Finite Group Databasebeta

← #11895964

Subgroups — #11895964

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5553C211yesmaximal, characteristic
2#10593864C211yesmaximal, characteristic, complemented
3C4×#3754C211yesmaximal, characteristic, complemented
4C3×#5007C211yesmaximal, characteristic, complemented
5#10591477C212yesmaximal, complemented
6#10591439C212yesmaximal, complemented
7#10590590C212yesmaximal, complemented
8#10590542C212yesmaximal, complemented
9#10590377C211yesmaximal, characteristic, complemented
10#10590277C211yesmaximal, characteristic, complemented
11#10590259C211yesmaximal, characteristic, complemented
12#83587—31nomaximal
13#80995—31nomaximal
14C2×C3×#235—21no—
15C32×C4×D4C2211yescharacteristic
16C2×#3754C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C3×#940C2212yes—
19C3×#930—21no—
20C3×#893C2212yes—
21C3×#884—22no—
22C3×#874C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63873—21no—
26#63869C2212yes—
27#63847—22no—
28#63844C2212yes—
29#63843—21no—
30C2×#3716C2212yes—
31#63659C2211yescharacteristic
32#63637C2211yescharacteristic
33#63635C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#832C2212yes—
36C3×#807C2212yes—
37C3×C4⋊(C3⋊C8)C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63563C2212yes—
40#63562C2212yes—
41#63562C2212yes—
42#63554C2212yes—
43C3×#550—31no—
44#5721—31no—
45#5567—31no—
46#5553D311yescharacteristic
47C3×#474—31no—
48#5088—31no—
49#5075—32no—
50#5075—31no—
51#5071—32no—
52#5070—31no—
53#5024—31no—
54#5018—32no—
55C4×#214—31no—
56C4×#214—31no—
57C4×#214—61no—
58#5009—32no—
59#5007D311yescharacteristic, complemented
60#4891—32no—
61#4889—32no—
62#4848—31no—
63#4831—31no—
64#4764—32no—
65#4762—32no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634C2311yescharacteristic
69C2×C3×#67—22no—
70C2×C3×#67—22no—
71C3×#235—44no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×C4×D3—22no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6D411yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80C32×C42C2311yescharacteristic
81#3754—22no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—21no—
84C4×C3⋊Dic3—21no—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
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—
95#3724—22no—
96Dic3⋊Dic3—22no—
97Dic32—22no—
98#3716—24no—
99#3368—91noSylow
100C2×C3×#41—61no—
101C2×#235—21no—
102C3×C4⋊Q8—31no—
103C3×#127—32no—
104C3×#127—31no—
105C3×#121—62no—
106C3×#121—61no—
107C3×C4×Q8—31no—
108C3×C4×D4—21no—
109C3×C4×D4—32no—
110C3×C4×D4C2×D311yescharacteristic
111C3×C4×D4C2×D311yescharacteristic
112Q8×Dic3—61no—
113#944—61no—
114#944—61no—
115#940C2×D312yes—
116C2×#214—31no—
117C2×#214—31no—
118C2×#214—32no—
119C2×#214—61no—
120#930—21no—
121C2×#204—32no—
122#893C2×D312yes—
123#890—32no—
124#889—62no—
125#889—62no—
126#887—32no—
127#887—61no—
128#884—22no—
129#874C2×D311yescharacteristic
130#870—32no—
131#869C2×D311yescharacteristic
132C4×Dic6—31no—
133C4×Dic6—31no—
134C4×Dic6—32no—
135C4×Dic6—61no—
136C4×Dic6C2×D311yescharacteristic
137C3×#107—32no—
138C3×C4⋊C8—31no—
139C3×#102—32no—
140#832—31no—
141#832—31no—
142#832—32no—
143#832—32no—
144#832—32no—
145#832—61no—
146#832C2×D312yes—
147#821—32no—
148#815—32no—
149Dic3⋊C8—32no—
150#810—31no—
151#810—31no—
152#810—61no—
153#809—32no—
154#809—32no—
155#808—31no—
156#808—31no—
157#808—61no—
158#807C2×D312yes—
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—22no—
167C32×D4—21no—
168C32×D4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—42no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176#634—21no—
177#634#4112yescomplemented
178C3×#67—44no—
179C3×#67—82no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3C2×D412yes—
183C3×D12—22no—
184C3×D12—22no—
185C3×D12—42no—
186C3×D12—81no—
187C3×C4×D3—44no—
188C3×Dic6—22no—
189C3×Dic6—42no—
190C3⋊(C3⋊C8)—21no—
191C3⋊(C3⋊C8)—21no—
192C3×C3⋊C8—22no—
193#557—91no—
194#550—31no—
195#490—92no—
196#486—91no—
197#478—92no—
198#474—31no—
199#460—92no—
200#460—91no—
201#446—91no—
202#440—92no—
203C4×SD16—91no—
204C3×#41—124no—
205C2×C3×Q8—31no—
206C2×C3×Q8—61no—
207C2×C3×D4—21no—
208C2×C3×D4—32no—
209C2×C3×D4—62no—
210C2×C3×D4—62no—
211C2×C3×D4—61no—
212C2×C3×D4—61no—
213C2×C3×D4C22×D311yescharacteristic
214C2×C3×D4C22×D311yescharacteristic
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—41no—
218C22×C3×C4—62no—
219C2×#67—22no—
220C2×#67—22no—
221#235—44no—
222C2×D12—21no—
223C2×D12—21no—
224C2×D12C22×D312yes—
225C2×C4×D3—22no—
226C2×Dic6—21no—
227C2×Dic6—31no—
228C2×Dic6—31no—
229C2×Dic6—61no—
230C2×Dic6#6711yescharacteristic
231C2×C3×C8—32no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4C22×D311yescharacteristic
238C3×C4⋊C4C22×D311yescharacteristic
239C3×C22⋊C4—21no—
240C3×C22⋊C4—21no—
241C3×C22⋊C4—41no—
242C3×C22⋊C4—62no—
243C3×C42—21no—
244C3×C42—32no—
245C3×C42C22×D311yescharacteristic
246C3×C42C22×D311yescharacteristic
247#214—64no—
248#214—62no—
249#214—62no—
250#214—64no—
251(C2×D3)⋊C4—22no—
252C4⋊Dic3—21no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—61no—
256C4⋊Dic3—62no—
257C4⋊Dic3#6711yescharacteristic
258C4⋊Dic3C22×D312yes—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—61no—
263Dic3⋊C4—61no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—121no—
267Dic3⋊C4#6712yes—
268C4×Dic3—62no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271C4×Dic3—62no—
272C4×Dic3—121no—
273C4×Dic3C22×D312yes—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—31no—
278C2×C3⋊C8—61no—
279C2×C3⋊C8—61no—
280C2×C3⋊C8C22×D312yes—
281#204—64no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32C22×D411yescharacteristic
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C32×C4—21no—
290C32×C4—41no—
291C32×C4AGL(1,ℤ/8)12yes—
292C32×C4C2×#4111yescharacteristic
293C32×C42−1+411yescharacteristic
294C3⋊Dic3—22no—
295C3⋊Dic3—41no—
296C3×Dic3—22no—
297C3×Dic3—22no—
298C3×Dic3—42no—
299C2×#41—61no—
300C2×SD16—92no—
301C2×SD16—91no—
302C4⋊Q8—31no—
303C4⋊Q8—181no—
304#127—32no—
305#127—31no—
306#125—92no—
307#125—182no—
308#121—62no—
309#121—61no—
310C4×Q8—31no—
311C4×Q8—92no—
312C4×Q8—91no—
313C4×Q8—181no—
314C4×D4—32no—
315C4×D4D3211yescharacteristic
316#107—32no—
317#106—91no—
318C4⋊C8—31no—
319C4⋊C8—92no—
320#103—91no—
321#102—32no—
322#102—92no—
323#102—92no—
324#102—92no—
325#102—91no—
326#97—92no—
327C4×C8—91no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—41no—
331C23×C3—62no—
332C22×D3—22no—
333C3×Q8—62no—
334C3×Q8—122no—
335C3×D4—22no—
336C3×D4—21no—
337C3×D4—21no—
338C3×D4—21no—
339C3×D4—21no—
340C3×D4—41no—
341C3×D4—62no—
342C3×D4—62no—
343C3×D4—124no—
344C3×D4—122no—
345C3×D4—241no—
346C3×D4—242no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—32no—
353C2×C3×C4—32no—
354C2×C3×C4—41no—
355C2×C3×C4—42no—
356C2×C3×C4—42no—
357C2×C3×C4—62no—
358C2×C3×C4—82no—
359C2×C3×C4—124no—
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366#67—44no—
367#67—82no—
368C2×Dic3—22no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—121no—
374C2×Dic3—121no—
375C2×Dic3C2×#6712yes—
376C2×Dic3C2×#6712yes—
377D12—22no—
378D12—22no—
379D12—42no—
380D12—81no—
381C4×D3—44no—
382Dic6—22no—
383Dic6—32no—
384Dic6—32no—
385Dic6—42no—
386Dic6—62no—
387Dic6—61no—
388Dic6—61no—
389Dic6—121no—
390C3×C8—62no—
391C3⋊C8—22no—
392C3⋊C8—62no—
393C3⋊C8—61no—
394C3⋊C8—61no—
395C3⋊C8—61no—
396C3⋊C8—61no—
397C3⋊C8—121no—
398C2×C32—81no—
399C2×C32#54811yescharacteristic
400C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
401C2×C32#57711yescharacteristic
402C3×D3—82no—
403#41—124no—
404C2×Q8—31no—
405C2×Q8—61no—
406C2×Q8—91no—
407C2×D4—32no—
408C2×D4—62no—
409C2×D4—62no—
410C2×D4—61no—
411C2×D4—61no—
412C2×D4C2×D3211yescharacteristic
413C22×C4—21no—
414C22×C4—62no—
415SD16—184no—
416SD16—182no—
417C2×C8—32no—
418C2×C8—91no—
419C2×C8—91no—
420C4⋊C4—31no—
421C4⋊C4—32no—
422C4⋊C4—32no—
423C4⋊C4—61no—
424C4⋊C4—91no—
425C4⋊C4—182no—
426C4⋊C4—182no—
427C4⋊C4—182no—
428C4⋊C4—181no—
429C4⋊C4C2×D3211yescharacteristic
430C22⋊C4—21no—
431C22⋊C4—62no—
432C42—32no—
433C42—182no—
434C42—181no—
435C42C2×D3211yescharacteristic
436C22×C3—21no—
437C22×C3—42no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—81no—
445C22×C3—81no—
446C22×C3—122no—
447C22×C3—122no—
448C22×C3—122no—
449C22×C3C2×D3×D411yescharacteristic
450C22×C3C22×#6711yescharacteristic
451C2×D3—42no—
452C2×D3—42no—
453C2×D3—42no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—22no—
459C3×C4—41no—
460C3×C4—41no—
461C3×C4—41no—
462C3×C4—62no—
463C3×C4—62no—
464C3×C4—81no—
465C3×C4—122no—
466C3×C4#91112yes—
467C3×C4#93212yes—
468C3×C4#100711yescharacteristic
469C3×C4D3×#4111yescharacteristic
470C3×C4D3×#4111yescharacteristic
471C3×C4#101011yescharacteristic
472Dic3—22no—
473Dic3—22no—
474Dic3—42no—
475Dic3—62no—
476Dic3—62no—
477Dic3—122no—
478Dic3—121no—
479Dic3—121no—
480Dic3—241no—
481C32#336811yescharacteristic, complemented, Sylow
482C23—21no—
483C23—62no—
484Q8—62no—
485Q8—92no—
486Q8—122no—
487Q8—181no—
488D4—21no—
489D4—21no—
490D4—62no—
491D4—62no—
492D4—124no—
493D4—122no—
494D4—241no—
495D4—242no—
496C2×C4—21no—
497C2×C4—32no—
498C2×C4—32no—
499C2×C4—42no—
500C2×C4—62no—
501C2×C4—124no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4D3×#6711yescharacteristic
505C2×C4D3×#6711yescharacteristic
506C2×C4C22×D3211yescharacteristic
507C8—62no—
508C8—181no—
509C8—181no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—82no—
514C2×C3—81no—
515C2×C3—81no—
516C2×C3—242no—
517C2×C3#563311yescharacteristic
518C2×C3C2×#91111yescharacteristic
519C2×C3#577811yescharacteristic
520C2×C3C2×#93211yescharacteristic
521C2×C3#583111yescharacteristic
522C2×C3#583611yescharacteristic
523D3—82no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—122no—
528C22—122no—
529C22—122no—
530C22C2×D3×#6711yescharacteristic
531C4—21no—
532C4—41no—
533C4—62no—
534C4—62no—
535C4—122no—
536C4—182no—
537C4—361no—
538C4#6393212yes—
539C4#6429711yescharacteristic
540C4#6430611yescharacteristic
541C3—21no—
542C3#8099511yescharacteristic, complemented
543C3#8358711yescharacteristic, complemented
544C2—81no—
545C2—242no—
546C2#1059483011yescharacteristic
547C2C2×#6393211yescharacteristic
548C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5553C2
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. #10593864C2semidirect
3. C4×#3754C2semidirect
4. C3×#5007C2semidirect
5. #10591477C2semidirect
6. #10591439C2semidirect
7. #10590590C2semidirect
8. #10590542C2semidirect
9. #10590377C2semidirect
10. #10590277C2semidirect
11. #10590259C2semidirect
59. #5007D3semidirect
177. #634#41semidirect
481. C32#3368semidirect
542. C3#80995semidirect
543. C3#83587semidirect

Maximal subgroups

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

subgroupindex
C3×#55532
#105938642
C4×#37542
C3×#50072
#105914772
#105914392
#105905902
#105905422
#105903772
#105902772
#105902592
#835873
#809953