Finite Group Databasebeta

← #11787649

Subgroups — #11787649

Order 1152.

749 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596216C211yesmaximal, characteristic, complemented
2#10594795C211yesmaximal, characteristic
3C3×#5129C211yesmaximal, characteristic, complemented
4#10591111C211yesmaximal, characteristic, complemented
5#10591105C211yesmaximal, characteristic, complemented
6C3×#4556C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70012—31nomaximal
9#69035—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14#64116—22no—
15M16×C3⋊D3—22no—
16#64110—22no—
17C3×#926C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20#63833C412yescomplemented
21#63831—21no—
22#63830C412yescomplemented
23#63829—22no—
24#63825—21no—
25C3×(C2×D3)⋊C8—22no—
26#63569—22no—
27#63567—21no—
28#63564—21no—
29#5822—31no—
30#5748—31no—
31#5745—31no—
32#5745—31no—
33#5745—61no—
34C3×#408—31no—
35#5236—31no—
36#5129D311yescharacteristic, complemented
37#5113—31no—
38#5005—31no—
39#5002—31no—
40C3×#344—31no—
41#4558—31no—
42#4556D311yescharacteristic, complemented
43#4552—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46#3828—21no—
47#3828—21no—
48#3828C2×C412yes—
49#3828D412yes—
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×#634D411yescharacteristic
53C2×C3×#67—21no—
54C3×#235—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235—21no—
58C2×C3×D12C2×C411yescharacteristic
59C2×C3×C4×D3—21no—
60C2×C3×Dic6C2×C411yescharacteristic
61C32×M16—21no—
62C32×M16—21no—
63C2×C32×C8D412yes—
64#3748—21no—
65#3748D412yes—
66C2×C3⋊(C3⋊C8)—21no—
67#3743—24no—
68C8×C3⋊D3—24no—
69C3×#217—21no—
70C3×C4⋊Dic3—21no—
71C3×C4×Dic3—21no—
72C3×#208—21no—
73C3×#208C2×C412yes—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
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
88C2×C3×M16—21no—
89C2×C3×M16—31no—
90C2×C3×M16C2×D311yescharacteristic
91C2×C3×M16C2×D311yescharacteristic
92C22×C3×C8—31no—
93C3×#117—31no—
94#951—61no—
95#950—62no—
96#949—61no—
97#942—32no—
98#932—32no—
99#926C2×D311yescharacteristic
100C2×#208—31no—
101C2×#208—31no—
102C2×#208—61no—
103C2×#208C2×D311yescharacteristic
104C22×C3⋊C8C2×D311yescharacteristic
105#909—32no—
106#909—61no—
107#908—32no—
108#908—61no—
109#907—62no—
110#907—62no—
111#907—64no—
112D3×M16—62no—
113D3×M16—62no—
114D3×M16—64no—
115#904—62no—
116#901—64no—
117#901—62no—
118#901—62no—
119C3×C22⋊C8—62no—
120#837—62no—
121#821—61no—
122(C2×D3)⋊C8—22no—
123#816—61no—
124#810—61no—
125#809—61no—
126#805—62no—
127C23×C32#4111yescharacteristic
128C22×C3⋊D3—21no—
129C22×C3×D3—21no—
130C2×C32×C4C22×C411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136#638—22no—
137#638—22no—
138C2×C3⋊Dic3—21no—
139C4⋊(C3⋊D3)—21no—
140C4⋊(C3⋊D3)C22⋊C412yes—
141C4×C3⋊D3—22no—
142C4×C3⋊D3—22no—
143#634—21no—
144#634C22⋊C412yes—
145C3×#67—41no—
146C3×#67—41no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—41no—
149C3×D12—21no—
150C3×D12—21no—
151C3×C4×D3—41no—
152C3×C4×D3—41no—
153C3×Dic6—21no—
154C3×Dic6—21no—
155C32×C8—22no—
156C3⋊(C3⋊C8)—22no—
157C3×C3⋊C8—22no—
158C3×C3⋊C8—41no—
159#575—91no—
160#568—91no—
161#421—91no—
162#416—91no—
163#408—31no—
164#344—31no—
165#341—91no—
166C3×#41—61no—
167C3×#41—61no—
168C3×#41—61no—
169C3×#41—61no—
170C2×C3×Q8—31no—
171C2×C3×D4—31no—
172C2×C3×D4—61no—
173C22×C3×C4—21no—
174C22×C3×C4—61no—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C2×#67—21no—
178C2×#67—62no—
179C2×#67—61no—
180C2×#67—61no—
181#235—21no—
182#235—21no—
183#235—21no—
184#235—21no—
185#235—32no—
186#235—32no—
187#235—32no—
188#235—32no—
189#235—62no—
190#235—62no—
191#235—62no—
192#235—62no—
193#235—61no—
194#235—61no—
195#235—61no—
196#235—61no—
197C2×D12—31no—
198C2×D12—31no—
199C2×D12—61no—
200C2×D12C4×D311yescharacteristic
201C2×C4×D3—21no—
202C2×C4×D3—62no—
203C2×C4×D3—61no—
204C2×C4×D3—61no—
205C2×Dic6—31no—
206C2×Dic6—31no—
207C2×Dic6—61no—
208C2×Dic6C4×D311yescharacteristic
209C3×M16—22no—
210C3×M16—22no—
211C3×M16—21no—
212C3×M16—21no—
213C3×M16—21no—
214C3×M16—21no—
215C3×M16—32no—
216C3×M16—61no—
217C2×C3×C8—22no—
218C2×C3×C8—61no—
219C2×C3×C8—61no—
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—32no—
236#208—32no—
237#208—62no—
238#208—62no—
239#208—61no—
240#208—61no—
241#208C4×D312yes—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—61no—
249Dic12—62no—
250D24—62no—
251#204—62no—
252#204—62no—
253ΓL(1,𝔽25)—68no—
254ΓL(1,𝔽25)—64no—
255ΓL(1,𝔽25)—64no—
256D3×C8—68no—
257D3×C8—64no—
258D3×C8—64no—
259C22×C32—41no—
260C22×C32C4×D411yescharacteristic
261C22×C32#12111yescharacteristic
262C22×C32#12311yescharacteristic
263C2×C3⋊D3—22no—
264C2×C3⋊D3—81no—
265C2×C3×D3—42no—
266C2×C3×D3—41no—
267C32×C4C2×C22⋊C411yescharacteristic
268C32×C4C4×D411yescharacteristic
269C32×C4#12011yescharacteristic
270C32×C4#12111yescharacteristic
271C3⋊Dic3—22no—
272C3×Dic3—41no—
273C3×Dic3—81no—
274C2×#41—31no—
275C2×#41—91no—
276#137—92no—
277#137—181no—
278AGL(1,ℤ/8)—92no—
279AGL(1,ℤ/8)—181no—
280#135—182no—
281#131—182no—
282#131—182no—
283C2×M16—31no—
284C2×M16—91no—
285C2×M16—182no—
286C2×M16D3211yescharacteristic
287C22×C8—31no—
288#117—31no—
289#104—182no—
290#103—181no—
291#102—181no—
292C22⋊C8—62no—
293C23×C3—21no—
294C23×C3—61no—
295C23×C3#23511yescharacteristic
296C23×C3#23511yescharacteristic
297C22×D3—21no—
298C22×D3—62no—
299C22×D3—61no—
300C22×D3—61no—
301C3×Q8—61no—
302C3×Q8—61no—
303C3×D4—61no—
304C3×D4—61no—
305C3×D4—121no—
306C3×D4—121no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—61no—
314C2×C3×C4—121no—
315C2×C3×C4—121no—
316C2×C3×C4—121no—
317C2×C3×C4C2×C4×D311yescharacteristic
318C2×C3×C4C2×C4×D311yescharacteristic
319C2×C3×C4C2×D1211yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4#23711yescharacteristic
327C2×C3×C4#23911yescharacteristic
328C2×C3×C4C2×#6711yescharacteristic
329#67—41no—
330#67—41no—
331#67—64no—
332#67—64no—
333#67—62no—
334#67—62no—
335#67—62no—
336#67—62no—
337C2×Dic3—21no—
338C2×Dic3—41no—
339C2×Dic3—62no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342D12—21no—
343D12—21no—
344D12—32no—
345D12—32no—
346D12—62no—
347D12—62no—
348D12—61no—
349D12—61no—
350C4×D3—41no—
351C4×D3—41no—
352C4×D3—64no—
353C4×D3—64no—
354C4×D3—62no—
355C4×D3—62no—
356C4×D3—62no—
357C4×D3—62no—
358Dic6—21no—
359Dic6—21no—
360Dic6—32no—
361Dic6—32no—
362Dic6—62no—
363Dic6—62no—
364Dic6—61no—
365Dic6—61no—
366C3×C8—24no—
367C3×C8—22no—
368C3×C8—22no—
369C3×C8—62no—
370C3×C8—121no—
371C3⋊C8—22no—
372C3⋊C8—41no—
373C3⋊C8—64no—
374C3⋊C8—62no—
375C3⋊C8—62no—
376C2×C32—21no—
377C2×C32—21no—
378C2×C32—21no—
379C2×C32#38611yescharacteristic
380C3⋊D3—42no—
381C3×D3—81no—
382#41—61no—
383#41—61no—
384#41—61no—
385#41—61no—
386#41—92no—
387#41—92no—
388#41—181no—
389#41—181no—
390C2×Q8—31no—
391C2×Q8—91no—
392C2×D4—31no—
393C2×D4—61no—
394C2×D4—91no—
395C2×D4—181no—
396C22×C4—61no—
397C22×C4—181no—
398C22×C4C2×D3211yescharacteristic
399Q16—182no—
400SD16—182no—
401SD16—182no—
402D8—182no—
403M16—21no—
404M16—21no—
405M16—32no—
406M16—61no—
407M16—92no—
408M16—184no—
409M16—181no—
410C2×C8—61no—
411C2×C8—61no—
412C2×C8—61no—
413C2×C8—61no—
414C2×C8—184no—
415C2×C8—181no—
416C2×C8#62612yes—
417C4⋊C4—61no—
418C22⋊C4—61no—
419C42—61no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—81no—
426C22×C3—122no—
427C22×C3—121no—
428C22×C3C4×D1211yescharacteristic
429C22×C3#88311yescharacteristic
430C22×C3#88411yescharacteristic
431C22×C3#88411yescharacteristic
432C22×C3#89411yescharacteristic
433C22×C3C4×#6711yescharacteristic
434C2×D3—42no—
435C2×D3—41no—
436C2×D3—64no—
437C2×D3—62no—
438C2×D3—62no—
439C2×D3—241no—
440C2×D3—241no—
441C2×D3—242no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—121no—
447C3×C4—241no—
448C3×C4D3×C22⋊C411yescharacteristic
449C3×C4D3×C22⋊C411yescharacteristic
450C3×C4#67⋊C411yescharacteristic
451C3×C4#88211yescharacteristic
452C3×C4#89311yescharacteristic
453C3×C4#89511yescharacteristic
454C3×C4#93711yescharacteristic
455C3×C4#93811yescharacteristic
456Dic3—41no—
457Dic3—64no—
458Dic3—62no—
459Dic3—62no—
460Dic3—81no—
461C32#188111yescharacteristic, complemented, Sylow
462C23—61no—
463C23—181no—
464C23#379811yescharacteristic
465Q8—61no—
466Q8—61no—
467Q8—92no—
468Q8—181no—
469D4—61no—
470D4—61no—
471D4—92no—
472D4—121no—
473D4—121no—
474D4—182no—
475D4—182no—
476D4—181no—
477C2×C4—61no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—121no—
481C2×C4—181no—
482C2×C4—182no—
483C2×C4—182no—
484C2×C4#379611yescharacteristic
485C2×C4C4×D3211yescharacteristic
486C2×C4#380211yescharacteristic
487C2×C4C2×#62611yescharacteristic
488C2×C4#381111yescharacteristic
489C2×C4#381111yescharacteristic
490C8—22no—
491C8—62no—
492C8—121no—
493C8—182no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—41no—
502C2×C3—41no—
503C2×C3—41no—
504C2×C3—241no—
505C2×C3#466511yescharacteristic
506C2×C3#495611yescharacteristic
507D3—81no—
508D3—124no—
509D3—122no—
510D3—122no—
511C22—41no—
512C22—122no—
513C22—121no—
514C22—182no—
515C22—721no—
516C22#6385311yescharacteristic
517C22C4×#62611yescharacteristic
518C22#6391211yescharacteristic
519C4—121no—
520C4—182no—
521C4—241no—
522C4#6388111yescharacteristic
523C4#6391611yescharacteristic
524C4#6392111yescharacteristic
525C4#6398111yescharacteristic
526C3—21no—
527C3#6903511yescharacteristic, complemented
528C3#7001211yescharacteristic, complemented
529C2—21no—
530C2—21no—
531C2—21no—
532C2—241no—
533C2—362no—
534C2#1059138711yescharacteristic
subgroupG/H
centerC4#63981
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. #10596216C2semidirect
3. C3×#5129C2semidirect
4. #10591111C2semidirect
5. #10591105C2semidirect
6. C3×#4556C2semidirect
7. #10589166C2semidirect
20. #63833C4semidirect
22. #63830C4semidirect
36. #5129D3semidirect
42. #4556D3semidirect
461. C32#1881semidirect
527. C3#69035semidirect
528. C3#70012semidirect

Maximal subgroups

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

subgroupindex
#105962162
#105947952
C3×#51292
#105911112
#105911052
C3×#45562
#105891662
#700123
#690353