Finite Group Databasebeta

← #11788008

Subgroups — #11788008

Order 1152.

729 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C211yesmaximal, characteristic, complemented
2#10595022C211yesmaximal, characteristic
3C3×#5126C211yesmaximal, characteristic, complemented
4#10591076C211yesmaximal, characteristic, complemented
5#10591069C211yesmaximal, characteristic, complemented
6#10589422C211yesmaximal, characteristic, complemented
7#10589171C211yesmaximal, characteristic, complemented
8#72029—31nomaximal
9#69992—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#907—22no—
18C3×D3×M16—22no—
19C3×#901—22no—
20#63976C412yes—
21#63961C412yes—
22#63908—21no—
23C4×#625—22no—
24#63856—21no—
25C3×(C2×D3)⋊C8—22no—
26#63560—21no—
27#63558—21no—
28(C2×D3)⋊(C3⋊C8)—22no—
29C3×#568—31no—
30#5828—31no—
31#5791—31no—
32#5745D311yescharacteristic, complemented
33C3×#407—31no—
34#5237—31no—
35#5207—31no—
36#5132—31no—
37#5126—31no—
38#5126D311yescharacteristic, complemented
39#4559—31no—
40#4556—31no—
41#4556—31no—
42#4556—31no—
43#4556—61no—
44C23×C3×D3C2×C411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C2×C3×#67C2×C412yes—
47C22×C3×Dic3C2×C411yescharacteristic
48C3×#235—21no—
49C3×#235—21no—
50C3×#235—21no—
51C3×#235—21no—
52C2×C3×D12D411yescharacteristic
53C2×C3×C4×D3—21no—
54C2×C3×C4×D3—21no—
55C2×C3×C4×D3—21no—
56C2×C3×C4×D3—21no—
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3D412yes—
60C2×C3×Dic6D411yescharacteristic
61C2×#625—22no—
62C32×M16—21no—
63C32×M16—21no—
64C2×C32×C8D412yescomplemented
65#3757C2×C412yes—
66C4⋊(C3⋊Dic3)—21no—
67C4×C3⋊Dic3—21no—
68#3748—21no—
69#3748—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208—21no—
74C3×#208—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8D412yescomplemented
77C3×ΓL(1,𝔽25)—24no—
78C3×D3×C8—24no—
79#3724—22no—
80(C2×D3)⋊Dic3—22no—
81(C2×D3)⋊Dic3—22no—
82#1891—91noSylow
83C2×C3×#41—31no—
84C23×C3×C4—31no—
85C2×#235C2×D311yescharacteristic
86C22×C4×D3C2×D311yescharacteristic
87C3×#131—62no—
88C3×#131—62no—
89C2×C3×M16—21no—
90C2×C3×M16—31no—
91C2×C3×M16—31no—
92C2×C3×M16—62no—
93C2×C3×M16C2×D311yescharacteristic
94C2×C3×M16C2×D311yescharacteristic
95#953—32no—
96#946—61no—
97#938—61no—
98#937—32no—
99#935—32no—
100#930—61no—
101#929—32no—
102C4×#67—62no—
103C4×#67—62no—
104#926—31no—
105#926—31no—
106#926—61no—
107#924—61no—
108C2×#208—31no—
109C2×#208—31no—
110C2×#208—61no—
111C2×#208C2×D311yescharacteristic
112C2×#208C2×D311yescharacteristic
113#907—22no—
114D3×M16—22no—
115#901—22no—
116C3×C22⋊C8—62no—
117#836—61no—
118#833—61no—
119#830—62no—
120#824—61no—
121#823—61no—
122(C2×D3)⋊C8—22no—
123(C2×D3)⋊C8—62no—
124C23×C32C22×C411yescharacteristic
125C22×C3×D3—21no—
126C22×C3×D3—21no—
127C22×C3×D3—21no—
128C22×C3×D3—42no—
129C22×C3×D3C22⋊C412yes—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C3⋊Dic3—22no—
137C3×#67—22no—
138C3×#67—22no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3C22⋊C412yes—
143C3×D12—21no—
144C3×D12—21no—
145C3×C4×D3—22no—
146C3×C4×D3—22no—
147C3×C4×D3—41no—
148C3×C4×D3—41no—
149C3×C4×D3—41no—
150C3×C4×D3—41no—
151C3×Dic6—21no—
152C3×Dic6—21no—
153#625—44no—
154C32×C8—22no—
155C3⋊(C3⋊C8)—41no—
156C3×C3⋊C8—22no—
157C3×C3⋊C8—41no—
158#568—31no—
159#525—91no—
160#413—91no—
161#407—31no—
162#407—91no—
163#344—91no—
164#344—91no—
165C24×C3—31no—
166C23×D3C4×D311yescharacteristic
167C3×#41—61no—
168C3×#41—61no—
169C3×#41—61no—
170C3×#41—61no—
171C2×C3×Q8—31no—
172C2×C3×D4—32no—
173C2×C3×D4—31no—
174C22×C3×C4—21no—
175C22×C3×C4—32no—
176C22×C3×C4—31no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C2×#67—62no—
186C2×#67—62no—
187C2×#67C4×D312yes—
188C22×Dic3C4×D311yescharacteristic
189#235—21no—
190#235—21no—
191#235—21no—
192#235—21no—
193C2×D12D1211yescharacteristic
194C2×C4×D3—21no—
195C2×C4×D3—21no—
196C2×C4×D3—21no—
197C2×C4×D3—21no—
198C2×C4×D3—21no—
199C2×C4×D3—21no—
200C2×C4×D3#6712yes—
201C2×Dic6D1211yescharacteristic
202C3×M16—21no—
203C3×M16—21no—
204C3×M16—21no—
205C3×M16—21no—
206C3×M16—41no—
207C3×M16—41no—
208C3×M16—64no—
209C3×M16—61no—
210C3×M16—61no—
211C3×M16—61no—
212C3×M16—61no—
213C2×C3×C8—22no—
214C2×C3×C8—32no—
215C2×C3×C8—64no—
216C2×C3×C8—61no—
217C2×C3×C8#6712yescomplemented
218C2×C3×C8#6712yescomplemented
219#217—32no—
220#217—32no—
221#217—62no—
222#217—62no—
223#217—62no—
224(C2×D3)⋊C4—62no—
225(C2×D3)⋊C4—62no—
226C4⋊Dic3—61no—
227C4⋊Dic3—61no—
228C4⋊Dic3—121no—
229Dic3⋊C4—62no—
230Dic3⋊C4—62no—
231C4×Dic3—61no—
232C4×Dic3—61no—
233C4×Dic3—121no—
234#208—21no—
235#208—21no—
236#208—21no—
237#208—21no—
238#208—62no—
239#208—61no—
240#208—61no—
241#208—61no—
242#208—61no—
243#208—121no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—121no—
248C2×C3⋊C8#6712yescomplemented
249ΓL(1,𝔽25)—24no—
250D3×C8—24no—
251C22×C32—41no—
252C22×C32C2×C22⋊C411yescharacteristic
253C22×C32C4×D411yescharacteristic
254C22×C32C4×D411yescharacteristic
255C2×C3×D3—22no—
256C2×C3×D3—22no—
257C2×C3×D3—22no—
258C2×C3×D3—22no—
259C2×C3×D3—41no—
260C2×C3×D3—41no—
261C2×C3×D3—41no—
262C2×C3×D3—41no—
263C2×C3×D3—42no—
264C32×C4#12011yescharacteristic
265C32×C4#12111yescharacteristic
266C32×C4#12111yescharacteristic
267C32×C4#12311yescharacteristic
268C3⋊Dic3—42no—
269C3×Dic3—22no—
270C3×Dic3—41no—
271C2×#41—31no—
272C23×C4—31no—
273#131—62no—
274#131—62no—
275C2×M16—31no—
276C2×M16—31no—
277C2×M16—62no—
278C2×M16—91no—
279C2×M16D3211yescharacteristic
280#123—92no—
281C22⋊Q8—181no—
282#121—181no—
283#120—92no—
284C4×D4—182no—
285#117—91no—
286#101—181no—
287#100—181no—
288C22⋊C8—62no—
289C22⋊C8—182no—
290C23×C3—21no—
291C23×C3—32no—
292C23×C3—61no—
293C23×C3—61no—
294C23×C3—61no—
295C23×C3—122no—
296C23×C3C2×C4×D311yescharacteristic
297C23×C3C2×C4×D311yescharacteristic
298C22×D3—21no—
299C22×D3—21no—
300C22×D3—21no—
301C22×D3—42no—
302C22×D3(C2×D3)⋊C412yes—
303C3×Q8—61no—
304C3×Q8—61no—
305C3×D4—62no—
306C3×D4—62no—
307C3×D4—61no—
308C3×D4—61no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—32no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—61no—
319C2×C3×C4—61no—
320C2×C3×C4—61no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4#23511yescharacteristic
327C2×C3×C4#23511yescharacteristic
328C2×C3×C4#23511yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4#23711yescharacteristic
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337#67—22no—
338#67—22no—
339#67—124no—
340#67—124no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—122no—
347C2×Dic3(C2×D3)⋊C412yes—
348D12—21no—
349D12—21no—
350C4×D3—22no—
351C4×D3—22no—
352C4×D3—41no—
353C4×D3—41no—
354C4×D3—41no—
355C4×D3—41no—
356Dic6—21no—
357Dic6—21no—
358C3×C8—22no—
359C3×C8—22no—
360C3×C8—42no—
361C3×C8—62no—
362C3×C8—121no—
363C3⋊C8—22no—
364C3⋊C8—41no—
365C3⋊C8—122no—
366C3⋊C8—121no—
367C3⋊C8—121no—
368C2×C32—21no—
369C2×C32—21no—
370C2×C32—21no—
371C2×C32#38611yescharacteristic
372C3×D3—42no—
373C3×D3—42no—
374C24—31no—
375#41—61no—
376#41—61no—
377#41—61no—
378#41—61no—
379C2×Q8—31no—
380C2×D4—32no—
381C2×D4—31no—
382C2×D4—182no—
383C22×C4—32no—
384C22×C4—31no—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4—61no—
388C22×C4—61no—
389C22×C4—61no—
390C22×C4—61no—
391C22×C4C2×D3211yescharacteristic
392M16—21no—
393M16—21no—
394M16—64no—
395M16—61no—
396M16—61no—
397M16—61no—
398M16—61no—
399M16—181no—
400M16—181no—
401C2×C8—32no—
402C2×C8—64no—
403C2×C8—61no—
404C2×C8—181no—
405C2×C8#62512yescomplemented
406C4⋊C4—182no—
407C4⋊C4—181no—
408C22⋊C4—92no—
409C22⋊C4—182no—
410C22⋊C4—182no—
411C42—181no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—62no—
418C22×C3—62no—
419C22×C3—62no—
420C22×C3—62no—
421C22×C3—81no—
422C22×C3—122no—
423C22×C3—121no—
424C22×C3—121no—
425C22×C3—121no—
426C22×C3—121no—
427C22×C3D3×C22⋊C411yescharacteristic
428C22×C3#67⋊C411yescharacteristic
429C22×C3C2×(C2×D3)⋊C411yescharacteristic
430C22×C3C4×#6711yescharacteristic
431C22×C3C4×#6711yescharacteristic
432C22×C3C4×#6711yescharacteristic
433C2×D3—22no—
434C2×D3—22no—
435C2×D3—22no—
436C2×D3—22no—
437C2×D3—41no—
438C2×D3—41no—
439C2×D3—41no—
440C2×D3—41no—
441C2×D3—42no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—62no—
447C3×C4—121no—
448C3×C4#88311yescharacteristic
449C3×C4#88411yescharacteristic
450C3×C4#92911yescharacteristic
451C3×C4#93011yescharacteristic
452C3×C4#93011yescharacteristic
453C3×C4#93711yescharacteristic
454C3×C4#93811yescharacteristic
455C3×C4#95311yescharacteristic
456Dic3—22no—
457Dic3—41no—
458Dic3—122no—
459Dic3—122no—
460Dic3—242no—
461C32#189111yescharacteristic, complemented, Sylow
462C23—32no—
463C23—61no—
464C23—61no—
465C23—61no—
466C23—122no—
467C23C4×D3211yescharacteristic
468Q8—61no—
469Q8—61no—
470D4—62no—
471D4—62no—
472D4—61no—
473D4—61no—
474D4—364no—
475C2×C4—32no—
476C2×C4—62no—
477C2×C4—62no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—121no—
482C2×C4—121no—
483C2×C4—121no—
484C2×C4—121no—
485C2×C4—182no—
486C2×C4#379511yescharacteristic
487C2×C4#379811yescharacteristic
488C2×C4D3×D1211yescharacteristic
489C2×C4C2×#62511yescharacteristic
490C2×C4D3×#6711yescharacteristic
491C2×C4D3×#6711yescharacteristic
492C8—22no—
493C8—62no—
494C8—121no—
495C8—361no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—41no—
504C2×C3—41no—
505C2×C3—41no—
506C2×C3—122no—
507C2×C3—122no—
508C2×C3#495611yescharacteristic
509C2×C3#521311yescharacteristic
510D3—42no—
511D3—42no—
512C22—41no—
513C22—62no—
514C22—62no—
515C22—62no—
516C22—62no—
517C22—122no—
518C22—121no—
519C22—121no—
520C22—121no—
521C22—121no—
522C22#6387911yescharacteristic
523C22C4×#62511yescharacteristic
524C22D3×(C2×D3)⋊C411yescharacteristic
525C4—62no—
526C4—121no—
527C4—362no—
528C4#6390511yescharacteristic
529C4#6390611yescharacteristic
530C4#6390811yescharacteristic
531C4#6397611yescharacteristic
532C3—21no—
533C3#6999211yescharacteristic, complemented
534C3#7202911yescharacteristic, complemented
535C2—21no—
536C2—21no—
537C2—21no—
538C2—122no—
539C2—122no—
540C2#1059138111yescharacteristic
subgroupG/H
centerC4#63976
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radical#10595022C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1891
LCSG ▷ C23×C32 ▷ 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. C3×#5126C2semidirect
4. #10591076C2semidirect
5. #10591069C2semidirect
6. #10589422C2semidirect
7. #10589171C2semidirect
32. #5745D3semidirect
38. #5126D3semidirect
64. C2×C32×C8D4semidirect
76. C2×C3×C3⋊C8D4semidirect
217. C2×C3×C8#67semidirect
218. C2×C3×C8#67semidirect
248. C2×C3⋊C8#67semidirect
405. C2×C8#625semidirect
461. C32#1891semidirect
533. C3#69992semidirect
534. C3#72029semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
#105950222
C3×#51262
#105910762
#105910692
#105894222
#105891712
#720293
#699923