Finite Group Databasebeta

← #11873494

Subgroups — #11873494

Order 1152.

879 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5832C211yesmaximal, characteristic
2#10595049C211yesmaximal, characteristic, complemented
3#10592932C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic, complemented
5#10591623C212yesmaximal, complemented
6#10591614C212yesmaximal, complemented
7#10591487C212yesmaximal, complemented
8#10591478C212yesmaximal, complemented
9#10591084C211yesmaximal, characteristic, complemented
10#10591083C211yesmaximal, characteristic, complemented
11C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
12#83281—31nomaximal
13#78825—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16#64135C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#947C2211yescharacteristic
19C3×#944C2211yescharacteristic
20C3×#940C2211yescharacteristic
21C3×#939—22no—
22C3×#936C2211yescharacteristic
23C3×C4×#67—22no—
24C3×#926C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27#63964—22no—
28#63918C2212yes—
29C4×#627—22no—
30#63869C2212yes—
31#63662C2212yes—
32#63659C2212yes—
33C3×#835C2212yes—
34C3×#832C2212yes—
35#63566C2212yes—
36#63565C2212yes—
37#63563C2212yes—
38#63562C2212yes—
39Dic3×C3⋊C8C2212yes—
40Dic3×C3⋊C8C2212yes—
41C3×#532—31no—
42#5832D311yescharacteristic
43#5517—31no—
44#5470—31no—
45C3×#416—31no—
46#5233—31no—
47#5233—31no—
48#5233—31no—
49#5233—31no—
50#5233—61no—
51#5233D311yescharacteristic, complemented
52#5113—31no—
53C2×C8×Dic3—31no—
54#5079—32no—
55#5070—32no—
56#5056—32no—
57#5056—32no—
58#5002—31no—
59C2×C4×C3⋊C8—31no—
60#4800—32no—
61#4792—32no—
62#4768—32no—
63#4760—32no—
64C32×#41—22no—
65C32×#41—22no—
66C2×C32×Q8C2311yescharacteristic
67C2×C32×D4—21no—
68C2×C32×D4C2311yescharacteristic
69C22×C32×C4—21no—
70C22×C32×C4C2311yescharacteristic
71C2×C3×#67—21no—
72C2×C3×#67—22no—
73C22×C3×Dic3D412yes—
74C3×#235—22no—
75C3×#235—22no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×Dic6C2311yescharacteristic
79C2×#627—22no—
80#3757—21no—
81C4⋊(C3⋊Dic3)C2312yes—
82C4×C3⋊Dic3—21no—
83C2×C3⋊(C3⋊C8)—22no—
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×#217—21no—
86C3×#217—22no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3C2312yes—
89C3×Dic3⋊C4—22no—
90C3×C4×Dic3—21no—
91C3×C4×Dic3D412yes—
92C3×C4×Dic3C2311yescharacteristic
93C3×C4×Dic3C2311yescharacteristic
94C2×C3×C3⋊C8—22no—
95C2×C3×C3⋊C8C2312yes—
96#3724—22no—
97Dic3⋊Dic3—22no—
98Dic3⋊Dic3—22no—
99#3131—91noSylow
100C2×C3×#41—21no—
101C2×C3×#41—31no—
102C2×C3×#41C2×D311yescharacteristic
103C2×C3×#41C2×D311yescharacteristic
104C2×#235C2×D311yescharacteristic
105C22×C3×C8—31no—
106C3×C4⋊Q8—31no—
107C3×#127—31no—
108C3×#124—31no—
109C3×#124—31no—
110C3×#121—62no—
111C3×C4×D4—62no—
112C3×#117—31no—
113C2×C3×C42—31no—
114#947C2×D311yescharacteristic
115#944C2×D311yescharacteristic
116#940C2×D311yescharacteristic
117#939—22no—
118#936C2×D311yescharacteristic
119C4×#67—22no—
120#926—31no—
121#926—31no—
122#926—61no—
123#926C2×D311yescharacteristic
124#924—62no—
125C2×C4×Dic3C2×D311yescharacteristic
126C22×C3⋊C8—31no—
127C22×C3⋊C8—31no—
128C22×C3⋊C8—61no—
129C22×C3⋊C8C2×D311yescharacteristic
130#890—32no—
131#888—32no—
132#878—62no—
133#870—32no—
134#869—32no—
135C4×Dic6—62no—
136C4×Dic6—62no—
137C3×#103—32no—
138C3×#102—32no—
139#835—32no—
140#835—32no—
141#835—32no—
142#835—32no—
143#835—62no—
144#835C2×D312yes—
145#832—32no—
146#832—32no—
147#832—32no—
148#832—32no—
149#832—62no—
150#832C2×D312yes—
151#821—32no—
152#816—32no—
153C8×Dic3—32no—
154C8×Dic3—32no—
155#810—32no—
156#809—32no—
157C4×C3⋊C8—32no—
158C4×C3⋊C8—32no—
159C23×C32—21no—
160C23×C32C2×D411yescharacteristic
161C22×C3×D3—21no—
162C32×Q8—21no—
163C32×Q8—21no—
164C32×D4—21no—
165C32×D4—21no—
166C32×D4—42no—
167C2×C32×C4—21no—
168C2×C32×C4—42no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4#4112yes—
171C2×C32×C4#4112yes—
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—22no—
174C3×#67—42no—
175C3×#67—44no—
176C2×C3×Dic3—24no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×D12—21no—
182C3×D12—21no—
183C3×C4×D3—42no—
184C3×Dic6—21no—
185C3×Dic6—21no—
186#627—44no—
187C3⋊(C3⋊C8)—22no—
188C3×C3⋊C8—22no—
189#533—91no—
190#532—31no—
191#488—92no—
192#488—92no—
193#487—92no—
194#486—92no—
195#416—31no—
196#416—91no—
197#416—91no—
198#416—91no—
199C2×C4×C8—91no—
200C3×#41—24no—
201C3×#41—22no—
202C3×#41—22no—
203C3×#41—22no—
204C3×#41—22no—
205C3×#41—42no—
206C3×#41—62no—
207C3×#41—62no—
208C2×C3×Q8—21no—
209C2×C3×Q8—31no—
210C2×C3×Q8C22×D311yescharacteristic
211C2×C3×Q8C22×D311yescharacteristic
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—31no—
216C2×C3×D4—41no—
217C2×C3×D4—62no—
218C2×C3×D4—61no—
219C2×C3×D4C22×D311yescharacteristic
220C2×C3×D4C22×D311yescharacteristic
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—32no—
225C22×C3×C4—41no—
226C22×C3×C4—61no—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C2×#67—21no—
230C2×#67—22no—
231C22×Dic3#6712yes—
232#235—22no—
233#235—22no—
234C2×D12C22×D311yescharacteristic
235C2×C4×D3—21no—
236C2×Dic6—62no—
237C2×Dic6—62no—
238C2×Dic6C22×D311yescharacteristic
239C2×C3×C8—32no—
240C2×C3×C8—62no—
241C3×C4⋊C4—32no—
242C3×C4⋊C4—62no—
243C3×C22⋊C4—62no—
244C3×C22⋊C4—62no—
245C3×C22⋊C4—61no—
246C3×C42—32no—
247C3×C42—31no—
248C3×C42—31no—
249C3×C42—61no—
250#217—21no—
251#217—22no—
252#217—61no—
253#217—61no—
254#217—121no—
255(C2×D3)⋊C4—22no—
256C4⋊Dic3—32no—
257C4⋊Dic3—32no—
258C4⋊Dic3—62no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3C22×D312yes—
262Dic3⋊C4—22no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267C4×Dic3—21no—
268C4×Dic3—61no—
269C4×Dic3—61no—
270C4×Dic3—121no—
271C4×Dic3#6712yes—
272C4×Dic3C22×D311yescharacteristic
273C4×Dic3C22×D311yescharacteristic
274C2×C3⋊C8—22no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—32no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8—62no—
279C2×C3⋊C8—62no—
280C2×C3⋊C8—122no—
281C2×C3⋊C8C22×D312yes—
282C22×C32—22no—
283C22×C32—41no—
284C22×C32—42no—
285C22×C32#12412yes—
286C22×C32C22×D411yescharacteristic
287C2×C3×D3—41no—
288C2×C3×D3—42no—
289C32×C4—41no—
290C32×C4#12412yes—
291C32×C4C2×#4111yescharacteristic
292C32×C4C2×#4111yescharacteristic
293C3⋊Dic3—42no—
294C3×Dic3—22no—
295C3×Dic3—41no—
296C3×Dic3—42no—
297C3×Dic3#13514yes—
298C2×#41—31no—
299C2×#41D3211yescharacteristic
300C22×C8—31no—
301C22×C8—91no—
302C4⋊Q8—31no—
303C4⋊Q8—92no—
304#127—31no—
305#125—92no—
306#124—31no—
307#124—31no—
308C22⋊Q8—182no—
309#121—62no—
310C4×Q8—182no—
311C4×D4—62no—
312#117—31no—
313#117—91no—
314C2×C42—31no—
315#103—32no—
316#103—92no—
317#103—92no—
318#103—92no—
319#102—32no—
320#102—92no—
321#102—92no—
322#102—92no—
323C4×C8—92no—
324C4×C8—92no—
325C23×C3—21no—
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—41no—
329C23×C3—61no—
330C23×C3D3×D411yescharacteristic
331C23×C3C2×#6711yescharacteristic
332C22×D3—21no—
333C3×Q8—22no—
334C3×Q8—21no—
335C3×Q8—21no—
336C3×Q8—21no—
337C3×Q8—21no—
338C3×Q8—41no—
339C3×Q8—61no—
340C3×Q8—61no—
341C3×D4—22no—
342C3×D4—21no—
343C3×D4—21no—
344C3×D4—21no—
345C3×D4—21no—
346C3×D4—41no—
347C3×D4—44no—
348C3×D4—42no—
349C3×D4—42no—
350C3×D4—61no—
351C3×D4—61no—
352C3×D4—124no—
353C3×D4—122no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—21no—
360C2×C3×C4—32no—
361C2×C3×C4—32no—
362C2×C3×C4—41no—
363C2×C3×C4—44no—
364C2×C3×C4—42no—
365C2×C3×C4—42no—
366C2×C3×C4—64no—
367C2×C3×C4—61no—
368C2×C3×C4—62no—
369C2×C3×C4—122no—
370C2×C3×C4#23512yes—
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4#23712yes—
373C2×C3×C4#23712yes—
374C2×C3×C4#23712yes—
375C2×C3×C4C2×#6711yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377C2×C3×C4C23×D311yescharacteristic
378#67—42no—
379#67—44no—
380C2×Dic3—24no—
381C2×Dic3—22no—
382C2×Dic3—21no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—122no—
386C2×Dic3C2×#6712yes—
387C2×Dic3C2×#6712yes—
388D12—21no—
389D12—21no—
390C4×D3—42no—
391Dic6—21no—
392Dic6—21no—
393Dic6—124no—
394Dic6—124no—
395C3×C8—62no—
396C3⋊C8—22no—
397C3⋊C8—62no—
398C3⋊C8—62no—
399C3⋊C8—122no—
400C2×C32—22no—
401C2×C32—81no—
402C2×C32C2×#12411yescharacteristic
403C2×C32C2×#13512yes—
404C3×D3—81no—
405#41—22no—
406#41—22no—
407#41—62no—
408#41—62no—
409C2×Q8—31no—
410C2×Q8—182no—
411C2×Q8C2×D3211yescharacteristic
412C2×D4—21no—
413C2×D4—31no—
414C2×D4—62no—
415C2×D4—61no—
416C2×D4C2×D3211yescharacteristic
417C22×C4—21no—
418C22×C4—32no—
419C22×C4—61no—
420C22×C4C2×D3211yescharacteristic
421C2×C8—32no—
422C2×C8—62no—
423C2×C8—92no—
424C2×C8—182no—
425C4⋊C4—32no—
426C4⋊C4—62no—
427C4⋊C4—92no—
428C4⋊C4—182no—
429C4⋊C4—182no—
430C4⋊C4—182no—
431C22⋊C4—62no—
432C22⋊C4—62no—
433C22⋊C4—61no—
434C22⋊C4—181no—
435C42—31no—
436C42—31no—
437C42—32no—
438C42—61no—
439C42—181no—
440C22×C3—22no—
441C22×C3—22no—
442C22×C3—21no—
443C22×C3—22no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—41no—
447C22×C3—42no—
448C22×C3—41no—
449C22×C3—42no—
450C22×C3—82no—
451C22×C3—121no—
452C22×C3—122no—
453C22×C3#88512yes—
454C22×C3#93612yes—
455C22×C3C2×D3×D411yescharacteristic
456C22×C3C22×#6711yescharacteristic
457C2×D3—41no—
458C2×D3—42no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—22no—
462C3×C4—34no—
463C3×C4—42no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—62no—
467C3×C4—121no—
468C3×C4—122no—
469C3×C4#88512yes—
470C3×C4#93612yes—
471C3×C4C2×#23511yescharacteristic
472C3×C4C2×#23711yescharacteristic
473C3×C4C2×#23711yescharacteristic
474C3×C4C2×#23711yescharacteristic
475Dic3—22no—
476Dic3—42no—
477Dic3—41no—
478Dic3—122no—
479Dic3—122no—
480Dic3—242no—
481Dic3#95014yes—
482C32#313111yescharacteristic, complemented, Sylow
483C23—21no—
484C23—61no—
485C23D3×#6711yescharacteristic
486Q8—21no—
487Q8—21no—
488Q8—61no—
489Q8—61no—
490Q8—364no—
491D4—21no—
492D4—21no—
493D4—42no—
494D4—61no—
495D4—61no—
496D4—124no—
497D4—122no—
498C2×C4—21no—
499C2×C4—32no—
500C2×C4—32no—
501C2×C4—42no—
502C2×C4—64no—
503C2×C4—62no—
504C2×C4—61no—
505C2×C4—122no—
506C2×C4—182no—
507C2×C4#380412yes—
508C2×C4#380512yes—
509C2×C4D3×#6711yescharacteristic
510C2×C4C22×D3211yescharacteristic
511C8—62no—
512C8—182no—
513C2×C3—22no—
514C2×C3—22no—
515C2×C3—22no—
516C2×C3—21no—
517C2×C3—42no—
518C2×C3—82no—
519C2×C3—81no—
520C2×C3—81no—
521C2×C3—241no—
522C2×C3C2×#88511yescharacteristic
523C2×C3D3×#13512yes—
524C2×C3C2×#93611yescharacteristic
525C2×C3C2×#95012yes—
526D3—81no—
527C22—22no—
528C22—42no—
529C22—41no—
530C22—122no—
531C22—121no—
532C22#6395912yes—
533C22C2×D3×#6711yescharacteristic
534C4—34no—
535C4—41no—
536C4—62no—
537C4—122no—
538C4—121no—
539C4—362no—
540C4#6395912yes—
541C4C2×#380411yescharacteristic
542C4C2×#380511yescharacteristic
543C3—21no—
544C3#7882511yescharacteristic, complemented
545C3#8328111yescharacteristic, complemented
546C2—22no—
547C2—81no—
548C2—241no—
549C2D3×#95012yes—
550C2C2×#6395911yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC3×#5832C2
hypercenterC2×#41D32
hypocenterC32#3131
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10595049C2semidirect
3. #10592932C2semidirect
4. C3×#5233C2semidirect
5. #10591623C2semidirect
6. #10591614C2semidirect
7. #10591487C2semidirect
8. #10591478C2semidirect
9. #10591084C2semidirect
10. #10591083C2semidirect
11. C2×Dic3×C3⋊C8C2semidirect
51. #5233D3semidirect
482. C32#3131semidirect
544. C3#78825semidirect
545. C3#83281semidirect

Maximal subgroups

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

subgroupindex
C3×#58322
#105950492
#105929322
C3×#52332
#105916232
#105916142
#105914872
#105914782
#105910842
#105910832
C2×Dic3×C3⋊C82
#832813
#788253