Finite Group Databasebeta

← #11788886

Subgroups — #11788886

Order 1152.

809 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596216C211yesmaximal, characteristic, complemented
2#10595042C211yesmaximal, characteristic
3C2×C3×#823C211yesmaximal, characteristic, complemented
4#10591078C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic, complemented
6C3×#4559C211yesmaximal, characteristic, complemented
7#10589169C211yesmaximal, characteristic, complemented
8#70089—31nomaximal
9#69040—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14#64116—22no—
15M16×C3⋊D3—22no—
16#64110—22no—
17C3×#926C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20#63977C414yes—
21#63916—22no—
22#63911—21no—
23#63860—21no—
24C3×#823—22no—
25#63561—21no—
26#63559—21no—
27#63558—22no—
28#5805—31no—
29#5745—31no—
30#5745—31no—
31#5745—61no—
32#5525—31no—
33C2×C3×#100—31no—
34C2×#833—31no—
35#5132—31no—
36#5132—31no—
37C2×#823—31no—
38C2×#823D311yescharacteristic, complemented
39C3×#344—31no—
40#4559D311yescharacteristic, complemented
41#4556—31no—
42#4533—31no—
43C23×C3×D3C2×C412yes—
44C22×C32×C4C2311yescharacteristic
45C2×#638C2×C412yes—
46#3828—21no—
47#3828—21no—
48#3828—21no—
49#3828—21no—
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C2×C4×C3⋊D3D412yes—
52C2×#634D411yescharacteristic
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×#626—24no—
60C32×M16—21no—
61C32×M16D412yescomplemented
62C2×C32×C8—21no—
63#3748—21no—
64#3748D412yescomplemented
65C2×C3⋊(C3⋊C8)—21no—
66#3743—24no—
67C8×C3⋊D3—24no—
68C3×#217C2×C412yes—
69C3×C4⋊Dic3—21no—
70C3×C4×Dic3—21no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208—21no—
74C3×#208—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77(C2×D3)⋊Dic3—24no—
78#1914—91noSylow
79C22×C3×D4—31no—
80C2×#235—31no—
81C2×#235—31no—
82C2×#235—61no—
83C22×D12C2×D311yescharacteristic
84C2×C3×M16—21no—
85C2×C3×M16—31no—
86C2×C3×M16—31no—
87C2×C3×M16C2×D311yescharacteristic
88C2×C3×M16C2×D311yescharacteristic
89C3×#117—31no—
90#953—34no—
91#940—61no—
92#938—62no—
93#936—61no—
94#926C2×D311yescharacteristic
95C2×#208—31no—
96C2×#208—31no—
97C2×#208—61no—
98C2×#208C2×D311yescharacteristic
99C2×#208C2×D311yescharacteristic
100#907—64no—
101#907—62no—
102#907—62no—
103D3×M16—62no—
104D3×M16—62no—
105D3×M16—64no—
106#901—62no—
107#901—62no—
108#901—64no—
109#895—62no—
110#882—34no—
111#875—61no—
112#874—61no—
113C3×#100—62no—
114#833—62no—
115#824—61no—
116#824—61no—
117#823—22no—
118#823—61no—
119#823—61no—
120#823—62no—
121C23×C32C22×C411yescharacteristic
122C22×C3⋊D3C22⋊C412yes—
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3—82no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133#638—22no—
134#638—22no—
135C2×C3⋊Dic3C22⋊C412yes—
136C4⋊(C3⋊D3)—21no—
137C4⋊(C3⋊D3)—21no—
138C4×C3⋊D3—22no—
139C4×C3⋊D3—22no—
140#634—21no—
141#634—21no—
142C2×C3×Dic3—22no—
143C3×D12—41no—
144C3×D12—41no—
145C3×D12—41no—
146C3×D12—41no—
147#626—84no—
148C32×C8—22no—
149C3⋊(C3⋊C8)—22no—
150C3×C3⋊C8—41no—
151C3×C3⋊C8—41no—
152#568—91no—
153#535—91no—
154#413—91no—
155C2×#100—31no—
156C2×#100—91no—
157#344—31no—
158#344—91no—
159C24×C3—32no—
160C23×D3C4×D312yes—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C22×C3×C4—21no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C2×#67—32no—
171C2×#67—32no—
172C2×#67—62no—
173C2×#67—64no—
174#235—62no—
175#235—62no—
176#235—62no—
177#235—62no—
178#235—61no—
179#235—61no—
180#235—61no—
181#235—61no—
182#235—61no—
183#235—61no—
184#235—61no—
185#235—61no—
186C2×D12—21no—
187C2×D12—21no—
188C2×D12—21no—
189C2×D12—21no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12—31no—
193C2×D12—31no—
194C2×D12—61no—
195C2×D12—64no—
196C2×C4×D3—32no—
197C2×C4×D3—32no—
198C2×C4×D3—62no—
199C2×Dic6—31no—
200C2×Dic6—31no—
201C2×Dic6—61no—
202C3×M16—22no—
203C3×M16—21no—
204C3×M16—21no—
205C3×M16—22no—
206C3×M16—61no—
207C3×M16—61no—
208C3×M16—61no—
209C3×M16—61no—
210C3×M16D1212yescomplemented
211C3×M16#6712yescomplemented
212C2×C3×C8—22no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C3×C4⋊C4—61no—
218C3×C22⋊C4—32no—
219C3×C42—61no—
220#217—64no—
221#217C4×D312yes—
222(C2×D3)⋊C4—64no—
223C4⋊Dic3—21no—
224C4×Dic3—21no—
225#208—21no—
226#208—21no—
227#208—21no—
228#208—21no—
229#208—32no—
230#208—32no—
231#208—62no—
232#208—62no—
233#208—61no—
234#208—61no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240ΓL(1,𝔽25)—68no—
241ΓL(1,𝔽25)—64no—
242ΓL(1,𝔽25)—64no—
243D3×C8—68no—
244D3×C8—64no—
245D3×C8—64no—
246C22×C32—41no—
247C22×C32C2×C22⋊C411yescharacteristic
248C22×C32C4×D411yescharacteristic
249C22×C32C4×D411yescharacteristic
250C2×C3⋊D3—22no—
251C2×C3⋊D3—42no—
252C2×C3×D3—44no—
253C2×C3×D3—42no—
254C2×C3×D3—82no—
255C2×C3×D3—82no—
256C32×C4#12011yescharacteristic
257C32×C4#12111yescharacteristic
258C32×C4#12111yescharacteristic
259C32×C4#12311yescharacteristic
260C3⋊Dic3—22no—
261C3×Dic3—42no—
262C2×#41—91no—
263C22×D4—31no—
264#131—182no—
265#131—182no—
266C2×M16—31no—
267C2×M16—31no—
268C2×M16—91no—
269C2×M16—182no—
270C2×M16D3211yescharacteristic
271#127—181no—
272#124—181no—
273#121—182no—
274#120—94no—
275#117—31no—
276#101—181no—
277#100—62no—
278#100—181no—
279#100—182no—
280C23×C3—21no—
281C23×C3—62no—
282C23×C3—62no—
283C23×C3—62no—
284C23×C3—242no—
285C23×C3C2×C4×D311yescharacteristic
286C23×C3C2×C4×D311yescharacteristic
287C22×D3—22no—
288C22×D3—22no—
289C22×D3—22no—
290C22×D3—32no—
291C22×D3—32no—
292C22×D3—62no—
293C22×D3—82no—
294C3×D4—121no—
295C3×D4—121no—
296C3×D4—121no—
297C3×D4—121no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—62no—
305C2×C3×C4C2×D1211yescharacteristic
306C2×C3×C4#23511yescharacteristic
307C2×C3×C4#23511yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4#23711yescharacteristic
315C2×C3×C4#23911yescharacteristic
316C2×C3×C4C2×#6711yescharacteristic
317#67—64no—
318#67—64no—
319#67—62no—
320#67—62no—
321#67—62no—
322#67—62no—
323#67—244no—
324C2×Dic3—22no—
325C2×Dic3—32no—
326C2×Dic3—32no—
327C2×Dic3—62no—
328D12—41no—
329D12—41no—
330D12—41no—
331D12—41no—
332D12—62no—
333D12—62no—
334D12—61no—
335D12—61no—
336D12—61no—
337D12—61no—
338D12—244no—
339C4×D3—64no—
340C4×D3—64no—
341C4×D3—62no—
342C4×D3—62no—
343C4×D3—62no—
344C4×D3—62no—
345Dic6—62no—
346Dic6—62no—
347Dic6—61no—
348Dic6—61no—
349Dic6—61no—
350Dic6—61no—
351C3×C8—24no—
352C3×C8—22no—
353C3×C8—22no—
354C3×C8—121no—
355C3×C8—121no—
356C3⋊C8—41no—
357C3⋊C8—41no—
358C3⋊C8—64no—
359C3⋊C8—62no—
360C3⋊C8—62no—
361C2×C32—21no—
362C2×C32—21no—
363C2×C32—21no—
364C2×C32#38611yescharacteristic
365C3⋊D3—42no—
366C3×D3—82no—
367C24—32no—
368#41—181no—
369#41—181no—
370#41—181no—
371#41—181no—
372C2×Q8—91no—
373C2×D4—61no—
374C2×D4—61no—
375C2×D4—61no—
376C2×D4—61no—
377C2×D4—61no—
378C2×D4—61no—
379C2×D4—92no—
380C2×D4—91no—
381C2×D4—184no—
382C22×C4—92no—
383C22×C4C2×D3211yescharacteristic
384M16—21no—
385M16—61no—
386M16—61no—
387M16—61no—
388M16—61no—
389M16—92no—
390M16—184no—
391M16—181no—
392M16#62612yescomplemented
393C2×C8—21no—
394C2×C8—61no—
395C2×C8—61no—
396C2×C8—184no—
397C2×C8—181no—
398C4⋊C4—61no—
399C22⋊C4—32no—
400C22⋊C4—184no—
401C42—61no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—81no—
408C22×C3—124no—
409C22×C3—122no—
410C22×C3—242no—
411C22×C3—242no—
412C22×C3C4×D1211yescharacteristic
413C22×C3D3×C22⋊C411yescharacteristic
414C22×C3D3×C22⋊C411yescharacteristic
415C22×C3#67⋊C411yescharacteristic
416C22×C3#89311yescharacteristic
417C22×C3C4×#6711yescharacteristic
418C2×D3—44no—
419C2×D3—42no—
420C2×D3—64no—
421C2×D3—62no—
422C2×D3—62no—
423C2×D3—82no—
424C2×D3—82no—
425C2×D3—122no—
426C2×D3—122no—
427C2×D3—242no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—122no—
433C3×C4#88211yescharacteristic
434C3×C4#88311yescharacteristic
435C3×C4#88411yescharacteristic
436C3×C4#88411yescharacteristic
437C3×C4#89411yescharacteristic
438C3×C4#89511yescharacteristic
439C3×C4#93711yescharacteristic
440C3×C4#93811yescharacteristic
441Dic3—42no—
442Dic3—64no—
443Dic3—62no—
444Dic3—62no—
445C32#191411yescharacteristic, complemented, Sylow
446C23—62no—
447C23—62no—
448C23—62no—
449C23—92no—
450C23—242no—
451C23C4×D3211yescharacteristic
452Q8—181no—
453Q8—181no—
454D4—121no—
455D4—121no—
456D4—121no—
457D4—121no—
458D4—182no—
459D4—182no—
460D4—181no—
461D4—181no—
462D4—724no—
463C2×C4—62no—
464C2×C4—92no—
465C2×C4—182no—
466C2×C4—182no—
467C2×C4#379611yescharacteristic
468C2×C4#379811yescharacteristic
469C2×C4#380211yescharacteristic
470C2×C4C2×#62611yescharacteristic
471C2×C4#381111yescharacteristic
472C2×C4#381111yescharacteristic
473C8—22no—
474C8—121no—
475C8—121no—
476C8—182no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—41no—
485C2×C3—41no—
486C2×C3—41no—
487C2×C3—242no—
488C2×C3#466511yescharacteristic
489C2×C3#495611yescharacteristic
490D3—82no—
491D3—124no—
492D3—122no—
493D3—122no—
494C22—41no—
495C22—124no—
496C22—122no—
497C22—182no—
498C22—242no—
499C22—242no—
500C22—362no—
501C22#6388111yescharacteristic
502C22C4×#62611yescharacteristic
503C22#6392111yescharacteristic
504C4—122no—
505C4—182no—
506C4#6385311yescharacteristic
507C4#6391211yescharacteristic
508C4#6391611yescharacteristic
509C4#6398111yescharacteristic
510C3—21no—
511C3#6904011yescharacteristic, complemented
512C3#7008911yescharacteristic, complemented
513C2—21no—
514C2—21no—
515C2—21no—
516C2—242no—
517C2—362no—
518C2#1059138711yescharacteristic
subgroupG/H
centerC2#10591387
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radical#10595042C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1914
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10596216C2semidirect
3. C2×C3×#823C2semidirect
4. #10591078C2semidirect
5. C2×#63558C2semidirect
6. C3×#4559C2semidirect
7. #10589169C2semidirect
38. C2×#823D3semidirect
40. #4559D3semidirect
61. C32×M16D4semidirect
64. #3748D4semidirect
210. C3×M16D12semidirect
211. C3×M16#67semidirect
392. M16#626semidirect
445. C32#1914semidirect
511. C3#69040semidirect
512. C3#70089semidirect

Maximal subgroups

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

subgroupindex
#105962162
#105950422
C2×C3×#8232
#105910782
C2×#635582
C3×#45592
#105891692
#700893
#690403