Finite Group Databasebeta

← #11868005

Subgroups — #11868005

Order 1152.

1356 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#575C211yesmaximal, characteristic, complemented
2#10596293C211yesmaximal, characteristic, complemented
3C2×#64159C211yesmaximal, characteristic, complemented
4C2×#64157C211yesmaximal, characteristic, complemented
5#10592936C211yesmaximal, characteristic, complemented
6#10592903C212yesmaximal, complemented
7#10592902C212yesmaximal, complemented
8#10592899C212yesmaximal, complemented
9#10592898C212yesmaximal, complemented
10#10592831C211yesmaximal, characteristic, complemented
11C2×#63649C211yesmaximal, characteristic, complemented
12#84001—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C2×C32×#41C2211yescharacteristic
15C2×#3828C2211yescharacteristic
16C32×#137—21no—
17C32×#137C2212yes—
18C32×AGL(1,ℤ/8)—21no—
19C32×AGL(1,ℤ/8)C2212yes—
20C32×#135—22no—
21C2×C32×M16C2211yescharacteristic
22#64160C2212yes—
23#64159—22no—
24#64159—21no—
25#64159—21no—
26#64159—21no—
27#64159—21no—
28#64158C2212yes—
29#64157—21no—
30#64157—21no—
31#64157C2212yes—
32#64157C2212yes—
33C2×#3756C2211yescharacteristic, complemented
34#64151—21no—
35C2×#3755C2211yescharacteristic, complemented
36C2×#3754C2211yescharacteristic, complemented
37#64141—21no—
38C2×#3753C2211yescharacteristic, complemented
39C2×#3748—21no—
40C2×#3748C2211yescharacteristic
41C2×#3748C2211yescharacteristic
42C22×C3⋊(C3⋊C8)—21no—
43C22×C3⋊(C3⋊C8)C2211yescharacteristic
44#63663C2212yescomplemented
45#63660C2212yescomplemented
46#63651C2212yescomplemented
47#63650C2212yescomplemented
48#63649C2212yescomplemented
49#63649C2212yescomplemented
50C3×#575D314yescomplemented
51#5822—34no—
52C2×#950—34no—
53C2×#948—34no—
54#5237—34no—
55#5204—38no—
56#5203—38no—
57#5200—38no—
58#5199—38no—
59#5132—34no—
60C2×#822—34no—
61C32×#41—21no—
62C32×#41—21no—
63C32×#41—21no—
64C32×#41—21no—
65C32×#41—21no—
66C32×#41—21no—
67C32×#41D412yes—
68C32×#41C2312yes—
69C2×C32×Q8D411yescharacteristic
70C2×C32×Q8C2311yescharacteristic
71C2×C32×D4—21no—
72C2×C32×D4—21no—
73C2×C32×D4D411yescharacteristic
74C2×C32×D4C2311yescharacteristic
75C22×C32×C4—21no—
76C22×C32×C4—21no—
77C22×C32×C4C2311yescharacteristic
78C2×#638—21no—
79#3828—21no—
80#3828—21no—
81#3828—21no—
82#3828—21no—
83C2×C4⋊(C3⋊D3)C2311yescharacteristic
84C2×C4×C3⋊D3—21no—
85C2×#634C2311yescharacteristic
86C32×Q16—22no—
87C32×SD16—22no—
88C32×SD16—22no—
89C32×D8—22no—
90C32×M16—21no—
91C32×M16C2312yes—
92C2×C32×C8—21no—
93#3756—22no—
94#3756—21no—
95#3756—21no—
96#3755—22no—
97#3755—21no—
98#3755—21no—
99#3754—22no—
100#3754—21no—
101#3754—21no—
102#3753—22no—
103#3753—21no—
104#3753—21no—
105#3748—21no—
106#3748—21no—
107#3748—22no—
108#3748—22no—
109#3748C2312yes—
110#3748C2312yes—
111C2×C3⋊(C3⋊C8)—21no—
112C2×C3⋊(C3⋊C8)—21no—
113C2×C3⋊(C3⋊C8)—22no—
114C2×C3⋊(C3⋊C8)—22no—
115C2×C3⋊(C3⋊C8)D411yescharacteristic
116C2×C3⋊(C3⋊C8)D411yescharacteristic
117C2×C3⋊(C3⋊C8)D411yescharacteristic
118C2×C3⋊(C3⋊C8)D411yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3067—91noSylow
122C2×C3×#41C2×D314yes—
123C2×C3×#41C2×D314yes—
124C2×#235—34no—
125C3×#137—24no—
126C3×#137C2×D318yes—
127C3×AGL(1,ℤ/8)—24no—
128C3×AGL(1,ℤ/8)C2×D318yes—
129C3×#135—28no—
130C2×C3×M16C2×D314yes—
131#951—38no—
132#950—64no—
133#950—64no—
134#950—64no—
135#950—64no—
136#950—68no—
137#949—38no—
138#948—38no—
139#948—38no—
140#948—64no—
141#948—64no—
142C2×#216—34no—
143#942—64no—
144C2×#215—34no—
145C2×#214—34no—
146#932—64no—
147C2×#213—34no—
148C2×#208—34no—
149C2×#208—34no—
150C2×#208—64no—
151C22×C3⋊C8—34no—
152C22×C3⋊C8—64no—
153#836—38no—
154#833—38no—
155#824—38no—
156#823—38no—
157#822—38no—
158#822—38no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32#4111yescharacteristic
162C22×C3⋊D3—21no—
163C32×Q8—21no—
164C32×Q8—21no—
165C32×Q8—21no—
166C32×Q8C2×D412yes—
167C32×D4—22no—
168C32×D4—22no—
169C32×D4—21no—
170C32×D4—21no—
171C32×D4—21no—
172C32×D4—41no—
173C32×D4—41no—
174C32×D4C2×D412yes—
175C2×C32×C4—21no—
176C2×C32×C4—22no—
177C2×C32×C4—22no—
178C2×C32×C4—21no—
179C2×C32×C4—41no—
180C2×C32×C4—41no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4#4111yescharacteristic
186C2×C32×C4C2411yescharacteristic
187#638—41no—
188#638—41no—
189C2×C3⋊Dic3—21no—
190C4⋊(C3⋊D3)—21no—
191C4⋊(C3⋊D3)—21no—
192C4×C3⋊D3—41no—
193C4×C3⋊D3—41no—
194#634—21no—
195#634—21no—
196C32×C8—22no—
197C3⋊(C3⋊C8)—22no—
198C3⋊(C3⋊C8)—22no—
199C3⋊(C3⋊C8)C2×D411yescharacteristic
200C3⋊(C3⋊C8)C2×D411yescharacteristic
201C3⋊(C3⋊C8)C2×D411yescharacteristic
202C3⋊(C3⋊C8)C2×D411yescharacteristic
203#575—91no—
204#575C3⋊D311yescharacteristic, complemented
205C2×#135—91no—
206C2×#131—91no—
207#473—92no—
208#472—92no—
209#471—92no—
210#471—92no—
211C2×#108—91no—
212#413—91no—
213#413—91no—
214C3×#41—24no—
215C3×#41—24no—
216C3×#41—24no—
217C3×#41—24no—
218C3×#41—24no—
219C3×#41—24no—
220C3×#41#6718yes—
221C3×#41C22×D318yes—
222C2×C3×Q8#6714yes—
223C2×C3×Q8C22×D314yes—
224C2×C3×D4—24no—
225C2×C3×D4—24no—
226C2×C3×D4#6714yes—
227C2×C3×D4C22×D314yes—
228C22×C3×C4—24no—
229C22×C3×C4—24no—
230C22×C3×C4C22×D314yes—
231C2×#67—64no—
232#235—64no—
233#235—64no—
234#235—64no—
235#235—64no—
236C2×D12—34no—
237C2×C4×D3—64no—
238C2×Dic6—34no—
239C3×Q16—28no—
240C3×SD16—28no—
241C3×SD16—28no—
242C3×D8—28no—
243C3×M16—24no—
244C3×M16C22×D318yes—
245C2×C3×C8—24no—
246#216—64no—
247#216—64no—
248#216—68no—
249#215—64no—
250#215—64no—
251#215—68no—
252#214—64no—
253#214—64no—
254#214—68no—
255#213—64no—
256#213—64no—
257#213—68no—
258#208—38no—
259#208—38no—
260#208—68no—
261#208—68no—
262#208—64no—
263#208—64no—
264C2×C3⋊C8—34no—
265C2×C3⋊C8—34no—
266C2×C3⋊C8—34no—
267C2×C3⋊C8—34no—
268C2×C3⋊C8—34no—
269C2×C3⋊C8—34no—
270C2×C3⋊C8—68no—
271C2×C3⋊C8—68no—
272C2×C3⋊C8—64no—
273C2×C3⋊C8—64no—
274C22×C32—22no—
275C22×C32—41no—
276C22×C32—42no—
277C22×C32—41no—
278C22×C32—81no—
279C22×C32#12111yescharacteristic
280C22×C32#12111yescharacteristic
281C22×C32C2×#4111yescharacteristic
282C2×C3⋊D3—41no—
283C2×C3⋊D3—81no—
284C32×C4—22no—
285C32×C4—41no—
286C32×C4#12111yescharacteristic
287C32×C4#12111yescharacteristic
288C32×C4C22×D411yescharacteristic
289C32×C4C22×D411yescharacteristic
290C3⋊Dic3—41no—
291C2×#41—91no—
292C2×#41C2×C3⋊D311yescharacteristic
293C2×#41C2×C3⋊D311yescharacteristic
294#137—21no—
295#137—92no—
296#137—181no—
297#137C2×C3⋊D312yes—
298AGL(1,ℤ/8)—21no—
299AGL(1,ℤ/8)—92no—
300AGL(1,ℤ/8)—181no—
301AGL(1,ℤ/8)C2×C3⋊D312yes—
302#135—22no—
303#135—181no—
304#135—181no—
305#135—181no—
306#135—181no—
307#135—182no—
308C2×Q16—91no—
309C2×SD16—91no—
310C2×SD16—91no—
311C2×D8—91no—
312#131—92no—
313#131—92no—
314#131—181no—
315#131—181no—
316C2×M16—91no—
317C2×M16—91no—
318C2×M16—181no—
319C2×M16C2×C3⋊D311yescharacteristic
320C22×C8—91no—
321C22×C8—181no—
322#108—92no—
323#108—92no—
324#101—92no—
325#101—92no—
326#100—92no—
327#100—92no—
328C23×C3—24no—
329C23×C3—24no—
330C23×C3#23714yes—
331C22×D3—64no—
332C3×Q8—24no—
333C3×Q8—24no—
334C3×Q8—24no—
335C3×Q8C2×#6718yes—
336C3×D4—28no—
337C3×D4—28no—
338C3×D4—24no—
339C3×D4—24no—
340C3×D4—24no—
341C3×D4—44no—
342C3×D4—44no—
343C3×D4C2×#6718yes—
344C2×C3×C4—24no—
345C2×C3×C4—28no—
346C2×C3×C4—28no—
347C2×C3×C4—24no—
348C2×C3×C4—44no—
349C2×C3×C4—44no—
350C2×C3×C4D3×D414yes—
351C2×C3×C4D3×D414yes—
352C2×C3×C4#23714yes—
353C2×C3×C4C2×#6714yes—
354C2×C3×C4C2×#6714yes—
355C2×C3×C4C23×D314yes—
356#67—124no—
357#67—124no—
358C2×Dic3—64no—
359D12—64no—
360D12—64no—
361C4×D3—124no—
362C4×D3—124no—
363Dic6—64no—
364Dic6—64no—
365C3×C8—28no—
366C3⋊C8—34no—
367C3⋊C8—34no—
368C3⋊C8—34no—
369C3⋊C8—34no—
370C3⋊C8—68no—
371C3⋊C8—68no—
372C2×C32—21no—
373C2×C32—21no—
374C2×C32—21no—
375C2×C32—42no—
376C2×C32—81no—
377C2×C32C2×#12111yescharacteristic
378C3⋊D3—81no—
379#41—21no—
380#41—21no—
381#41—21no—
382#41—21no—
383#41—21no—
384#41—21no—
385#41—181no—
386#41—181no—
387#41—181no—
388#41—181no—
389#41#63812yes—
390#41C22×C3⋊D312yes—
391C2×Q8—91no—
392C2×Q8#63811yescharacteristic
393C2×Q8C22×C3⋊D311yescharacteristic
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—91no—
397C2×D4—181no—
398C2×D4#63811yescharacteristic
399C2×D4C22×C3⋊D311yescharacteristic
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—181no—
403C22×C4C22×C3⋊D311yescharacteristic
404Q16—22no—
405Q16—181no—
406Q16—181no—
407Q16—182no—
408SD16—22no—
409SD16—22no—
410SD16—181no—
411SD16—181no—
412SD16—181no—
413SD16—181no—
414SD16—182no—
415SD16—182no—
416D8—22no—
417D8—181no—
418D8—181no—
419D8—182no—
420M16—21no—
421M16—92no—
422M16—92no—
423M16—182no—
424M16—182no—
425M16—181no—
426M16—181no—
427M16C22×C3⋊D312yes—
428C2×C8—21no—
429C2×C8—91no—
430C2×C8—91no—
431C2×C8—91no—
432C2×C8—91no—
433C2×C8—91no—
434C2×C8—91no—
435C2×C8—182no—
436C2×C8—182no—
437C2×C8—181no—
438C2×C8—181no—
439C22×C3—28no—
440C22×C3—44no—
441C22×C3—48no—
442C22×C3—44no—
443C22×C3—84no—
444C22×C3#93914yes—
445C22×C3#93914yes—
446C22×C3C2×#23714yes—
447C2×D3—124no—
448C2×D3—244no—
449C3×C4—28no—
450C3×C4—44no—
451C3×C4#93914yes—
452C3×C4#93914yes—
453C3×C4C2×D3×D414yes—
454C3×C4C22×#6714yes—
455Dic3—124no—
456C32#306711yescharacteristic, complemented, Sylow
457C23—21no—
458C23—21no—
459C23—181no—
460C23#383011yescharacteristic
461Q8—21no—
462Q8—21no—
463Q8—21no—
464Q8—181no—
465Q8—181no—
466Q8C2×#63812yes—
467D4—22no—
468D4—22no—
469D4—21no—
470D4—21no—
471D4—21no—
472D4—41no—
473D4—41no—
474D4—181no—
475D4—181no—
476D4—361no—
477D4—361no—
478D4C2×#63812yes—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—181no—
486C2×C4—361no—
487C2×C4—361no—
488C2×C4D4×C3⋊D311yescharacteristic
489C2×C4D4×C3⋊D311yescharacteristic
490C2×C4#383011yescharacteristic
491C2×C4C2×#63811yescharacteristic
492C2×C4C2×#63811yescharacteristic
493C2×C4C23×C3⋊D311yescharacteristic
494C8—22no—
495C8—91no—
496C8—91no—
497C8—91no—
498C8—91no—
499C8—182no—
500C8—182no—
501C2×C3—24no—
502C2×C3—24no—
503C2×C3—24no—
504C2×C3—48no—
505C2×C3—84no—
506C2×C3C2×#93914yes—
507D3—244no—
508C22—22no—
509C22—41no—
510C22—42no—
511C22—41no—
512C22—81no—
513C22—361no—
514C22—721no—
515C22#6414811yescharacteristic
516C22#6414811yescharacteristic
517C22C2×#383011yescharacteristic
518C4—22no—
519C4—41no—
520C4—361no—
521C4#6414811yescharacteristic
522C4#6414811yescharacteristic
523C4C2×D4×C3⋊D311yescharacteristic
524C4C22×#63811yescharacteristic
525C3#8400114yescomplemented
526C2—21no—
527C2—21no—
528C2—21no—
529C2—42no—
530C2—81no—
531C2—721no—
532C2C2×#6414811yescharacteristic
subgroupG/H
centerC4#64148
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#575C2
socleC2×C32C2×#121
hypercenter#575C3⋊D3
hypocenterC32#3067
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C32×#575C2semidirect
2. #10596293C2semidirect
3. C2×#64159C2semidirect
4. C2×#64157C2semidirect
5. #10592936C2semidirect
6. #10592903C2semidirect
7. #10592902C2semidirect
8. #10592899C2semidirect
9. #10592898C2semidirect
10. #10592831C2semidirect
11. C2×#63649C2semidirect
33. C2×#3756C22semidirect
35. C2×#3755C22semidirect
36. C2×#3754C22semidirect
38. C2×#3753C22semidirect
44. #63663C22semidirect
45. #63660C22semidirect
46. #63651C22semidirect
47. #63650C22semidirect
48. #63649C22semidirect
49. #63649C22semidirect
50. C3×#575D3semidirect
204. #575C3⋊D3semidirect
456. C32#3067semidirect
525. C3#84001semidirect

Maximal subgroups

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

subgroupindex
C32×#5752
#105962932
C2×#641592
C2×#641572
#105929362
#105929032
#105929022
#105928992
#105928982
#105928312
C2×#636492
#840013