Finite Group Databasebeta

← #11882337

Subgroups — #11882337

Order 1152.

866 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5716C211yesmaximal, characteristic, complemented
2#10593870C211yesmaximal, characteristic, complemented
3#10592771C211yesmaximal, characteristic, complemented
4C3×#5075C211yesmaximal, characteristic, complemented
5#10591499C212yesmaximal, complemented
6#10591471C212yesmaximal, complemented
7#10591449C212yesmaximal, complemented
8#10591409C212yesmaximal, complemented
9D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#10590310C211yesmaximal, characteristic, complemented
11#10590300C211yesmaximal, characteristic, complemented
12#83311—31nomaximal
13#80401—31nomaximal
14C2×C3×#237—21no—
15C32×#127C2211yescharacteristic
16C2×#3753C2212yes—
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×#938—21no—
19C3×#938C2212yes—
20C3×#936—21no—
21C3×D4×Dic3—21no—
22C3×D4×Dic3C2212yes—
23C2×C3×#214C2212yes—
24C3×C42×D3C2211yescharacteristic
25C3×#869C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27#63909C2211yescharacteristic
28C4×#626—21no—
29#63874—21no—
30#63869C2211yescharacteristic
31#63868—21no—
32#63864C2211yescharacteristic
33#63856C2211yescharacteristic
34#63850—21no—
35C2×D3×C3⋊C8C2212yes—
36#63659C2212yes—
37C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
38C3×#832C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63576C2212yes—
41#63573C2212yes—
42Dic3⋊(C3⋊C8)C2212yes—
43#63565C2212yes—
44#63564C2212yes—
45C3×#532—31no—
46#5716D311yescharacteristic, complemented
47#5580—31no—
48#5479—31no—
49C3×#460—31no—
50#5171—32no—
51#5165—32no—
52#5091—31no—
53#5084—31no—
54#5075D311yescharacteristic, complemented
55#5072—31no—
56#5072—31no—
57#5072—61no—
58#5041—32no—
59#5038—32no—
60#5021—31no—
61#5016—32no—
62#5009—32no—
63C2×C4⋊(C3⋊C8)—31no—
64#4842—31no—
65D3×C4⋊C8—31no—
66#4775—32no—
67#4763—32no—
68C2×C32×D4—21no—
69C2×C32×D4—21no—
70C2×C32×D4C2312yes—
71C2×C4⋊(C3⋊D3)C2311yescharacteristic
72C2×C4×C3⋊D3—21no—
73C2×C3×#67—22no—
74C22×C3×Dic3—22no—
75C3×#237—44no—
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79C2×C3×Dic6—21no—
80C2×C3×Dic6C2311yescharacteristic
81C2×#626—21no—
82C32×C42C2311yescharacteristic
83#3753—42no—
84#3752—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#217—22no—
88C3×#217—22no—
89C3×#214—42no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—21no—
94C3×C4×Dic3—21no—
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99#3724—21no—
100#3724—21no—
101Dic3⋊Dic3—21no—
102#3722—21no—
103#3722—21no—
104#3722—21no—
105(C2×D3)⋊Dic3—21no—
106D3×C3⋊C8—42no—
107#3247—91noSylow
108C2×C3×#41—61no—
109C2×#237—21no—
110C2×C3×SD16—32no—
111C3×C4⋊Q8—31no—
112C3×#127—21no—
113C3×#127C2×D311yescharacteristic
114C3×#127C2×D311yescharacteristic
115C3×#124—61no—
116C3×#121—32no—
117C3×#121—61no—
118C3×C4×Q8—31no—
119C3×C4×D4—32no—
120C3×C4×D4—61no—
121C2×C3×C42—31no—
122#947—31no—
123#946—31no—
124#938—21no—
125#938C2×D312yes—
126#936—21no—
127D4×Dic3—21no—
128D4×Dic3C2×D312yes—
129C2×#214C2×D312yes—
130C2×#213—32no—
131C2×#213—32no—
132C2×#213—62no—
133#930—31no—
134#929—61no—
135C4×#67—61no—
136#924—31no—
137C22×C3⋊C8—32no—
138C2×D3×C8—32no—
139#898—61no—
140#895—31no—
141#894—61no—
142#890—31no—
143#876—61no—
144#875—31no—
145C4×D12—31no—
146C4×D12—31no—
147C4×D12—61no—
148C4×D12—61no—
149#872—61no—
150#872—61no—
151C42×D3C2×D311yescharacteristic
152#870—31no—
153#869C2×D311yescharacteristic
154C4×Dic6C2×D311yescharacteristic
155C3×C4⋊C8—31no—
156C3×#102—32no—
157#835—32no—
158#832—32no—
159#832—32no—
160#832—62no—
161#832C2×D312yes—
162#821—32no—
163#817—32no—
164Dic3⋊C8—32no—
165#810—32no—
166#809—32no—
167#808—32no—
168#807—32no—
169#807—32no—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—32no—
173C4⋊(C3⋊C8)—61no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C23×C32—22no—
176C22×C3⋊D3—21no—
177C22×C3×D3C2×D411yescharacteristic
178C32×D4—22no—
179C32×D4—22no—
180C32×D4—42no—
181C32×D4—42no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3—21no—
186C4⋊(C3⋊D3)—21no—
187C4⋊(C3⋊D3)—21no—
188C4×C3⋊D3—42no—
189C3×#67—44no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—44no—
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C3×C4×D3—22no—
198C3×C4×D3—22no—
199C3×C4×D3—21no—
200C3×C4×D3—21no—
201C3×Dic6—21no—
202C3×Dic6—21no—
203C3×Dic6—42no—
204#626—42no—
205C3⋊(C3⋊C8)—22no—
206C3×C3⋊C8—22no—
207#532—31no—
208#529—91no—
209#478—92no—
210#477—91no—
211#476—91no—
212#466—92no—
213#465—92no—
214#463—92no—
215#460—31no—
216#459—91no—
217C2×C4⋊C8—91no—
218C3×#41—124no—
219C2×C3×Q8—31no—
220C2×C3×Q8—61no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—22no—
226C2×C3×D4—41no—
227C2×C3×D4—41no—
228C2×C3×D4—62no—
229C2×C3×D4C22×D312yes—
230C2×C3×D4C22×D312yes—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—62no—
235C2×#67—22no—
236C2×#67—61no—
237C22×Dic3—22no—
238#237—44no—
239C2×D12—31no—
240C2×D12—31no—
241C2×D12—61no—
242C2×D12—61no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C2×C4×D3—121no—
246C2×C4×D3#6711yescharacteristic
247C2×C4×D3#6711yescharacteristic
248C2×C4×D3C22×D311yescharacteristic
249C2×Dic6—21no—
250C2×Dic6C22×D311yescharacteristic
251C3×SD16—122no—
252C2×C3×C8—32no—
253C3×C4⋊C4—31no—
254C3×C4⋊C4—32no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4—61no—
257C3×C22⋊C4—62no—
258C3×C22⋊C4—62no—
259C3×C42—21no—
260C3×C42—31no—
261C3×C42—31no—
262C3×C42—31no—
263C3×C42—61no—
264C3×C42C22×D311yescharacteristic
265C3×C42C22×D311yescharacteristic
266#217—22no—
267#217—22no—
268#217—61no—
269#214—42no—
270#213—122no—
271#213—122no—
272#213—124no—
273(C2×D3)⋊C4—61no—
274(C2×D3)⋊C4—61no—
275(C2×D3)⋊C4—61no—
276(C2×D3)⋊C4—61no—
277(C2×D3)⋊C4—61no—
278(C2×D3)⋊C4—61no—
279(C2×D3)⋊C4—61no—
280(C2×D3)⋊C4—61no—
281(C2×D3)⋊C4—61no—
282(C2×D3)⋊C4—121no—
283C4⋊Dic3—21no—
284C4⋊Dic3—31no—
285C4⋊Dic3—31no—
286C4⋊Dic3—61no—
287C4⋊Dic3—61no—
288C4⋊Dic3C22×D311yescharacteristic
289C4⋊Dic3C22×D312yes—
290Dic3⋊C4—21no—
291Dic3⋊C4—61no—
292Dic3⋊C4—61no—
293Dic3⋊C4—61no—
294Dic3⋊C4—61no—
295Dic3⋊C4—61no—
296C4×Dic3—21no—
297C4×Dic3#6711yescharacteristic
298C4×Dic3#6711yescharacteristic
299C4×Dic3C22×D311yescharacteristic
300C2×C3⋊C8—32no—
301C2×C3⋊C8—32no—
302C2×C3⋊C8—62no—
303C2×C3⋊C8—122no—
304C2×C3⋊C8C22×D312yes—
305D3×C8—122no—
306C22×C32—42no—
307C22×C32—42no—
308C22×C32—42no—
309C22×C32C22×D411yescharacteristic
310C2×C3⋊D3—41no—
311C2×C3⋊D3—41no—
312C2×C3⋊D3—41no—
313C2×C3×D3—21no—
314C2×C3×D3—21no—
315C2×C3×D3AGL(1,ℤ/8)12yes—
316C32×C4—21no—
317C32×C4#13512yes—
318C32×C4H(5,𝔽2)11yescharacteristic
319C32×C42−1+411yescharacteristic
320C3⋊Dic3—41no—
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—41no—
325C3×Dic3—41no—
326C3×Dic3—42no—
327C2×#41—61no—
328C2×SD16—32no—
329C2×D8—92no—
330C22×C8—92no—
331C4⋊Q8—31no—
332#127D3211yescharacteristic
333#126—181no—
334#125—91no—
335#124—61no—
336#124—91no—
337#123—181no—
338C22⋊Q8—91no—
339#121—32no—
340#121—61no—
341#121—91no—
342C4×Q8—31no—
343C4×D4—32no—
344C4×D4—61no—
345C4×D4—91no—
346C4×D4—181no—
347#117—181no—
348C2×C42—31no—
349#107—92no—
350#106—92no—
351C4⋊C8—31no—
352C4⋊C8—92no—
353C4⋊C8—91no—
354#103—92no—
355#102—32no—
356#102—92no—
357#102—92no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—31no—
361C23×C3—42no—
362C22×D3—61no—
363C22×D3—61no—
364C22×D3—121no—
365C22×D3C2×#6711yescharacteristic
366C3×Q8—61no—
367C3×Q8—61no—
368C3×Q8—122no—
369C3×D4—22no—
370C3×D4—22no—
371C3×D4—22no—
372C3×D4—22no—
373C3×D4—42no—
374C3×D4—42no—
375C3×D4—42no—
376C3×D4—42no—
377C3×D4—42no—
378C3×D4—42no—
379C3×D4—82no—
380C3×D4—82no—
381C3×D4—124no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—31no—
386C2×C3×C4—31no—
387C2×C3×C4—31no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—61no—
391C2×C3×C4—61no—
392C2×C3×C4—62no—
393C2×C3×C4—61no—
394C2×C3×C4—61no—
395C2×C3×C4—124no—
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4C2×#6711yescharacteristic
399C2×C3×C4C2×#6711yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402#67—44no—
403#67—122no—
404C2×Dic3—21no—
405C2×Dic3—21no—
406C2×Dic3—22no—
407C2×Dic3—44no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—121no—
411C2×Dic3C2×#6711yescharacteristic
412C2×Dic3C2×#6711yescharacteristic
413C2×Dic3C2×#6711yescharacteristic
414D12—62no—
415D12—61no—
416D12—61no—
417D12—61no—
418D12—61no—
419D12—121no—
420D12—122no—
421C4×D3—22no—
422C4×D3—22no—
423C4×D3—21no—
424C4×D3—21no—
425C4×D3—122no—
426C4×D3—122no—
427C4×D3—242no—
428Dic6—21no—
429Dic6—21no—
430Dic6—42no—
431C3×C8—62no—
432C3⋊C8—22no—
433C3⋊C8—62no—
434C3⋊C8—62no—
435C3⋊C8—122no—
436C2×C32—82no—
437C2×C32#53711yescharacteristic
438C2×C32C2×#13511yescharacteristic
439C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
440C3⋊D3—81no—
441C3×D3—22no—
442#41—124no—
443C2×Q8—31no—
444C2×Q8—61no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—62no—
448C2×D4—91no—
449C2×D4—181no—
450C2×D4C2×D3212yes—
451C22×C4—31no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—62no—
455C22×C4—181no—
456SD16—122no—
457D8—362no—
458C2×C8—32no—
459C2×C8—92no—
460C2×C8—362no—
461C4⋊C4—31no—
462C4⋊C4—32no—
463C4⋊C4—61no—
464C4⋊C4—61no—
465C4⋊C4—91no—
466C4⋊C4—181no—
467C4⋊C4—181no—
468C4⋊C4—181no—
469C22⋊C4—62no—
470C22⋊C4—62no—
471C22⋊C4—181no—
472C22⋊C4—181no—
473C22⋊C4—181no—
474C22⋊C4—181no—
475C22⋊C4—181no—
476C42—31no—
477C42—31no—
478C42—31no—
479C42—61no—
480C42C2×D3211yescharacteristic
481C22×C3—21no—
482C22×C3—32no—
483C22×C3—42no—
484C22×C3—42no—
485C22×C3—42no—
486C22×C3—42no—
487C22×C3—42no—
488C22×C3—42no—
489C22×C3—61no—
490C22×C3—61no—
491C22×C3—82no—
492C22×C3—82no—
493C22×C3—82no—
494C22×C3C2×D3×D411yescharacteristic
495C22×C3C22×#6711yescharacteristic
496C2×D3—21no—
497C2×D3—21no—
498C2×D3—122no—
499C2×D3—121no—
500C2×D3—121no—
501C2×D3—121no—
502C2×D3—121no—
503C2×D3—121no—
504C2×D3—121no—
505C2×D3—241no—
506C2×D3—241no—
507C2×D3#93212yes—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—22no—
513C3×C4—41no—
514C3×C4—61no—
515C3×C4—61no—
516C3×C4—61no—
517C3×C4—122no—
518C3×C4—121no—
519C3×C4—121no—
520C3×C4#91612yes—
521C3×C4#95012yes—
522C3×C4#100411yescharacteristic
523C3×C4#100911yescharacteristic
524C3×C4#101011yescharacteristic
525C3×C4#101011yescharacteristic
526Dic3—21no—
527Dic3—21no—
528Dic3—21no—
529Dic3—41no—
530Dic3—42no—
531Dic3—41no—
532Dic3—121no—
533Dic3—121no—
534Dic3—241no—
535C32#324711yescharacteristic, complemented, Sylow
536C23—22no—
537C23—31no—
538C23—181no—
539Q8—61no—
540Q8—61no—
541Q8—122no—
542D4—22no—
543D4—22no—
544D4—42no—
545D4—42no—
546D4—124no—
547D4—181no—
548D4—181no—
549D4—362no—
550C2×C4—31no—
551C2×C4—31no—
552C2×C4—31no—
553C2×C4—62no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—62no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—62no—
560C2×C4—124no—
561C2×C4—181no—
562C2×C4—362no—
563C2×C4D3×#6711yescharacteristic
564C2×C4D3×#6711yescharacteristic
565C2×C4C22×D3211yescharacteristic
566C8—62no—
567C8—182no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—62no—
572C2×C3—82no—
573C2×C3—82no—
574C2×C3—162no—
575C2×C3#560811yescharacteristic
576C2×C3C2×#91611yescharacteristic
577C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
578C2×C3C2×#93211yescharacteristic
579C2×C3C2×#95011yescharacteristic
580C2×C3#583311yescharacteristic
581D3—22no—
582D3—242no—
583D3—241no—
584D3—241no—
585C22—32no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—61no—
590C22—61no—
591C22—361no—
592C22—361no—
593C22—361no—
594C22C2×D3×#6711yescharacteristic
595C4—21no—
596C4—61no—
597C4—61no—
598C4—61no—
599C4—122no—
600C4—121no—
601C4—121no—
602C4—361no—
603C4#6393512yes—
604C4#6430911yescharacteristic
605C4#6431411yescharacteristic
606C3—21no—
607C3#8040111yescharacteristic, complemented
608C3#8331111yescharacteristic, complemented
609C2—62no—
610C2—82no—
611C2—721no—
612C2D3×#93211yescharacteristic
613C2C2×#6393511yescharacteristic
614C2#1059523211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3247
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5716C2semidirect
2. #10593870C2semidirect
3. #10592771C2semidirect
4. C3×#5075C2semidirect
5. #10591499C2semidirect
6. #10591471C2semidirect
7. #10591449C2semidirect
8. #10591409C2semidirect
9. D3×C4⋊(C3⋊C8)C2semidirect
10. #10590310C2semidirect
11. #10590300C2semidirect
46. #5716D3semidirect
54. #5075D3semidirect
535. C32#3247semidirect
607. C3#80401semidirect
608. C3#83311semidirect

Maximal subgroups

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

subgroupindex
C3×#57162
#105938702
#105927712
C3×#50752
#105914992
#105914712
#105914492
#105914092
D3×C4⋊(C3⋊C8)2
#105903102
#105903002
#833113
#804013