Finite Group Databasebeta

← #11882340

Subgroups — #11882340

Order 1152.

913 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595950C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic, complemented
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#10591175C212yesmaximal, complemented
5#10591164C212yesmaximal, complemented
6#10590377C211yesmaximal, characteristic, complemented
7#10590366C212yesmaximal, complemented
8#10590355C211yesmaximal, characteristic, complemented
9#10590300C211yesmaximal, characteristic, complemented
10#10590284C211yesmaximal, characteristic, complemented
11#10590271C212yesmaximal, complemented
12#83311—31nomaximal
13#79028—31nomaximal
14C2×C3×#235—21no—
15C2×C32×C42C2211yescharacteristic
16#64139C2211yescharacteristic
17#64138—21no—
18C4×#638—21no—
19#64133C2211yescharacteristic
20#64085—21no—
21#64084C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23#64081—21no—
24#64079C2211yescharacteristic
25C4×#634C2211yescharacteristic
26C3×#930—21no—
27C3×#930C2212yes—
28C22×C3×C3⋊C8C2212yes—
29C3×#875—21no—
30C3×#874C2211yescharacteristic
31C3×C4×D12—21no—
32C3×C4×D12C2212yes—
33C3×#869C2211yescharacteristic
34C2×#3716C2212yes—
35C2×#3714C2212yes—
36C3×C4⋊(C3⋊C8)C2212yes—
37C3×C4⋊(C3⋊C8)C2211yescharacteristic
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39#63575C2212yes—
40#63573C2212yes—
41#63567C2212yes—
42#63564C2212yes—
43#63563C2212yes—
44#63563C2212yes—
45C3×#532—31no—
46#5479—31no—
47#5479—31no—
48#5479—61no—
49#5477D311yescharacteristic, complemented
50C2×C3×C4⋊C8—31no—
51#5115—32no—
52#5114—32no—
53#5091—31no—
54#5084—31no—
55#5075—31no—
56#5072—31no—
57#5041—32no—
58#5038—32no—
59#5016—32no—
60#5009—32no—
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—21no—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×#634C2311yescharacteristic
75C2×C3×#67—22no—
76C3×#235—44no—
77C2×C3×D12—21no—
78C2×C3×D12—21no—
79C2×C3×D12C2312yes—
80C2×C3×C4×D3—22no—
81C2×C3×Dic6—21no—
82C32×C42D411yescharacteristic
83C32×C42D411yescharacteristic
84C32×C42C2311yescharacteristic
85C32×C42C2311yescharacteristic
86#3757—21no—
87#3752—21no—
88#3752—21no—
89#3752—21no—
90#3752—21no—
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92C4⋊(C3⋊Dic3)C2311yescharacteristic
93#3750—21no—
94#3750—21no—
95#3750—21no—
96#3750—21no—
97C4×C3⋊Dic3—21no—
98C3×(C2×D3)⋊C4—22no—
99C3×(C2×D3)⋊C4—22no—
100C3×C4⋊Dic3—21no—
101C3×C4⋊Dic3C2312yes—
102C2×C3×C3⋊C8—42no—
103C2×C3×C3⋊C8C2312yes—
104C2×C3×C3⋊C8C2312yes—
105#3716—42no—
106#3714—42no—
107#3247—91noSylow
108C2×C3×#41—61no—
109C2×#235—21no—
110C22×C3×C8—32no—
111C3×C4⋊Q8—31no—
112C3×#127—31no—
113C3×#124—61no—
114C3×#121—32no—
115C3×#121—61no—
116C3×C4×D4—32no—
117C3×C4×D4—61no—
118C2×C3×C42—21no—
119C2×C3×C42C2×D311yescharacteristic
120C2×C3×C42C2×D311yescharacteristic
121C2×#214—32no—
122C2×#213—32no—
123#930—21no—
124#930—31no—
125#930—31no—
126#930—61no—
127#930C2×D312yes—
128#929—62no—
129#929—61no—
130#929—61no—
131C4×#67—62no—
132C4×#67—61no—
133C4×#67—61no—
134#924—31no—
135#924—31no—
136#924—61no—
137C22×C3⋊C8C2×D312yes—
138C2×D24—32no—
139C2×#204—32no—
140#876—62no—
141#876—61no—
142#876—61no—
143#875—21no—
144#875—31no—
145#875—31no—
146#875—61no—
147#874C2×D311yescharacteristic
148C4×D12—21no—
149C4×D12—31no—
150C4×D12—31no—
151C4×D12—61no—
152C4×D12C2×D312yes—
153#872—62no—
154#872—61no—
155#872—61no—
156#870—31no—
157#870—31no—
158#870—61no—
159#869C2×D311yescharacteristic
160C4×Dic6—31no—
161C4×Dic6—31no—
162C4×Dic6—61no—
163C3×C4⋊C8—31no—
164C3×C4⋊C8—31no—
165C3×C4⋊C8—32no—
166#832—32no—
167#832—32no—
168#821—32no—
169#821—32no—
170#821—32no—
171#818—32no—
172#817—32no—
173#816—32no—
174#810—32no—
175#809—32no—
176#808—32no—
177#807—32no—
178C4⋊(C3⋊C8)C2×D312yes—
179C4⋊(C3⋊C8)C2×D311yescharacteristic
180C4⋊(C3⋊C8)C2×D311yescharacteristic
181C23×C32C2×D411yescharacteristic
182C22×C3⋊D3—21no—
183C22×C3×D3—22no—
184C2×C32×C4—22no—
185C2×C32×C4—22no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2411yescharacteristic
194#638—42no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C4⋊(C3⋊D3)—21no—
199C4⋊(C3⋊D3)—21no—
200C4×C3⋊D3—42no—
201#634—21no—
202#634—21no—
203C3×#67—44no—
204C2×C3×Dic3—22no—
205C3×D12—22no—
206C3×D12—22no—
207C3×D12—42no—
208C3×D12—42no—
209C3×C4×D3—44no—
210C3×Dic6—42no—
211C3×C3⋊C8—22no—
212C3×C3⋊C8—22no—
213#532—31no—
214#529—91no—
215#478—92no—
216#477—91no—
217#476—91no—
218#466—92no—
219#465—92no—
220#463—92no—
221#460—91no—
222#459—91no—
223C2×C4⋊C8—31no—
224C3×#41—124no—
225C2×C3×Q8—61no—
226C2×C3×D4—32no—
227C2×C3×D4—62no—
228C2×C3×D4—61no—
229C2×C3×D4—61no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—62no—
234C22×C3×C4D1211yescharacteristic
235C22×C3×C4D1211yescharacteristic
236C22×C3×C4#6711yescharacteristic
237C22×C3×C4#6711yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C2×#67—22no—
241C2×#67—62no—
242C2×#67—61no—
243C2×#67—61no—
244#235—44no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—31no—
248C2×D12—31no—
249C2×D12—61no—
250C2×D12C22×D312yes—
251C2×C4×D3—22no—
252C2×C4×D3—62no—
253C2×C4×D3—61no—
254C2×C4×D3—61no—
255C2×Dic6—21no—
256C2×Dic6—31no—
257C2×Dic6—31no—
258C2×Dic6—61no—
259C2×C3×C8—32no—
260C2×C3×C8—32no—
261C2×C3×C8—122no—
262C3×C4⋊C4—32no—
263C3×C4⋊C4—61no—
264C3×C22⋊C4—62no—
265C3×C22⋊C4—62no—
266C3×C42—21no—
267C3×C42—21no—
268C3×C42—21no—
269C3×C42—21no—
270C3×C42D1211yescharacteristic
271C3×C42D1211yescharacteristic
272C3×C42#6711yescharacteristic
273C3×C42#6711yescharacteristic
274C3×C42C22×D311yescharacteristic
275C3×C42C22×D311yescharacteristic
276C3×C42C22×D311yescharacteristic
277C3×C42C22×D311yescharacteristic
278#217—62no—
279#217—61no—
280#217—61no—
281#214—122no—
282#213—122no—
283(C2×D3)⋊C4—22no—
284(C2×D3)⋊C4—22no—
285(C2×D3)⋊C4—62no—
286(C2×D3)⋊C4—62no—
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—61no—
295(C2×D3)⋊C4—61no—
296(C2×D3)⋊C4—61no—
297C4⋊Dic3—21no—
298C4⋊Dic3—31no—
299C4⋊Dic3—31no—
300C4⋊Dic3—31no—
301C4⋊Dic3—31no—
302C4⋊Dic3—61no—
303C4⋊Dic3—61no—
304C4⋊Dic3C22×D312yes—
305Dic3⋊C4—62no—
306Dic3⋊C4—62no—
307Dic3⋊C4—62no—
308Dic3⋊C4—62no—
309Dic3⋊C4—61no—
310Dic3⋊C4—61no—
311Dic3⋊C4—61no—
312Dic3⋊C4—61no—
313Dic3⋊C4—61no—
314Dic3⋊C4—61no—
315Dic3⋊C4—61no—
316Dic3⋊C4—61no—
317C4×Dic3—62no—
318C4×Dic3—61no—
319C4×Dic3—61no—
320C2×C3⋊C8—42no—
321C2×C3⋊C8C22×D312yes—
322C2×C3⋊C8C22×D312yes—
323D24—122no—
324#204—122no—
325C22×C32—21no—
326C22×C32—21no—
327C22×C32AGL(1,ℤ/8)12yes—
328C22×C32C22×D411yescharacteristic
329C2×C3⋊D3—41no—
330C2×C3⋊D3—41no—
331C2×C3⋊D3—41no—
332C2×C3×D3—42no—
333C2×C3×D3—42no—
334C2×C3×D3—42no—
335C32×C4—21no—
336C32×C4—21no—
337C32×C4—21no—
338C32×C4—21no—
339C32×C4#13512yes—
340C32×C4H(5,𝔽2)11yescharacteristic
341C32×C42−1+411yescharacteristic
342C3⋊Dic3—41no—
343C3⋊Dic3—41no—
344C3⋊Dic3—41no—
345C3×Dic3—42no—
346C2×#41—61no—
347C2×SD16—92no—
348C2×D8—92no—
349C22×C8—32no—
350C4⋊Q8—31no—
351#127—31no—
352#126—181no—
353#125—91no—
354#124—61no—
355#124—91no—
356#123—181no—
357C22⋊Q8—91no—
358#121—32no—
359#121—61no—
360#121—91no—
361C4×Q8—91no—
362C4×D4—32no—
363C4×D4—61no—
364C4×D4—91no—
365C4×D4—181no—
366#117—181no—
367C2×C42D3211yescharacteristic
368#107—92no—
369#106—92no—
370C4⋊C8—31no—
371C4⋊C8—31no—
372C4⋊C8—32no—
373#103—92no—
374#102—92no—
375#102—92no—
376#102—92no—
377C23×C3—21no—
378C23×C3—62no—
379C23×C3C2×D1211yescharacteristic
380C23×C3C2×#6711yescharacteristic
381C22×D3—22no—
382C22×D3—62no—
383C22×D3—61no—
384C22×D3—61no—
385C3×Q8—122no—
386C3×D4—62no—
387C3×D4—62no—
388C3×D4—122no—
389C3×D4—124no—
390C3×D4—122no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—62no—
410C2×C3×C4—124no—
411C2×C3×C4C2×D1211yescharacteristic
412C2×C3×C4C2×D1211yescharacteristic
413C2×C3×C4C2×D1211yescharacteristic
414C2×C3×C4C2×D1211yescharacteristic
415C2×C3×C4C2×D1211yescharacteristic
416C2×C3×C4C2×#6711yescharacteristic
417C2×C3×C4C2×#6711yescharacteristic
418C2×C3×C4C2×#6711yescharacteristic
419C2×C3×C4C2×#6711yescharacteristic
420C2×C3×C4C2×#6711yescharacteristic
421C2×C3×C4C23×D311yescharacteristic
422C2×C3×C4C23×D311yescharacteristic
423#67—44no—
424#67—124no—
425#67—122no—
426#67—122no—
427C2×Dic3—22no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—61no—
432C2×Dic3—61no—
433C2×Dic3—61no—
434C2×Dic3—61no—
435C2×Dic3—61no—
436C2×Dic3—61no—
437D12—22no—
438D12—22no—
439D12—42no—
440D12—42no—
441D12—61no—
442D12—61no—
443D12—61no—
444D12—61no—
445D12—121no—
446D12—121no—
447C4×D3—44no—
448C4×D3—124no—
449C4×D3—122no—
450C4×D3—122no—
451Dic6—42no—
452Dic6—61no—
453Dic6—61no—
454Dic6—61no—
455Dic6—61no—
456Dic6—121no—
457Dic6—121no—
458C3×C8—62no—
459C3×C8—62no—
460C3⋊C8—22no—
461C3⋊C8—22no—
462C2×C32—22no—
463C2×C32#53711yescharacteristic
464C2×C32C2×#13511yescharacteristic
465C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
466C3⋊D3—81no—
467C3×D3—82no—
468#41—124no—
469C2×Q8—61no—
470C2×Q8—91no—
471C2×D4—32no—
472C2×D4—62no—
473C2×D4—61no—
474C2×D4—61no—
475C2×D4—91no—
476C2×D4—181no—
477C22×C4—62no—
478C22×C4—181no—
479C22×C4#62611yescharacteristic
480C22×C4#62611yescharacteristic
481C22×C4C2×D3211yescharacteristic
482SD16—362no—
483D8—362no—
484C2×C8—32no—
485C2×C8—32no—
486C2×C8—122no—
487C4⋊C4—32no—
488C4⋊C4—61no—
489C4⋊C4—91no—
490C4⋊C4—91no—
491C4⋊C4—181no—
492C4⋊C4—181no—
493C4⋊C4—181no—
494C4⋊C4—181no—
495C22⋊C4—62no—
496C22⋊C4—62no—
497C22⋊C4—181no—
498C22⋊C4—181no—
499C22⋊C4—181no—
500C22⋊C4—181no—
501C22⋊C4—181no—
502C42—181no—
503C42#62611yescharacteristic
504C42#62611yescharacteristic
505C42C2×D3211yescharacteristic
506C42C2×D3211yescharacteristic
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—22no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—122no—
516C22×C3—122no—
517C22×C3—122no—
518C22×C3#90812yes—
519C22×C3#93212yes—
520C22×C3C22×D1211yescharacteristic
521C22×C3C22×#6711yescharacteristic
522C2×D3—42no—
523C2×D3—42no—
524C2×D3—42no—
525C2×D3—122no—
526C2×D3—122no—
527C2×D3—122no—
528C2×D3—121no—
529C2×D3—121no—
530C2×D3—121no—
531C2×D3—121no—
532C2×D3—121no—
533C2×D3—121no—
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—22no—
545C3×C4—41no—
546C3×C4—41no—
547C3×C4—41no—
548C3×C4—41no—
549C3×C4—122no—
550C3×C4#90412yes—
551C3×C4#95012yes—
552C3×C4#100411yescharacteristic
553C3×C4#100711yescharacteristic
554C3×C4#100911yescharacteristic
555C3×C4#101011yescharacteristic
556Dic3—42no—
557Dic3—122no—
558Dic3—122no—
559Dic3—122no—
560Dic3—121no—
561Dic3—121no—
562Dic3—121no—
563Dic3—121no—
564Dic3—121no—
565Dic3—121no—
566C32#324711yescharacteristic, complemented, Sylow
567C23—62no—
568C23—181no—
569C23C2×#62611yescharacteristic
570Q8—122no—
571Q8—181no—
572Q8—181no—
573D4—62no—
574D4—62no—
575D4—122no—
576D4—124no—
577D4—122no—
578D4—181no—
579D4—181no—
580D4—362no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—62no—
586C2×C4—124no—
587C2×C4—181no—
588C2×C4—181no—
589C2×C4—181no—
590C2×C4—362no—
591C2×C4C2×#62611yescharacteristic
592C2×C4C2×#62611yescharacteristic
593C2×C4C2×#62611yescharacteristic
594C2×C4C2×#62611yescharacteristic
595C2×C4C2×#62611yescharacteristic
596C2×C4C22×D3211yescharacteristic
597C8—62no—
598C8—62no—
599C2×C3—22no—
600C2×C3—22no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—42no—
605C2×C3—242no—
606C2×C3#551011yescharacteristic
607C2×C3C2×#90411yescharacteristic
608C2×C3C2×#90811yescharacteristic
609C2×C3C2×#93211yescharacteristic
610C2×C3C2×#95011yescharacteristic
611C2×C3#583311yescharacteristic
612D3—82no—
613D3—242no—
614D3—241no—
615D3—241no—
616C22—21no—
617C22—21no—
618C22—122no—
619C22—122no—
620C22—122no—
621C22—361no—
622C22—361no—
623C22—361no—
624C22#6383012yes—
625C22C22×#62611yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—122no—
631C4—361no—
632C4—361no—
633C4—361no—
634C4#6382912yes—
635C4#6429711yescharacteristic
636C4#6430711yescharacteristic
637C3—21no—
638C3#7902811yescharacteristic, complemented
639C3#8331111yescharacteristic, complemented
640C2—22no—
641C2—242no—
642C2—721no—
643C2C2×#6382911yescharacteristic
644C2C2×#6383011yescharacteristic
645C2#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. #10595950C2semidirect
2. C3×#5477C2semidirect
3. C2×C3×C4⋊(C3⋊C8)C2semidirect
4. #10591175C2semidirect
5. #10591164C2semidirect
6. #10590377C2semidirect
7. #10590366C2semidirect
8. #10590355C2semidirect
9. #10590300C2semidirect
10. #10590284C2semidirect
11. #10590271C2semidirect
49. #5477D3semidirect
61. C2×C4⋊(C3⋊C8)D3semidirect
566. C32#3247semidirect
638. C3#79028semidirect
639. C3#83311semidirect

Maximal subgroups

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

subgroupindex
#105959502
C3×#54772
C2×C3×C4⋊(C3⋊C8)2
#105911752
#105911642
#105903772
#105903662
#105903552
#105903002
#105902842
#105902712
#833113
#790283