—34no—
430D12—64no—
431D12—64no—
432D12—64no—
433D12—62no—
434D12—62no—
435D12—62no—
436D12—62no—
437D12—122no—
438D12—122no—
439D12—124no—
440D12—122no—
441D12—122no—
442C4×D3—124no—
443C4×D3—124no—
444C4×D3—122no—
445C4×D3—122no—
446C4×D3—124no—
447C4×D3—124no—
448C4×D3—122no—
449Dic6—122no—
450Dic6—122no—
451C3×C8—22no—
452C3×C8—22no—
453C3×C8—42no—
454C3×C8—62no—
455C3⋊C8—22no—
456C2×C32—22no—
457C2×C32#52511yescharacteristic
458C2×C32C22×D811yescharacteristic
459C2×C32#57511yescharacteristic
460C3⋊D3—44no—
461C3⋊D3—81no—
462C3×D3—81no—
463C24—181no—
464#41—364no—
465C2×Q8—181no—
466C2×D4—31no—
467C2×D4—61no—
468C2×D4—92no—
469C2×D4—91no—
470C2×D4—184no—
471C2×D4—181no—
472C2×D4—181no—
473C2×D4—181no—
474C2×D4—181no—
475C22×C4—31no—
476C22×C4—31no—
477C22×C4—61no—
478C22×C4—182no—
479C22×C4—182no—
480C22×C4—181no—
481C22×C4—181no—
482C22×C4—364no—
483C22×C4C2×D3211yescharacteristic
484D8—184no—
485D8—184no—
486C2×C8—32no—
487C2×C8C2×D3212yes—
488C4⋊C4—32no—
489C4⋊C4—31no—
490C4⋊C4—61no—
491C4⋊C4—91no—
492C4⋊C4—181no—
493C22⋊C4—61no—
494C22⋊C4—182no—
495C22⋊C4—182no—
496C22⋊C4—181no—
497C22⋊C4—181no—
498C22⋊C4—181no—
499C42—31no—
500C42—31no—
501C42—31no—
502C42—31no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—22no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—121no—
512C22×C3—121no—
513C22×C3—121no—
514C22×C3C2×D2412yes—
515C22×C3D3×D812yes—
516C22×C3C22×D1211yescharacteristic
517C22×C3C2×D3×D411yescharacteristic
518C2×D3—41no—
519C2×D3—41no—
520C2×D3—41no—
521C2×D3—64no—
522C2×D3—64no—
523C2×D3—124no—
524C2×D3—128no—
525C2×D3—128no—
526C2×D3—122no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—121no—
531C2×D3—121no—
532C2×D3—121no—
533C2×D3—121no—
534C2×D3—121no—
535C2×D3—121no—
536C2×D3—242no—
537C2×D3—242no—
538C2×D3—248no—
539C2×D3—241no—
540C2×D3—241no—
541C2×D3—241no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—22no—
545C3×C4—32no—
546C3×C4—32no—
547C3×C4—41no—
548C3×C4—61no—
549C3×C4—61no—
550C3×C4—121no—
551C3×C4—122no—
552C3×C4D3×#4112yes—
553C3×C4D3×#4112yes—
554Dic3—21no—
555Dic3—21no—
556Dic3—41no—
557Dic3—42no—
558Dic3—121no—
559Dic3—121no—
560Dic3—241no—
561Dic3C2×D2412yes—
562Dic3C2×D2412yes—
563C32#310011yescharacteristic, complemented, Sylow
564C23—61no—
565C23—184no—
566C23—182no—
567C23—181no—
568C23—362no—
569C23—362no—
570C23D3×D1211yescharacteristic
571Q8—362no—
572D4—62no—
573D4—94no—
574D4—122no—
575D4—184no—
576D4—182no—
577D4—182no—
578D4—362no—
579D4—362no—
580D4—362no—
581C2×C4—22no—
582C2×C4—31no—
583C2×C4—31no—
584C2×C4—34no—
585C2×C4—31no—
586C2×C4—31no—
587C2×C4—61no—
588C2×C4—62no—
589C2×C4—121no—
590C2×C4—122no—
591C2×C4—181no—
592C2×C4—364no—
593C2×C4—364no—
594C2×C4—362no—
595C2×C4—362no—
596C2×C4D3×D1211yescharacteristic
597C2×C4C22×D3211yescharacteristic
598C8—22no—
599C8—62no—
600C2×C3—22no—
601C2×C3—22no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—42no—
606C2×C3—241no—
607C2×C3#552411yescharacteristic
608C2×C3#565611yescharacteristic
609C2×C3C22×D2411yescharacteristic
610C2×C3#574811yescharacteristic
611C2×C3C2×D3×D811yescharacteristic
612C2×C3#577711yescharacteristic
613D3—81no—
614D3—124no—
615D3—124no—
616D3—244no—
617D3—241no—
618D3—241no—
619D3—481no—
620C22—21no—
621C22—21no—
622C22—121no—
623C22—121no—
624C22—121no—
625C22—184no—
626C22—368no—
627C22—362no—
628C22—362no—
629C22—361no—
630C22—361no—
631C22—361no—
632C22D3×D2412yes—
633C22C2×D3×D1211yescharacteristic
634C4—21no—
635C4—32no—
636C4—32no—
637C4—61no—
638C4—61no—
639C4—122no—
640C4—121no—
641C4—361no—
642C4#6431212yes—
643C3—21no—
644C3#7929711yescharacteristic, complemented
645C3#8126811yescharacteristic, complemented
646C2—22no—
647C2—241no—
648C2—364no—
649C2—721no—
650C2#1059407911yescharacteristic
651C2C2×D3×D2411yescharacteristic
652C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63894C2semidirect
2. #10594910C2semidirect
3. #10592431C2semidirect
4. C3×#4736C2semidirect
5. C3×#4718C2semidirect
6. #10591168C2semidirect
7. #10591133C2semidirect
8. #10590765C2semidirect
9. #10590764C2semidirect
10. #10590763C2semidirect
11. #10590745C2semidirect
24. #63918C22semidirect
25. #63911C22semidirect
30. #63894C22semidirect
31. Dic3×D12C22semidirect
38. C3×#821C22semidirect
39. C3×#818C22semidirect
40. C3×Dic3⋊C8C22semidirect
41. C3×C8×Dic3C22semidirect
42. #63575C22semidirect
44. #63564C22semidirect
60. #4736D3semidirect
65. #4718D3semidirect
168. #821C2×D3semidirect
170. #818C2×D3semidirect
171. Dic3⋊C8C2×D3semidirect
172. C8×Dic3C2×D3semidirect
191. C4⋊(C3⋊D3)#41semidirect
197. C2×C3×Dic3D8semidirect
422. C2×Dic3D24semidirect
563. C32#3100semidirect
644. C3#79297semidirect
645. C3#81268semidirect

Maximal subgroups

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

subgroupindex
C2×#638942
#105949102
#105924312
C3×#47362
C3×#47182
#105911682
#105911332
#105907652
#105907642
#105907632
#105907452
#812683
#792973