Finite Group Databasebeta

← #11882339

Subgroups — #11882339

Order 1152.

951 conjugacy classes of subgroups.

The subgroup lattice has 637 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic, complemented
2C3×#5479C211yesmaximal, characteristic, complemented
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#10591177C212yesmaximal, complemented
5#10591164C212yesmaximal, complemented
6#10590367C211yesmaximal, characteristic, complemented
7#10590356C212yesmaximal, complemented
8#10590349C211yesmaximal, characteristic, complemented
9#10590308C212yesmaximal, complemented
10#10590283C211yesmaximal, characteristic, complemented
11#10590268C211yesmaximal, characteristic, complemented
12#83148—31nomaximal
13#79028—31nomaximal
14C2×#3828—21no—
15C2×C32×C42C2211yescharacteristic
16#64139—21no—
17#64139C2212yes—
18#64084—21no—
19#64083C2211yescharacteristic
20C4×C4⋊(C3⋊D3)—21no—
21C4×C4⋊(C3⋊D3)C2212yes—
22#64078C2211yescharacteristic
23C3×#930C2211yescharacteristic
24C3×#929—21no—
25C3×C4×#67—21no—
26C3×#924C2211yescharacteristic
27C22×C3×C3⋊C8C2212yes—
28C3×#876—21no—
29C3×#875C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×#872—21no—
32C3×#870C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34C2×#3717C2212yes—
35C2×#3714C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×C4⋊(C3⋊C8)C2211yescharacteristic
38C3×C4⋊(C3⋊C8)C2212yes—
39#63575C2212yes—
40#63573C2212yes—
41#63566C2212yes—
42#63564C2212yes—
43#63564C2212yes—
44#63563C2212yes—
45C3×#529—31no—
46#5479D311yescharacteristic, complemented
47#5477—31no—
48#5477—31no—
49#5477—61no—
50C2×C3×C4⋊C8—31no—
51#5115—32no—
52#5114—32no—
53#5066—32no—
54#5057—32no—
55#5048—32no—
56#5038—32no—
57#5027—31no—
58#5021—31no—
59#5015—31no—
60#5008—31no—
61C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
62#4850—31no—
63#4848—31no—
64#4847—32no—
65#4844—32no—
66#4843—31no—
67#4842—31no—
68C22×C32×C4D411yescharacteristic
69C22×C32×C4D411yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C2×#638—22no—
72#3828—44no—
73C2×C4⋊(C3⋊D3)—21no—
74C2×C4⋊(C3⋊D3)—21no—
75C2×C4⋊(C3⋊D3)C2312yes—
76C2×C4×C3⋊D3—22no—
77C2×#634—21no—
78C2×C3×#67—21no—
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×Dic6C2311yescharacteristic
82C32×C42D411yescharacteristic
83C32×C42D411yescharacteristic
84C32×C42C2311yescharacteristic
85C32×C42C2311yescharacteristic
86#3752—22no—
87#3752—22no—
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2312yes—
90C3×#217—21no—
91C3×(C2×D3)⋊C4—21no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×(C2×D3)⋊C4—21no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2311yescharacteristic
97C3×Dic3⋊C4—21no—
98C3×Dic3⋊C4—21no—
99C3×Dic3⋊C4—21no—
100C3×Dic3⋊C4—21no—
101C3×C4×Dic3—21no—
102C2×C3×C3⋊C8—42no—
103C2×C3×C3⋊C8C2312yes—
104C2×C3×C3⋊C8C2312yes—
105#3717—42no—
106#3714—42no—
107#3247—91noSylow
108C2×#235—62no—
109C2×#235—61no—
110C2×#235—61no—
111C22×C3×C8—32no—
112C3×#126—61no—
113C3×#125—31no—
114C3×#124—31no—
115C3×#123—61no—
116C3×C22⋊Q8—31no—
117C3×#121—31no—
118C3×C4×Q8—31no—
119C3×C4×D4—31no—
120C3×C4×D4—61no—
121C3×#117—61no—
122C2×C3×C42—21no—
123C2×C3×C42C2×D311yescharacteristic
124C2×C3×C42C2×D311yescharacteristic
125C2×#215—32no—
126C2×#213—32no—
127#930—32no—
128#930—32no—
129#930—62no—
130#930—62no—
131#930—61no—
132#930—61no—
133#930C2×D311yescharacteristic
134#929—21no—
135C4×#67—21no—
136#924C2×D311yescharacteristic
137C22×C3⋊C8C2×D312yes—
138C2×D24—32no—
139C2×#204—32no—
140#876—21no—
141#875—62no—
142#875—61no—
143#875—61no—
144#875C2×D311yescharacteristic
145#874—31no—
146#874—31no—
147#874—61no—
148C4×D12—32no—
149C4×D12—32no—
150C4×D12—62no—
151C4×D12—62no—
152C4×D12—61no—
153C4×D12—61no—
154C4×D12C2×D311yescharacteristic
155#872—21no—
156#870C2×D311yescharacteristic
157#869—31no—
158#869—31no—
159#869—61no—
160C4×Dic6C2×D311yescharacteristic
161C3×C4⋊C8—31no—
162C3×C4⋊C8—31no—
163C3×C4⋊C8—32no—
164#835—32no—
165#832—32no—
166#821—32no—
167#821—32no—
168#821—32no—
169#818—32no—
170#817—32no—
171#816—32no—
172#809—32no—
173#809—32no—
174#808—32no—
175#807—32no—
176C4⋊(C3⋊C8)C2×D311yescharacteristic
177C4⋊(C3⋊C8)C2×D311yescharacteristic
178C4⋊(C3⋊C8)C2×D312yes—
179C23×C32C2×D411yescharacteristic
180C22×C3⋊D3—22no—
181C22×C3×D3—21no—
182C2×C32×C4—22no—
183C2×C32×C4—22no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2411yescharacteristic
192#638—44no—
193C2×C3⋊Dic3—22no—
194C4⋊(C3⋊D3)—22no—
195C4⋊(C3⋊D3)—22no—
196C4⋊(C3⋊D3)—42no—
197C4⋊(C3⋊D3)—42no—
198C4×C3⋊D3—44no—
199#634—42no—
200C3×#67—42no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C3×D12—21no—
205C3×D12—21no—
206C3×C4×D3—42no—
207C3×Dic6—21no—
208C3×Dic6—21no—
209C3×C3⋊C8—22no—
210C3×C3⋊C8—22no—
211#532—91no—
212#529—31no—
213#478—92no—
214#477—91no—
215#476—91no—
216#466—92no—
217#465—92no—
218#463—92no—
219#460—91no—
220#459—91no—
221C2×C4⋊C8—31no—
222C2×C3×Q8—31no—
223C2×C3×D4—31no—
224C2×C3×D4—61no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—61no—
229C22×C3×C4D1211yescharacteristic
230C22×C3×C4D1211yescharacteristic
231C22×C3×C4#6711yescharacteristic
232C22×C3×C4#6711yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—21no—
236C2×#67—64no—
237C2×#67—62no—
238C2×#67—62no—
239#235—128no—
240#235—124no—
241#235—124no—
242C2×D12—32no—
243C2×D12—32no—
244C2×D12—62no—
245C2×D12—62no—
246C2×D12—62no—
247C2×D12—61no—
248C2×D12—61no—
249C2×D12—61no—
250C2×D12—61no—
251C2×D12C22×D311yescharacteristic
252C2×C4×D3—21no—
253C2×C4×D3—64no—
254C2×C4×D3—62no—
255C2×C4×D3—62no—
256C2×Dic6—62no—
257C2×Dic6—61no—
258C2×Dic6—61no—
259C2×Dic6C22×D311yescharacteristic
260C2×C3×C8—32no—
261C2×C3×C8—32no—
262C2×C3×C8—122no—
263C3×C4⋊C4—31no—
264C3×C4⋊C4—31no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4—61no—
267C3×C4⋊C4—61no—
268C3×C4⋊C4—61no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—61no—
271C3×C22⋊C4—61no—
272C3×C22⋊C4—61no—
273C3×C22⋊C4—61no—
274C3×C42—21no—
275C3×C42—21no—
276C3×C42—21no—
277C3×C42—21no—
278C3×C42—61no—
279C3×C42D1211yescharacteristic
280C3×C42D1211yescharacteristic
281C3×C42#6711yescharacteristic
282C3×C42#6711yescharacteristic
283C3×C42C22×D311yescharacteristic
284C3×C42C22×D311yescharacteristic
285C3×C42C22×D311yescharacteristic
286C3×C42C22×D311yescharacteristic
287#217—21no—
288#215—122no—
289#213—122no—
290(C2×D3)⋊C4—21no—
291(C2×D3)⋊C4—21no—
292(C2×D3)⋊C4—21no—
293(C2×D3)⋊C4—21no—
294(C2×D3)⋊C4—64no—
295(C2×D3)⋊C4—64no—
296(C2×D3)⋊C4—62no—
297(C2×D3)⋊C4—62no—
298(C2×D3)⋊C4—62no—
299(C2×D3)⋊C4—62no—
300C4⋊Dic3—32no—
301C4⋊Dic3—32no—
302C4⋊Dic3—62no—
303C4⋊Dic3—62no—
304C4⋊Dic3—61no—
305C4⋊Dic3—61no—
306C4⋊Dic3C22×D311yescharacteristic
307C4⋊Dic3C22×D311yescharacteristic
308Dic3⋊C4—21no—
309Dic3⋊C4—21no—
310Dic3⋊C4—21no—
311Dic3⋊C4—21no—
312C4×Dic3—21no—
313C2×C3⋊C8—42no—
314C2×C3⋊C8C22×D312yes—
315C2×C3⋊C8C22×D312yes—
316D24—122no—
317#204—122no—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32AGL(1,ℤ/8)12yes—
321C22×C32C22×D411yescharacteristic
322C2×C3⋊D3—42no—
323C2×C3⋊D3—42no—
324C2×C3⋊D3—42no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C32×C4—21no—
329C32×C4—21no—
330C32×C4—21no—
331C32×C4—21no—
332C32×C4#13512yes—
333C32×C4H(5,𝔽2)11yescharacteristic
334C32×C42−1+411yescharacteristic
335C3⋊Dic3—42no—
336C3×Dic3—41no—
337C3×Dic3—41no—
338C3×Dic3—41no—
339C2×#41—181no—
340C2×SD16—92no—
341C2×D8—92no—
342C22×C8—32no—
343C4⋊Q8—91no—
344#127—91no—
345#126—61no—
346#125—31no—
347#124—31no—
348#124—181no—
349#123—61no—
350C22⋊Q8—31no—
351#121—31no—
352#121—92no—
353#121—181no—
354C4×Q8—31no—
355C4×D4—31no—
356C4×D4—61no—
357C4×D4—92no—
358C4×D4—181no—
359#117—61no—
360C2×C42D3211yescharacteristic
361#107—92no—
362#106—92no—
363C4⋊C8—31no—
364C4⋊C8—31no—
365C4⋊C8—32no—
366#103—92no—
367#102—92no—
368#102—92no—
369#102—92no—
370C23×C3—21no—
371C23×C3—61no—
372C23×C3C2×D1211yescharacteristic
373C23×C3C2×#6711yescharacteristic
374C22×D3—21no—
375C22×D3—64no—
376C22×D3—62no—
377C22×D3—62no—
378C3×Q8—61no—
379C3×Q8—61no—
380C3×D4—61no—
381C3×D4—61no—
382C3×D4—122no—
383C2×C3×C4—24no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—42no—
401C2×C3×C4—61no—
402C2×C3×C4—61no—
403C2×C3×C4—61no—
404C2×C3×C4—122no—
405C2×C3×C4C2×D1211yescharacteristic
406C2×C3×C4C2×D1211yescharacteristic
407C2×C3×C4C2×D1211yescharacteristic
408C2×C3×C4C2×D1211yescharacteristic
409C2×C3×C4C2×D1211yescharacteristic
410C2×C3×C4C2×#6711yescharacteristic
411C2×C3×C4C2×#6711yescharacteristic
412C2×C3×C4C2×#6711yescharacteristic
413C2×C3×C4C2×#6711yescharacteristic
414C2×C3×C4C2×#6711yescharacteristic
415C2×C3×C4C23×D311yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417#67—42no—
418#67—128no—
419#67—124no—
420#67—124no—
421C2×Dic3—21no—
422C2×Dic3—21no—
423C2×Dic3—21no—
424C2×Dic3—64no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427D12—21no—
428D12—21no—
429D12—62no—
430D12—62no—
431D12—62no—
432D12—62no—
433D12—122no—
434D12—122no—
435D12—124no—
436D12—124no—
437D12—122no—
438D12—122no—
439D12—122no—
440D12—122no—
441C4×D3—42no—
442C4×D3—128no—
443C4×D3—124no—
444C4×D3—124no—
445Dic6—21no—
446Dic6—21no—
447Dic6—124no—
448Dic6—122no—
449Dic6—122no—
450C3×C8—62no—
451C3×C8—62no—
452C3⋊C8—22no—
453C3⋊C8—22no—
454C2×C32—22no—
455C2×C32#53711yescharacteristic
456C2×C32C2×#13511yescharacteristic
457C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
458C3⋊D3—82no—
459C3×D3—81no—
460#41—364no—
461C2×Q8—31no—
462C2×Q8—181no—
463C2×D4—31no—
464C2×D4—61no—
465C2×D4—92no—
466C2×D4—182no—
467C2×D4—181no—
468C2×D4—181no—
469C22×C4—61no—
470C22×C4—182no—
471C22×C4#62611yescharacteristic
472C22×C4#62611yescharacteristic
473C22×C4C2×D3211yescharacteristic
474SD16—362no—
475D8—362no—
476C2×C8—32no—
477C2×C8—32no—
478C2×C8—122no—
479C4⋊C4—31no—
480C4⋊C4—31no—
481C4⋊C4—61no—
482C4⋊C4—61no—
483C4⋊C4—61no—
484C4⋊C4—61no—
485C4⋊C4—92no—
486C4⋊C4—181no—
487C22⋊C4—61no—
488C22⋊C4—61no—
489C22⋊C4—61no—
490C22⋊C4—61no—
491C22⋊C4—61no—
492C22⋊C4—182no—
493C22⋊C4—182no—
494C42—61no—
495C42#62611yescharacteristic
496C42#62611yescharacteristic
497C42C2×D3211yescharacteristic
498C42C2×D3211yescharacteristic
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—22no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3—121no—
508C22×C3—121no—
509C22×C3—121no—
510C22×C3#90812yes—
511C22×C3#94912yes—
512C22×C3C22×D1211yescharacteristic
513C22×C3C22×#6711yescharacteristic
514C2×D3—41no—
515C2×D3—41no—
516C2×D3—41no—
517C2×D3—124no—
518C2×D3—124no—
519C2×D3—124no—
520C2×D3—122no—
521C2×D3—122no—
522C2×D3—122no—
523C2×D3—122no—
524C2×D3—122no—
525C2×D3—122no—
526C3×C4—22no—
527C3×C4—22no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—22no—
539C3×C4—41no—
540C3×C4—41no—
541C3×C4—121no—
542C3×C4—121no—
543C3×C4—121no—
544C3×C4#90412yes—
545C3×C4#95012yes—
546C3×C4#100411yescharacteristic
547C3×C4#100711yescharacteristic
548C3×C4#100911yescharacteristic
549C3×C4#101011yescharacteristic
550Dic3—41no—
551Dic3—41no—
552Dic3—41no—
553Dic3—124no—
554Dic3—122no—
555Dic3—122no—
556C32#324711yescharacteristic, complemented, Sylow
557C23—61no—
558C23—182no—
559C23C2×#62611yescharacteristic
560Q8—61no—
561Q8—61no—
562Q8—362no—
563D4—61no—
564D4—61no—
565D4—122no—
566D4—182no—
567D4—182no—
568D4—362no—
569D4—364no—
570D4—362no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—61no—
576C2×C4—61no—
577C2×C4—61no—
578C2×C4—122no—
579C2×C4—182no—
580C2×C4—364no—
581C2×C4C2×#62611yescharacteristic
582C2×C4C2×#62611yescharacteristic
583C2×C4C2×#62611yescharacteristic
584C2×C4C2×#62611yescharacteristic
585C2×C4C2×#62611yescharacteristic
586C2×C4C22×D3211yescharacteristic
587C8—62no—
588C8—62no—
589C2×C3—22no—
590C2×C3—22no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—42no—
595C2×C3—241no—
596C2×C3#551011yescharacteristic
597C2×C3C2×#90411yescharacteristic
598C2×C3C2×#90811yescharacteristic
599C2×C3C2×#94911yescharacteristic
600C2×C3C2×#95011yescharacteristic
601C2×C3#583311yescharacteristic
602D3—81no—
603D3—244no—
604D3—242no—
605D3—242no—
606C22—21no—
607C22—21no—
608C22—121no—
609C22—121no—
610C22—121no—
611C22—362no—
612C22—362no—
613C22—362no—
614C22#6382512yes—
615C22C22×#62611yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—121no—
621C4—121no—
622C4—121no—
623C4—362no—
624C4#6382912yes—
625C4#6429711yescharacteristic
626C4#6430711yescharacteristic
627C3—21no—
628C3#7902811yescharacteristic, complemented
629C3#8314811yescharacteristic, complemented
630C2—22no—
631C2—241no—
632C2—722no—
633C2C2×#6382511yescharacteristic
634C2C2×#6382911yescharacteristic
635C2#1059504311yescharacteristic
subgroupG/H
centerC22C22×#626
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. #10595948C2semidirect
2. C3×#5479C2semidirect
3. C2×C3×C4⋊(C3⋊C8)C2semidirect
4. #10591177C2semidirect
5. #10591164C2semidirect
6. #10590367C2semidirect
7. #10590356C2semidirect
8. #10590349C2semidirect
9. #10590308C2semidirect
10. #10590283C2semidirect
11. #10590268C2semidirect
46. #5479D3semidirect
61. C2×C4⋊(C3⋊C8)D3semidirect
556. C32#3247semidirect
628. C3#79028semidirect
629. C3#83148semidirect

Maximal subgroups

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

subgroupindex
#105959482
C3×#54792
C2×C3×C4⋊(C3⋊C8)2
#105911772
#105911642
#105903672
#105903562
#105903492
#105903082
#105902832
#105902682
#831483
#790283