Finite Group Databasebeta

← #11878653

Subgroups — #11878653

Order 1152.

1123 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#874C211yesmaximal, characteristic, complemented
2#10593897C211yesmaximal, characteristic, complemented
3#10592393C211yesmaximal, characteristic, complemented
4C3×#4695C211yesmaximal, characteristic, complemented
5C3×#4685C211yesmaximal, characteristic, complemented
6#10590944C214yesmaximal, complemented
7#10590753C214yesmaximal, complemented
8#10590350C211yesmaximal, characteristic, complemented
9#10590273C211yesmaximal, characteristic, complemented
10#81785—31nomaximal
11#79303—31nomaximal
12C2×D3×D12—21no—
13C2×D3×D12—21no—
14C2×D3×D12C2212yes—
15C2×#3795—21no—
16#64083C2211yescharacteristic
17#64078C2211yescharacteristic, complemented
18C2×C3×D24C2214yescomplemented
19C3×#874C2211yescharacteristic
20C3×#874C2211yescharacteristic, complemented
21C3×C42×D3C2211yescharacteristic
22#63911—21no—
23#63911—21no—
24#63911C2212yes—
25#63908—21no—
26#63908C2212yes—
27Dic3×D12—21no—
28Dic3×D12C2212yescomplemented
29#63860—21no—
30C2×#3714C2214yescomplemented
31C32×C4×C8C2211yescharacteristic, complemented
32#63648C2214yescomplemented
33C3×(C2×D3)⋊C8C2212yes—
34C3×Dic3⋊C8C2212yescomplemented
35C3×C4×C3⋊C8C2211yescharacteristic, complemented
36#63563C2214yescomplemented
37#5716—31no—
38D3×#127—31no—
39#5477—31no—
40C2×#874—31no—
41C3×#493—31no—
42C3×#431—31no—
43#5156—34no—
44#5150—34no—
45#5073—31no—
46#5070—31no—
47#4843—34no—
48#4732—34no—
49#4695—31no—
50#4695D311yescharacteristic, complemented
51#4694—31no—
52#4694—31no—
53#4694—31no—
54#4694—61no—
55#4685D311yescharacteristic, complemented
56C22×D32—22no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×#634—21no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12—21no—
65C2×C3×D12C2312yes—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3D411yescharacteristic
68C2×C3×C4×D3D411yescharacteristic
69C2×C3×C4×D3C2311yescharacteristic
70C2×#626—22no—
71C2×#626—22no—
72C2×#626—22no—
73C2×#625—22no—
74C2×D3×Dic3—22no—
75D3×D12—44no—
76D3×D12—44no—
77D3×D12—44no—
78#3795—44no—
79C2×C32×C8C2312yes—
80C32×C42C2311yescharacteristic
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)C2312yes—
83C3×C4×Dic3D411yescharacteristic
84C3×C4×Dic3D411yescharacteristic
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2312yes—
87C3×D24—44no—
88(C2×D3)⋊Dic3—22no—
89(C2×D3)⋊Dic3—22no—
90#3714—44no—
91#3205—91noSylow
92C2×#237—61no—
93C2×D3×D4—32no—
94C2×D3×D4—61no—
95C2×D3×D4—61no—
96C2×#235—61no—
97C22×D12—32no—
98C22×D12—61no—
99C22×D12—61no—
100C2×C3×D8—34no—
101C3×#127—31no—
102C3×#127—31no—
103C2×C3×C42—31no—
104#940—32no—
105#940—61no—
106#940—61no—
107#938—32no—
108#938—61no—
109#936—61no—
110D4×Dic3—32no—
111D4×Dic3—61no—
112C2×#213—34no—
113#930—32no—
114#930—61no—
115C2×D24—34no—
116C2×D24C2×D314yescomplemented
117#875—61no—
118#874—32no—
119#874—31no—
120#874—31no—
121#874—61no—
122#874—61no—
123#874—61no—
124#874C2×D311yescharacteristic
125#874C2×D311yescharacteristic, complemented
126C4×D12—32no—
127C4×D12—61no—
128C42×D3C2×D311yescharacteristic
129#869—31no—
130#869—31no—
131#869—61no—
132C3×C4⋊C8—32no—
133C3×C22⋊C8—32no—
134C3×C4×C8—21no—
135C3×C4×C8—31no—
136C3×C4×C8C2×D311yescharacteristic, complemented
137C3×C4×C8C2×D311yescharacteristic, complemented
138#832—34no—
139#821—34no—
140#821—34no—
141#821—34no—
142#821—64no—
143(C2×D3)⋊C8C2×D312yes—
144Dic3⋊C8C2×D312yescomplemented
145C4×C3⋊C8C2×D311yescharacteristic, complemented
146C22×C3⋊D3—22no—
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3C2×D411yescharacteristic
150C2×D32—44no—
151C2×D32—44no—
152C2×D32—44no—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2411yescharacteristic
156C2×C3⋊Dic3—22no—
157C4⋊(C3⋊D3)—24no—
158C4⋊(C3⋊D3)—42no—
159C4⋊(C3⋊D3)—42no—
160#634—42no—
161C2×C3×Dic3C2×D411yescharacteristic
162C2×C3×Dic3C2×D411yescharacteristic
163C2×C3×Dic3C2×D411yescharacteristic
164C3×D12—24no—
165C3×D12—24no—
166C3×D12—42no—
167C3×D12—42no—
168C3×D12—42no—
169C3×D12—42no—
170C3×C4×D3—22no—
171C3×C4×D3—22no—
172C3×C4×D3D814yescomplemented
173#626—44no—
174#626—44no—
175#626—44no—
176#625—44no—
177D3×Dic3—44no—
178C32×C8—22no—
179C3×C3⋊C8—22no—
180#532—91no—
181C2×#127—91no—
182#493—31no—
183#493—91no—
184#486—91no—
185#486—91no—
186#459—94no—
187#447—94no—
188#431—31no—
189C23×D3—62no—
190C23×D3—62no—
191C2×C3×D4—32no—
192C2×C3×D4—32no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C2×C3×D4—61no—
196C2×C3×D4—61no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—31no—
200C2×#67—62no—
201C2×#67—62no—
202C2×#67—62no—
203C2×#67—62no—
204C2×#67—62no—
205C22×Dic3—62no—
206#237—124no—
207D3×D4—124no—
208D3×D4—124no—
209D3×D4—124no—
210#235—124no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12—32no—
216C2×D12—32no—
217C2×D12—62no—
218C2×D12—62no—
219C2×D12—62no—
220C2×D12—62no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—61no—
224C2×D12—61no—
225C2×D12—121no—
226C2×D12—121no—
227C2×D12—124no—
228C2×D12—124no—
229C2×D12—124no—
230C2×D12C22×D312yes—
231C2×D12C22×D312yes—
232C2×C4×D3—62no—
233C2×C4×D3D1211yescharacteristic
234C2×C4×D3D1211yescharacteristic
235C2×C4×D3C22×D311yescharacteristic
236C2×Dic6—61no—
237C2×Dic6—61no—
238C2×Dic6—121no—
239C3×D8—124no—
240C2×C3×C8—22no—
241C2×C3×C8—32no—
242C2×C3×C8C22×D312yes—
243C2×C3×C8C22×D312yes—
244C3×C42—21no—
245C3×C42—31no—
246C3×C42—31no—
247C3×C42—31no—
248C3×C42C22×D311yescharacteristic
249C3×C42C22×D311yescharacteristic
250#217—62no—
251#217—62no—
252#213—124no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—62no—
255C4⋊Dic3—32no—
256C4⋊Dic3—32no—
257C4⋊Dic3—62no—
258C4⋊Dic3—61no—
259C4⋊Dic3—61no—
260C4⋊Dic3—121no—
261C4×Dic3D1211yescharacteristic
262C4×Dic3D1211yescharacteristic
263C4×Dic3C22×D311yescharacteristic
264C2×C3⋊C8C22×D312yes—
265D24—44no—
266D24—124no—
267C22×C32C22×D411yescharacteristic
268C2×C3⋊D3—42no—
269C2×C3⋊D3—42no—
270C2×C3⋊D3—42no—
271C2×C3×D3—21no—
272C2×C3×D3—21no—
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×D3C2×D812yes—
280D32—88no—
281C32×C4C2×D812yes—
282C32×C4AGL(1,ℤ/8)12yes—
283C32×C4H(5,𝔽2)12yes—
284C3⋊Dic3—42no—
285C3×Dic3—21no—
286C3×Dic3—21no—
287C3×Dic3C2×D812yes—
288C2×#41—181no—
289C22×D4—92no—
290C22×D4—181no—
291C22×D4—181no—
292C2×D8—34no—
293C2×D8—94no—
294C4⋊Q8—91no—
295#127—31no—
296#127—31no—
297#127—92no—
298#127—91no—
299#127—181no—
300#127—181no—
301#124—181no—
302#121—92no—
303#121—181no—
304C4×D4—92no—
305C4×D4—181no—
306C2×C42—31no—
307C4⋊C8—32no—
308#102—94no—
309#102—94no—
310C22⋊C8—32no—
311C4×C8—31no—
312C4×C8D3211yescharacteristic, complemented
313C23×C3—31no—
314C23×C3—62no—
315C23×C3—62no—
316C22×D3—22no—
317C22×D3—22no—
318C22×D3—62no—
319C22×D3—62no—
320C22×D3—122no—
321C22×D3—124no—
322C22×D3—124no—
323C22×D3—124no—
324C22×D3—124no—
325C22×D3—124no—
326C22×D3—124no—
327C22×D3C2×D1211yescharacteristic
328C3×D4—64no—
329C3×D4—64no—
330C3×D4—122no—
331C3×D4—122no—
332C3×D4—122no—
333C3×D4—122no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—31no—
338C2×C3×C4—34no—
339C2×C3×C4—31no—
340C2×C3×C4—31no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349#67—124no—
350#67—124no—
351#67—124no—
352#67—124no—
353#67—124no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—122no—
357C2×Dic3—124no—
358C2×Dic3C2×D1211yescharacteristic
359C2×Dic3C2×D1211yescharacteristic
360C2×Dic3C2×D1211yescharacteristic
361D12—24no—
362D12—24no—
363D12—42no—
364D12—42no—
365D12—42no—
366D12—42no—
367D12—64no—
368D12—64no—
369D12—124no—
370D12—124no—
371D12—124no—
372D12—124no—
373D12—122no—
374D12—122no—
375D12—122no—
376D12—122no—
377D12—242no—
378D12—242no—
379C4×D3—22no—
380C4×D3—22no—
381C4×D3—124no—
382C4×D3D2414yescomplemented
383Dic6—122no—
384Dic6—122no—
385Dic6—242no—
386C3×C8—22no—
387C3×C8—22no—
388C3×C8—42no—
389C3×C8—62no—
390C3⋊C8—22no—
391C2×C32#53511yescharacteristic
392C2×C32C22×D811yescharacteristic
393C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
394C3⋊D3—82no—
395C3×D3—22no—
396C3×D3—82no—
397C3×D3—82no—
398C24—182no—
399#41—364no—
400C2×Q8—181no—
401C2×D4—32no—
402C2×D4—32no—
403C2×D4—61no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—61no—
407C2×D4—92no—
408C2×D4—182no—
409C2×D4—182no—
410C2×D4—182no—
411C2×D4—182no—
412C2×D4—181no—
413C2×D4—181no—
414C2×D4—364no—
415C2×D4—364no—
416C2×D4—364no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—182no—
421D8—124no—
422D8—364no—
423C2×C8—32no—
424C2×C8C2×D3212yes—
425C4⋊C4—92no—
426C4⋊C4—181no—
427C22⋊C4—182no—
428C22⋊C4—182no—
429C42—31no—
430C42—31no—
431C42—31no—
432C42C2×D3211yescharacteristic
433C22×C3—21no—
434C22×C3—32no—
435C22×C3—61no—
436C22×C3—61no—
437C22×C3—122no—
438C22×C3—122no—
439C22×C3—122no—
440C22×C3—122no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3C22×D1211yescharacteristic
444C22×C3C2×D3×D411yescharacteristic
445C2×D3—21no—
446C2×D3—21no—
447C2×D3—42no—
448C2×D3—42no—
449C2×D3—42no—
450C2×D3—42no—
451C2×D3—42no—
452C2×D3—42no—
453C2×D3—122no—
454C2×D3—122no—
455C2×D3—122no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—242no—
460C2×D3—242no—
461C2×D3—242no—
462C2×D3—248no—
463C2×D3—248no—
464C2×D3C2×D2412yes—
465C3×C4—22no—
466C3×C4—22no—
467C3×C4—22no—
468C3×C4—32no—
469C3×C4—61no—
470C3×C4—61no—
471C3×C4C2×D2412yes—
472C3×C4#90812yes—
473C3×C4D3×D812yes—
474C3×C4#91112yes—
475C3×C4#100412yes—
476C3×C4#100912yes—
477Dic3—21no—
478Dic3—21no—
479Dic3—122no—
480Dic3—122no—
481Dic3—242no—
482Dic3C2×D2412yes—
483C32#320511yescharacteristic, complemented, Sylow
484C23—31no—
485C23—62no—
486C23—62no—
487C23—182no—
488C23—364no—
489C23—364no—
490C23—364no—
491Q8—362no—
492D4—64no—
493D4—64no—
494D4—122no—
495D4—122no—
496D4—122no—
497D4—122no—
498D4—184no—
499D4—364no—
500D4—364no—
501D4—364no—
502D4—364no—
503D4—362no—
504D4—362no—
505C2×C4—31no—
506C2×C4—34no—
507C2×C4—31no—
508C2×C4—31no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—182no—
512C2×C4—364no—
513C2×C4D3×D1211yescharacteristic
514C2×C4D3×D1211yescharacteristic
515C2×C4C22×D3211yescharacteristic
516C8—22no—
517C8—62no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—62no—
522C2×C3—242no—
523C2×C3—242no—
524C2×C3#552511yescharacteristic
525C2×C3#571511yescharacteristic
526C2×C3C22×D2411yescharacteristic
527C2×C3C2×#90811yescharacteristic
528C2×C3C2×D3×D811yescharacteristic
529C2×C3C2×#91111yescharacteristic
530D3—22no—
531D3—82no—
532D3—82no—
533D3—242no—
534D3—242no—
535D3—482no—
536C22—32no—
537C22—61no—
538C22—61no—
539C22—122no—
540C22—122no—
541C22—122no—
542C22—122no—
543C22—122no—
544C22—122no—
545C22—362no—
546C22—362no—
547C22—362no—
548C22—728no—
549C22C2×D3×D1211yescharacteristic
550C4—32no—
551C4—61no—
552C4—61no—
553C4—362no—
554C4D3×D2412yes—
555C4#6379512yes—
556C4#6430712yes—
557C3—21no—
558C3#7930311yescharacteristic, complemented
559C3#8178511yescharacteristic, complemented
560C2—62no—
561C2—242no—
562C2—242no—
563C2—722no—
564C2#1059400011yescharacteristic
565C2C2×D3×D2411yescharacteristic
566C2C2×#6379511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
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. D3×#874C2semidirect
2. #10593897C2semidirect
3. #10592393C2semidirect
4. C3×#4695C2semidirect
5. C3×#4685C2semidirect
6. #10590944C2semidirect
7. #10590753C2semidirect
8. #10590350C2semidirect
9. #10590273C2semidirect
17. #64078C22semidirect
18. C2×C3×D24C22semidirect
20. C3×#874C22semidirect
28. Dic3×D12C22semidirect
30. C2×#3714C22semidirect
31. C32×C4×C8C22semidirect
32. #63648C22semidirect
34. C3×Dic3⋊C8C22semidirect
35. C3×C4×C3⋊C8C22semidirect
36. #63563C22semidirect
50. #4695D3semidirect
55. #4685D3semidirect
116. C2×D24C2×D3semidirect
125. #874C2×D3semidirect
136. C3×C4×C8C2×D3semidirect
137. C3×C4×C8C2×D3semidirect
144. Dic3⋊C8C2×D3semidirect
145. C4×C3⋊C8C2×D3semidirect
172. C3×C4×D3D8semidirect
312. C4×C8D32semidirect
382. C4×D3D24semidirect
483. C32#3205semidirect
558. C3#79303semidirect
559. C3#81785semidirect

Maximal subgroups

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

subgroupindex
D3×#8742
#105938972
#105923932
C3×#46952
C3×#46852
#105909442
#105907532
#105903502
#105902732
#817853
#793033