Finite Group Databasebeta

← #11895870

Subgroups — #11895870

Order 1152.

804 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×Dic6C211yesmaximal, characteristic, complemented
2#10593879C211yesmaximal, characteristic, complemented
3#10592718C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic
5#10591468C212yesmaximal
6#10591405C212yesmaximal, complemented
7#10590531C212yesmaximal, complemented
8#10590488C212yesmaximal, complemented
9#10590288C211yesmaximal, characteristic, complemented
10#10590269C211yesmaximal, characteristic, complemented
11#10590258C211yesmaximal, characteristic, complemented
12#83563—31nomaximal
13#79571—31nomaximal
14C22×C3×Dic6—21no—
15C32×C4×D4C2211yescharacteristic
16C2×#3754C2212yes—
17#64078C2211yescharacteristic
18C3×D4×Dic3C2212yes—
19C2×C3×#213C2211yescharacteristic
20C3×#924—21no—
21C3×#888C2212yes—
22C3×#878—22no—
23C3×C4×D12C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63861—22no—
27#63860C2212yes—
28#63856—21no—
29#63844C2212yes—
30#63841—21no—
31#63637C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#832C2211yescharacteristic
34C3×#809C2211yescharacteristic
35C3×#807C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63576C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2212yes—
40#63567C2212yes—
41#63562C2212yes—
42#63554C2212yes—
43C3×D4×Q8—31no—
44#5584—31no—
45#5542—31no—
46D4×Dic6D311yescharacteristic, complemented
47C3×C4×D8—31no—
48#5153—32no—
49#5093—31no—
50#5091—32no—
51#5089—32no—
52#5087—31no—
53#5024—31no—
54#5019—31no—
55#5019—31no—
56#5019—61no—
57#5018—32no—
58#5016—32no—
59C4×#213D311yescharacteristic
60#5007—31no—
61#4875—32no—
62#4765—32no—
63#4757—32no—
64#4681—31no—
65#4679—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634C2312yes—
69C22×C3×Dic3—22no—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6—22no—
74C2×C3×Dic6—44no—
75C2×C3×Dic6D411yescharacteristic
76C32×C4⋊C4C2311yescharacteristic
77C32×C22⋊C4—21no—
78C32×C42C2311yescharacteristic
79#3754—24no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)—21no—
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×#217—22no—
84C3×#213—22no—
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95#3724—22no—
96(C2×D3)⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98Dic32—22no—
99#3367—91noSylow
100C22×C3×Q8—61no—
101C22×Dic6—21no—
102C2×C3×D8—31no—
103C3×C4⋊Q8—32no—
104C3×C4⋊Q8—31no—
105C3×C22⋊Q8—62no—
106C3×C22⋊Q8—61no—
107C3×C4×Q8—31no—
108C3×C4×D4—21no—
109C3×C4×D4—32no—
110C3×C4×D4—31no—
111C3×C4×D4C2×D311yescharacteristic
112C3×C4×D4C2×D311yescharacteristic
113#946—61no—
114#936—32no—
115D4×Dic3C2×D312yes—
116C2×#214—32no—
117C2×#214—32no—
118C2×#214—62no—
119C2×#213C2×D311yescharacteristic
120#926—61no—
121#924—21no—
122#924—61no—
123#898—62no—
124#892—61no—
125#888C2×D312yes—
126#887—32no—
127#879—62no—
128#878—22no—
129#875—32no—
130C4×D12C2×D311yescharacteristic
131#869—31no—
132#869—31no—
133#869—61no—
134#869C2×D311yescharacteristic
135C4×Dic6—32no—
136C4×Dic6C2×D311yescharacteristic
137C3×#107—31no—
138C3×#102—31no—
139C3×#102—31no—
140C3×C4×C8—31no—
141#832—32no—
142#832C2×D311yescharacteristic
143#816—32no—
144#816—32no—
145#815—32no—
146Dic3⋊C8—32no—
147#810—32no—
148#810—32no—
149#810—32no—
150#810—32no—
151#810—62no—
152#809—32no—
153#809C2×D311yescharacteristic
154#807—32no—
155#807—32no—
156#807C2×D311yescharacteristic
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—61no—
161#803—32no—
162C4×C3⋊C8C2×D311yescharacteristic
163C23×C32—21no—
164C22×C3×D3—21no—
165C32×D4—21no—
166C32×D4#4112yes—
167C2×C32×C4—21no—
168C2×C32×C4—42no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—22no—
173#634—22no—
174#634—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—44no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×D12—21no—
181C3×D12—21no—
182C3×C4×D3—42no—
183C3×Dic6—22no—
184C3×Dic6—44no—
185C3×Dic6—42no—
186C3⋊(C3⋊C8)—22no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—21no—
189#556—91no—
190D4×Q8—31no—
191#489—92no—
192#487—91no—
193#477—92no—
194#474—91no—
195#463—92no—
196#461—91no—
197#446—91no—
198#440—92no—
199C4×D8—31no—
200C2×C3×Q8—31no—
201C2×C3×Q8—62no—
202C2×C3×Q8—61no—
203C2×C3×Q8—124no—
204C2×C3×D4—21no—
205C2×C3×D4—31no—
206C2×C3×D4C22×D311yescharacteristic
207C2×C3×D4C22×D311yescharacteristic
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—41no—
211C22×C3×C4—62no—
212C22×C3×C4—61no—
213C22×Dic3—22no—
214C2×D12C22×D311yescharacteristic
215C2×C4×D3—21no—
216C2×Dic6—21no—
217C2×Dic6—22no—
218C2×Dic6—32no—
219C2×Dic6—32no—
220C2×Dic6—44no—
221C2×Dic6—62no—
222C2×Dic6#6711yescharacteristic
223C3×D8—62no—
224C2×C3×C8—31no—
225C2×C3×C8—31no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4C22×D311yescharacteristic
234C3×C4⋊C4C22×D311yescharacteristic
235C3×C22⋊C4—21no—
236C3×C22⋊C4—21no—
237C3×C22⋊C4—41no—
238C3×C22⋊C4—62no—
239C3×C22⋊C4—61no—
240C3×C42—21no—
241C3×C42—32no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#217—22no—
245#217—62no—
246#217—62no—
247#214—64no—
248#214—64no—
249#214—124no—
250#213—22no—
251(C2×D3)⋊C4—21no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254C4⋊Dic3—21no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259C4⋊Dic3—121no—
260C4⋊Dic3—121no—
261C4⋊Dic3#6711yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263C4⋊Dic3C22×D312yes—
264Dic3⋊C4—22no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4#6712yes—
268C4×Dic3—62no—
269C4×Dic3—62no—
270C4×Dic3C22×D312yes—
271C2×C3⋊C8—32no—
272C2×C3⋊C8—32no—
273C2×C3⋊C8—62no—
274C2×C3⋊C8C22×D311yescharacteristic
275C2×C3⋊C8C22×D311yescharacteristic
276C22×C32—22no—
277C22×C32—41no—
278C22×C32—41no—
279C22×C32C22×D411yescharacteristic
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C2×C3×D3—41no—
283C32×C4—21no—
284C32×C4—41no—
285C32×C4AGL(1,ℤ/8)12yes—
286C32×C4C2×#4111yescharacteristic
287C32×C42−1+411yescharacteristic
288C3⋊Dic3—42no—
289C3×Dic3—22no—
290C3×Dic3—22no—
291C3×Dic3—42no—
292C3×Dic3—41no—
293C22×Q8—61no—
294C2×SD16—92no—
295C2×D8—31no—
296C4⋊Q8—32no—
297C4⋊Q8—31no—
298C4⋊Q8—91no—
299#126—182no—
300#124—92no—
301C22⋊Q8—62no—
302C22⋊Q8—61no—
303C22⋊Q8—181no—
304C4×Q8—31no—
305C4×Q8—92no—
306C4×D4—32no—
307C4×D4—31no—
308C4×D4D3211yescharacteristic
309#117—181no—
310#107—31no—
311#107—92no—
312C4⋊C8—92no—
313C4⋊C8—91no—
314#103—92no—
315#103—92no—
316#103—92no—
317#102—31no—
318#102—31no—
319#102—92no—
320#97—92no—
321C4×C8—31no—
322C23×C3—21no—
323C23×C3—21no—
324C23×C3—41no—
325C23×C3—61no—
326C22×D3—21no—
327C3×Q8—62no—
328C3×Q8—124no—
329C3×Q8—122no—
330C3×D4—21no—
331C3×D4—21no—
332C3×D4—22no—
333C3×D4—41no—
334C3×D4—61no—
335C3×D4—61no—
336C3×D4#23512yes—
337C3×D4#23912yes—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—41no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—62no—
349C2×C3×C4—61no—
350C2×C3×C4—82no—
351C2×C3×C4—124no—
352C2×C3×C4—122no—
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×Dic3—21no—
360C2×Dic3—22no—
361C2×Dic3—44no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—122no—
365C2×Dic3C2×#6712yes—
366C2×Dic3C2×#6712yes—
367D12—21no—
368D12—21no—
369C4×D3—42no—
370Dic6—22no—
371Dic6—44no—
372Dic6—42no—
373Dic6—62no—
374Dic6—62no—
375Dic6—62no—
376Dic6—62no—
377Dic6—122no—
378Dic6—122no—
379C3×C8—61no—
380C3×C8—61no—
381C3⋊C8—21no—
382C3⋊C8—21no—
383C3⋊C8—62no—
384C3⋊C8—62no—
385C3⋊C8—122no—
386C2×C32—42no—
387C2×C32#54811yescharacteristic
388C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
389C2×C32#57811yescharacteristic
390C3×D3—81no—
391C2×Q8—31no—
392C2×Q8—62no—
393C2×Q8—61no—
394C2×Q8—92no—
395C2×Q8—124no—
396C2×D4—31no—
397C2×D4C2×D3211yescharacteristic
398C22×C4—21no—
399C22×C4—62no—
400C22×C4—61no—
401SD16—184no—
402D8—62no—
403C2×C8—31no—
404C2×C8—31no—
405C2×C8—92no—
406C4⋊C4—31no—
407C4⋊C4—32no—
408C4⋊C4—31no—
409C4⋊C4—32no—
410C4⋊C4—62no—
411C4⋊C4—61no—
412C4⋊C4—182no—
413C4⋊C4—181no—
414C4⋊C4—181no—
415C4⋊C4C2×D3211yescharacteristic
416C22⋊C4—21no—
417C22⋊C4—62no—
418C22⋊C4—61no—
419C22⋊C4—182no—
420C22⋊C4—182no—
421C42—32no—
422C42—182no—
423C42C2×D3211yescharacteristic
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—21no—
427C22×C3—42no—
428C22×C3—41no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—81no—
433C22×C3—81no—
434C22×C3—121no—
435C22×C3—121no—
436C22×C3—121no—
437C22×C3C2×D3×D411yescharacteristic
438C22×C3C22×#6711yescharacteristic
439C2×D3—41no—
440C2×D3—41no—
441C2×D3—41no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—22no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4—41no—
450C3×C4—62no—
451C3×C4—62no—
452C3×C4—81no—
453C3×C4—122no—
454C3×C4—121no—
455C3×C4#91112yes—
456C3×C4#93212yes—
457C3×C4C2×#23511yescharacteristic
458C3×C4C2×#23911yescharacteristic
459C3×C4#100711yescharacteristic
460C3×C4#101011yescharacteristic
461Dic3—22no—
462Dic3—22no—
463Dic3—41no—
464Dic3—42no—
465Dic3—122no—
466Dic3—122no—
467Dic3—242no—
468C32#336711yescharacteristic, complemented, Sylow
469C23—21no—
470C23—61no—
471Q8—62no—
472Q8—124no—
473Q8—122no—
474Q8—182no—
475Q8—182no—
476D4—21no—
477D4—61no—
478D4—61no—
479D4#379912yes—
480C2×C4—21no—
481C2×C4—32no—
482C2×C4—32no—
483C2×C4—42no—
484C2×C4—61no—
485C2×C4—62no—
486C2×C4—124no—
487C2×C4—122no—
488C2×C4—182no—
489C2×C4D3×#6711yescharacteristic
490C2×C4D3×#6711yescharacteristic
491C2×C4C22×D3211yescharacteristic
492C8—61no—
493C8—61no—
494C8—182no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—42no—
499C2×C3—42no—
500C2×C3—82no—
501C2×C3—241no—
502C2×C3#555211yescharacteristic
503C2×C3C2×#91111yescharacteristic
504C2×C3#577111yescharacteristic
505C2×C3C2×#93211yescharacteristic
506C2×C3#581711yescharacteristic
507C2×C3#583811yescharacteristic
508D3—81no—
509C22—22no—
510C22—41no—
511C22—41no—
512C22—121no—
513C22—121no—
514C22—121no—
515C22C2×D3×#6711yescharacteristic
516C4—21no—
517C4—41no—
518C4—62no—
519C4—62no—
520C4—122no—
521C4—121no—
522C4—362no—
523C4#6393212yes—
524C4#6429711yescharacteristic
525C4C2×#379911yescharacteristic
526C3—21no—
527C3#7957111yescharacteristic, complemented
528C3#8356311yescharacteristic, complemented
529C2—42no—
530C2—241no—
531C2#1059490211yescharacteristic
532C2C2×#6393211yescharacteristic
533C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC4×D4D32
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×D4×Dic6C2semidirect
2. #10593879C2semidirect
3. #10592718C2semidirect
6. #10591405C2semidirect
7. #10590531C2semidirect
8. #10590488C2semidirect
9. #10590288C2semidirect
10. #10590269C2semidirect
11. #10590258C2semidirect
46. D4×Dic6D3semidirect
468. C32#3367semidirect
527. C3#79571semidirect
528. C3#83563semidirect

Maximal subgroups

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

subgroupindex
C3×D4×Dic62
#105938792
#105927182
C3×C4×#2132
#105914682
#105914052
#105905312
#105904882
#105902882
#105902692
#105902582
#835633
#795713