Finite Group Databasebeta

← #11786590

Subgroups — #11786590

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594996C211yesmaximal, characteristic
2C2×#63650C211yesmaximal, characteristic
3C3×#5121C211yesmaximal, characteristic, complemented
4#10591320C211yesmaximal, characteristic
5#10591139C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70674—31nomaximal
9#68758—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17#63974—22no—
18C2×#3722—22no—
19#63894—21no—
20#63894—21no—
21#63894—21no—
22#63894—21no—
23#63650C414yescomplemented
24C3×#818—21no—
25C3×#817—21no—
26#63576—21no—
27#63574—21no—
28#5521—31no—
29#5521—31no—
30C3×#428—31no—
31C2×#823—31no—
32C2×#823—31no—
33C2×#823—61no—
34#5121D311yescharacteristic, complemented
35#4995—31no—
36#4988—31no—
37#4964—31no—
38#4939—31no—
39C3×#339—31no—
40#4555D311yescharacteristic, complemented
41#4532—31no—
42#4523—31no—
43C23×C3⋊D3D412yes—
44C22×C32×C4C2311yescharacteristic
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)C2×C412yes—
50C2×C4⋊(C3⋊D3)Q812yes—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C2×#624—22no—
54C2×#624—22no—
55C32×M16—21no—
56C32×M16C2×C412yescomplemented
57C2×C32×C8—21no—
58#3748—21no—
59#3748C2×C412yescomplemented
60C2×C3⋊(C3⋊C8)—21no—
61C3×#217—21no—
62C3×#217—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×C4⋊Dic3D411yescharacteristic
67C3×C4⋊Dic3D411yescharacteristic
68C3×C4⋊Dic3D411yescharacteristic
69C3×C4×Dic3—21no—
70C3×C4×Dic3—21no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3—21no—
73#3722—22no—
74#3722—22no—
75#3722—44no—
76#1856—91noSylow
77C22×D12—31no—
78C22×D12—31no—
79C22×D12—61no—
80C2×C3×M16—21no—
81C2×C3×M16C2×D311yescharacteristic
82C2×C3×M16C2×D311yescharacteristic
83C3×#117—31no—
84C3×#117—31no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C42—31no—
87C2×(C2×D3)⋊C4—62no—
88C2×(C2×D3)⋊C4—62no—
89#926C2×D311yescharacteristic
90#926C2×D311yescharacteristic
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×C4×Dic3C2×D311yescharacteristic
93C2×#208—31no—
94C2×#208—31no—
95C2×#208—61no—
96#893—61no—
97#893—61no—
98#893—61no—
99#893—61no—
100D3×C22⋊C4—62no—
101D3×C22⋊C4—62no—
102C4×D12—61no—
103C4×D12—61no—
104C4×D12—61no—
105C4×D12—61no—
106C3×#107—61no—
107C3×#106—61no—
108#823—34no—
109#823—34no—
110#823—64no—
111#818—21no—
112#817—21no—
113#808—61no—
114#808—61no—
115#807—61no—
116#807—61no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—22no—
119C22×C3⋊D3—22no—
120C22×C3⋊D3—42no—
121C22×C3⋊D3—42no—
122C22×C3⋊D3C4⋊C414yes—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×Q811yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C4⋊(C3⋊D3)—22no—
130C4⋊(C3⋊D3)—22no—
131C4⋊(C3⋊D3)—22no—
132C4⋊(C3⋊D3)—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—41no—
142#624—82no—
143#624—82no—
144C32×C8—22no—
145C3⋊(C3⋊C8)—22no—
146#518—91no—
147#428—31no—
148#428—91no—
149C2×#100—91no—
150#390—91no—
151#339—31no—
152#339—91no—
153C23×D3—32no—
154C23×D3—32no—
155C23×D3—62no—
156C22×C3×C4—21no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×Dic3—21no—
162C22×Dic3—21no—
163C2×D12—32no—
164C2×D12—32no—
165C2×D12—32no—
166C2×D12—32no—
167C2×D12—62no—
168C2×D12—62no—
169C2×D12—61no—
170C2×D12—61no—
171C2×D12—61no—
172C2×D12—61no—
173C2×D12—61no—
174C2×D12—61no—
175C2×D12—61no—
176C2×D12—61no—
177C2×D12—121no—
178C2×D12—121no—
179C2×D12—121no—
180C2×D12—121no—
181C2×C4×D3—62no—
182C2×C4×D3—62no—
183C2×C4×D3—62no—
184C2×C4×D3—62no—
185C3×M16—21no—
186C3×M16—21no—
187C3×M16—22no—
188C3×M16—41no—
189C3×M16C4×D312yescomplemented
190C3×M16C4×D312yescomplemented
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—41no—
194C3×C4⋊C4—31no—
195C3×C4⋊C4—31no—
196C3×C4⋊C4—31no—
197C3×C4⋊C4—31no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—61no—
200C3×C22⋊C4—61no—
201C3×C22⋊C4—61no—
202C3×C42—61no—
203C3×C42—61no—
204C3×C42—61no—
205C3×C42—61no—
206#217—21no—
207#217—21no—
208(C2×D3)⋊C4—62no—
209(C2×D3)⋊C4—62no—
210(C2×D3)⋊C4—62no—
211(C2×D3)⋊C4—62no—
212(C2×D3)⋊C4—124no—
213(C2×D3)⋊C4—124no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3D1211yescharacteristic
217C4⋊Dic3D1211yescharacteristic
218C4⋊Dic3#6711yescharacteristic
219C4⋊Dic3#6711yescharacteristic
220C4×Dic3—21no—
221C4×Dic3—21no—
222C4×Dic3—21no—
223C4×Dic3—21no—
224#208—32no—
225#208—32no—
226#208—62no—
227#208—61no—
228#208—61no—
229#208—121no—
230C2×C3⋊C8—61no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8—121no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32C2×C4⋊C411yescharacteristic
236C22×C32#12011yescharacteristic
237C22×C32#12311yescharacteristic
238C2×C3⋊D3—24no—
239C2×C3⋊D3—42no—
240C2×C3⋊D3—42no—
241C2×C3⋊D3—44no—
242C2×C3⋊D3—82no—
243C32×C4C4×D411yescharacteristic
244C32×C4C4×D411yescharacteristic
245C32×C4C22⋊Q811yescharacteristic
246C32×C4C22⋊Q811yescharacteristic
247C3×Dic3—42no—
248C3×Dic3—41no—
249C3×Dic3—41no—
250C3×Dic3—41no—
251C3×Dic3—41no—
252C3×Dic3—81no—
253C22×D4—91no—
254C2×M16—91no—
255C2×M16D3211yescharacteristic
256C4×D4—181no—
257C4×D4—181no—
258C4×D4—181no—
259C4×D4—181no—
260#117—31no—
261#117—31no—
262C2×C4⋊C4—31no—
263C2×C22⋊C4—182no—
264C2×C22⋊C4—182no—
265C2×C42—31no—
266#107—61no—
267#107—181no—
268#106—61no—
269#106—181no—
270#100—94no—
271C23×C3—21no—
272C23×C3D3×D411yescharacteristic
273C23×C3D3×D411yescharacteristic
274C22×D3—34no—
275C22×D3—34no—
276C22×D3—64no—
277C22×D3—62no—
278C22×D3—62no—
279C22×D3—62no—
280C22×D3—62no—
281C22×D3—122no—
282C22×D3—122no—
283C22×D3—122no—
284C22×D3—122no—
285C22×D3—122no—
286C22×D3—122no—
287C22×D3—242no—
288C22×D3—242no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—62no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—61no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4—122no—
303C2×C3×C4—121no—
304C2×C3×C4C2×C4×D311yescharacteristic
305C2×C3×C4C2×C4×D311yescharacteristic
306C2×C3×C4C2×D1211yescharacteristic
307C2×C3×C4#23511yescharacteristic
308C2×C3×C4#23511yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4#23711yescharacteristic
312C2×C3×C4D3×Q811yescharacteristic
313C2×C3×C4D3×Q811yescharacteristic
314C2×C3×C4#23911yescharacteristic
315C2×C3×C4C2×#6711yescharacteristic
316C2×Dic3—22no—
317C2×Dic3—21no—
318C2×Dic3—21no—
319C2×Dic3—21no—
320C2×Dic3—21no—
321C2×Dic3—41no—
322C2×Dic3—41no—
323C2×Dic3—42no—
324C2×Dic3—41no—
325D12—62no—
326D12—62no—
327D12—62no—
328D12—62no—
329D12—62no—
330D12—62no—
331D12—62no—
332D12—62no—
333D12—122no—
334D12—122no—
335D12—122no—
336D12—122no—
337C4×D3—242no—
338C4×D3—242no—
339C4×D3—242no—
340C4×D3—242no—
341C3×C8—22no—
342C3×C8—22no—
343C3×C8—42no—
344C3⋊C8—62no—
345C3⋊C8—62no—
346C3⋊C8—122no—
347C2×C32—21no—
348C2×C32—21no—
349C2×C32#38511yescharacteristic
350C2×C32#45311yescharacteristic
351C2×C32#45511yescharacteristic
352C3⋊D3—44no—
353C24—92no—
354C2×D4—92no—
355C2×D4—92no—
356C2×D4—181no—
357C2×D4—181no—
358C2×D4—181no—
359C2×D4—181no—
360C22×C4—61no—
361C22×C4—61no—
362C22×C4—182no—
363C22×C4—182no—
364C22×C4C2×D3211yescharacteristic
365M16—21no—
366M16—92no—
367M16—181no—
368M16#62412yescomplemented
369C2×C8—21no—
370C2×C8—181no—
371C4⋊C4—31no—
372C4⋊C4—31no—
373C4⋊C4—31no—
374C4⋊C4—31no—
375C4⋊C4—61no—
376C4⋊C4—61no—
377C22⋊C4—61no—
378C22⋊C4—61no—
379C22⋊C4—182no—
380C22⋊C4—182no—
381C22⋊C4—364no—
382C42—61no—
383C42—61no—
384C42—61no—
385C42—61no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—41no—
394C22×C3—41no—
395C22×C3#88211yescharacteristic
396C22×C3#88311yescharacteristic
397C22×C3D3×C4⋊C411yescharacteristic
398C22×C3D3×C4⋊C411yescharacteristic
399C22×C3#89411yescharacteristic
400C22×C3#93711yescharacteristic
401C2×D3—64no—
402C2×D3—64no—
403C2×D3—124no—
404C2×D3—122no—
405C2×D3—122no—
406C2×D3—122no—
407C2×D3—122no—
408C2×D3—124no—
409C2×D3—124no—
410C2×D3—242no—
411C2×D3—242no—
412C2×D3—244no—
413C2×D3—242no—
414C2×D3—242no—
415C2×D3—244no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—122no—
421C3×C4—121no—
422C3×C4—121no—
423C3×C4—121no—
424C3×C4—121no—
425C3×C4—241no—
426C3×C4C4×D1211yescharacteristic
427C3×C4#67⋊C411yescharacteristic
428C3×C4#89311yescharacteristic
429C3×C4#89611yescharacteristic
430C3×C4#89611yescharacteristic
431C3×C4#89711yescharacteristic
432C3×C4C4×#6711yescharacteristic
433C3×C4#94611yescharacteristic
434Dic3—42no—
435Dic3—41no—
436Dic3—41no—
437Dic3—41no—
438Dic3—41no—
439Dic3—81no—
440C32#185611yescharacteristic, complemented, Sylow
441C23—94no—
442C23—182no—
443C23—182no—
444C23—362no—
445C23—362no—
446C23#380211yescharacteristic
447D4—182no—
448D4—182no—
449D4—182no—
450D4—182no—
451C2×C4—62no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—121no—
457C2×C4—121no—
458C2×C4—122no—
459C2×C4—121no—
460C2×C4—722no—
461C2×C4—722no—
462C2×C4#379711yescharacteristic
463C2×C4#379911yescharacteristic
464C2×C4D3×D1211yescharacteristic
465C2×C4#380411yescharacteristic
466C2×C4C2×#62411yescharacteristic
467C2×C4D3×#6711yescharacteristic
468C8—22no—
469C8—182no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—41no—
478C2×C3—41no—
479C2×C3#466811yescharacteristic
480C2×C3#482211yescharacteristic
481C2×C3#482511yescharacteristic
482C2×C3#498911yescharacteristic
483C2×C3#519811yescharacteristic
484C2×C3#520211yescharacteristic
485D3—124no—
486D3—124no—
487D3—244no—
488C22—21no—
489C22—21no—
490C22—184no—
491C22—364no—
492C22—362no—
493C22—362no—
494C22—722no—
495C22#6385411yescharacteristic
496C22#6390011yescharacteristic
497C22#6392211yescharacteristic
498C4—122no—
499C4—121no—
500C4—121no—
501C4—121no—
502C4—121no—
503C4—241no—
504C4#6388811yescharacteristic
505C4#6389411yescharacteristic
506C4#6389511yescharacteristic
507C4#6395211yescharacteristic
508C3—21no—
509C3#6875811yescharacteristic, complemented
510C3#7067411yescharacteristic, complemented
511C2—21no—
512C2—21no—
513C2—364no—
514C2#1059101111yescharacteristic
515C2#1059101311yescharacteristic
516C2#1059137811yescharacteristic
subgroupG/H
centerC22#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1856
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C3×#5121C2semidirect
5. #10591139C2semidirect
6. C3×#4555C2semidirect
7. #10589161C2semidirect
23. #63650C4semidirect
34. #5121D3semidirect
40. #4555D3semidirect
56. C32×M16C2×C4semidirect
59. #3748C2×C4semidirect
189. C3×M16C4×D3semidirect
190. C3×M16C4×D3semidirect
368. M16#624semidirect
440. C32#1856semidirect
509. C3#68758semidirect
510. C3#70674semidirect

Maximal subgroups

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

subgroupindex
#105949962
C2×#636502
C3×#51212
#105913202
#105911392
C3×#45552
#105891612
#706743
#687583