Finite Group Databasebeta

← #11882341

Subgroups — #11882341

Order 1152.

865 conjugacy classes of subgroups.

The subgroup lattice has 613 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5479C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic, complemented
3C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
4#10591179C212yesmaximal, complemented
5#10591166C212yesmaximal, complemented
6#10590364C211yesmaximal, characteristic, complemented
7#10590348C212yesmaximal, complemented
8#10590347C211yesmaximal, characteristic, complemented
9#10590310C211yesmaximal, characteristic, complemented
10#10590270C212yesmaximal, complemented
11#10590266C211yesmaximal, characteristic, complemented
12#83311—31nomaximal
13#83148—31nomaximal
14C2×C3×#235—21no—
15C2×C32×C42C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2212yes—
17C3×#930—21no—
18C3×#930C2211yescharacteristic
19C3×#930C2212yes—
20C3×#929—21no—
21C3×C4×#67—21no—
22C3×#924C2211yescharacteristic
23C3×#876—21no—
24C3×#875—21no—
25C3×#875C2211yescharacteristic
26C3×#874C2211yescharacteristic
27C3×C4×D12—21no—
28C3×C4×D12C2211yescharacteristic
29C3×C4×D12C2212yes—
30C3×#872—21no—
31C3×#870C2211yescharacteristic
32C3×#869C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34C2×#3715C2212yes—
35C2×#3713C2212yes—
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
37C4⋊(C3⋊(C3⋊C8))C2212yes—
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39#63576C2212yes—
40#63574C2212yes—
41#63565C2212yes—
42#63562C2212yes—
43#63562C2212yes—
44#63562C2212yes—
45C3×#532—31no—
46C3×#529—31no—
47#5479D311yescharacteristic, complemented
48#5477D311yescharacteristic, complemented
49#5091—31no—
50#5084—31no—
51#5075—31no—
52#5072—31no—
53#5066—32no—
54#5057—32no—
55#5048—32no—
56#5041—32no—
57#5038—32no—
58#5038—32no—
59#5027—31no—
60#5021—31no—
61#5016—32no—
62#5015—31no—
63#5009—32no—
64#5008—31no—
65C2×C4⋊(C3⋊C8)—31no—
66C2×C4⋊(C3⋊C8)—31no—
67C2×C4⋊(C3⋊C8)—61no—
68C22×C32×C4D411yescharacteristic
69C22×C32×C4D411yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C2×C3×#67—21no—
72C2×C3×#67—22no—
73C3×#235—44no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×D12C2312yes—
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—22no—
80C2×C3×Dic6—21no—
81C2×C3×Dic6C2311yescharacteristic
82C32×C42D411yescharacteristic
83C32×C42D411yescharacteristic
84C32×C42C2311yescharacteristic
85C32×C42C2311yescharacteristic
86C2×C3⋊(C3⋊C8)—42no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C2×C3⋊(C3⋊C8)C2312yes—
89C3×#217—21no—
90C3×(C2×D3)⋊C4—21no—
91C3×(C2×D3)⋊C4—21no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—22no—
94C3×(C2×D3)⋊C4—21no—
95C3×(C2×D3)⋊C4—22no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4⋊Dic3C2312yes—
100C3×Dic3⋊C4—21no—
101C3×Dic3⋊C4—21no—
102C3×Dic3⋊C4—21no—
103C3×Dic3⋊C4—21no—
104C3×C4×Dic3—21no—
105#3715—42no—
106#3713—42no—
107#3247—91noSylow
108C2×C3×#41—61no—
109C2×#235—21no—
110C3×C4⋊Q8—31no—
111C3×#127—31no—
112C3×#126—61no—
113C3×#125—31no—
114C3×#124—31no—
115C3×#124—61no—
116C3×#123—61no—
117C3×C22⋊Q8—31no—
118C3×#121—31no—
119C3×#121—32no—
120C3×#121—61no—
121C3×C4×Q8—31no—
122C3×C4×D4—31no—
123C3×C4×D4—32no—
124C3×C4×D4—61no—
125C3×C4×D4—61no—
126C3×#117—61no—
127C2×C3×C42—21no—
128C2×C3×C42C2×D311yescharacteristic
129C2×C3×C42C2×D311yescharacteristic
130C2×#215—32no—
131C2×#214—32no—
132C2×#213—32no—
133C2×#213—32no—
134#930—21no—
135#930C2×D312yes—
136#930C2×D311yescharacteristic
137#929—21no—
138C4×#67—21no—
139#924C2×D311yescharacteristic
140C22×C3⋊C8—32no—
141C22×C3⋊C8—32no—
142C22×C3⋊C8—62no—
143#876—21no—
144#875—21no—
145#875C2×D311yescharacteristic
146#874C2×D311yescharacteristic
147C4×D12—21no—
148C4×D12C2×D312yes—
149C4×D12C2×D311yescharacteristic
150#872—21no—
151#870C2×D311yescharacteristic
152#869C2×D311yescharacteristic
153C4×Dic6C2×D311yescharacteristic
154#835—32no—
155#832—32no—
156#832—32no—
157#832—32no—
158#810—32no—
159#809—32no—
160#809—32no—
161#809—32no—
162#808—32no—
163#808—32no—
164#807—32no—
165#807—32no—
166C4⋊(C3⋊C8)—31no—
167C4⋊(C3⋊C8)—32no—
168C4⋊(C3⋊C8)—31no—
169C4⋊(C3⋊C8)—32no—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—61no—
173C4⋊(C3⋊C8)—61no—
174C4⋊(C3⋊C8)—62no—
175C23×C32C2×D411yescharacteristic
176C22×C3×D3—21no—
177C22×C3×D3—22no—
178C2×C32×C4—22no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—22no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2411yescharacteristic
188C3×#67—44no—
189C3×#67—42no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C3×D12—21no—
195C3×D12—22no—
196C3×D12—21no—
197C3×D12—22no—
198C3×D12—42no—
199C3×D12—42no—
200C3×C4×D3—44no—
201C3×C4×D3—42no—
202C3×Dic6—21no—
203C3×Dic6—21no—
204C3×Dic6—42no—
205C3⋊(C3⋊C8)—22no—
206C3⋊(C3⋊C8)—22no—
207#532—31no—
208#529—31no—
209#478—92no—
210#477—91no—
211#476—91no—
212#466—92no—
213#465—92no—
214#463—92no—
215#460—91no—
216#459—91no—
217C2×C4⋊C8—91no—
218C3×#41—124no—
219C2×C3×Q8—31no—
220C2×C3×Q8—61no—
221C2×C3×D4—31no—
222C2×C3×D4—32no—
223C2×C3×D4—61no—
224C2×C3×D4—62no—
225C2×C3×D4—61no—
226C2×C3×D4—61no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—61no—
231C22×C3×C4—62no—
232C22×C3×C4#6711yescharacteristic
233C22×C3×C4#6711yescharacteristic
234C22×C3×C4#6711yescharacteristic
235C22×C3×C4#6711yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C2×#67—21no—
239C2×#67—22no—
240#235—44no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12C22×D312yes—
244C2×D12C22×D311yescharacteristic
245C2×C4×D3—21no—
246C2×C4×D3—22no—
247C2×Dic6—21no—
248C2×Dic6C22×D311yescharacteristic
249C3×C4⋊C4—31no—
250C3×C4⋊C4—32no—
251C3×C4⋊C4—31no—
252C3×C4⋊C4—61no—
253C3×C4⋊C4—61no—
254C3×C4⋊C4—61no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4—61no—
257C3×C22⋊C4—61no—
258C3×C22⋊C4—61no—
259C3×C22⋊C4—61no—
260C3×C22⋊C4—62no—
261C3×C22⋊C4—61no—
262C3×C22⋊C4—62no—
263C3×C22⋊C4—61no—
264C3×C42—21no—
265C3×C42—21no—
266C3×C42—21no—
267C3×C42—21no—
268C3×C42—61no—
269C3×C42#6711yescharacteristic
270C3×C42#6711yescharacteristic
271C3×C42#6711yescharacteristic
272C3×C42#6711yescharacteristic
273C3×C42C22×D311yescharacteristic
274C3×C42C22×D311yescharacteristic
275C3×C42C22×D311yescharacteristic
276C3×C42C22×D311yescharacteristic
277#217—21no—
278#215—122no—
279#214—122no—
280#213—122no—
281#213—122no—
282(C2×D3)⋊C4—21no—
283(C2×D3)⋊C4—21no—
284(C2×D3)⋊C4—22no—
285(C2×D3)⋊C4—22no—
286(C2×D3)⋊C4—21no—
287(C2×D3)⋊C4—21no—
288C4⋊Dic3—21no—
289C4⋊Dic3C22×D311yescharacteristic
290C4⋊Dic3C22×D312yes—
291C4⋊Dic3C22×D311yescharacteristic
292Dic3⋊C4—21no—
293Dic3⋊C4—21no—
294Dic3⋊C4—21no—
295Dic3⋊C4—21no—
296C4×Dic3—21no—
297C2×C3⋊C8—32no—
298C2×C3⋊C8—32no—
299C2×C3⋊C8—32no—
300C2×C3⋊C8—32no—
301C2×C3⋊C8—62no—
302C2×C3⋊C8—62no—
303C2×C3⋊C8—122no—
304C2×C3⋊C8—122no—
305C2×C3⋊C8—124no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32AGL(1,ℤ/8)12yes—
309C22×C32C22×D411yescharacteristic
310C2×C3×D3—41no—
311C2×C3×D3—42no—
312C2×C3×D3—41no—
313C2×C3×D3—42no—
314C2×C3×D3—42no—
315C2×C3×D3—41no—
316C32×C4—21no—
317C32×C4—21no—
318C32×C4—21no—
319C32×C4—21no—
320C32×C4#13512yes—
321C32×C4H(5,𝔽2)11yescharacteristic
322C32×C42−1+411yescharacteristic
323C3×Dic3—41no—
324C3×Dic3—41no—
325C3×Dic3—42no—
326C3×Dic3—41no—
327C2×#41—61no—
328C2×SD16—92no—
329C2×D8—92no—
330C22×C8—92no—
331C4⋊Q8—31no—
332#127—31no—
333#126—61no—
334#125—31no—
335#124—31no—
336#124—61no—
337#123—61no—
338C22⋊Q8—31no—
339#121—31no—
340#121—32no—
341#121—61no—
342C4×Q8—31no—
343C4×D4—31no—
344C4×D4—32no—
345C4×D4—61no—
346C4×D4—61no—
347#117—61no—
348C2×C42D3211yescharacteristic
349#107—92no—
350#106—92no—
351C4⋊C8—91no—
352C4⋊C8—91no—
353C4⋊C8—92no—
354#103—92no—
355#102—92no—
356#102—92no—
357#102—92no—
358C23×C3—21no—
359C23×C3—61no—
360C23×C3—62no—
361C23×C3C2×#6711yescharacteristic
362C23×C3C2×#6711yescharacteristic
363C22×D3—21no—
364C22×D3—22no—
365C3×Q8—61no—
366C3×Q8—61no—
367C3×Q8—122no—
368C3×D4—61no—
369C3×D4—62no—
370C3×D4—62no—
371C3×D4—61no—
372C3×D4—122no—
373C3×D4—122no—
374C3×D4—124no—
375C3×D4—122no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—24no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—42no—
394C2×C3×C4—61no—
395C2×C3×C4—61no—
396C2×C3×C4—61no—
397C2×C3×C4—62no—
398C2×C3×C4—124no—
399C2×C3×C4—122no—
400C2×C3×C4C2×#6711yescharacteristic
401C2×C3×C4C2×#6711yescharacteristic
402C2×C3×C4C2×#6711yescharacteristic
403C2×C3×C4C2×#6711yescharacteristic
404C2×C3×C4C2×#6711yescharacteristic
405C2×C3×C4C2×#6711yescharacteristic
406C2×C3×C4C2×#6711yescharacteristic
407C2×C3×C4C2×#6711yescharacteristic
408C2×C3×C4C2×#6711yescharacteristic
409C2×C3×C4C2×#6711yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411C2×C3×C4C23×D311yescharacteristic
412#67—44no—
413#67—42no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—21no—
417C2×Dic3—22no—
418D12—21no—
419D12—22no—
420D12—21no—
421D12—22no—
422D12—42no—
423D12—42no—
424C4×D3—44no—
425C4×D3—42no—
426Dic6—21no—
427Dic6—21no—
428Dic6—42no—
429C3⋊C8—62no—
430C3⋊C8—62no—
431C3⋊C8—62no—
432C3⋊C8—62no—
433C3⋊C8—122no—
434C3⋊C8—122no—
435C2×C32—22no—
436C2×C32#53711yescharacteristic
437C2×C32C2×#13511yescharacteristic
438C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
439C3×D3—82no—
440C3×D3—81no—
441#41—124no—
442C2×Q8—31no—
443C2×Q8—61no—
444C2×D4—31no—
445C2×D4—32no—
446C2×D4—61no—
447C2×D4—62no—
448C2×D4—61no—
449C2×D4—61no—
450C22×C4—61no—
451C22×C4—62no—
452C22×C4#62511yescharacteristic
453C22×C4#62511yescharacteristic
454C22×C4C2×D3211yescharacteristic
455SD16—362no—
456D8—362no—
457C2×C8—92no—
458C2×C8—92no—
459C2×C8—362no—
460C4⋊C4—31no—
461C4⋊C4—31no—
462C4⋊C4—32no—
463C4⋊C4—61no—
464C4⋊C4—61no—
465C4⋊C4—61no—
466C4⋊C4—61no—
467C4⋊C4—61no—
468C22⋊C4—61no—
469C22⋊C4—61no—
470C22⋊C4—61no—
471C22⋊C4—62no—
472C22⋊C4—61no—
473C22⋊C4—62no—
474C22⋊C4—61no—
475C42—61no—
476C42#62511yescharacteristic
477C42#62511yescharacteristic
478C42C2×D3211yescharacteristic
479C42C2×D3211yescharacteristic
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—22no—
488C22×C3—121no—
489C22×C3—122no—
490C22×C3—121no—
491C22×C3—122no—
492C22×C3—121no—
493C22×C3—122no—
494C22×C3#93212yes—
495C22×C3#94912yes—
496C22×C3C22×#6711yescharacteristic
497C22×C3C22×#6711yescharacteristic
498C2×D3—42no—
499C2×D3—41no—
500C2×D3—41no—
501C2×D3—42no—
502C2×D3—42no—
503C2×D3—41no—
504C3×C4—22no—
505C3×C4—22no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—21no—
516C3×C4—22no—
517C3×C4—41no—
518C3×C4—41no—
519C3×C4—121no—
520C3×C4—122no—
521C3×C4—121no—
522C3×C4—121no—
523C3×C4#95012yes—
524C3×C4#95012yes—
525C3×C4#100911yescharacteristic
526C3×C4#100911yescharacteristic
527C3×C4#101011yescharacteristic
528C3×C4#101011yescharacteristic
529Dic3—42no—
530Dic3—41no—
531Dic3—41no—
532Dic3—41no—
533C32#324711yescharacteristic, complemented, Sylow
534C23—61no—
535C23—62no—
536C23C2×#62511yescharacteristic
537Q8—61no—
538Q8—61no—
539Q8—122no—
540D4—61no—
541D4—62no—
542D4—61no—
543D4—62no—
544D4—122no—
545D4—124no—
546D4—122no—
547D4—122no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—61no—
553C2×C4—61no—
554C2×C4—61no—
555C2×C4—62no—
556C2×C4—124no—
557C2×C4—122no—
558C2×C4C2×#62511yescharacteristic
559C2×C4C2×#62511yescharacteristic
560C2×C4C2×#62511yescharacteristic
561C2×C4C2×#62511yescharacteristic
562C2×C4C2×#62511yescharacteristic
563C2×C4C22×D3211yescharacteristic
564C8—182no—
565C8—182no—
566C2×C3—24no—
567C2×C3—22no—
568C2×C3—22no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—241no—
573C2×C3—242no—
574C2×C3C2×#93211yescharacteristic
575C2×C3C2×#94911yescharacteristic
576C2×C3C2×#95011yescharacteristic
577C2×C3C2×#95011yescharacteristic
578C2×C3#583311yescharacteristic
579C2×C3#583311yescharacteristic
580D3—82no—
581D3—81no—
582C22—21no—
583C22—21no—
584C22—121no—
585C22—122no—
586C22—122no—
587C22—121no—
588C22—121no—
589C22—122no—
590C22#6382312yes—
591C22C22×#62511yescharacteristic
592C4—21no—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—121no—
597C4—122no—
598C4—121no—
599C4—121no—
600C4#6382212yes—
601C4#6429811yescharacteristic
602C4#6430811yescharacteristic
603C3—21no—
604C3#8314811yescharacteristic, complemented
605C3#8331111yescharacteristic, complemented
606C2—22no—
607C2—241no—
608C2—242no—
609C2C2×#6382211yescharacteristic
610C2C2×#6382311yescharacteristic
611C2#1059504411yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
hypercenterC2×C42D32
hypocenterC32#3247
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C3×#5479C2semidirect
2. C3×#5477C2semidirect
3. C2×C4⋊(C3⋊(C3⋊C8))C2semidirect
4. #10591179C2semidirect
5. #10591166C2semidirect
6. #10590364C2semidirect
7. #10590348C2semidirect
8. #10590347C2semidirect
9. #10590310C2semidirect
10. #10590270C2semidirect
11. #10590266C2semidirect
47. #5479D3semidirect
48. #5477D3semidirect
533. C32#3247semidirect
604. C3#83148semidirect
605. C3#83311semidirect

Maximal subgroups

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

subgroupindex
C3×#54792
C3×#54772
C2×C4⋊(C3⋊(C3⋊C8))2
#105911792
#105911662
#105903642
#105903482
#105903472
#105903102
#105902702
#105902662
#833113
#831483