Finite Group Databasebeta

← #11895963

Subgroups — #11895963

Order 1152.

920 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596024C211yesmaximal, characteristic
2#10593861C211yesmaximal, characteristic, complemented
3C3×C4×#214C211yesmaximal, characteristic, complemented
4C3×#5007C211yesmaximal, characteristic, complemented
5#10591480C212yesmaximal, complemented
6#10591444C212yesmaximal, complemented
7#10590484C212yesmaximal, complemented
8#10590435C212yesmaximal, complemented
9#10590367C211yesmaximal, characteristic, complemented
10#10590296C211yesmaximal, characteristic, complemented
11#10590281C211yesmaximal, characteristic, complemented
12#80995—31nomaximal
13#79625—31nomaximal
14C2×#3828—21no—
15C32×C4×D4C2211yescharacteristic
16#64149C2212yes—
17#64139—21no—
18#64102C2212yes—
19#64093—22no—
20#64083C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63872C2212yes—
26#63866—21no—
27#63846—22no—
28#63843C2212yes—
29Dic3×Dic6—21no—
30C2×#3717C2212yes—
31C3×#832C2212yes—
32C3×#832C2211yescharacteristic
33C3×#810C2211yescharacteristic
34C3×#808C2211yescharacteristic
35C3×#807C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38#63572C2212yes—
39#63564C2212yes—
40#63564C2212yes—
41#63564C2212yes—
42#63555C2212yes—
43#5721—31no—
44#5570—31no—
45#5553—31no—
46#5553—31no—
47#5553—61no—
48C3×#474—31no—
49C3×C4×SD16—31no—
50#5163—32no—
51#5088—31no—
52#5027—31no—
53C4×#214D311yescharacteristic, complemented
54#5007D311yescharacteristic, complemented
55#4891—32no—
56#4889—32no—
57#4871—32no—
58#4848—31no—
59#4831—31no—
60#4817—32no—
61#4764—32no—
62#4764—32no—
63#4762—32no—
64#4694—31no—
65#4679—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#638—22no—
69C2×#638—22no—
70#3828—44no—
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)C2312yes—
74C2×C4×C3⋊D3—22no—
75C2×#634D411yescharacteristic
76C2×C3×Dic6—21no—
77C2×C3×Dic6C2311yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80C32×C42C2311yescharacteristic
81#3752—22no—
82C4⋊(C3⋊Dic3)D411yescharacteristic
83#3750D412yes—
84C4×C3⋊Dic3C2312yes—
85C3×#214—22no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—21no—
90C3×C4×Dic3—21no—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2312yes—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96Dic3⋊Dic3—22no—
97Dic32—22no—
98#3717—24no—
99#3368—91noSylow
100C2×#235—61no—
101C2×#235—61no—
102C2×#235—62no—
103C2×C3×SD16—31no—
104C3×C4⋊Q8—31no—
105C3×C4×Q8—31no—
106C3×C4×D4—21no—
107C3×C4×D4C2×D311yescharacteristic
108C3×C4×D4C2×D311yescharacteristic
109Q8×Dic3—32no—
110Q8×Dic3—61no—
111#944—61no—
112C2×#215—32no—
113#940—32no—
114#940—32no—
115#940—62no—
116C2×#214C2×D311yescharacteristic
117#930—61no—
118#930—61no—
119#930—62no—
120C2×#204—32no—
121#893—32no—
122#893—32no—
123#893—62no—
124#890—32no—
125#890—32no—
126#890—62no—
127#889—62no—
128#887—32no—
129#884—62no—
130#884—62no—
131#884—64no—
132#874—31no—
133#874—31no—
134#874—61no—
135#869—61no—
136#869C2×D311yescharacteristic
137C4×Dic6—31no—
138C4×Dic6—31no—
139C4×Dic6—61no—
140C4×Dic6—61no—
141C4×Dic6C2×D311yescharacteristic
142C3×#107—32no—
143C3×#106—31no—
144C3×C4⋊C8—31no—
145C3×#103—31no—
146C3×#102—32no—
147C3×#102—31no—
148C3×C4×C8—31no—
149#832C2×D312yes—
150#832C2×D311yescharacteristic
151#821—32no—
152#821—32no—
153#821—32no—
154#815—32no—
155#815—32no—
156Dic3⋊C8—32no—
157Dic3⋊C8—32no—
158#810C2×D311yescharacteristic
159#809—32no—
160#809—32no—
161#809—32no—
162#808C2×D311yescharacteristic
163#807C2×D312yes—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C23×C32—21no—
167C22×C3⋊D3—22no—
168C32×D4—21no—
169C32×D4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—42no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175#638—44no—
176#638—82no—
177C2×C3⋊Dic3C2×D412yes—
178C2×C3⋊Dic3C2×D412yes—
179C4⋊(C3⋊D3)—22no—
180C4⋊(C3⋊D3)—22no—
181C4⋊(C3⋊D3)—42no—
182C4⋊(C3⋊D3)—81no—
183C4×C3⋊D3—44no—
184#634—22no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C3×Dic6—21no—
189C3×Dic6—42no—
190C3×Dic6#4112yescomplemented
191C3×C3⋊C8—22no—
192C3×C3⋊C8—21no—
193C3×C3⋊C8—21no—
194#557—91no—
195#550—91no—
196#490—92no—
197#486—91no—
198#478—92no—
199#474—31no—
200#460—92no—
201#460—91no—
202#446—91no—
203#440—92no—
204C4×SD16—31no—
205C2×C3×Q8—31no—
206C2×C3×Q8—61no—
207C2×C3×D4—21no—
208C2×C3×D4C22×D311yescharacteristic
209C2×C3×D4C22×D311yescharacteristic
210C22×C3×C4—22no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C2×#67—62no—
214C2×#67—62no—
215C2×#67—62no—
216C2×#67—62no—
217C2×#67—64no—
218C2×#67—64no—
219#235—128no—
220#235—124no—
221#235—124no—
222C2×D12—32no—
223C2×D12—32no—
224C2×D12—62no—
225C2×D12—62no—
226C2×D12—61no—
227C2×D12—61no—
228C2×D12—62no—
229C2×D12—61no—
230C2×D12—61no—
231C2×C4×D3—62no—
232C2×C4×D3—62no—
233C2×C4×D3—64no—
234C2×Dic6—21no—
235C2×Dic6—31no—
236C2×Dic6—31no—
237C2×Dic6—61no—
238C2×Dic6C22×D311yescharacteristic
239C3×SD16—62no—
240C2×C3×C8—31no—
241C2×C3×C8—32no—
242C2×C3×C8—31no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—31no—
245C3×C4⋊C4—32no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C22⋊C4—22no—
251C3×C22⋊C4—21no—
252C3×C22⋊C4—21no—
253C3×C42—21no—
254C3×C42—61no—
255C3×C42C22×D311yescharacteristic
256C3×C42C22×D311yescharacteristic
257#215—64no—
258#214—22no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—62no—
261(C2×D3)⋊C4—64no—
262C4⋊Dic3—21no—
263C4⋊Dic3—31no—
264C4⋊Dic3—31no—
265C4⋊Dic3—61no—
266C4⋊Dic3—62no—
267C4⋊Dic3—62no—
268C4⋊Dic3—62no—
269C4⋊Dic3C22×D312yes—
270C4⋊Dic3C22×D311yescharacteristic
271Dic3⋊C4—21no—
272Dic3⋊C4—32no—
273Dic3⋊C4—32no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276Dic3⋊C4—62no—
277Dic3⋊C4—62no—
278C4×Dic3—21no—
279C4×Dic3—32no—
280C4×Dic3—32no—
281C4×Dic3—62no—
282C4×Dic3—62no—
283C4×Dic3—62no—
284C2×C3⋊C8C22×D311yescharacteristic
285C2×C3⋊C8C22×D311yescharacteristic
286C2×C3⋊C8C22×D312yes—
287#204—64no—
288C22×C32—41no—
289C22×C32—41no—
290C22×C32—41no—
291C22×C32C22×D411yescharacteristic
292C2×C3⋊D3—42no—
293C2×C3⋊D3—42no—
294C2×C3⋊D3—42no—
295C32×C4—21no—
296C32×C4—41no—
297C32×C4AGL(1,ℤ/8)12yes—
298C32×C4C2×#4111yescharacteristic
299C32×C42−1+411yescharacteristic
300C3⋊Dic3—22no—
301C3⋊Dic3—22no—
302C3×Dic3—22no—
303C3×Dic3—42no—
304C3×Dic3—41no—
305C2×#41—181no—
306C2×SD16—31no—
307C2×SD16—92no—
308C4⋊Q8—31no—
309C4⋊Q8—181no—
310#127—92no—
311#127—91no—
312#125—92no—
313#125—182no—
314#121—182no—
315#121—181no—
316C4×Q8—31no—
317C4×Q8—91no—
318C4×Q8—92no—
319C4×Q8—181no—
320C4×D4—92no—
321C4×D4D3211yescharacteristic
322#107—32no—
323#106—31no—
324C4⋊C8—31no—
325C4⋊C8—92no—
326#103—31no—
327#102—31no—
328#102—32no—
329#102—92no—
330#102—92no—
331#102—92no—
332#97—92no—
333C4×C8—31no—
334C23×C3—22no—
335C23×C3—21no—
336C23×C3—21no—
337C22×D3—64no—
338C22×D3—62no—
339C22×D3—62no—
340C3×Q8—32no—
341C3×Q8—61no—
342C3×Q8—122no—
343C3×D4—21no—
344C3×D4—21no—
345C3×D4—21no—
346C3×D4—21no—
347C3×D4—41no—
348C3×D4—41no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—44no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—61no—
359C2×C3×C4—62no—
360C2×C3×C4—61no—
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367#67—128no—
368#67—124no—
369#67—124no—
370#67—242no—
371#67—242no—
372#67—244no—
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3—22no—
376C2×Dic3—32no—
377C2×Dic3—32no—
378C2×Dic3—32no—
379C2×Dic3—32no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382D12—62no—
383D12—62no—
384D12—62no—
385D12—62no—
386D12—122no—
387D12—122no—
388D12—124no—
389D12—122no—
390D12—122no—
391D12—241no—
392D12—241no—
393D12—242no—
394C4×D3—128no—
395C4×D3—124no—
396C4×D3—124no—
397Dic6—21no—
398Dic6—42no—
399Dic6—64no—
400Dic6—62no—
401Dic6—62no—
402Dic6#23512yescomplemented
403C3×C8—62no—
404C3×C8—61no—
405C3×C8—61no—
406C3⋊C8—21no—
407C3⋊C8—22no—
408C3⋊C8—21no—
409C2×C32—81no—
410C2×C32#54811yescharacteristic
411C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
412C2×C32#57711yescharacteristic
413C3⋊D3—82no—
414#41—364no—
415C2×Q8—31no—
416C2×Q8—61no—
417C2×Q8—91no—
418C2×D4—92no—
419C2×D4—182no—
420C2×D4—182no—
421C2×D4—181no—
422C2×D4—181no—
423C2×D4C2×D3211yescharacteristic
424C22×C4—21no—
425C22×C4—182no—
426SD16—62no—
427SD16—184no—
428C2×C8—31no—
429C2×C8—31no—
430C2×C8—32no—
431C4⋊C4—31no—
432C4⋊C4—32no—
433C4⋊C4—61no—
434C4⋊C4—61no—
435C4⋊C4—91no—
436C4⋊C4—92no—
437C4⋊C4—182no—
438C4⋊C4—182no—
439C4⋊C4—182no—
440C4⋊C4C2×D3211yescharacteristic
441C22⋊C4—21no—
442C22⋊C4—182no—
443C42—61no—
444C42—92no—
445C42—182no—
446C42C2×D3211yescharacteristic
447C22×C3—21no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—41no—
454C22×C3—41no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3C2×D3×D411yescharacteristic
458C22×C3C2×D3×D411yescharacteristic
459C2×D3—124no—
460C2×D3—124no—
461C2×D3—124no—
462C2×D3—122no—
463C2×D3—122no—
464C2×D3—122no—
465C2×D3—122no—
466C2×D3—122no—
467C2×D3—122no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—22no—
473C3×C4—41no—
474C3×C4—42no—
475C3×C4—41no—
476C3×C4—41no—
477C3×C4—62no—
478C3×C4—122no—
479C3×C4—121no—
480C3×C4#91112yes—
481C3×C4#91412yes—
482C3×C4C2×#23511yescharacteristic
483C3×C4#100711yescharacteristic
484C3×C4D3×#4111yescharacteristic
485C3×C4#101011yescharacteristic
486Dic3—22no—
487Dic3—42no—
488Dic3—41no—
489Dic3—64no—
490Dic3—62no—
491Dic3—62no—
492Dic3—62no—
493Dic3—62no—
494Dic3—122no—
495C32#336811yescharacteristic, complemented, Sylow
496C23—21no—
497C23—182no—
498Q8—32no—
499Q8—61no—
500Q8—122no—
501Q8—182no—
502D4—21no—
503D4—21no—
504D4—182no—
505D4—182no—
506D4—364no—
507D4—362no—
508D4—721no—
509D4—722no—
510C2×C4—21no—
511C2×C4—42no—
512C2×C4—61no—
513C2×C4—61no—
514C2×C4—62no—
515C2×C4—92no—
516C2×C4—92no—
517C2×C4—364no—
518C2×C4#381111yescharacteristic
519C2×C4#381111yescharacteristic
520C2×C4C22×D3211yescharacteristic
521C8—61no—
522C8—61no—
523C8—62no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—82no—
528C2×C3—81no—
529C2×C3—81no—
530C2×C3#555211yescharacteristic
531C2×C3#563311yescharacteristic
532C2×C3C2×#91111yescharacteristic
533C2×C3C2×#91411yescharacteristic
534C2×C3#577011yescharacteristic
535C2×C3#577811yescharacteristic
536D3—244no—
537D3—242no—
538D3—242no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—362no—
543C22—362no—
544C22—362no—
545C22C2×#381111yescharacteristic
546C4—21no—
547C4—41no—
548C4—62no—
549C4—122no—
550C4—121no—
551C4—182no—
552C4—182no—
553C4#6393712yes—
554C4#6429711yescharacteristic
555C4D3×#23511yescharacteristic
556C3—21no—
557C3#7962511yescharacteristic, complemented
558C3#8099511yescharacteristic, complemented
559C2—81no—
560C2—722no—
561C2#1059491611yescharacteristic
562C2C2×#6393711yescharacteristic
563C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radical#10596024C2
hypercenterC4×D4D32
hypocenterC32#3368
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
2. #10593861C2semidirect
3. C3×C4×#214C2semidirect
4. C3×#5007C2semidirect
5. #10591480C2semidirect
6. #10591444C2semidirect
7. #10590484C2semidirect
8. #10590435C2semidirect
9. #10590367C2semidirect
10. #10590296C2semidirect
11. #10590281C2semidirect
53. C4×#214D3semidirect
54. #5007D3semidirect
190. C3×Dic6#41semidirect
402. Dic6#235semidirect
495. C32#3368semidirect
557. C3#79625semidirect
558. C3#80995semidirect

Maximal subgroups

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

subgroupindex
#105960242
#105938612
C3×C4×#2142
C3×#50072
#105914802
#105914442
#105904842
#105904352
#105903672
#105902962
#105902812
#809953
#796253