Finite Group Databasebeta

← #11787650

Subgroups — #11787650

Order 1152.

699 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C211yesmaximal, characteristic, complemented
2#10594795C211yesmaximal, characteristic
3#10592828C211yesmaximal, characteristic, complemented
4#10591113C211yesmaximal, characteristic, complemented
5#10591083C211yesmaximal, characteristic, complemented
6C3×#4556C211yesmaximal, characteristic, complemented
7#10589165C211yesmaximal, characteristic, complemented
8#72020—31nomaximal
9#69035—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#907—22no—
18C3×D3×M16—22no—
19C3×#901—22no—
20#63833—21no—
21#63831C412yescomplemented
22#63830—21no—
23#63829—22no—
24#63825C412yescomplemented
25#63647—22no—
26#63570—22no—
27#63565—21no—
28#63562—21no—
29C3×#568—31no—
30#5822—31no—
31#5748—31no—
32#5745D311yescharacteristic, complemented
33#5233—31no—
34#5139—31no—
35#5129—31no—
36#5129—31no—
37#5129—61no—
38#5005—31no—
39#5002—31no—
40C3×#344—31no—
41#4558—31no—
42#4558—31no—
43#4556D311yescharacteristic, complemented
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46#3828—21no—
47#3828—21no—
48#3828—21no—
49#3828—21no—
50C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×#634C2×C411yescharacteristic
53C2×C3×#67—21no—
54C3×#235—21no—
55C3×#235—21no—
56C3×#235C2×C412yes—
57C3×#235D412yes—
58C2×C3×D12D411yescharacteristic
59C2×C3×C4×D3—21no—
60C2×C3×Dic6D411yescharacteristic
61C32×M16—21no—
62C32×M16—21no—
63C2×C32×C8D412yes—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C3×#217—21no—
68C3×C4⋊Dic3—21no—
69C3×C4×Dic3—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208C2×C412yes—
73C3×#208D412yes—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C3×ΓL(1,𝔽25)—24no—
77C3×D3×C8—24no—
78#3719—22no—
79#3717—22no—
80#3716—22no—
81#3714—22no—
82#1881—91noSylow
83C2×C3×#41—31no—
84C2×#235—31no—
85C2×#235—31no—
86C2×#235—61no—
87C2×#235C2×D311yescharacteristic
88C3×#131—62no—
89C3×#131—62no—
90C2×C3×M16—21no—
91C2×C3×M16—31no—
92C2×C3×M16—31no—
93C2×C3×M16—62no—
94C2×C3×M16C2×D311yescharacteristic
95C2×C3×M16C2×D311yescharacteristic
96C3×#117—31no—
97#951—32no—
98#950—62no—
99#949—32no—
100#942—61no—
101#932—61no—
102#926C2×D311yescharacteristic
103C2×#208C2×D311yescharacteristic
104C2×#208C2×D311yescharacteristic
105C22×C3⋊C8—31no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—61no—
108#909—32no—
109#909—61no—
110#908—32no—
111#908—61no—
112#907—22no—
113D3×M16—22no—
114#904—62no—
115#901—22no—
116#835—61no—
117#832—61no—
118#825—62no—
119(C2×D3)⋊C8—64no—
120(C2×D3)⋊C8—62no—
121(C2×D3)⋊C8—62no—
122#810—61no—
123#809—61no—
124#805—62no—
125C23×C32#4111yescharacteristic
126C22×C3⋊D3—21no—
127C22×C3×D3—21no—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4111yescharacteristic
134#638—41no—
135#638—41no—
136C2×C3⋊Dic3—21no—
137C4⋊(C3⋊D3)—21no—
138C4⋊(C3⋊D3)—21no—
139C4×C3⋊D3—41no—
140C4×C3⋊D3—41no—
141#634—21no—
142#634—21no—
143C3×#67—22no—
144C3×#67—22no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—41no—
147C3×D12—21no—
148C3×D12C22⋊C412yes—
149C3×C4×D3—22no—
150C3×C4×D3—22no—
151C3×Dic6—21no—
152C3×Dic6C22⋊C412yes—
153C32×C8—22no—
154C3⋊(C3⋊C8)—41no—
155C3×C3⋊C8—22no—
156C3×C3⋊C8—22no—
157#575—91no—
158#568—31no—
159#421—91no—
160#416—91no—
161#408—91no—
162#344—31no—
163#341—91no—
164C3×#41—32no—
165C3×#41—32no—
166C3×#41—61no—
167C3×#41—61no—
168C2×C3×Q8—31no—
169C2×C3×D4—31no—
170C2×C3×D4—61no—
171C22×C3×C4—21no—
172C22×C3×C4—61no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C2×#67—21no—
176C2×#67—62no—
177C2×#67—61no—
178C2×#67—61no—
179#235—21no—
180#235—21no—
181#235—61no—
182#235—61no—
183#235—61no—
184#235—61no—
185#235—61no—
186#235—61no—
187#235—61no—
188#235—61no—
189#235—121no—
190#235—121no—
191#235—121no—
192#235—121no—
193#235C4×D312yes—
194#235#6712yes—
195C2×D12—31no—
196C2×D12—31no—
197C2×D12—61no—
198C2×D12D1211yescharacteristic
199C2×C4×D3—21no—
200C2×C4×D3—62no—
201C2×C4×D3—61no—
202C2×C4×D3—61no—
203C2×Dic6—31no—
204C2×Dic6—31no—
205C2×Dic6—61no—
206C2×Dic6D1211yescharacteristic
207C3×M16—21no—
208C3×M16—21no—
209C3×M16—21no—
210C3×M16—21no—
211C3×M16—32no—
212C3×M16—32no—
213C3×M16—41no—
214C3×M16—41no—
215C3×M16—64no—
216C3×M16—61no—
217C3×M16—61no—
218C2×C3×C8—22no—
219C2×C3×C8—64no—
220C2×C3×C8—61no—
221C2×C3×C8—61no—
222C2×C3×C8D1212yes—
223C2×C3×C8#6712yes—
224C3×C4⋊C4—61no—
225C3×C22⋊C4—61no—
226C3×C42—61no—
227#217—21no—
228#216—62no—
229#215—62no—
230#214—62no—
231#213—62no—
232C4⋊Dic3—21no—
233C4×Dic3—21no—
234#208—21no—
235#208—21no—
236#208C4×D312yes—
237#208#6712yes—
238C2×C3⋊C8—21no—
239C2×C3⋊C8—21no—
240C2×C3⋊C8—62no—
241C2×C3⋊C8—61no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—121no—
248C2×C3⋊C8—121no—
249Dic12—62no—
250D24—62no—
251#204—62no—
252#204—62no—
253ΓL(1,𝔽25)—24no—
254D3×C8—24no—
255C22×C32—41no—
256C22×C32C4×D411yescharacteristic
257C22×C32#12111yescharacteristic
258C22×C32#12311yescharacteristic
259C2×C3⋊D3—42no—
260C2×C3⋊D3—41no—
261C2×C3×D3—22no—
262C2×C3×D3—81no—
263C32×C4C2×C22⋊C411yescharacteristic
264C32×C4C4×D411yescharacteristic
265C32×C4#12011yescharacteristic
266C32×C4#12111yescharacteristic
267C3⋊Dic3—41no—
268C3×Dic3—22no—
269C3×Dic3—81no—
270C2×#41—31no—
271C2×#41—91no—
272#137—92no—
273#137—181no—
274AGL(1,ℤ/8)—92no—
275AGL(1,ℤ/8)—181no—
276#135—182no—
277#131—62no—
278#131—62no—
279C2×M16—31no—
280C2×M16—31no—
281C2×M16—62no—
282C2×M16D3211yescharacteristic
283C22×C8—91no—
284#117—31no—
285#104—182no—
286#103—181no—
287#102—181no—
288C22⋊C8—182no—
289C23×C3—21no—
290C23×C3—61no—
291C23×C3#23511yescharacteristic
292C23×C3#23511yescharacteristic
293C22×D3—21no—
294C22×D3—62no—
295C22×D3—61no—
296C22×D3—61no—
297C3×Q8—32no—
298C3×Q8—61no—
299C3×D4—32no—
300C3×D4—62no—
301C3×D4—62no—
302C3×D4—61no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—61no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4—121no—
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×D1211yescharacteristic
316C2×C3×C4C2×D1211yescharacteristic
317C2×C3×C4#23511yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4#23911yescharacteristic
322C2×C3×C4C2×#6711yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325#67—22no—
326#67—22no—
327#67—122no—
328#67—122no—
329#67—121no—
330#67—121no—
331#67—121no—
332#67—121no—
333C2×Dic3—21no—
334C2×Dic3—41no—
335C2×Dic3—62no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338D12—21no—
339D12—61no—
340D12—61no—
341D12—61no—
342D12—61no—
343D12—121no—
344D12—121no—
345D12(C2×D3)⋊C412yes—
346C4×D3—22no—
347C4×D3—22no—
348C4×D3—122no—
349C4×D3—122no—
350C4×D3—121no—
351C4×D3—121no—
352C4×D3—121no—
353C4×D3—121no—
354Dic6—21no—
355Dic6—61no—
356Dic6—61no—
357Dic6—61no—
358Dic6—61no—
359Dic6—121no—
360Dic6—121no—
361Dic6(C2×D3)⋊C412yes—
362C3×C8—22no—
363C3×C8—22no—
364C3×C8—42no—
365C3×C8—62no—
366C3×C8—62no—
367C3⋊C8—22no—
368C3⋊C8—22no—
369C3⋊C8—122no—
370C3⋊C8—121no—
371C3⋊C8—121no—
372C2×C32—21no—
373C2×C32—21no—
374C2×C32—21no—
375C2×C32#38611yescharacteristic
376C3⋊D3—81no—
377C3×D3—42no—
378#41—32no—
379#41—32no—
380#41—61no—
381#41—61no—
382#41—181no—
383#41—181no—
384#41—181no—
385#41—181no—
386C2×Q8—31no—
387C2×Q8—91no—
388C2×D4—31no—
389C2×D4—61no—
390C2×D4—91no—
391C2×D4—181no—
392C22×C4—61no—
393C22×C4—181no—
394C22×C4C2×D3211yescharacteristic
395Q16—182no—
396SD16—182no—
397SD16—182no—
398D8—182no—
399M16—21no—
400M16—21no—
401M16—32no—
402M16—32no—
403M16—64no—
404M16—61no—
405M16—61no—
406C2×C8—64no—
407C2×C8—61no—
408C2×C8—61no—
409C2×C8—181no—
410C2×C8—181no—
411C2×C8—181no—
412C2×C8#62612yes—
413C4⋊C4—61no—
414C22⋊C4—61no—
415C42—61no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—42no—
422C22×C3—62no—
423C22×C3—241no—
424C22×C3C4×D1211yescharacteristic
425C22×C3#88411yescharacteristic
426C22×C3#89411yescharacteristic
427C22×C3C4×#6711yescharacteristic
428C22×C3#92911yescharacteristic
429C22×C3#93011yescharacteristic
430C2×D3—22no—
431C2×D3—81no—
432C2×D3—122no—
433C2×D3—124no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—121no—
437C2×D3—121no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—62no—
443C3×C4—241no—
444C3×C4D3×C22⋊C411yescharacteristic
445C3×C4#88211yescharacteristic
446C3×C4#89311yescharacteristic
447C3×C4#89511yescharacteristic
448C3×C4C2×(C2×D3)⋊C411yescharacteristic
449C3×C4C4×#6711yescharacteristic
450C3×C4#93011yescharacteristic
451C3×C4#95311yescharacteristic
452Dic3—22no—
453Dic3—81no—
454Dic3—122no—
455Dic3—121no—
456Dic3—121no—
457C32#188111yescharacteristic, complemented, Sylow
458C23—61no—
459C23—181no—
460C23#379811yescharacteristic
461Q8—32no—
462Q8—61no—
463Q8—181no—
464Q8—181no—
465D4—32no—
466D4—62no—
467D4—62no—
468D4—61no—
469D4—181no—
470D4—181no—
471D4—361no—
472D4—361no—
473C2×C4—61no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—121no—
477C2×C4—181no—
478C2×C4—361no—
479C2×C4—361no—
480C2×C4#379911yescharacteristic
481C2×C4C4×D3211yescharacteristic
482C2×C4D3×D1211yescharacteristic
483C2×C4C2×#62611yescharacteristic
484C2×C4D3×#6711yescharacteristic
485C2×C4D3×#6711yescharacteristic
486C8—22no—
487C8—62no—
488C8—62no—
489C8—361no—
490C2×C3—22no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—41no—
499C2×C3—41no—
500C2×C3—122no—
501C2×C3#466511yescharacteristic
502C2×C3#521311yescharacteristic
503D3—42no—
504D3—242no—
505D3—241no—
506D3—241no—
507C22—41no—
508C22—62no—
509C22—241no—
510C22—362no—
511C22—361no—
512C22#6385011yescharacteristic
513C22C4×#62611yescharacteristic
514C22#6390611yescharacteristic
515C4—62no—
516C4—241no—
517C4—361no—
518C4#6390411yescharacteristic
519C4#6390911yescharacteristic
520C4D3×(C2×D3)⋊C411yescharacteristic
521C4#6397711yescharacteristic
522C3—21no—
523C3#6903511yescharacteristic, complemented
524C3#7202011yescharacteristic, complemented
525C2—21no—
526C2—21no—
527C2—21no—
528C2—122no—
529C2—721no—
530C2#1059138211yescharacteristic
subgroupG/H
centerC4#63977
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radical#10594795C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1881
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C3×#5745C2semidirect
3. #10592828C2semidirect
4. #10591113C2semidirect
5. #10591083C2semidirect
6. C3×#4556C2semidirect
7. #10589165C2semidirect
21. #63831C4semidirect
24. #63825C4semidirect
32. #5745D3semidirect
43. #4556D3semidirect
457. C32#1881semidirect
523. C3#69035semidirect
524. C3#72020semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
#105947952
#105928282
#105911132
#105910832
C3×#45562
#105891652
#720203
#690353