Finite Group Databasebeta

← #11878661

Subgroups — #11878661

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
1C3×D3×#127C211yesmaximal, characteristic, complemented
2#10593897C211yesmaximal, characteristic, complemented
3#10592769C211yesmaximal, characteristic, complemented
4C3×#5073C211yesmaximal, characteristic, complemented
5#10591447C214yesmaximal, complemented
6#10591428C214yesmaximal, complemented
7#10590352C211yesmaximal, characteristic, complemented
8#10590273C211yesmaximal, characteristic, complemented
9#10590261C211yesmaximal, characteristic, complemented
10#83166—31nomaximal
11#81785—31nomaximal
12C2×C3×D3×D4—21no—
13C2×C3×D3×D4—21no—
14C2×C3×D3×D4C2212yes—
15C2×#3795—21no—
16C32×#127C2211yescharacteristic
17#64078C2211yescharacteristic, complemented
18C3×#940—21no—
19C3×#940—21no—
20C3×#940C2212yes—
21C2×C3×#213C2214yescomplemented
22C3×#874C2211yescharacteristic
23C3×#874C2211yescharacteristic, complemented
24C3×C42×D3C2211yescharacteristic
25#63908—21no—
26#63908C2212yes—
27Dic3×D12—21no—
28Dic3×D12C2212yescomplemented
29#63860—21no—
30C2×#3713C2214yescomplemented
31#63659C2214yescomplemented
32C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
33C3×C4×C3⋊C8C2211yescharacteristic, complemented
34Dic3⋊(C3⋊C8)C2212yescomplemented
35#63563C2214yescomplemented
36(C2×D3)⋊(C3⋊C8)C2212yes—
37C2×C3×#127—31no—
38#5716—31no—
39D3×#127D311yescharacteristic, complemented
40#5477—31no—
41C3×#493—31no—
42#5217—34no—
43#5156—34no—
44#5150—34no—
45#5073—31no—
46#5073—31no—
47#5073D311yescharacteristic, complemented
48#5072—34no—
49#5070—31no—
50#5070—31no—
51#5070—31no—
52#5070—61no—
53#4925—31no—
54#4694—31no—
55#4685—31no—
56C23×C3×D3—22no—
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4C2312yes—
60C2×#634—21no—
61C2×C3×#67—22no—
62C2×C3×#67—22no—
63C2×C3×#67—22no—
64C3×D3×D4—44no—
65C3×D3×D4—44no—
66C3×D3×D4—44no—
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×D12C2312yes—
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3C2311yescharacteristic
76C2×#625—22no—
77C2×D3×Dic3—22no—
78#3795—44no—
79C32×C42C2311yescharacteristic
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)C2312yes—
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×#213—44no—
84C3×C4×Dic3D411yescharacteristic
85C3×C4×Dic3D411yescharacteristic
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2312yes—
88(C2×D3)⋊Dic3—22no—
89(C2×D3)⋊Dic3—22no—
90#3713—44no—
91#3205—91noSylow
92C22×C3×D4—32no—
93C22×C3×D4—61no—
94C22×C3×D4—61no—
95C2×#237—61no—
96C2×D3×D4—21no—
97C2×D3×D4—21no—
98C2×D3×D4C2×D312yes—
99C2×#235—61no—
100C2×C3×D8—34no—
101C3×#127—21no—
102C3×#127—32no—
103C3×#127—31no—
104C3×#127—31no—
105C3×#127—61no—
106C3×#127—61no—
107C3×#127C2×D311yescharacteristic
108C3×#127C2×D311yescharacteristic
109C2×C3×C42—31no—
110#940—21no—
111#940—21no—
112#940C2×D312yes—
113#938—32no—
114#938—61no—
115#936—61no—
116D4×Dic3—32no—
117D4×Dic3—61no—
118C2×#213—34no—
119C2×#213—34no—
120C2×#213C2×D314yescomplemented
121#930—32no—
122#930—61no—
123#875—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—31no—
133#832—34no—
134#832—34no—
135#832—34no—
136#832—64no—
137#830—32no—
138#821—34no—
139(C2×D3)⋊C8—32no—
140Dic3⋊C8—32no—
141C4⋊(C3⋊C8)—32no—
142C4×C3⋊C8—31no—
143C4×C3⋊C8—31no—
144C4×C3⋊C8—61no—
145C4×C3⋊C8C2×D311yescharacteristic, complemented
146C23×C32—22no—
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3—44no—
150C22×C3×D3—44no—
151C22×C3×D3—44no—
152C22×C3×D3C2×D411yescharacteristic
153C32×D4—24no—
154C32×D4—42no—
155C32×D4—42no—
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2411yescharacteristic
159C2×C3⋊Dic3—22no—
160#634—42no—
161C3×#67—44no—
162C3×#67—44no—
163C3×#67—44no—
164C2×C3×Dic3C2×D411yescharacteristic
165C2×C3×Dic3C2×D411yescharacteristic
166C2×C3×Dic3C2×D411yescharacteristic
167C3×D12—24no—
168C3×D12—24no—
169C3×D12—42no—
170C3×D12—42no—
171C3×D12—42no—
172C3×D12—42no—
173C3×C4×D3—22no—
174C3×C4×D3—22no—
175C3×C4×D3D814yescomplemented
176#625—44no—
177D3×Dic3—44no—
178C3⋊(C3⋊C8)—22no—
179C3×C3⋊C8—22no—
180#532—91no—
181C2×#127—31no—
182#493—31no—
183#493—91no—
184#486—91no—
185#486—91no—
186#459—94no—
187#447—94no—
188#431—91no—
189C24×C3—62no—
190C23×D3—22no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—22no—
196C2×C3×D4—32no—
197C2×C3×D4—32no—
198C2×C3×D4—41no—
199C2×C3×D4—41no—
200C2×C3×D4—62no—
201C2×C3×D4—62no—
202C2×C3×D4—62no—
203C2×C3×D4—61no—
204C2×C3×D4—61no—
205C2×C3×D4—61no—
206C2×C3×D4—61no—
207C2×C3×D4—124no—
208C2×C3×D4—124no—
209C2×C3×D4—124no—
210C2×C3×D4C22×D312yes—
211C2×C3×D4C22×D312yes—
212C22×C3×C4—31no—
213C22×C3×C4—31no—
214C22×C3×C4—31no—
215C2×#67—22no—
216C2×#67—22no—
217C2×#67—22no—
218C2×#67—62no—
219C2×#67—62no—
220C22×Dic3—62no—
221#237—124no—
222D3×D4—44no—
223D3×D4—44no—
224D3×D4—44no—
225#235—124no—
226C2×D12—21no—
227C2×D12—21no—
228C2×D12—21no—
229C2×D12—21no—
230C2×D12C22×D312yes—
231C2×D12C22×D312yes—
232C2×C4×D3—62no—
233C2×C4×D3#6711yescharacteristic
234C2×C4×D3#6711yescharacteristic
235C2×C4×D3C22×D311yescharacteristic
236C2×Dic6—61no—
237C2×Dic6—61no—
238C2×Dic6—121no—
239C3×D8—124no—
240C2×C3×C8—32no—
241C3×C42—21no—
242C3×C42—31no—
243C3×C42—31no—
244C3×C42—31no—
245C3×C42C22×D311yescharacteristic
246C3×C42C22×D311yescharacteristic
247#217—62no—
248#217—62no—
249#213—44no—
250#213—124no—
251#213—124no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254C4⋊Dic3—32no—
255C4⋊Dic3—32no—
256C4⋊Dic3—62no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259C4⋊Dic3—121no—
260C4×Dic3#6711yescharacteristic
261C4×Dic3#6711yescharacteristic
262C4×Dic3C22×D311yescharacteristic
263C2×C3⋊C8—32no—
264C2×C3⋊C8—32no—
265C2×C3⋊C8—62no—
266C2×C3⋊C8C22×D312yes—
267C22×C32—42no—
268C22×C32—42no—
269C22×C32—42no—
270C22×C32C22×D411yescharacteristic
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×D3—88no—
280C2×C3×D3C2×D812yes—
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—32no—
290C22×D4—61no—
291C22×D4—61no—
292C2×D8—34no—
293C2×D8—94no—
294C4⋊Q8—91no—
295#127—32no—
296#127—31no—
297#127—31no—
298#127—61no—
299#127—61no—
300#127D3211yescharacteristic
301#124—181no—
302#121—92no—
303#121—181no—
304C4×D4—92no—
305C4×D4—181no—
306C2×C42—31no—
307C4⋊C8—92no—
308#102—94no—
309#102—94no—
310C22⋊C8—92no—
311C4×C8—31no—
312C4×C8—91no—
313C23×C3—22no—
314C23×C3—22no—
315C23×C3—31no—
316C23×C3—42no—
317C23×C3—62no—
318C23×C3—62no—
319C23×C3—124no—
320C23×C3—124no—
321C23×C3—124no—
322C22×D3—22no—
323C22×D3—22no—
324C22×D3—44no—
325C22×D3—44no—
326C22×D3—44no—
327C22×D3C2×#6711yescharacteristic
328C3×D4—24no—
329C3×D4—24no—
330C3×D4—44no—
331C3×D4—42no—
332C3×D4—42no—
333C3×D4—42no—
334C3×D4—42no—
335C3×D4—64no—
336C3×D4—64no—
337C3×D4—82no—
338C3×D4—82no—
339C3×D4—124no—
340C3×D4—124no—
341C3×D4—124no—
342C3×D4—122no—
343C3×D4—122no—
344C3×D4—122no—
345C3×D4—122no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—31no—
350C2×C3×C4—34no—
351C2×C3×C4—31no—
352C2×C3×C4—31no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361#67—44no—
362#67—44no—
363#67—44no—
364#67—124no—
365#67—124no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—122no—
369C2×Dic3—124no—
370C2×Dic3C2×#6711yescharacteristic
371C2×Dic3C2×#6711yescharacteristic
372C2×Dic3C2×#6711yescharacteristic
373D12—24no—
374D12—24no—
375D12—42no—
376D12—42no—
377D12—42no—
378D12—42no—
379C4×D3—22no—
380C4×D3—22no—
381C4×D3—124no—
382C4×D3#21314yescomplemented
383Dic6—122no—
384Dic6—122no—
385Dic6—242no—
386C3×C8—62no—
387C3⋊C8—22no—
388C3⋊C8—62no—
389C3⋊C8—62no—
390C3⋊C8—122no—
391C2×C32—82no—
392C2×C32#53511yescharacteristic
393C2×C32C22×D811yescharacteristic
394C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
395C3×D3—22no—
396C3×D3—82no—
397C3×D3—82no—
398C24—62no—
399#41—364no—
400C2×Q8—181no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—32no—
404C2×D4—32no—
405C2×D4—62no—
406C2×D4—62no—
407C2×D4—62no—
408C2×D4—61no—
409C2×D4—61no—
410C2×D4—61no—
411C2×D4—61no—
412C2×D4—124no—
413C2×D4—124no—
414C2×D4—124no—
415C2×D4—182no—
416C2×D4C2×D3212yes—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—182no—
421D8—124no—
422D8—364no—
423C2×C8—32no—
424C2×C8—92no—
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—42no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—61no—
442C22×C3—61no—
443C22×C3—82no—
444C22×C3—82no—
445C22×C3—82no—
446C22×C3—122no—
447C22×C3—122no—
448C22×C3—122no—
449C22×C3—122no—
450C22×C3—122no—
451C22×C3—122no—
452C22×C3—248no—
453C22×C3C2×D3×D411yescharacteristic
454C22×C3C22×#6711yescharacteristic
455C2×D3—21no—
456C2×D3—21no—
457C2×D3—42no—
458C2×D3—42no—
459C2×D3—42no—
460C2×D3—42no—
461C2×D3—42no—
462C2×D3—42no—
463C2×D3—88no—
464C2×D3C2×#21312yes—
465C3×C4—22no—
466C3×C4—22no—
467C3×C4—22no—
468C3×C4—32no—
469C3×C4—61no—
470C3×C4—61no—
471C3×C4D3×D812yes—
472C3×C4#91112yes—
473C3×C4C2×#21312yes—
474C3×C4#93212yes—
475C3×C4#100412yes—
476C3×C4#100412yes—
477Dic3—21no—
478Dic3—21no—
479Dic3—122no—
480Dic3—122no—
481Dic3—242no—
482Dic3C2×#21312yes—
483C32#320511yescharacteristic, complemented, Sylow
484C23—22no—
485C23—31no—
486C23—62no—
487C23—62no—
488C23—124no—
489C23—124no—
490C23—124no—
491Q8—362no—
492D4—24no—
493D4—42no—
494D4—42no—
495D4—64no—
496D4—64no—
497D4—124no—
498D4—124no—
499D4—124no—
500D4—122no—
501D4—122no—
502D4—122no—
503D4—122no—
504D4—364no—
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×#6711yescharacteristic
514C2×C4D3×#6711yescharacteristic
515C2×C4C22×D3211yescharacteristic
516C8—62no—
517C8—182no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—62no—
522C2×C3—82no—
523C2×C3—82no—
524C2×C3—162no—
525C2×C3—242no—
526C2×C3—242no—
527C2×C3#571511yescharacteristic
528C2×C3C2×D3×D811yescharacteristic
529C2×C3C2×#91111yescharacteristic
530C2×C3C22×#21311yescharacteristic
531C2×C3C2×#93211yescharacteristic
532C2×C3#580511yescharacteristic
533D3—22no—
534D3—82no—
535D3—82no—
536C22—32no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—61no—
541C22—61no—
542C22—122no—
543C22—122no—
544C22—122no—
545C22—122no—
546C22—122no—
547C22—122no—
548C22—248no—
549C22C2×D3×#6711yescharacteristic
550C4—32no—
551C4—61no—
552C4—61no—
553C4—362no—
554C4D3×#21312yes—
555C4#6393212yes—
556C4#6431312yes—
557C3—21no—
558C3#8178511yescharacteristic, complemented
559C3#8316611yescharacteristic, complemented
560C2—62no—
561C2—82no—
562C2—242no—
563C2—242no—
564C2C2×D3×#21311yescharacteristic
565C2C2×#6393211yescharacteristic
566C2#1059523311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×D3×#127C2semidirect
2. #10593897C2semidirect
3. #10592769C2semidirect
4. C3×#5073C2semidirect
5. #10591447C2semidirect
6. #10591428C2semidirect
7. #10590352C2semidirect
8. #10590273C2semidirect
9. #10590261C2semidirect
17. #64078C22semidirect
21. C2×C3×#213C22semidirect
23. C3×#874C22semidirect
28. Dic3×D12C22semidirect
30. C2×#3713C22semidirect
31. #63659C22semidirect
32. C4×C3⋊(C3⋊C8)C22semidirect
33. C3×C4×C3⋊C8C22semidirect
34. Dic3⋊(C3⋊C8)C22semidirect
35. #63563C22semidirect
39. D3×#127D3semidirect
47. #5073D3semidirect
120. C2×#213C2×D3semidirect
125. #874C2×D3semidirect
145. C4×C3⋊C8C2×D3semidirect
175. C3×C4×D3D8semidirect
382. C4×D3#213semidirect
483. C32#3205semidirect
558. C3#81785semidirect
559. C3#83166semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1272
#105938972
#105927692
C3×#50732
#105914472
#105914282
#105903522
#105902732
#105902612
#831663
#817853