Finite Group Databasebeta

← #11895350

Subgroups — #11895350

Order 1152.

785 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5585C211yesmaximal, characteristic, complemented
2#10593958C211yesmaximal, characteristic, complemented
3C4×#3755C211yesmaximal, characteristic, complemented
4C3×#5021C211yesmaximal, characteristic, complemented
5#10591614C212yesmaximal, complemented
6#10591568C212yesmaximal, complemented
7#10590542C212yesmaximal, complemented
8#10590456C212yesmaximal, complemented
9#10590355C211yesmaximal, characteristic
10#10590277C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83713—31nomaximal
13#81134—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15C2×#3755C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×#947C2212yes—
18C3×#894—22no—
19C3×#893C2212yes—
20C3×#875—21no—
21C3×#874C2211yescharacteristic
22C3×C4×D12—21no—
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63900—21no—
26#63894C2212yes—
27#63888—22no—
28#63871—21no—
29#63869C2212yes—
30C2×#3714C2212yes—
31#63662C2211yescharacteristic
32#63636C2211yescharacteristic
33#63635C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#835C2212yes—
36C3×#807C2212yes—
37C3×C4⋊(C3⋊C8)C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63563C2212yes—
40#63562C2212yes—
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#559—31no—
44#5730—31no—
45#5585D311yescharacteristic, complemented
46#5579—31no—
47C3×#477—31no—
48#5088—31no—
49#5072—31no—
50#5070—31no—
51#5057—32no—
52#5056—32no—
53C4×#215—31no—
54C4×#215—31no—
55C4×#215—61no—
56Q8×C3⋊C8—31no—
57#5021D311yescharacteristic, complemented
58C4×#213—32no—
59#5009—32no—
60#4891—32no—
61#4872—32no—
62#4843—31no—
63#4830—31no—
64#4819—32no—
65#4800—32no—
66C2×C32×Q8C2311yescharacteristic
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×C4×D3—22no—
73C2×C3×Dic6—21no—
74C2×C3×Dic6D411yescharacteristic
75C2×#624—22no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2311yescharacteristic
78C32×C42—21no—
79C32×C42C2311yescharacteristic
80#3755—22no—
81#3752—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2312yes—
94#3724—22no—
95Dic3⋊Dic3—22no—
96#3722—22no—
97#3714—24no—
98#3361—91noSylow
99C3×C4⋊Q8—31no—
100C3×#127—31no—
101C3×#124—32no—
102C3×#124—61no—
103C3×#123—62no—
104C3×C4×Q8—21no—
105C3×C4×Q8—31no—
106C3×C4×Q8C2×D311yescharacteristic
107C3×C4×Q8C2×D311yescharacteristic
108C3×C4×D4—32no—
109C3×C4×D4—61no—
110#947C2×D312yes—
111#946—61no—
112#946—62no—
113C2×#215—31no—
114C2×#215—31no—
115C2×#215—61no—
116C2×#213—32no—
117C2×D24—32no—
118#897—61no—
119#896—62no—
120#894—22no—
121#893—32no—
122#893C2×D312yes—
123D3×C4⋊C4—61no—
124D3×C4⋊C4—61no—
125#890—32no—
126#875—21no—
127#874C2×D311yescharacteristic
128C4×D12—21no—
129C4×D12—31no—
130C4×D12—31no—
131C4×D12—32no—
132C4×D12—61no—
133#870—32no—
134#869C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#107—32no—
137C3×C4⋊C8—31no—
138C3×#103—32no—
139#835—31no—
140#835—31no—
141#835—61no—
142#835C2×D312yes—
143#832—32no—
144#832—32no—
145#832—32no—
146#821—32no—
147Dic3⋊C8—32no—
148C8×Dic3—32no—
149#809—32no—
150#809—32no—
151#809—31no—
152#809—31no—
153#809—61no—
154#808—31no—
155#808—31no—
156#808—61no—
157#807C2×D312yes—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)C2×D311yescharacteristic
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—32no—
163C4×C3⋊C8—61no—
164C22×C3⋊D3—21no—
165C22×C3×D3—22no—
166C32×Q8—21no—
167C32×Q8—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C4⋊(C3⋊D3)—21no—
175C4⋊(C3⋊D3)#4112yes—
176C4×C3⋊D3—42no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×D12—22no—
181C3×D12—22no—
182C3×D12—42no—
183C3×D12—81no—
184C3×C4×D3—82no—
185C3×Dic6—22no—
186C3×Dic6—81no—
187#624—82no—
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)—21no—
190C3×C3⋊C8—22no—
191#559—31no—
192#554—91no—
193#488—92no—
194#486—91no—
195#478—92no—
196#477—31no—
197#463—92no—
198#459—91no—
199C8×Q8—91no—
200C4×SD16—91no—
201C4×D8—92no—
202C2×C3×Q8—21no—
203C2×C3×Q8—31no—
204C2×C3×Q8—61no—
205C2×C3×Q8C22×D311yescharacteristic
206C2×C3×Q8C22×D311yescharacteristic
207C2×C3×D4—32no—
208C2×C3×D4—61no—
209C2×C3×D4—61no—
210C22×C3×C4—62no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—31no—
214C2×D12—31no—
215C2×D12—61no—
216C2×D12C22×D312yes—
217C2×C4×D3—22no—
218C2×C4×D3—61no—
219C2×C4×D3—61no—
220C2×C4×D3—62no—
221C2×C4×D3—62no—
222C2×C4×D3—121no—
223C2×Dic6—21no—
224C2×Dic6#6711yescharacteristic
225C2×C3×C8—32no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—41no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4C22×D311yescharacteristic
235C3×C4⋊C4C22×D311yescharacteristic
236C3×C22⋊C4—62no—
237C3×C22⋊C4—62no—
238C3×C22⋊C4—62no—
239C3×C42—21no—
240C3×C42—21no—
241C3×C42—21no—
242C3×C42—32no—
243C3×C42—41no—
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246#215—62no—
247#215—62no—
248#215—64no—
249#213—64no—
250(C2×D3)⋊C4—22no—
251(C2×D3)⋊C4—22no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—61no—
255(C2×D3)⋊C4—61no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—121no—
258C4⋊Dic3—21no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—61no—
262C4⋊Dic3—62no—
263C4⋊Dic3#6711yescharacteristic
264C4⋊Dic3C22×D312yes—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4#6712yes—
269C4×Dic3C22×D312yes—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—61no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8C22×D312yes—
277D24—64no—
278C22×C32C22×D411yescharacteristic
279C2×C3⋊D3—22no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C32×C4—21no—
286C32×C4—41no—
287C32×C4—41no—
288C32×C4#13512yes—
289C32×C4C2×#4111yescharacteristic
290C32×C42−1+411yescharacteristic
291C3⋊Dic3—41no—
292C3×Dic3—22no—
293C3×Dic3—22no—
294C3×Dic3—42no—
295C2×SD16—91no—
296C2×D8—92no—
297C4⋊Q8—31no—
298#127—31no—
299#125—92no—
300#124—32no—
301#124—61no—
302#123—62no—
303C22⋊Q8—182no—
304C22⋊Q8—181no—
305C4×Q8—31no—
306C4×Q8D3211yescharacteristic
307C4×D4—32no—
308C4×D4—61no—
309C4×D4—92no—
310C4×D4—91no—
311C2×C4⋊C4—181no—
312#107—32no—
313#106—91no—
314C4⋊C8—31no—
315C4⋊C8—92no—
316#103—32no—
317#103—91no—
318#102—92no—
319#102—92no—
320#102—92no—
321#102—91no—
322C4×C8—92no—
323C4×C8—91no—
324C23×C3—62no—
325C22×D3—22no—
326C22×D3—61no—
327C22×D3—61no—
328C22×D3—121no—
329C3×Q8—22no—
330C3×Q8—21no—
331C3×Q8—21no—
332C3×Q8—21no—
333C3×Q8—21no—
334C3×Q8—41no—
335C3×Q8—62no—
336C3×Q8—241no—
337C3×D4—62no—
338C3×D4—62no—
339C3×D4—122no—
340C3×D4—241no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
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—41no—
352C2×C3×C4—62no—
353C2×C3×C4—242no—
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×Dic3—22no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—121no—
364C2×Dic3C2×#6712yes—
365C2×Dic3C2×#6712yes—
366D12—22no—
367D12—22no—
368D12—32no—
369D12—32no—
370D12—42no—
371D12—62no—
372D12—61no—
373D12—61no—
374D12—81no—
375D12—121no—
376C4×D3—82no—
377C4×D3—122no—
378C4×D3—122no—
379C4×D3—242no—
380C4×D3—242no—
381C4×D3—242no—
382Dic6—22no—
383Dic6—81no—
384C3×C8—62no—
385C3⋊C8—22no—
386C3⋊C8—62no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C3⋊C8—61no—
390C3⋊C8—61no—
391C3⋊C8—121no—
392C2×C32#54811yescharacteristic
393C2×C32C2×#13511yescharacteristic
394C2×C32#57611yescharacteristic
395C3⋊D3—42no—
396C3×D3—82no—
397C2×Q8—31no—
398C2×Q8—61no—
399C2×Q8C2×D3211yescharacteristic
400C2×D4—32no—
401C2×D4—61no—
402C2×D4—61no—
403C2×D4—91no—
404C22×C4—62no—
405C22×C4—182no—
406C22×C4—181no—
407SD16—182no—
408D8—184no—
409C2×C8—32no—
410C2×C8—91no—
411C2×C8—91no—
412C4⋊C4—21no—
413C4⋊C4—31no—
414C4⋊C4—32no—
415C4⋊C4—32no—
416C4⋊C4—61no—
417C4⋊C4—91no—
418C4⋊C4—182no—
419C4⋊C4—182no—
420C4⋊C4C2×D3211yescharacteristic
421C22⋊C4—62no—
422C22⋊C4—62no—
423C22⋊C4—62no—
424C22⋊C4—182no—
425C22⋊C4—181no—
426C42—21no—
427C42—32no—
428C42C2×D3211yescharacteristic
429C22×C3—21no—
430C22×C3—122no—
431C22×C3—122no—
432C22×C3—122no—
433C22×C3C2×D3×D411yescharacteristic
434C22×C3C22×#6711yescharacteristic
435C2×D3—42no—
436C2×D3—42no—
437C2×D3—42no—
438C2×D3—62no—
439C2×D3—62no—
440C2×D3—122no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—241no—
446C2×D3—241no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—22no—
452C3×C4—41no—
453C3×C4—42no—
454C3×C4—41no—
455C3×C4—41no—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4—62no—
459C3×C4—62no—
460C3×C4—81no—
461C3×C4—122no—
462C3×C4#91912yes—
463C3×C4#95012yes—
464C3×C4#100711yescharacteristic
465C3×C4D3×#4111yescharacteristic
466C3×C4D3×#4111yescharacteristic
467C3×C4#101011yescharacteristic
468Dic3—22no—
469Dic3—22no—
470Dic3—42no—
471Dic3—121no—
472Dic3—121no—
473Dic3—241no—
474C32#336111yescharacteristic, complemented, Sylow
475C23—62no—
476C23—181no—
477Q8—21no—
478Q8—21no—
479Q8—62no—
480Q8—241no—
481D4—62no—
482D4—62no—
483D4—92no—
484D4—122no—
485D4—181no—
486D4—241no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—32no—
490C2×C4—32no—
491C2×C4—62no—
492C2×C4—181no—
493C2×C4—242no—
494C2×C4—362no—
495C2×C4—722no—
496C2×C4D3×#6711yescharacteristic
497C2×C4D3×#6711yescharacteristic
498C2×C4C22×D3211yescharacteristic
499C8—62no—
500C8—181no—
501C8—181no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—242no—
506C2×C3#563311yescharacteristic
507C2×C3C2×#91911yescharacteristic
508C2×C3#577411yescharacteristic
509C2×C3C2×#95011yescharacteristic
510C2×C3#583111yescharacteristic
511C2×C3#583511yescharacteristic
512D3—82no—
513D3—122no—
514D3—122no—
515D3—242no—
516C22—122no—
517C22—122no—
518C22—122no—
519C22—182no—
520C22—361no—
521C22—361no—
522C22C2×D3×#6711yescharacteristic
523C4—21no—
524C4—41no—
525C4—41no—
526C4—62no—
527C4—62no—
528C4—122no—
529C4—361no—
530C4#6394912yes—
531C4#6429711yescharacteristic
532C4#6430611yescharacteristic
533C3—21no—
534C3#8113411yescharacteristic, complemented
535C3#8371311yescharacteristic, complemented
536C2—242no—
537C2—362no—
538C2#1059483011yescharacteristic
539C2C2×#6394911yescharacteristic
540C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10590355C2
hypercenterC4×Q8D32
hypocenterC32#3361
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5585C2semidirect
2. #10593958C2semidirect
3. C4×#3755C2semidirect
4. C3×#5021C2semidirect
5. #10591614C2semidirect
6. #10591568C2semidirect
7. #10590542C2semidirect
8. #10590456C2semidirect
10. #10590277C2semidirect
11. #10590250C2semidirect
45. #5585D3semidirect
57. #5021D3semidirect
474. C32#3361semidirect
534. C3#81134semidirect
535. C3#83713semidirect

Maximal subgroups

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

subgroupindex
C3×#55852
#105939582
C4×#37552
C3×#50212
#105916142
#105915682
#105905422
#105904562
#105903552
#105902772
#105902502
#837133
#811343