Finite Group Databasebeta

← #11878652

Subgroups — #11878652

Order 1152.

1123 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594008C211yesmaximal, characteristic, complemented
2#10593907C211yesmaximal, characteristic, complemented
3#10592384C211yesmaximal, characteristic, complemented
4C3×#4695C211yesmaximal, characteristic, complemented
5C3×#4694C211yesmaximal, characteristic, complemented
6#10590945C214yesmaximal, complemented
7#10590749C214yesmaximal, complemented
8#10590352C211yesmaximal, characteristic, complemented
9#10590277C211yesmaximal, characteristic, complemented
10#81785—31nomaximal
11#81566—31nomaximal
12C2×#3802—21no—
13C2×#3802—21no—
14C2×#3802C2212yes—
15C2×#3796—21no—
16C42×C3⋊D3C2211yescharacteristic
17C2×C3×D24C2214yescomplemented
18C3×#874C2211yescharacteristic
19C3×#874C2211yescharacteristic
20C3×#874C2211yescharacteristic, complemented
21C3×#869C2211yescharacteristic, complemented
22#63916—21no—
23#63916C2212yes—
24#63914—21no—
25#63914—21no—
26#63914C2212yes—
27#63898—21no—
28#63898C2212yescomplemented
29#63863—21no—
30C2×#3713C2214yescomplemented
31C32×C4×C8C2211yescharacteristic, complemented
32#63647C2212yes—
33#63641C2212yescomplemented
34C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
35C3×#821C2214yescomplemented
36#63562C2214yescomplemented
37#5725—31no—
38#5716—31no—
39D3×#127—31no—
40D3×#127—31no—
41C3×#493—31no—
42C3×#486—31no—
43#5156—34no—
44#5150—34no—
45#5088—31no—
46#5073—31no—
47#5073—31no—
48#5070—31no—
49#4786—34no—
50#4773—34no—
51#4695D311yescharacteristic, complemented
52#4694D311yescharacteristic, complemented
53#4685—31no—
54#4685—31no—
55#4685—61no—
56C22×D32—22no—
57C2×C4×C3⋊D3D411yescharacteristic
58C2×C4×C3⋊D3D411yescharacteristic
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12—21no—
65C2×C3×D12—21no—
66C2×C3×D12C2312yes—
67C2×C3×D12C2312yes—
68C2×C3×D12C2312yes—
69C2×C3×Dic6—21no—
70C2×#626—22no—
71C2×#625—22no—
72C2×#625—22no—
73C2×#625—22no—
74C2×D3×Dic3—22no—
75#3802—44no—
76#3802—44no—
77#3802—44no—
78#3796—44no—
79C2×C32×C8C2312yes—
80C32×C42C2311yescharacteristic
81C4×C3⋊Dic3D411yescharacteristic
82C4×C3⋊Dic3D411yescharacteristic
83C4×C3⋊Dic3C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2312yes—
87C3×D24—44no—
88(C2×D3)⋊Dic3—22no—
89(C2×D3)⋊Dic3—22no—
90#3713—44no—
91#3205—91noSylow
92C2×#239—61no—
93C2×#237—61no—
94C2×D3×D4—32no—
95C2×D3×D4—32no—
96C2×D3×D4—61no—
97C2×D3×D4—61no—
98C2×D3×D4—61no—
99C2×D3×D4—61no—
100C2×C3×D8—34no—
101C3×C4⋊Q8—31no—
102C3×#127—31no—
103C3×#127—31no—
104C3×#127—31no—
105#947—61no—
106#940—32no—
107#940—32no—
108#940—61no—
109#940—61no—
110#940—61no—
111#940—61no—
112#938—32no—
113#938—61no—
114#936—61no—
115D4×Dic3—32no—
116D4×Dic3—61no—
117C2×#213—34no—
118C2×#213—34no—
119C2×D24C2×D314yescomplemented
120#895—32no—
121#895—61no—
122#893—32no—
123#893—61no—
124#874C2×D311yescharacteristic
125#874C2×D311yescharacteristic
126#874C2×D311yescharacteristic, complemented
127C42×D3—31no—
128C42×D3—31no—
129C42×D3—61no—
130#869C2×D311yescharacteristic, complemented
131C3×#102—34no—
132C3×C4×C8—21no—
133C3×C4×C8C2×D311yescharacteristic, complemented
134C3×C4×C8C2×D311yescharacteristic, complemented
135#832—34no—
136#821C2×D314yescomplemented
137(C2×D3)⋊C8—32no—
138(C2×D3)⋊C8—32no—
139(C2×D3)⋊C8—62no—
140Dic3⋊C8—32no—
141Dic3⋊C8—32no—
142Dic3⋊C8—62no—
143#809—34no—
144C4×C3⋊C8—31no—
145C4×C3⋊C8—31no—
146C4×C3⋊C8—61no—
147C22×C3⋊D3C2×D411yescharacteristic
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C2×D32—44no—
152C2×D32—44no—
153C2×D32—44no—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2411yescharacteristic
157C2×C3⋊Dic3C2×D411yescharacteristic
158C2×C3⋊Dic3C2×D411yescharacteristic
159C2×C3⋊Dic3C2×D411yescharacteristic
160C4×C3⋊D3—22no—
161C4×C3⋊D3—22no—
162C4×C3⋊D3D814yescomplemented
163C2×C3×Dic3—22no—
164C3×D12—24no—
165C3×D12—24no—
166C3×D12—24no—
167C3×D12—42no—
168C3×D12—42no—
169C3×D12—42no—
170C3×D12—42no—
171C3×D12—42no—
172C3×D12—42no—
173C3×Dic6—42no—
174#626—44no—
175#625—44no—
176#625—44no—
177#625—44no—
178D3×Dic3—44no—
179C32×C8—22no—
180C3⋊(C3⋊C8)—22no—
181#532—91no—
182C2×#127—91no—
183#493—31no—
184#493—91no—
185#486—31no—
186#486—91no—
187#459—94no—
188#447—94no—
189#431—91no—
190C23×D3—62no—
191C23×D3—62no—
192C2×C3×Q8—61no—
193C2×C3×D4—32no—
194C2×C3×D4—32no—
195C2×C3×D4—32no—
196C2×C3×D4—61no—
197C2×C3×D4—61no—
198C2×C3×D4—61no—
199C2×C3×D4—61no—
200C2×C3×D4—61no—
201C2×C3×D4—61no—
202C2×#67—62no—
203C2×#67—62no—
204C2×#67—62no—
205C2×#67—62no—
206C2×#67—62no—
207C2×#67—62no—
208C2×#67—62no—
209C22×Dic3—62no—
210#239—124no—
211#237—124no—
212D3×D4—124no—
213D3×D4—124no—
214D3×D4—124no—
215D3×D4—124no—
216D3×D4—124no—
217D3×D4—124no—
218C2×D12—21no—
219C2×D12—21no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12—21no—
224C2×D12—62no—
225C2×D12C22×D312yes—
226C2×D12C22×D312yes—
227C2×D12C22×D312yes—
228C2×C4×D3—31no—
229C2×C4×D3—31no—
230C2×C4×D3—31no—
231C2×C4×D3—31no—
232C2×C4×D3—31no—
233C2×C4×D3—31no—
234C2×C4×D3—61no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×C4×D3—62no—
238C2×Dic6—21no—
239C3×D8—124no—
240C2×C3×C8—22no—
241C2×C3×C8C22×D312yes—
242C2×C3×C8C22×D312yes—
243C3×C4⋊C4—32no—
244C3×C4⋊C4—61no—
245C3×C42—21no—
246C3×C42C22×D311yescharacteristic
247C3×C42C22×D311yescharacteristic
248#217—62no—
249#217—62no—
250#213—124no—
251#213—124no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254C4⋊Dic3—21no—
255C4⋊Dic3C22×D312yes—
256C4×Dic3—31no—
257C4×Dic3—31no—
258C4×Dic3—31no—
259C4×Dic3—31no—
260C4×Dic3—31no—
261C4×Dic3—31no—
262C4×Dic3—61no—
263C4×Dic3—61no—
264C4×Dic3—61no—
265C2×C3⋊C8—32no—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—62no—
268D24—44no—
269C22×C32C22×D411yescharacteristic
270C2×C3⋊D3—21no—
271C2×C3⋊D3—21no—
272C2×C3⋊D3C2×D812yes—
273C2×C3×D3—42no—
274C2×C3×D3—42no—
275C2×C3×D3—42no—
276C2×C3×D3—42no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C2×C3×D3—42no—
282D32—88no—
283C32×C4C2×D812yes—
284C32×C4AGL(1,ℤ/8)12yes—
285C32×C4H(5,𝔽2)12yes—
286C3⋊Dic3—21no—
287C3⋊Dic3—21no—
288C3⋊Dic3C2×D812yes—
289C3×Dic3—42no—
290C2×#41—181no—
291C22×D4—92no—
292C22×D4—181no—
293C22×D4—181no—
294C2×D8—34no—
295C2×D8—94no—
296C4⋊Q8—31no—
297#127—31no—
298#127—31no—
299#127—31no—
300#127—92no—
301#127—181no—
302#127—181no—
303#124—181no—
304#121—92no—
305#121—181no—
306C4×D4—92no—
307C4×D4—181no—
308C2×C42—91no—
309C4⋊C8—92no—
310#102—34no—
311#102—94no—
312C22⋊C8—92no—
313C4×C8—91no—
314C4×C8D3211yescharacteristic, complemented
315C23×C3—62no—
316C23×C3—62no—
317C23×C3—62no—
318C22×D3—22no—
319C22×D3—22no—
320C22×D3—22no—
321C22×D3—31no—
322C22×D3—31no—
323C22×D3—61no—
324C22×D3—124no—
325C22×D3—124no—
326C22×D3—124no—
327C22×D3—124no—
328C22×D3—124no—
329C22×D3—124no—
330C3×Q8—122no—
331C3×D4—64no—
332C3×D4—64no—
333C3×D4—64no—
334C3×D4—122no—
335C3×D4—122no—
336C3×D4—122no—
337C3×D4—122no—
338C3×D4—122no—
339C3×D4—122no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—62no—
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350#67—124no—
351#67—124no—
352#67—124no—
353#67—124no—
354#67—124no—
355#67—124no—
356#67—124no—
357C2×Dic3—22no—
358C2×Dic3—31no—
359C2×Dic3—31no—
360C2×Dic3—31no—
361C2×Dic3—31no—
362C2×Dic3—31no—
363C2×Dic3—31no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—124no—
368D12—24no—
369D12—24no—
370D12—24no—
371D12—42no—
372D12—42no—
373D12—42no—
374D12—42no—
375D12—42no—
376D12—42no—
377D12—124no—
378C4×D3—34no—
379C4×D3—34no—
380C4×D3—64no—
381C4×D3—62no—
382C4×D3—62no—
383C4×D3—62no—
384C4×D3—62no—
385C4×D3—122no—
386C4×D3—122no—
387C4×D3—124no—
388Dic6—42no—
389C3×C8—22no—
390C3×C8—22no—
391C3×C8—42no—
392C3⋊C8—62no—
393C3⋊C8—62no—
394C3⋊C8—122no—
395C2×C32#53511yescharacteristic
396C2×C32C22×D811yescharacteristic
397C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
398C3⋊D3—22no—
399C3×D3—82no—
400C3×D3—82no—
401C3×D3—82no—
402C24—182no—
403#41—364no—
404C2×Q8—61no—
405C2×D4—32no—
406C2×D4—32no—
407C2×D4—32no—
408C2×D4—61no—
409C2×D4—61no—
410C2×D4—61no—
411C2×D4—61no—
412C2×D4—61no—
413C2×D4—61no—
414C2×D4—182no—
415C2×D4—182no—
416C2×D4—182no—
417C2×D4—182no—
418C2×D4—364no—
419C2×D4—364no—
420C2×D4—364no—
421C22×C4—91no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—182no—
425D8—124no—
426D8—364no—
427C2×C8—92no—
428C2×C8C2×D3212yes—
429C4⋊C4—32no—
430C4⋊C4—61no—
431C22⋊C4—182no—
432C22⋊C4—182no—
433C42—91no—
434C42—91no—
435C42—91no—
436C42C2×D3211yescharacteristic
437C22×C3—21no—
438C22×C3—122no—
439C22×C3—122no—
440C22×C3—122no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3—122no—
444C22×C3—122no—
445C22×C3—122no—
446C22×C3—122no—
447C22×C3C2×D3×D411yescharacteristic
448C22×C3C2×D3×D411yescharacteristic
449C2×D3—32no—
450C2×D3—32no—
451C2×D3—42no—
452C2×D3—42no—
453C2×D3—42no—
454C2×D3—42no—
455C2×D3—42no—
456C2×D3—42no—
457C2×D3—42no—
458C2×D3—42no—
459C2×D3—42no—
460C2×D3—62no—
461C2×D3—61no—
462C2×D3—61no—
463C2×D3—61no—
464C2×D3—61no—
465C2×D3—121no—
466C2×D3—121no—
467C2×D3—248no—
468C2×D3—248no—
469C3×C4—22no—
470C3×C4—22no—
471C3×C4—22no—
472C3×C4—122no—
473C3×C4D3×D812yes—
474C3×C4D3×D812yes—
475C3×C4#91112yes—
476C3×C4#91412yes—
477C3×C4#100412yes—
478C3×C4#100912yes—
479Dic3—32no—
480Dic3—32no—
481Dic3—42no—
482Dic3—62no—
483Dic3—61no—
484Dic3—61no—
485Dic3—61no—
486Dic3—61no—
487Dic3—121no—
488Dic3—121no—
489C32#320511yescharacteristic, complemented, Sylow
490C23—62no—
491C23—62no—
492C23—62no—
493C23—91no—
494C23—364no—
495C23—364no—
496C23—364no—
497Q8—122no—
498D4—64no—
499D4—64no—
500D4—64no—
501D4—122no—
502D4—122no—
503D4—122no—
504D4—122no—
505D4—122no—
506D4—122no—
507D4—364no—
508D4—364no—
509D4—364no—
510D4—364no—
511C2×C4—62no—
512C2×C4—91no—
513C2×C4—94no—
514C2×C4—91no—
515C2×C4—91no—
516C2×C4—182no—
517C2×C4—182no—
518C2×C4—364no—
519C2×C4#380211yescharacteristic
520C2×C4#380211yescharacteristic
521C2×C4C22×D3211yescharacteristic
522C8—22no—
523C8—182no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—242no—
528C2×C3—242no—
529C2×C3—242no—
530C2×C3#567411yescharacteristic
531C2×C3#571511yescharacteristic
532C2×C3C2×D3×D811yescharacteristic
533C2×C3C2×D3×D811yescharacteristic
534C2×C3C2×#91111yescharacteristic
535C2×C3C2×#91411yescharacteristic
536D3—62no—
537D3—62no—
538D3—82no—
539D3—82no—
540D3—82no—
541D3—122no—
542C22—92no—
543C22—122no—
544C22—122no—
545C22—122no—
546C22—122no—
547C22—122no—
548C22—122no—
549C22—122no—
550C22—122no—
551C22—122no—
552C22—181no—
553C22—181no—
554C22—728no—
555C22C2×#380211yescharacteristic
556C4—92no—
557C4—122no—
558C4—181no—
559C4—181no—
560C4#6379712yes—
561C4#6379812yes—
562C4#6430712yes—
563C3—21no—
564C3#8156611yescharacteristic, complemented
565C3#8178511yescharacteristic, complemented
566C2—182no—
567C2—242no—
568C2—242no—
569C2—242no—
570C2#1059401011yescharacteristic
571C2C2×#6379711yescharacteristic
572C2C2×#6379811yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
hypercenterC4×C8D32
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10594008C2semidirect
2. #10593907C2semidirect
3. #10592384C2semidirect
4. C3×#4695C2semidirect
5. C3×#4694C2semidirect
6. #10590945C2semidirect
7. #10590749C2semidirect
8. #10590352C2semidirect
9. #10590277C2semidirect
17. C2×C3×D24C22semidirect
20. C3×#874C22semidirect
21. C3×#869C22semidirect
28. #63898C22semidirect
30. C2×#3713C22semidirect
31. C32×C4×C8C22semidirect
33. #63641C22semidirect
34. C4×C3⋊(C3⋊C8)C22semidirect
35. C3×#821C22semidirect
36. #63562C22semidirect
51. #4695D3semidirect
52. #4694D3semidirect
119. C2×D24C2×D3semidirect
126. #874C2×D3semidirect
130. #869C2×D3semidirect
133. C3×C4×C8C2×D3semidirect
134. C3×C4×C8C2×D3semidirect
136. #821C2×D3semidirect
162. C4×C3⋊D3D8semidirect
314. C4×C8D32semidirect
489. C32#3205semidirect
564. C3#81566semidirect
565. C3#81785semidirect

Maximal subgroups

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

subgroupindex
#105940082
#105939072
#105923842
C3×#46952
C3×#46942
#105909452
#105907492
#105903522
#105902772
#817853
#815663