Finite Group Databasebeta

← #11788885

Subgroups — #11788885

Order 1152.

773 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C211yesmaximal, characteristic, complemented
2#10595045C211yesmaximal, characteristic
3C2×#63650C211yesmaximal, characteristic, complemented
4C2×#63559C211yesmaximal, characteristic, complemented
5#10591076C211yesmaximal, characteristic, complemented
6C3×#4559C211yesmaximal, characteristic, complemented
7#10589170C211yesmaximal, characteristic, complemented
8#72030—31nomaximal
9#69040—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#907—22no—
18C3×D3×M16—22no—
19C3×#901—22no—
20#63981C414yes—
21#63911—21no—
22#63909—22no—
23#63864—21no—
24#63650—22no—
25#63560—21no—
26#63559—22no—
27#63558—21no—
28C3×#568—31no—
29#5830—31no—
30#5745D311yescharacteristic, complemented
31#5525—31no—
32#5237—31no—
33#5132—31no—
34C2×#823—31no—
35C2×#823—31no—
36C2×#823—31no—
37C2×#823—31no—
38C2×#823—61no—
39C3×#344—31no—
40#4559—31no—
41#4559D311yescharacteristic, complemented
42#4533—31no—
43C23×C3⋊D3C2×C412yes—
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)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C3×#67C2×C412yes—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C2×C3×D12D411yescharacteristic
57C2×C3×C4×D3D412yes—
58C2×C3×Dic6D411yescharacteristic
59C2×#626—24no—
60C32×M16—21no—
61C32×M16D412yescomplemented
62C2×C32×C8—21no—
63#3748—21no—
64#3748—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C3×#217C2×C412yes—
67C3×C4⋊Dic3—21no—
68C3×C4×Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208D412yescomplemented
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C3×ΓL(1,𝔽25)—24no—
76C3×D3×C8—24no—
77#3722—24no—
78#1914—91noSylow
79C2×C3×#41—31no—
80C2×#235C2×D311yescharacteristic
81C22×D12—31no—
82C22×D12—31no—
83C22×D12—61no—
84C3×#131—62no—
85C3×#131—62no—
86C2×C3×M16—21no—
87C2×C3×M16—31no—
88C2×C3×M16—31no—
89C2×C3×M16—62no—
90C2×C3×M16C2×D311yescharacteristic
91C2×C3×M16C2×D311yescharacteristic
92C3×#117—31no—
93#947—61no—
94#940—61no—
95#937—34no—
96#930—62no—
97#926C2×D311yescharacteristic
98C2×#208—31no—
99C2×#208—31no—
100C2×#208—61no—
101C2×#208C2×D311yescharacteristic
102C2×#208C2×D311yescharacteristic
103#907—22no—
104D3×M16—22no—
105#901—22no—
106#895—62no—
107#882—34no—
108#875—61no—
109#874—61no—
110#836—61no—
111#833—61no—
112#824—61no—
113#823—62no—
114#823—64no—
115#823—61no—
116#823—62no—
117#823—62no—
118#823—62no—
119C23×C32C22×C411yescharacteristic
120C22×C3⋊D3—22no—
121C22×C3⋊D3—22no—
122C22×C3⋊D3—22no—
123C22×C3⋊D3—82no—
124C22×C3×D3C22⋊C412yes—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C4⋊(C3⋊D3)—41no—
132C4⋊(C3⋊D3)—41no—
133C4⋊(C3⋊D3)—41no—
134C4⋊(C3⋊D3)—41no—
135C3×#67—22no—
136C3×#67—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3C22⋊C412yes—
139C3×D12—21no—
140C3×D12—21no—
141C3×C4×D3—22no—
142C3×C4×D3—22no—
143C3×Dic6—21no—
144C3×Dic6—21no—
145#626—84no—
146C32×C8—22no—
147C3⋊(C3⋊C8)—41no—
148C3×C3⋊C8—22no—
149C3×C3⋊C8—41no—
150#568—31no—
151#535—91no—
152#413—91no—
153C2×#100—91no—
154C2×#100—91no—
155#344—31no—
156#344—91no—
157C23×D3—32no—
158C23×D3—32no—
159C23×D3—62no—
160C3×#41—61no—
161C3×#41—61no—
162C3×#41—61no—
163C3×#41—61no—
164C2×C3×Q8—31no—
165C2×C3×D4—32no—
166C2×C3×D4—31no—
167C22×C3×C4—21no—
168C22×C3×C4—32no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C2×#67—64no—
172C2×#67C4×D312yes—
173#235—21no—
174#235—21no—
175#235—21no—
176#235—21no—
177C2×D12—62no—
178C2×D12—62no—
179C2×D12—61no—
180C2×D12—61no—
181C2×D12—61no—
182C2×D12—61no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—61no—
186C2×D12—61no—
187C2×D12—61no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—61no—
191C2×D12—64no—
192C2×D12—121no—
193C2×D12—121no—
194C2×D12—121no—
195C2×D12—121no—
196C2×D12D1211yescharacteristic
197C2×C4×D3#6712yes—
198C2×Dic6D1211yescharacteristic
199C3×M16—21no—
200C3×M16—21no—
201C3×M16—22no—
202C3×M16—32no—
203C3×M16—41no—
204C3×M16—64no—
205C3×M16—61no—
206C3×M16—61no—
207C3×M16—61no—
208C3×M16D1212yescomplemented
209C3×M16#6712yescomplemented
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—41no—
213C2×C3×C8—64no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C3×C4⋊C4—61no—
217C3×C22⋊C4—32no—
218C3×C42—61no—
219#217C4×D312yes—
220(C2×D3)⋊C4—64no—
221(C2×D3)⋊C4—64no—
222C4⋊Dic3—21no—
223C4×Dic3—21no—
224#208—21no—
225#208—21no—
226#208—21no—
227#208—62no—
228#208—61no—
229#208—61no—
230#208—61no—
231#208—61no—
232#208—121no—
233#208#6712yescomplemented
234C2×C3⋊C8—21no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—121no—
239ΓL(1,𝔽25)—24no—
240D3×C8—24no—
241C22×C32—41no—
242C22×C32C2×C22⋊C411yescharacteristic
243C22×C32C4×D411yescharacteristic
244C22×C32C4×D411yescharacteristic
245C2×C3⋊D3—42no—
246C2×C3⋊D3—44no—
247C2×C3⋊D3—82no—
248C2×C3⋊D3—82no—
249C2×C3×D3—22no—
250C2×C3×D3—42no—
251C32×C4#12011yescharacteristic
252C32×C4#12111yescharacteristic
253C32×C4#12111yescharacteristic
254C32×C4#12311yescharacteristic
255C3×Dic3—22no—
256C3×Dic3—42no—
257C2×#41—31no—
258C22×D4—91no—
259#131—62no—
260#131—62no—
261C2×M16—31no—
262C2×M16—31no—
263C2×M16—62no—
264C2×M16—91no—
265C2×M16D3211yescharacteristic
266#127—181no—
267#124—181no—
268#121—182no—
269#120—94no—
270#117—31no—
271#101—181no—
272#100—182no—
273#100—181no—
274#100—182no—
275C23×C3—21no—
276C23×C3—32no—
277C23×C3C2×C4×D311yescharacteristic
278C23×C3C2×C4×D311yescharacteristic
279C22×D3—62no—
280C22×D3—62no—
281C22×D3—64no—
282C22×D3—62no—
283C22×D3—62no—
284C22×D3—62no—
285C22×D3—62no—
286C22×D3—122no—
287C22×D3—122no—
288C22×D3—242no—
289C22×D3—242no—
290C22×D3—244no—
291C22×D3(C2×D3)⋊C412yes—
292C3×Q8—61no—
293C3×Q8—61no—
294C3×D4—62no—
295C3×D4—62no—
296C3×D4—61no—
297C3×D4—61no—
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—32no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4C2×D1211yescharacteristic
309C2×C3×C4C2×D1211yescharacteristic
310C2×C3×C4#23511yescharacteristic
311C2×C3×C4#23511yescharacteristic
312C2×C3×C4#23511yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4#23911yescharacteristic
317C2×C3×C4C2×#6711yescharacteristic
318C2×C3×C4C2×#6711yescharacteristic
319C2×C3×C4C2×#6711yescharacteristic
320#67—22no—
321#67—22no—
322#67—244no—
323C2×Dic3—22no—
324C2×Dic3(C2×D3)⋊C412yes—
325D12—21no—
326D12—21no—
327D12—122no—
328D12—122no—
329D12—122no—
330D12—122no—
331D12—121no—
332D12—121no—
333D12—121no—
334D12—121no—
335D12—121no—
336D12—121no—
337D12—121no—
338D12—121no—
339D12—244no—
340C4×D3—22no—
341C4×D3—22no—
342Dic6—21no—
343Dic6—21no—
344C3×C8—22no—
345C3×C8—22no—
346C3×C8—42no—
347C3×C8—62no—
348C3×C8—121no—
349C3⋊C8—22no—
350C3⋊C8—41no—
351C3⋊C8—122no—
352C3⋊C8—121no—
353C3⋊C8—121no—
354C2×C32—21no—
355C2×C32—21no—
356C2×C32—21no—
357C2×C32#38611yescharacteristic
358C3⋊D3—82no—
359C3×D3—42no—
360C24—92no—
361#41—61no—
362#41—61no—
363#41—61no—
364#41—61no—
365C2×Q8—31no—
366C2×D4—32no—
367C2×D4—31no—
368C2×D4—184no—
369C2×D4—181no—
370C2×D4—181no—
371C2×D4—181no—
372C2×D4—181no—
373C2×D4—181no—
374C2×D4—181no—
375C22×C4—32no—
376C22×C4C2×D3211yescharacteristic
377M16—21no—
378M16—32no—
379M16—64no—
380M16—61no—
381M16—61no—
382M16—61no—
383M16—181no—
384M16—181no—
385M16#62612yescomplemented
386C2×C8—21no—
387C2×C8—64no—
388C2×C8—61no—
389C2×C8—61no—
390C2×C8—181no—
391C4⋊C4—61no—
392C22⋊C4—32no—
393C22⋊C4—184no—
394C42—61no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—42no—
401C22×C3—62no—
402C22×C3—122no—
403C22×C3C4×D1211yescharacteristic
404C22×C3D3×C22⋊C411yescharacteristic
405C22×C3#89311yescharacteristic
406C22×C3C2×(C2×D3)⋊C411yescharacteristic
407C22×C3C4×#6711yescharacteristic
408C22×C3C4×#6711yescharacteristic
409C2×D3—22no—
410C2×D3—42no—
411C2×D3—124no—
412C2×D3—124no—
413C2×D3—124no—
414C2×D3—122no—
415C2×D3—122no—
416C2×D3—244no—
417C2×D3—244no—
418C2×D3—242no—
419C2×D3—242no—
420C2×D3—242no—
421C2×D3—242no—
422C2×D3—244no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—62no—
428C3×C4—122no—
429C3×C4#88211yescharacteristic
430C3×C4#88411yescharacteristic
431C3×C4#89411yescharacteristic
432C3×C4#89511yescharacteristic
433C3×C4#92911yescharacteristic
434C3×C4#93011yescharacteristic
435C3×C4#93011yescharacteristic
436C3×C4#95311yescharacteristic
437Dic3—22no—
438Dic3—42no—
439C32#191411yescharacteristic, complemented, Sylow
440C23—32no—
441C23—182no—
442C23—182no—
443C23—182no—
444C23—722no—
445C23C4×D3211yescharacteristic
446Q8—61no—
447Q8—61no—
448D4—62no—
449D4—62no—
450D4—61no—
451D4—61no—
452D4—361no—
453D4—361no—
454D4—361no—
455D4—361no—
456D4—724no—
457C2×C4—32no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4#379811yescharacteristic
462C2×C4#379911yescharacteristic
463C2×C4D3×D1211yescharacteristic
464C2×C4C2×#62611yescharacteristic
465C2×C4D3×#6711yescharacteristic
466C2×C4D3×#6711yescharacteristic
467C8—22no—
468C8—62no—
469C8—121no—
470C8—361no—
471C2×C3—22no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—41no—
480C2×C3—41no—
481C2×C3—122no—
482C2×C3#466511yescharacteristic
483C2×C3#521311yescharacteristic
484D3—42no—
485D3—244no—
486D3—242no—
487D3—242no—
488C22—41no—
489C22—62no—
490C22—122no—
491C22—364no—
492C22—362no—
493C22—722no—
494C22—722no—
495C22C4×#62611yescharacteristic
496C22#6390411yescharacteristic
497C22D3×(C2×D3)⋊C411yescharacteristic
498C4—62no—
499C4—122no—
500C4#6385011yescharacteristic
501C4#6390611yescharacteristic
502C4#6390911yescharacteristic
503C4#6397711yescharacteristic
504C3—21no—
505C3#6904011yescharacteristic, complemented
506C3#7203011yescharacteristic, complemented
507C2—21no—
508C2—21no—
509C2—21no—
510C2—122no—
511C2—722no—
512C2#1059138211yescharacteristic
subgroupG/H
centerC2#10591382
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radical#10595045C2
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. C3×#5745C2semidirect
3. C2×#63650C2semidirect
4. C2×#63559C2semidirect
5. #10591076C2semidirect
6. C3×#4559C2semidirect
7. #10589170C2semidirect
30. #5745D3semidirect
41. #4559D3semidirect
61. C32×M16D4semidirect
72. C3×#208D4semidirect
208. C3×M16D12semidirect
209. C3×M16#67semidirect
233. #208#67semidirect
385. M16#626semidirect
439. C32#1914semidirect
505. C3#69040semidirect
506. C3#72030semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
#105950452
C2×#636502
C2×#635592
#105910762
C3×#45592
#105891702
#720303
#690403