Finite Group Databasebeta

← #11895868

Subgroups — #11895868

Order 1152.

811 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×Dic6C211yesmaximal, characteristic, complemented
2#10593865C211yesmaximal, characteristic, complemented
3C4×#3753C211yesmaximal, characteristic
4C3×#5019C211yesmaximal, characteristic, complemented
5#10591471C212yesmaximal
6#10591440C212yesmaximal, complemented
7#10590535C212yesmaximal, complemented
8#10590489C212yesmaximal, complemented
9#10590313C211yesmaximal, characteristic, complemented
10#10590290C211yesmaximal, characteristic, complemented
11#10590259C211yesmaximal, characteristic, complemented
12#83563—31nomaximal
13#80416—31nomaximal
14C22×C3×Dic6—21no—
15C32×C4×D4C2211yescharacteristic
16C2×#3753C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×D4×Dic3C2212yes—
19C2×C3×#214C2212yes—
20C3×#924—21no—
21C3×#888C2212yes—
22C3×#878—22no—
23C3×#869C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63871—21no—
27#63864C2212yes—
28#63849—21no—
29#63848—22no—
30Dic3×Dic6C2212yes—
31#63659C2211yescharacteristic
32#63636C2211yescharacteristic
33#63634C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#810C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63575C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63565C2212yes—
40#63565C2212yes—
41#63564C2212yes—
42#63554C2212yes—
43C3×D4×Q8—31no—
44#5732—31no—
45#5584—31no—
46D4×Dic6D311yescharacteristic, complemented
47C3×#461—31no—
48#5165—32no—
49#5164—32no—
50#5093—31no—
51#5091—32no—
52#5089—32no—
53#5087—31no—
54#5079—31no—
55#5024—31no—
56#5019D311yescharacteristic, complemented
57#5018—32no—
58#5016—32no—
59C4×#213—31no—
60C4×#213—31no—
61C4×#213—61no—
62#4846—31no—
63#4831—31no—
64#4794—32no—
65#4793—32no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C22×C3×Dic3—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6—44no—
74C2×C3×Dic6D411yescharacteristic
75C2×C3×Dic6C2312yes—
76C32×C4⋊C4C2311yescharacteristic
77C32×C22⋊C4—21no—
78C32×C42C2311yescharacteristic
79#3753—22no—
80#3752—21no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C3×#217—22no—
85C3×#214—24no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2312yes—
95Dic3⋊Dic3—22no—
96#3722—22no—
97#3722—22no—
98Dic32—22no—
99#3367—91noSylow
100C22×C3×Q8—61no—
101C22×Dic6—21no—
102C2×C3×SD16—32no—
103C3×C4⋊Q8—32no—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8—31no—
106C3×C22⋊Q8—62no—
107C3×C22⋊Q8—61no—
108C3×C4×Q8—31no—
109C3×C4×D4—21no—
110C3×C4×D4—32no—
111C3×C4×D4C2×D311yescharacteristic
112C3×C4×D4C2×D311yescharacteristic
113#947—32no—
114#946—61no—
115Q8×Dic3—32no—
116D4×Dic3C2×D312yes—
117C2×#214C2×D312yes—
118C2×#213—31no—
119C2×#213—31no—
120C2×#213—61no—
121#924—21no—
122#898—62no—
123#898—62no—
124#897—61no—
125#892—61no—
126#892—61no—
127#888C2×D312yes—
128#878—22no—
129#875—32no—
130C4×D12—31no—
131C4×D12—31no—
132C4×D12—61no—
133#869C2×D311yescharacteristic
134#869C2×D311yescharacteristic
135C4×Dic6—32no—
136C4×Dic6C2×D311yescharacteristic
137C3×C4⋊C8—31no—
138C3×#103—32no—
139#835—32no—
140#835—32no—
141#832—31no—
142#832—31no—
143#832—61no—
144#821—32no—
145#818—32no—
146#815—32no—
147Dic3⋊C8—32no—
148#810—32no—
149#810—32no—
150#810C2×D312yes—
151#809—31no—
152#809—31no—
153#809—32no—
154#809—61no—
155#807—31no—
156#807—31no—
157#807—32no—
158#807—61no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)C2×D311yescharacteristic
161#803—32no—
162C4×C3⋊C8—31no—
163C4×C3⋊C8—31no—
164C4×C3⋊C8—61no—
165C23×C32—21no—
166C22×C3⋊D3—21no—
167C32×D4—21no—
168C32×D4#4112yes—
169C2×C32×C4—21no—
170C2×C32×C4—42no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—21no—
175C4⋊(C3⋊D3)—21no—
176C4⋊(C3⋊D3)—21no—
177C4×C3⋊D3—42no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—44no—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3C2×D412yes—
183C3×Dic6—22no—
184C3×Dic6—22no—
185C3×Dic6—22no—
186C3×Dic6—44no—
187C3×Dic6—42no—
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)—21no—
190C3×C3⋊C8—22no—
191#556—91no—
192D4×Q8—31no—
193#489—92no—
194#487—91no—
195#477—92no—
196#474—91no—
197#463—92no—
198#461—31no—
199#446—91no—
200#440—92no—
201C4×D8—91no—
202C2×C3×Q8—31no—
203C2×C3×Q8—32no—
204C2×C3×Q8—62no—
205C2×C3×Q8—61no—
206C2×C3×Q8—124no—
207C2×C3×D4—21no—
208C2×C3×D4C22×D311yescharacteristic
209C2×C3×D4C22×D311yescharacteristic
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—41no—
213C22×C3×C4—62no—
214C22×Dic3—22no—
215C2×D12—31no—
216C2×D12—31no—
217C2×D12—61no—
218C2×C4×D3—61no—
219C2×C4×D3—61no—
220C2×C4×D3—121no—
221C2×Dic6—21no—
222C2×Dic6—22no—
223C2×Dic6—44no—
224C2×Dic6#6711yescharacteristic
225C2×Dic6C22×D312yes—
226C3×SD16—64no—
227C2×C3×C8—32no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4—61no—
236C3×C4⋊C4C22×D311yescharacteristic
237C3×C4⋊C4C22×D311yescharacteristic
238C3×C22⋊C4—21no—
239C3×C22⋊C4—21no—
240C3×C22⋊C4—41no—
241C3×C22⋊C4—62no—
242C3×C42—21no—
243C3×C42—32no—
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246#217—22no—
247#214—24no—
248#213—64no—
249#213—62no—
250#213—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—61no—
254(C2×D3)⋊C4—61no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—121no—
258C4⋊Dic3—21no—
259C4⋊Dic3—21no—
260C4⋊Dic3—21no—
261C4⋊Dic3—31no—
262C4⋊Dic3—31no—
263C4⋊Dic3—61no—
264C4⋊Dic3—62no—
265C4⋊Dic3#6711yescharacteristic
266C4⋊Dic3C22×D312yes—
267Dic3⋊C4—22no—
268Dic3⋊C4—62no—
269Dic3⋊C4#6712yes—
270C4×Dic3—62no—
271C4×Dic3—62no—
272C4×Dic3C22×D312yes—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—61no—
278C2×C3⋊C8—61no—
279C2×C3⋊C8C22×D312yes—
280C22×C32—22no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32C22×D411yescharacteristic
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C2×C3⋊D3—41no—
287C32×C4—21no—
288C32×C4—41no—
289C32×C4AGL(1,ℤ/8)12yes—
290C32×C4C2×#4111yescharacteristic
291C32×C42−1+411yescharacteristic
292C3⋊Dic3—41no—
293C3×Dic3—22no—
294C3×Dic3—22no—
295C3×Dic3—42no—
296C3×Dic3—42no—
297C22×Q8—61no—
298C2×SD16—32no—
299C2×D8—91no—
300C4⋊Q8—32no—
301C4⋊Q8—31no—
302C4⋊Q8—31no—
303#126—182no—
304#124—92no—
305C22⋊Q8—62no—
306C22⋊Q8—61no—
307C22⋊Q8—181no—
308C4×Q8—31no—
309C4×Q8—92no—
310C4×D4—32no—
311C4×D4—91no—
312C4×D4D3211yescharacteristic
313#117—181no—
314#107—92no—
315#107—91no—
316C4⋊C8—31no—
317C4⋊C8—92no—
318#103—32no—
319#103—92no—
320#103—92no—
321#102—92no—
322#102—91no—
323#102—91no—
324#97—92no—
325C4×C8—91no—
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—41no—
329C22×D3—61no—
330C22×D3—61no—
331C22×D3—121no—
332C3×Q8—62no—
333C3×Q8—62no—
334C3×Q8—62no—
335C3×Q8—124no—
336C3×Q8—122no—
337C3×D4—21no—
338C3×D4—21no—
339C3×D4—22no—
340C3×D4—41no—
341C3×D4#23712yes—
342C3×D4#23912yes—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—41no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—82no—
356C2×C3×C4—124no—
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—44no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—121no—
369C2×Dic3C2×#6712yes—
370C2×Dic3C2×#6712yes—
371D12—62no—
372D12—61no—
373D12—61no—
374D12—61no—
375D12—61no—
376D12—121no—
377C4×D3—122no—
378C4×D3—122no—
379C4×D3—242no—
380Dic6—22no—
381Dic6—22no—
382Dic6—22no—
383Dic6—44no—
384Dic6—42no—
385C3×C8—62no—
386C3⋊C8—22no—
387C3⋊C8—62no—
388C3⋊C8—61no—
389C3⋊C8—61no—
390C3⋊C8—61no—
391C3⋊C8—61no—
392C3⋊C8—121no—
393C2×C32—42no—
394C2×C32#54811yescharacteristic
395C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
396C2×C32#57811yescharacteristic
397C3⋊D3—81no—
398C2×Q8—31no—
399C2×Q8—32no—
400C2×Q8—62no—
401C2×Q8—61no—
402C2×Q8—124no—
403C2×D4—91no—
404C2×D4C2×D3211yescharacteristic
405C22×C4—21no—
406C22×C4—62no—
407C22×C4—181no—
408SD16—64no—
409D8—182no—
410C2×C8—32no—
411C2×C8—91no—
412C2×C8—91no—
413C4⋊C4—31no—
414C4⋊C4—32no—
415C4⋊C4—32no—
416C4⋊C4—62no—
417C4⋊C4—61no—
418C4⋊C4—61no—
419C4⋊C4—61no—
420C4⋊C4—91no—
421C4⋊C4—182no—
422C4⋊C4C2×D3211yescharacteristic
423C22⋊C4—21no—
424C22⋊C4—62no—
425C22⋊C4—182no—
426C22⋊C4—182no—
427C22⋊C4—181no—
428C42—32no—
429C42—182no—
430C42C2×D3211yescharacteristic
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—21no—
434C22×C3—42no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—81no—
440C22×C3—81no—
441C22×C3C2×D3×D411yescharacteristic
442C22×C3C22×#6711yescharacteristic
443C2×D3—122no—
444C2×D3—121no—
445C2×D3—121no—
446C2×D3—121no—
447C2×D3—121no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—241no—
451C2×D3—241no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—41no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—62no—
461C3×C4—62no—
462C3×C4—81no—
463C3×C4—122no—
464C3×C4—122no—
465C3×C4#91412yes—
466C3×C4#93212yes—
467C3×C4C2×#23711yescharacteristic
468C3×C4C2×#23911yescharacteristic
469C3×C4#100711yescharacteristic
470C3×C4#101011yescharacteristic
471Dic3—22no—
472Dic3—22no—
473Dic3—42no—
474Dic3—42no—
475Dic3—121no—
476Dic3—121no—
477Dic3—241no—
478C32#336711yescharacteristic, complemented, Sylow
479C23—21no—
480C23—181no—
481Q8—62no—
482Q8—62no—
483Q8—62no—
484Q8—124no—
485Q8—122no—
486D4—21no—
487D4—181no—
488D4—181no—
489D4#379612yes—
490C2×C4—21no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—42no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—124no—
497C2×C4—181no—
498C2×C4—362no—
499C2×C4D3×#6711yescharacteristic
500C2×C4D3×#6711yescharacteristic
501C2×C4C22×D3211yescharacteristic
502C8—62no—
503C8—181no—
504C8—181no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—42no—
509C2×C3—42no—
510C2×C3—82no—
511C2×C3#559811yescharacteristic
512C2×C3C2×#91411yescharacteristic
513C2×C3#577911yescharacteristic
514C2×C3C2×#93211yescharacteristic
515C2×C3#581711yescharacteristic
516C2×C3#583811yescharacteristic
517D3—242no—
518D3—241no—
519D3—241no—
520C22—22no—
521C22—41no—
522C22—41no—
523C22—361no—
524C22—361no—
525C22—361no—
526C22C2×D3×#6711yescharacteristic
527C4—21no—
528C4—41no—
529C4—62no—
530C4—62no—
531C4—122no—
532C4—122no—
533C4—361no—
534C4#6393412yes—
535C4C2×#379611yescharacteristic
536C4#6429711yescharacteristic
537C3—21no—
538C3#8041611yescharacteristic, complemented
539C3#8356311yescharacteristic, complemented
540C2—42no—
541C2—721no—
542C2#1059490011yescharacteristic
543C2C2×#6393411yescharacteristic
544C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#3753C22
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. #10593865C2semidirect
4. C3×#5019C2semidirect
6. #10591440C2semidirect
7. #10590535C2semidirect
8. #10590489C2semidirect
9. #10590313C2semidirect
10. #10590290C2semidirect
11. #10590259C2semidirect
46. D4×Dic6D3semidirect
56. #5019D3semidirect
478. C32#3367semidirect
538. C3#80416semidirect
539. 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
#105938652
C4×#37532
C3×#50192
#105914712
#105914402
#105905352
#105904892
#105903132
#105902902
#105902592
#835633
#804163