Finite Group Databasebeta

← #11869659

Subgroups — #11869659

Order 1152.

941 conjugacy classes of subgroups.

The subgroup lattice has 633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594922C211yesmaximal, characteristic
2C2×#63849C211yesmaximal, characteristic, complemented
3C3⋊D3×C22⋊C8C211yesmaximal, characteristic, complemented
4C3×#4736C211yesmaximal, characteristic, complemented
5C3×#4722C211yesmaximal, characteristic, complemented
6#10591101C211yesmaximal, characteristic, complemented
7#10591091C211yesmaximal, characteristic, complemented
8#10590956C212yesmaximal, complemented
9#10590715C212yesmaximal, complemented
10#10590714C212yesmaximal, complemented
11#10590651C212yesmaximal, complemented
12#81467—31nomaximal
13#81281—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C2×#3796C2211yescharacteristic
16C2×C8×C3⋊D3C2212yes—
17C3×#930C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C3×#924C2211yescharacteristic
21#63981—21no—
22#67⋊Dic3—21no—
23C2×#3722—21no—
24C2×Dic32—21no—
25#63916C2211yescharacteristic
26#63881—21no—
27#63871C2211yescharacteristic
28#63853—21no—
29#63849—21no—
30#63849—21no—
31#63849C2212yes—
32#63849C2212yes—
33#63849C2211yescharacteristic
34C32×C22⋊C8C2211yescharacteristic
35#63657C2211yescharacteristic
36#63647C2212yes—
37C3×#821C2212yescomplemented
38C3×#818C2212yescomplemented
39C3×#818C2212yescomplemented
40C3×#816C2212yescomplemented
41#63574C2212yescomplemented
42#63574C2212yescomplemented
43#63565C2212yescomplemented
44#63562C2212yescomplemented
45#5627—31no—
46#5606—31no—
47C2×#892—31no—
48C2×#892—31no—
49C3×#484—31no—
50C3×#480—31no—
51#5043—31no—
52#5034—31no—
53#4971—31no—
54#4968—31no—
55#4888—32no—
56#4885—32no—
57#4880—32no—
58#4880—32no—
59#4814—32no—
60#4804—32no—
61#4784—32no—
62#4772—32no—
63#4736D311yescharacteristic, complemented
64D3×C22⋊C8—31no—
65D3×C22⋊C8—31no—
66D3×C22⋊C8—61no—
67#4722D311yescharacteristic, complemented
68C23×C3⋊D3D411yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3D411yescharacteristic
71C2×C4×C3⋊D3—24no—
72C2×C4×C3⋊D3D411yescharacteristic
73C2×C4×C3⋊D3D411yescharacteristic
74C2×C4×C3⋊D3C2311yescharacteristic
75C2×C4×C3⋊D3C2311yescharacteristic
76C2×C3×#67—21no—
77C22×C3×Dic3—21no—
78C22×C3×Dic3—21no—
79C2×C3×D12C2311yescharacteristic
80C2×C3×Dic6C2311yescharacteristic
81C2×#626—21no—
82C2×#626—21no—
83C2×D3×Dic3—21no—
84#3796—24no—
85C2×C32×C8C2312yes—
86C2×C3⋊(C3⋊C8)C2312yes—
87C8×C3⋊D3—24no—
88C3×#217—21no—
89C3×(C2×D3)⋊C4—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4⋊Dic3C2312yes—
94C3×C4⋊Dic3C2312yes—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×Dic3⋊C4—21no—
97Dic3⋊Dic3—21no—
98#3722—22no—
99#3722—22no—
100#3722—21no—
101#3722—21no—
102(C2×D3)⋊Dic3—21no—
103Dic32—22no—
104Dic32—22no—
105Dic32—21no—
106#3091—91noSylow
107C2×#239—31no—
108C2×#237—31no—
109C22×C4×D3—31no—
110C22×C4×D3—31no—
111C22×C4×D3—61no—
112C3×C22⋊Q8—31no—
113C3×#121—31no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—31no—
116#946—31no—
117#938—31no—
118#937—61no—
119D4×Dic3—61no—
120#930C2×D311yescharacteristic
121C2×(C2×D3)⋊C4—61no—
122C2×(C2×D3)⋊C4—61no—
123C2×C4⋊Dic3C2×D311yescharacteristic
124C2×C4⋊Dic3C2×D311yescharacteristic
125#924C2×D311yescharacteristic
126C2×C4×Dic3—61no—
127C2×C4×Dic3—61no—
128C2×D3×C8—32no—
129C2×D3×C8—32no—
130C2×D3×C8—62no—
131#897—31no—
132#895—31no—
133#894—61no—
134#893—61no—
135#892—31no—
136#892—31no—
137#892—32no—
138#892—32no—
139#892—32no—
140#892—32no—
141#892—61no—
142#892—61no—
143#892—61no—
144#892—61no—
145#883—61no—
146#882—61no—
147#67⋊C4—61no—
148#67⋊C4—61no—
149C3×#107—32no—
150C3×#107—32no—
151C3×#103—32no—
152C3×#102—32no—
153C3×C22⋊C8—21no—
154C3×C22⋊C8C2×D311yescharacteristic
155C3×C22⋊C8C2×D311yescharacteristic
156#835—32no—
157#832—32no—
158#830—31no—
159#830—31no—
160#830—61no—
161#821C2×D312yescomplemented
162(C2×D3)⋊C8—32no—
163(C2×D3)⋊C8—32no—
164(C2×D3)⋊C8—62no—
165#818C2×D312yescomplemented
166#818C2×D312yescomplemented
167#816C2×D312yescomplemented
168#810—32no—
169#809—32no—
170#808—32no—
171#808—32no—
172#808—32no—
173#808—32no—
174C23×C32C2×D411yescharacteristic
175C22×C3⋊D3—22no—
176C22×C3⋊D3—22no—
177C22×C3⋊D3—41no—
178C22×C3⋊D3C2×D411yescharacteristic
179C22×C3⋊D3C2×D411yescharacteristic
180C22×C3×D3—21no—
181C2×C32×C4—22no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3C2×D411yescharacteristic
186C2×C3⋊Dic3C2×D411yescharacteristic
187C4×C3⋊D3—22no—
188C4×C3⋊D3—22no—
189C4×C3⋊D3—22no—
190C4×C3⋊D3#4114yes—
191C3×#67—42no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—42no—
198C2×C3×Dic3—42no—
199C3×D12—22no—
200C3×Dic6—22no—
201#626—42no—
202#626—42no—
203D3×Dic3—42no—
204C32×C8—22no—
205C3⋊(C3⋊C8)—22no—
206#525—91no—
207C2×#117—91no—
208#485—92no—
209#484—31no—
210#483—91no—
211#482—92no—
212#481—91no—
213#480—31no—
214#427—92no—
215#416—92no—
216C2×C22⋊C8—91no—
217C23×D3—31no—
218C23×D3—31no—
219C23×D3—61no—
220C2×C3×Q8—31no—
221C2×C3×D4—31no—
222C2×C3×D4—61no—
223C22×C3×C4—21no—
224C22×C3×C4—61no—
225C22×C3×C4—61no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C2×#67—21no—
229C2×#67—61no—
230C2×#67—61no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—61no—
236C22×Dic3—61no—
237#239—64no—
238#237—64no—
239C2×D12—61no—
240C2×D12—61no—
241C2×D12C22×D311yescharacteristic
242C2×C4×D3—31no—
243C2×C4×D3—31no—
244C2×C4×D3—31no—
245C2×C4×D3—31no—
246C2×C4×D3—31no—
247C2×C4×D3—31no—
248C2×C4×D3—31no—
249C2×C4×D3—31no—
250C2×C4×D3—61no—
251C2×C4×D3—61no—
252C2×C4×D3—61no—
253C2×C4×D3—61no—
254C2×C4×D3—64no—
255C2×C4×D3—64no—
256C2×C4×D3—61no—
257C2×C4×D3—124no—
258C2×Dic6C22×D311yescharacteristic
259C2×C3×C8—22no—
260C2×C3×C8C22×D312yes—
261C2×C3×C8C22×D312yes—
262C3×C4⋊C4—31no—
263C3×C4⋊C4—31no—
264C3×C4⋊C4—32no—
265C3×C4⋊C4—32no—
266C3×C4⋊C4—61no—
267C3×C4⋊C4—61no—
268C3×C4⋊C4—61no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—61no—
271#217—21no—
272#217—61no—
273(C2×D3)⋊C4—21no—
274(C2×D3)⋊C4—61no—
275(C2×D3)⋊C4—61no—
276(C2×D3)⋊C4—61no—
277(C2×D3)⋊C4—61no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—62no—
280(C2×D3)⋊C4—62no—
281(C2×D3)⋊C4—62no—
282(C2×D3)⋊C4—61no—
283C4⋊Dic3—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3—61no—
286C4⋊Dic3C22×D311yescharacteristic
287C4⋊Dic3C22×D311yescharacteristic
288C4⋊Dic3C22×D312yes—
289C4⋊Dic3C22×D312yes—
290Dic3⋊C4—21no—
291Dic3⋊C4—61no—
292C4×Dic3—61no—
293C4×Dic3—61no—
294C4×Dic3—62no—
295C4×Dic3—62no—
296C4×Dic3—62no—
297C4×Dic3—62no—
298C2×C3⋊C8—32no—
299C2×C3⋊C8—32no—
300C2×C3⋊C8—62no—
301D3×C8—64no—
302D3×C8—64no—
303D3×C8—124no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32#13512yes—
307C22×C32C22×D411yescharacteristic
308C2×C3⋊D3—21no—
309C2×C3⋊D3—21no—
310C2×C3⋊D3—21no—
311C2×C3⋊D3—21no—
312C2×C3⋊D3—21no—
313C2×C3⋊D3—44no—
314C2×C3⋊D3#12312yes—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C2×C3×D3—41no—
318C32×C4—21no—
319C32×C4C2×#4112yes—
320C3⋊Dic3—21no—
321C3⋊Dic3#12312yes—
322C3×Dic3—41no—
323C3×Dic3—42no—
324C3×Dic3—41no—
325C3×Dic3—41no—
326C3×Dic3—42no—
327C2×#41—91no—
328C23×C4—91no—
329C22×C8—92no—
330#123—181no—
331C22⋊Q8—31no—
332C22⋊Q8—91no—
333#121—31no—
334#121—91no—
335#120—181no—
336C4×D4—181no—
337C4×D4—181no—
338#117—92no—
339#117—92no—
340#117—91no—
341#117—181no—
342#117—181no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—31no—
345C2×C22⋊C4—181no—
346C2×C42—181no—
347#107—32no—
348#107—32no—
349#106—92no—
350#106—92no—
351#103—32no—
352#103—92no—
353#102—32no—
354#102—92no—
355C22⋊C8—91no—
356C22⋊C8—92no—
357C22⋊C8D3211yescharacteristic
358C23×C3—21no—
359C23×C3—61no—
360C23×C3D3×D411yescharacteristic
361C23×C3D3×D411yescharacteristic
362C22×D3—21no—
363C22×D3—31no—
364C22×D3—31no—
365C22×D3—31no—
366C22×D3—31no—
367C22×D3—61no—
368C22×D3—61no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—64no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—122no—
375C22×D3—121no—
376C22×D3—121no—
377C22×D3—122no—
378C3×Q8—62no—
379C3×D4—62no—
380C3×D4—122no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—42no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—61no—
389C2×C3×C4—61no—
390C2×C3×C4—61no—
391C2×C3×C4—122no—
392C2×C3×C4—122no—
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397#67—42no—
398#67—122no—
399#67—122no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—21no—
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3—31no—
406C2×Dic3—31no—
407C2×Dic3—31no—
408C2×Dic3—31no—
409C2×Dic3—42no—
410C2×Dic3—42no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—122no—
416C2×Dic3—122no—
417D12—22no—
418D12—122no—
419D12—122no—
420C4×D3—34no—
421C4×D3—34no—
422C4×D3—64no—
423C4×D3—62no—
424C4×D3—62no—
425C4×D3—62no—
426C4×D3—62no—
427C4×D3—62no—
428C4×D3—62no—
429C4×D3—122no—
430C4×D3—122no—
431C4×D3—122no—
432C4×D3—122no—
433Dic6—22no—
434C3×C8—22no—
435C3×C8—22no—
436C3×C8—42no—
437C3⋊C8—62no—
438C3⋊C8—62no—
439C3⋊C8—122no—
440C2×C32—22no—
441C2×C32C2×#12311yescharacteristic
442C2×C32C2×#13511yescharacteristic
443C2×C32#57511yescharacteristic
444C3⋊D3—22no—
445C3⋊D3—41no—
446C3×D3—81no—
447C24—91no—
448#41—184no—
449C2×Q8—31no—
450C2×D4—31no—
451C2×D4—61no—
452C2×D4—181no—
453C2×D4—181no—
454C22×C4—61no—
455C22×C4—61no—
456C22×C4—91no—
457C22×C4—91no—
458C22×C4—91no—
459C22×C4—91no—
460C22×C4—91no—
461C22×C4—184no—
462C22×C4—181no—
463C22×C4C2×D3211yescharacteristic
464C2×C8—92no—
465C2×C8—184no—
466C2×C8C2×D3212yes—
467C4⋊C4—32no—
468C4⋊C4—32no—
469C4⋊C4—31no—
470C4⋊C4—31no—
471C4⋊C4—61no—
472C4⋊C4—61no—
473C4⋊C4—61no—
474C4⋊C4—181no—
475C22⋊C4—61no—
476C22⋊C4—61no—
477C22⋊C4—182no—
478C22⋊C4—182no—
479C22⋊C4—181no—
480C22⋊C4—181no—
481C22⋊C4—181no—
482C42—182no—
483C42—182no—
484C42—181no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—22no—
491C22×C3—41no—
492C22×C3—41no—
493C22×C3—121no—
494C22×C3—121no—
495C22×C3—121no—
496C22×C3#91212yes—
497C22×C3#91912yes—
498C22×C3C2×D3×D411yescharacteristic
499C22×C3C2×D3×D411yescharacteristic
500C2×D3—32no—
501C2×D3—32no—
502C2×D3—41no—
503C2×D3—41no—
504C2×D3—41no—
505C2×D3—62no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—61no—
509C2×D3—61no—
510C2×D3—61no—
511C2×D3—61no—
512C2×D3—62no—
513C2×D3—61no—
514C2×D3—61no—
515C2×D3—61no—
516C2×D3—61no—
517C2×D3—61no—
518C2×D3—61no—
519C2×D3—121no—
520C2×D3—121no—
521C2×D3—124no—
522C2×D3—124no—
523C2×D3—128no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—22no—
527C3×C4—41no—
528C3×C4—121no—
529C3×C4—122no—
530C3×C4—121no—
531C3×C4—121no—
532C3×C4—122no—
533C3×C4D3×#4112yes—
534C3×C4D3×#4112yes—
535Dic3—32no—
536Dic3—32no—
537Dic3—41no—
538Dic3—42no—
539Dic3—41no—
540Dic3—42no—
541Dic3—41no—
542Dic3—62no—
543Dic3—61no—
544Dic3—61no—
545Dic3—121no—
546C32#309111yescharacteristic, complemented, Sylow
547C23—61no—
548C23—91no—
549C23—91no—
550C23—182no—
551C23—182no—
552C23—361no—
553C23#380211yescharacteristic
554Q8—62no—
555D4—62no—
556D4—122no—
557D4—362no—
558D4—362no—
559C2×C4—22no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—61no—
563C2×C4—61no—
564C2×C4—61no—
565C2×C4—91no—
566C2×C4—94no—
567C2×C4—91no—
568C2×C4—122no—
569C2×C4—122no—
570C2×C4—182no—
571C2×C4—182no—
572C2×C4—182no—
573C2×C4—182no—
574C2×C4—362no—
575C2×C4#380211yescharacteristic
576C2×C4C22×D3211yescharacteristic
577C8—22no—
578C8—182no—
579C2×C3—22no—
580C2×C3—22no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—42no—
585C2×C3—241no—
586C2×C3D3×#12311yescharacteristic
587C2×C3D3×#12311yescharacteristic
588C2×C3C2×#91211yescharacteristic
589C2×C3C2×#91911yescharacteristic
590C2×C3#577311yescharacteristic
591C2×C3#577711yescharacteristic
592D3—64no—
593D3—62no—
594D3—62no—
595D3—81no—
596D3—122no—
597D3—121no—
598D3—121no—
599C22—21no—
600C22—21no—
601C22—92no—
602C22—121no—
603C22—121no—
604C22—121no—
605C22—181no—
606C22—181no—
607C22—181no—
608C22—181no—
609C22—181no—
610C22—364no—
611C22#6381012yes—
612C22C2×#380211yescharacteristic
613C4—21no—
614C4—92no—
615C4—122no—
616C4—121no—
617C4—122no—
618C4—121no—
619C4—121no—
620C4—181no—
621C4#6431212yes—
622C3—21no—
623C3#8128111yescharacteristic, complemented
624C3#8146711yescharacteristic, complemented
625C2—22no—
626C2—182no—
627C2—241no—
628C2—361no—
629C2#1059429511yescharacteristic
630C2C2×#6381011yescharacteristic
631C2#1059471811yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10594922C2
hypercenterC22⋊C8D32
hypocenterC32#3091
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
2. C2×#63849C2semidirect
3. C3⋊D3×C22⋊C8C2semidirect
4. C3×#4736C2semidirect
5. C3×#4722C2semidirect
6. #10591101C2semidirect
7. #10591091C2semidirect
8. #10590956C2semidirect
9. #10590715C2semidirect
10. #10590714C2semidirect
11. #10590651C2semidirect
37. C3×#821C22semidirect
38. C3×#818C22semidirect
39. C3×#818C22semidirect
40. C3×#816C22semidirect
41. #63574C22semidirect
42. #63574C22semidirect
43. #63565C22semidirect
44. #63562C22semidirect
63. #4736D3semidirect
67. #4722D3semidirect
161. #821C2×D3semidirect
165. #818C2×D3semidirect
166. #818C2×D3semidirect
167. #816C2×D3semidirect
546. C32#3091semidirect
623. C3#81281semidirect
624. C3#81467semidirect

Maximal subgroups

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

subgroupindex
#105949222
C2×#638492
C3⋊D3×C22⋊C82
C3×#47362
C3×#47222
#105911012
#105910912
#105909562
#105907152
#105907142
#105906512
#814673
#812813