Finite Group Databasebeta

← #11870523

Subgroups — #11870523

Order 1152.

955 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3802C211yesmaximal, characteristic
2#10593866C211yesmaximal, characteristic, complemented
3#10592532C211yesmaximal, characteristic, complemented
4C3×#4842C211yesmaximal, characteristic, complemented
5C3×#4841C211yesmaximal, characteristic, complemented
6#10590943C212yesmaximal
7#10590775C212yesmaximal, complemented
8#10590742C212yesmaximal, complemented
9#10590686C212yesmaximal, complemented
10#10590363C211yesmaximal, characteristic, complemented
11#10590266C211yesmaximal, characteristic, complemented
12#81044—31nomaximal
13#80408—31nomaximal
14C2×#3802C2211yescharacteristic
15C2×C4×D32—21no—
16C42×C3⋊D3C2211yescharacteristic
17C2×C3×#204C2212yes—
18C3×C4×D12C2211yescharacteristic
19C3×C4×D12C2211yescharacteristic
20C3×#869C2211yescharacteristic, complemented
21C3×#869C2211yescharacteristic, complemented
22#63921—21no—
23#63902—21no—
24C4×#625—21no—
25#63900C2211yescharacteristic
26#63898C2211yescharacteristic
27#63898C2211yescharacteristic
28#63872—21no—
29#63871—21no—
30#63871C2212yes—
31#63849—21no—
32#63843—21no—
33#63843C2212yescomplemented
34C2×#3715C2212yes—
35C32×C4⋊C8C2211yescharacteristic, complemented
36#63647C2212yes—
37C8×C3⋊Dic3C2212yescomplemented
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
39C3×#821C2212yes—
40C3×#817C2212yescomplemented
41C3×#816C2212yescomplemented
42#63574C2212yescomplemented
43#63565C2212yescomplemented
44#63562C2212yes—
45#5728—31no—
46#5728—31no—
47C4×D3×D4—31no—
48C4×D3×D4—31no—
49C3×#476—31no—
50C3×#461—31no—
51#5169—32no—
52Dic3×SD16—32no—
53#5084—31no—
54#5083—31no—
55#5019—31no—
56#5008—31no—
57#4862—32no—
58#4852—32no—
59#4842D311yescharacteristic, complemented
60#4841D311yescharacteristic, complemented
61#4833—31no—
62#4833—31no—
63#4833—61no—
64#4805—32no—
65#4788—32no—
66#4776—32no—
67#4758—32no—
68C22×D32—21no—
69C2×C4×C3⋊D3D411yescharacteristic
70C2×C4×C3⋊D3D411yescharacteristic
71C2×C4×C3⋊D3C2311yescharacteristic
72C2×C3×D12C2311yescharacteristic
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×C4×D3—21no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6C2312yes—
78C2×#625—21no—
79C2×#624—21no—
80C2×D3×Dic3—21no—
81C2×D3×Dic3—21no—
82#3802—22no—
83#3802—22no—
84C4×D32—44no—
85C2×C32×C8C2312yes—
86C32×C42C2311yescharacteristic
87C4×C3⋊Dic3D411yescharacteristic
88C4×C3⋊Dic3D411yescharacteristic
89C4×C3⋊Dic3C2311yescharacteristic
90C2×C3⋊(C3⋊C8)C2312yes—
91C3×(C2×D3)⋊C4—21no—
92C3×(C2×D3)⋊C4—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3C2312yes—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4⋊Dic3C2311yescharacteristic
99C3×#204—24no—
100#3724—21no—
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3—22no—
103#3722—22no—
104(C2×D3)⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106Dic32—22no—
107#3715—24no—
108#3101—91noSylow
109C2×D3×D4—31no—
110C2×D3×D4—31no—
111C22×C4×D3—61no—
112C22×C4×D3—61no—
113C2×C3×SD16—32no—
114C3×C4⋊Q8—31no—
115C3×C4⋊Q8—31no—
116C3×C4×D4—31no—
117C3×C4×D4—31no—
118#946—32no—
119#946—61no—
120Q8×Dic3—32no—
121Q8×Dic3—61no—
122C2×#215—32no—
123D4×Dic3—31no—
124D4×Dic3—31no—
125C2×#214—32no—
126C4×#67—61no—
127C4×#67—61no—
128C2×#204C2×D312yes—
129#897—32no—
130#897—61no—
131#893—31no—
132#893—31no—
133#892—61no—
134#892—61no—
135D3×C4⋊C4—31no—
136D3×C4⋊C4—31no—
137#890—61no—
138#890—61no—
139#887—32no—
140#887—61no—
141#67⋊C4—61no—
142#67⋊C4—61no—
143D3×C22⋊C4—61no—
144D3×C22⋊C4—61no—
145C4×D12C2×D311yescharacteristic
146C4×D12C2×D311yescharacteristic
147C42×D3—31no—
148C42×D3—31no—
149C42×D3—61no—
150#869C2×D311yescharacteristic, complemented
151#869C2×D311yescharacteristic, complemented
152C3×#106—32no—
153C3×C4⋊C8—21no—
154C3×C4⋊C8C2×D311yescharacteristic, complemented
155C3×C4⋊C8C2×D311yescharacteristic, complemented
156C3×#103—32no—
157C3×#102—32no—
158#835—32no—
159#832—32no—
160#821C2×D312yes—
161(C2×D3)⋊C8—32no—
162(C2×D3)⋊C8—32no—
163(C2×D3)⋊C8—62no—
164#817C2×D312yescomplemented
165#816C2×D312yescomplemented
166C8×Dic3—32no—
167C8×Dic3—32no—
168C8×Dic3—62no—
169#810—32no—
170#809—32no—
171#808—32no—
172#808—32no—
173C4⋊(C3⋊C8)—31no—
174C4⋊(C3⋊C8)—31no—
175C4⋊(C3⋊C8)—61no—
176C22×C3⋊D3C2×D411yescharacteristic
177C22×C3×D3—21no—
178C22×C3×D3—21no—
179C2×D32—24no—
180C2×D32—42no—
181C2×D32—42no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3C2×D411yescharacteristic
186C2×C3⋊Dic3C2×D411yescharacteristic
187C2×C3⋊Dic3C2×D411yescharacteristic
188C4×C3⋊D3—21no—
189C4×C3⋊D3—21no—
190C4×C3⋊D3—41no—
191C4×C3⋊D3SD1614yescomplemented
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C3×D12—21no—
197C3×D12—21no—
198C3×D12#4112yes—
199C3×D12#4112yes—
200C3×C4×D3—42no—
201C3×C4×D3—42no—
202C3×Dic6—22no—
203C3×Dic6—22no—
204C3×Dic6—42no—
205#625—24no—
206#624—42no—
207D3×Dic3—42no—
208D3×Dic3—42no—
209C32×C8—22no—
210C3⋊(C3⋊C8)—22no—
211#533—91no—
212C2×C4×D4—91no—
213#483—92no—
214#476—31no—
215#476—91no—
216#461—31no—
217#461—91no—
218#450—92no—
219C4×SD16—92no—
220C4×SD16—92no—
221#431—91no—
222C23×D3—61no—
223C23×D3—61no—
224C2×C3×Q8—32no—
225C2×C3×Q8—61no—
226C2×C3×D4—31no—
227C2×C3×D4—31no—
228C22×C3×C4—61no—
229C22×C3×C4—61no—
230C2×#67—61no—
231C2×#67—61no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234D3×D4—62no—
235D3×D4—62no—
236D3×D4—62no—
237D3×D4—62no—
238C2×D12C22×D311yescharacteristic
239C2×D12C22×D311yescharacteristic
240C2×C4×D3—21no—
241C2×C4×D3—21no—
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—61no—
249C2×C4×D3—61no—
250C2×C4×D3—61no—
251C2×C4×D3—61no—
252C2×C4×D3—61no—
253C2×C4×D3—61no—
254C2×C4×D3—61no—
255C2×C4×D3—124no—
256C2×C4×D3—124no—
257C2×Dic6—21no—
258C2×Dic6C22×D312yes—
259C3×SD16—64no—
260C2×C3×C8—22no—
261C2×C3×C8C22×D312yes—
262C2×C3×C8C22×D312yes—
263C3×C4⋊C4—31no—
264C3×C4⋊C4—32no—
265C3×C4⋊C4—31no—
266C3×C4⋊C4—61no—
267C3×C4⋊C4—61no—
268C3×C4⋊C4—61no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—61no—
271C3×C42—21no—
272C3×C42C22×D311yescharacteristic
273C3×C42C22×D311yescharacteristic
274#217—61no—
275#217—61no—
276#215—64no—
277#214—64no—
278(C2×D3)⋊C4—21no—
279(C2×D3)⋊C4—21no—
280(C2×D3)⋊C4—62no—
281(C2×D3)⋊C4—62no—
282(C2×D3)⋊C4—61no—
283(C2×D3)⋊C4—61no—
284C4⋊Dic3—21no—
285C4⋊Dic3—21no—
286C4⋊Dic3—21no—
287C4⋊Dic3—62no—
288C4⋊Dic3—62no—
289C4⋊Dic3C22×D311yescharacteristic
290C4⋊Dic3C22×D312yes—
291C4⋊Dic3C22×D311yescharacteristic
292Dic3⋊C4—61no—
293Dic3⋊C4—61no—
294Dic3⋊C4—62no—
295Dic3⋊C4—62no—
296C4×Dic3—31no—
297C4×Dic3—31no—
298C4×Dic3—31no—
299C4×Dic3—31no—
300C4×Dic3—31no—
301C4×Dic3—31no—
302C4×Dic3—61no—
303C4×Dic3—61no—
304C4×Dic3—61no—
305C4×Dic3—62no—
306C4×Dic3—62no—
307C2×C3⋊C8—32no—
308C2×C3⋊C8—32no—
309C2×C3⋊C8—62no—
310#204—24no—
311C22×C32C22×D411yescharacteristic
312C2×C3⋊D3—21no—
313C2×C3⋊D3—21no—
314C2×C3⋊D3C2×SD1612yes—
315C2×C3×D3—22no—
316C2×C3×D3—22no—
317C2×C3×D3—41no—
318C2×C3×D3—41no—
319C2×C3×D3—41no—
320C2×C3×D3—41no—
321D32—48no—
322C32×C4—21no—
323C32×C4C2×SD1612yes—
324C32×C4C2×#4111yescharacteristic
325C32×C4C2×#4111yescharacteristic
326C3⋊Dic3—21no—
327C3⋊Dic3—21no—
328C3⋊Dic3C2×SD1612yes—
329C3×Dic3—42no—
330C3×Dic3—41no—
331C3×Dic3—41no—
332C3×Dic3—42no—
333C22×D4—91no—
334C23×C4—181no—
335C2×SD16—32no—
336C2×SD16—92no—
337C4⋊Q8—31no—
338C4⋊Q8—31no—
339#125—181no—
340C22⋊Q8—92no—
341C22⋊Q8—181no—
342C4×Q8—92no—
343C4×Q8—181no—
344C4×D4—31no—
345C4×D4—31no—
346C4×D4—91no—
347C4×D4—91no—
348C4×D4—181no—
349C4×D4—181no—
350#117—181no—
351C2×C4⋊C4—91no—
352C2×C22⋊C4—181no—
353C2×C42—91no—
354#106—32no—
355#106—92no—
356C4⋊C8—91no—
357C4⋊C8D3211yescharacteristic, complemented
358#103—32no—
359#103—92no—
360#102—32no—
361#102—92no—
362C22⋊C8—92no—
363C4×C8—92no—
364C23×C3—61no—
365C23×C3—61no—
366C22×D3—21no—
367C22×D3—21no—
368C22×D3—31no—
369C22×D3—31no—
370C22×D3—61no—
371C22×D3—64no—
372C22×D3—64no—
373C22×D3—122no—
374C22×D3—122no—
375C22×D3—122no—
376C22×D3—122no—
377C3×Q8—62no—
378C3×Q8—62no—
379C3×Q8—122no—
380C3×D4—32no—
381C3×D4—32no—
382C3×D4—61no—
383C3×D4—61no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
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×C4D3×D411yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4C23×D311yescharacteristic
398C2×C3×C4C23×D311yescharacteristic
399#67—64no—
400#67—64no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3—31no—
406C2×Dic3—31no—
407C2×Dic3—31no—
408C2×Dic3—31no—
409C2×Dic3—31no—
410C2×Dic3—31no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—122no—
415C2×Dic3—122no—
416D12—21no—
417D12—21no—
418D12#23712yes—
419D12#23912yes—
420C4×D3—34no—
421C4×D3—34no—
422C4×D3—42no—
423C4×D3—42no—
424C4×D3—64no—
425C4×D3—61no—
426C4×D3—61no—
427C4×D3—61no—
428C4×D3—61no—
429C4×D3—121no—
430C4×D3—121no—
431C4×D3—122no—
432C4×D3—122no—
433C4×D3—122no—
434C4×D3—122no—
435C4×D3—121no—
436C4×D3—121no—
437C4×D3—122no—
438Dic6—22no—
439Dic6—22no—
440Dic6—42no—
441C3×C8—22no—
442C3×C8—22no—
443C3×C8—42no—
444C3⋊C8—62no—
445C3⋊C8—62no—
446C3⋊C8—122no—
447C2×C32#52511yescharacteristic
448C2×C32C22×SD1611yescharacteristic
449C2×C32#57511yescharacteristic
450C3⋊D3—22no—
451C3×D3—42no—
452C3×D3—42no—
453C24—181no—
454C2×Q8—32no—
455C2×Q8—61no—
456C2×D4—31no—
457C2×D4—31no—
458C2×D4—181no—
459C2×D4—182no—
460C2×D4—182no—
461C22×C4—61no—
462C22×C4—61no—
463C22×C4—91no—
464C22×C4—91no—
465C22×C4—91no—
466C22×C4—181no—
467C22×C4—181no—
468C22×C4—181no—
469C22×C4—364no—
470SD16—64no—
471SD16—184no—
472C2×C8—92no—
473C2×C8C2×D3212yes—
474C4⋊C4—32no—
475C4⋊C4—31no—
476C4⋊C4—31no—
477C4⋊C4—61no—
478C4⋊C4—61no—
479C4⋊C4—61no—
480C4⋊C4—181no—
481C4⋊C4—182no—
482C4⋊C4—182no—
483C22⋊C4—61no—
484C22⋊C4—61no—
485C22⋊C4—182no—
486C22⋊C4—181no—
487C22⋊C4—181no—
488C42—91no—
489C42—91no—
490C42—91no—
491C42—182no—
492C42C2×D3211yescharacteristic
493C22×C3—21no—
494C22×C3—62no—
495C22×C3—62no—
496C22×C3—121no—
497C22×C3—121no—
498C22×C3—121no—
499C22×C3—121no—
500C22×C3C2×D3×D411yescharacteristic
501C22×C3C2×D3×D411yescharacteristic
502C2×D3—22no—
503C2×D3—22no—
504C2×D3—32no—
505C2×D3—32no—
506C2×D3—41no—
507C2×D3—41no—
508C2×D3—41no—
509C2×D3—41no—
510C2×D3—62no—
511C2×D3—61no—
512C2×D3—61no—
513C2×D3—61no—
514C2×D3—61no—
515C2×D3—121no—
516C2×D3—121no—
517C2×D3—128no—
518C2×D3—128no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—22no—
522C3×C4—21no—
523C3×C4—21no—
524C3×C4—41no—
525C3×C4—121no—
526C3×C4—121no—
527C3×C4—122no—
528C3×C4—122no—
529C3×C4D3×SD1612yes—
530C3×C4D3×SD1612yes—
531C3×C4C2×#23711yescharacteristic
532C3×C4C2×#23911yescharacteristic
533C3×C4D3×#4111yescharacteristic
534C3×C4D3×#4111yescharacteristic
535Dic3—32no—
536Dic3—32no—
537Dic3—41no—
538Dic3—41no—
539Dic3—42no—
540Dic3—42no—
541Dic3—62no—
542Dic3—62no—
543Dic3—61no—
544Dic3—61no—
545Dic3—61no—
546Dic3—61no—
547Dic3—121no—
548C32#310111yescharacteristic, complemented, Sylow
549C23—61no—
550C23—61no—
551C23—91no—
552C23—184no—
553C23—362no—
554C23—362no—
555Q8—62no—
556Q8—62no—
557Q8—122no—
558D4—32no—
559D4—32no—
560D4—61no—
561D4—61no—
562D4—184no—
563C2×C4—62no—
564C2×C4—62no—
565C2×C4—61no—
566C2×C4—61no—
567C2×C4—91no—
568C2×C4—94no—
569C2×C4—91no—
570C2×C4—91no—
571C2×C4—122no—
572C2×C4—122no—
573C2×C4—181no—
574C2×C4—181no—
575C2×C4—361no—
576C2×C4—362no—
577C2×C4—362no—
578C2×C4—362no—
579C2×C4#380211yescharacteristic
580C2×C4#380211yescharacteristic
581C2×C4C22×D3211yescharacteristic
582C8—22no—
583C8—182no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—122no—
588C2×C3—122no—
589C2×C3#560611yescharacteristic
590C2×C3#562711yescharacteristic
591C2×C3C2×D3×SD1611yescharacteristic
592C2×C3C2×D3×SD1611yescharacteristic
593C2×C3#577311yescharacteristic
594C2×C3#577711yescharacteristic
595D3—42no—
596D3—42no—
597D3—62no—
598D3—62no—
599D3—122no—
600C22—62no—
601C22—62no—
602C22—92no—
603C22—121no—
604C22—121no—
605C22—121no—
606C22—121no—
607C22—181no—
608C22—181no—
609C22—368no—
610C22C2×#380211yescharacteristic
611C4—21no—
612C4—92no—
613C4—122no—
614C4—121no—
615C4—121no—
616C4—122no—
617C4—181no—
618C4—181no—
619C4#6379612yes—
620C4D3×#23711yescharacteristic
621C4D3×#23911yescharacteristic
622C3—21no—
623C3#8040811yescharacteristic, complemented
624C3#8104411yescharacteristic, complemented
625C2—122no—
626C2—122no—
627C2—182no—
628C2#1059463211yescharacteristic
629C2C2×#6379611yescharacteristic
630C2#1059471811yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC4⋊C8D32
hypocenterC32#3101
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
2. #10593866C2semidirect
3. #10592532C2semidirect
4. C3×#4842C2semidirect
5. C3×#4841C2semidirect
7. #10590775C2semidirect
8. #10590742C2semidirect
9. #10590686C2semidirect
10. #10590363C2semidirect
11. #10590266C2semidirect
20. C3×#869C22semidirect
21. C3×#869C22semidirect
33. #63843C22semidirect
35. C32×C4⋊C8C22semidirect
37. C8×C3⋊Dic3C22semidirect
38. C4⋊(C3⋊(C3⋊C8))C22semidirect
40. C3×#817C22semidirect
41. C3×#816C22semidirect
42. #63574C22semidirect
43. #63565C22semidirect
59. #4842D3semidirect
60. #4841D3semidirect
150. #869C2×D3semidirect
151. #869C2×D3semidirect
154. C3×C4⋊C8C2×D3semidirect
155. C3×C4⋊C8C2×D3semidirect
164. #817C2×D3semidirect
165. #816C2×D3semidirect
191. C4×C3⋊D3SD16semidirect
357. C4⋊C8D32semidirect
548. C32#3101semidirect
623. C3#80408semidirect
624. C3#81044semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
#105938662
#105925322
C3×#48422
C3×#48412
#105909432
#105907752
#105907422
#105906862
#105903632
#105902662
#810443
#804083