Finite Group Databasebeta

← #11861180

Subgroups — #11861180

Order 1152.

969 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594706C212yesmaximal, complemented
2#10594676C211yesmaximal, characteristic
3#10592594C211yesmaximal, characteristic, complemented
4C3×#4894C211yesmaximal, characteristic, complemented
5C3×#4893C211yesmaximal, characteristic, complemented
6D3×#825C212yesmaximal, complemented
7#10590995C212yesmaximal, complemented
8#10590978C212yesmaximal, complemented
9#10590919C211yesmaximal, characteristic, complemented
10#10590918C211yesmaximal, characteristic, complemented
11#10590667C211yesmaximal, characteristic, complemented
12#79898—31nomaximal
13#79258—31nomaximal
14D3×#235C2212yes—
15#64116C2212yescomplemented
16#64113C2211yescharacteristic
17C3×#907C2212yescomplemented
18C3×D3×M16C2212yes—
19C3×#904C2211yescharacteristic
20C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
21C4×D3×Dic3C2211yescharacteristic
22#63829C2212yes—
23C2×#3711C2211yescharacteristic
24#63817C2212yescomplemented
25#63815C2212yescomplemented
26#63804—22no—
27#63803—22no—
28#63801C412yescomplemented
29#63800C412yescomplemented
30#63795C412yescomplemented
31#63794C412yescomplemented
32#63791—22no—
33D3×ΓL(1,𝔽25)—22no—
34C32×#108C2211yescharacteristic, complemented
35#63652C2212yescomplemented
36C8×C3⋊Dic3C2211yescharacteristic, complemented
37C3×#825C2212yescomplemented
38C3×#822C2212yescomplemented
39C3×#819C2211yescharacteristic, complemented
40C3×#815C2211yescharacteristic, complemented
41#63570C2212yescomplemented
42#63568C2212yescomplemented
43#63554C2211yescharacteristic, complemented
44#63553C2211yescharacteristic, complemented
45#5768—31no—
46#5750—32no—
47#5748—31no—
48#5745—32no—
49C3×#444—31no—
50C3×#430—31no—
51#5196—31no—
52#5144—32no—
53C2×#825—32no—
54Dic3×M16—31no—
55#4895—32no—
56#4895—31no—
57#4895—31no—
58#4895—31no—
59#4895—61no—
60#4894—32no—
61#4894—31no—
62#4894D311yescharacteristic, complemented
63#4893D311yescharacteristic, complemented
64#4823—32no—
65D3×#104—32no—
66#4717—31no—
67#4707—31no—
68#3828C2312yes—
69C3×#235C2312yes—
70C2×C3×C4×D3C2311yescharacteristic
71D3×#67—22no—
72#3804—22no—
73C2×D3×Dic3—21no—
74D3×D12C2×C412yes—
75C4×D32—22no—
76#3799C2×C412yes—
77#3798—22no—
78#3795C2×C412yes—
79D3×Dic6C2×C412yes—
80C32×M16C2312yes—
81C2×C32×C8C2311yescharacteristic
82C4×C3⋊Dic3C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84#3746C2×C411yescharacteristic, complemented
85#3745C2×C411yescharacteristic, complemented
86#3744C2×C412yescomplemented
87#3743—22no—
88C8×C3⋊D3—22no—
89C3×C4×Dic3C2311yescharacteristic
90C3×#208C2312yes—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93C3×Dic12C2×C411yescharacteristic, complemented
94C3×D24C2×C411yescharacteristic, complemented
95C3×#204C2×C412yescomplemented
96C3×ΓL(1,𝔽25)—22no—
97C3×ΓL(1,𝔽25)—22no—
98C3×ΓL(1,𝔽25)C2×C412yes—
99C3×ΓL(1,𝔽25)C2×C412yes—
100C3×D3×C8—22no—
101C3×D3×C8—22no—
102Dic32—21no—
103#3719C2×C412yescomplemented
104#3717C2×C412yescomplemented
105#3716C2×C412yescomplemented
106#3714C2×C412yescomplemented
107#3712—22no—
108#3711—22no—
109#3711D412yes—
110#3711D412yes—
111#3710—22no—
112D3×C3⋊C8—22no—
113#2956—91noSylow
114D3×#41—32no—
115C2×#235—32no—
116C3×#135—31no—
117C3×#131—32no—
118C2×C3×M16—31no—
119C2×C3×M16—32no—
120#950—32no—
121#948—32no—
122C2×C4×Dic3—31no—
123C2×#208—31no—
124#918—32no—
125#915—32no—
126#914—32no—
127#911—32no—
128#909—32no—
129#909—32no—
130#908—32no—
131#908—32no—
132#907—32no—
133#907—32no—
134#907—32no—
135#907—32no—
136#907—62no—
137#907—62no—
138#907C2×D312yescomplemented
139D3×M16—62no—
140D3×M16—62no—
141D3×M16—62no—
142D3×M16C2×D312yes—
143#904—32no—
144#904—31no—
145#904—31no—
146#904—61no—
147#904C2×D311yescharacteristic
148#901—32no—
149#901—62no—
150#901—62no—
151#901—62no—
152C2×ΓL(1,𝔽25)—31no—
153C2×ΓL(1,𝔽25)—62no—
154C2×ΓL(1,𝔽25)C2×D311yescharacteristic
155C42×D3—31no—
156C3×#108—21no—
157C3×#108—32no—
158C3×#108—31no—
159C3×#108C2×D311yescharacteristic, complemented
160C3×#108C2×D311yescharacteristic, complemented
161C3×#104—32no—
162C3×#97—31no—
163#837—32no—
164#825—32no—
165#825—32no—
166#825—32no—
167#825—32no—
168#825—62no—
169#825C2×D312yescomplemented
170#822C2×D312yescomplemented
171#819C2×D311yescharacteristic, complemented
172#815—31no—
173#815C2×D311yescharacteristic, complemented
174C8×Dic3—31no—
175C8×Dic3—31no—
176C8×Dic3—31no—
177C8×Dic3—31no—
178C8×Dic3—61no—
179#805—32no—
180#803—31no—
181C22×C3×D3#4111yescharacteristic
182C2×D32—22no—
183C2×C32×C4C2411yescharacteristic
184#638—22no—
185C2×C3⋊Dic3—21no—
186C4⋊(C3⋊D3)C22×C412yes—
187C4×C3⋊D3—22no—
188#634C22×C412yes—
189C3×#67—22no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3#4111yescharacteristic
192C3×D12C22×C412yes—
193C3×C4×D3—22no—
194C3×C4×D3C22×C412yes—
195C3×C4×D3C2×D412yes—
196C3×Dic6C22×C412yes—
197#627—22no—
198#626—22no—
199#626—22no—
200#625—22no—
201#624—22no—
202D3×Dic3—22no—
203D3×Dic3—22no—
204D3×Dic3—42no—
205C32×C8—22no—
206C32×C8C22×C411yescharacteristic
207C32×C8C22×C411yescharacteristic
208C3⋊(C3⋊C8)C2×D411yescharacteristic
209C3⋊(C3⋊C8)C2×D411yescharacteristic
210C3×C3⋊C8—22no—
211C3×C3⋊C8C22×C412yes—
212C3×C3⋊C8C2×D412yes—
213#575—91no—
214#568—92no—
215#444—31no—
216#444—91no—
217#444—92no—
218#443—92no—
219#443—91no—
220#443—91no—
221#430—31no—
222C2×#104—92no—
223C4×M16—91no—
224C3×#41—32no—
225C22×C3×C4—31no—
226C2×#67—62no—
227C22×Dic3—61no—
228#239—32no—
229D3×Q8—32no—
230#237—32no—
231#237—62no—
232D3×D4—32no—
233D3×D4—62no—
234#235—32no—
235#235—32no—
236#235—32no—
237#235—32no—
238#235—62no—
239#235—62no—
240#235—62no—
241#235—62no—
242#235C22×D312yes—
243C2×D12—32no—
244C2×C4×D3—62no—
245C2×C4×D3—62no—
246C2×C4×D3—61no—
247C2×C4×D3C22×D311yescharacteristic
248C2×Dic6—32no—
249C3×Q16—31no—
250C3×SD16—32no—
251C3×D8—31no—
252C3×M16—22no—
253C3×M16—32no—
254C3×M16—32no—
255C3×M16—32no—
256C3×M16—62no—
257C3×M16—62no—
258C3×M16C22×D312yes—
259C3×M16C22×D312yes—
260C2×C3×C8—21no—
261C2×C3×C8—31no—
262C2×C3×C8—31no—
263C2×C3×C8—62no—
264C2×C3×C8—62no—
265C2×C3×C8C22×D311yescharacteristic
266C2×C3×C8C22×D311yescharacteristic
267C3×C42—31no—
268#216—32no—
269#215—32no—
270#214—32no—
271#213—32no—
272C4×Dic3—31no—
273C4×Dic3—31no—
274C4×Dic3—61no—
275C4×Dic3—61no—
276C4×Dic3—61no—
277C4×Dic3C22×D311yescharacteristic
278#208—32no—
279#208—32no—
280#208—62no—
281#208C22×D312yes—
282C2×C3⋊C8—31no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—61no—
285C2×C3⋊C8—62no—
286C2×C3⋊C8C22×D311yescharacteristic
287C2×C3⋊C8C22×D311yescharacteristic
288Dic12—32no—
289Dic12—31no—
290Dic12—31no—
291Dic12—61no—
292Dic12C4×D311yescharacteristic, complemented
293D24—32no—
294D24—31no—
295D24—31no—
296D24—61no—
297D24C4×D311yescharacteristic, complemented
298#204—32no—
299#204—32no—
300#204—32no—
301#204—32no—
302#204—62no—
303#204C4×D312yescomplemented
304ΓL(1,𝔽25)—22no—
305ΓL(1,𝔽25)—22no—
306ΓL(1,𝔽25)—32no—
307ΓL(1,𝔽25)—32no—
308ΓL(1,𝔽25)—62no—
309ΓL(1,𝔽25)—62no—
310ΓL(1,𝔽25)—62no—
311ΓL(1,𝔽25)—62no—
312ΓL(1,𝔽25)—62no—
313ΓL(1,𝔽25)—122no—
314ΓL(1,𝔽25)C4×D312yes—
315ΓL(1,𝔽25)C4×D312yes—
316D3×C8—22no—
317D3×C8—22no—
318D3×C8—62no—
319D3×C8—62no—
320D3×C8—62no—
321D3×C8—62no—
322D3×C8—62no—
323D3×C8—122no—
324C22×C32C2×#4111yescharacteristic
325C2×C3⋊D3—22no—
326C2×C3×D3—22no—
327C2×C3×D3—41no—
328C2×C3×D3C4×D412yes—
329D32—82no—
330C32×C4C23×C411yescharacteristic
331C32×C4C22×D411yescharacteristic
332C3⋊Dic3—22no—
333C3⋊Dic3—22no—
334C3×Dic3—22no—
335C3×Dic3—41no—
336C3×Dic3C4×D412yes—
337C2×#41—92no—
338#137—92no—
339#137—92no—
340AGL(1,ℤ/8)—92no—
341AGL(1,ℤ/8)—92no—
342#135—31no—
343#135—92no—
344#135—91no—
345#131—32no—
346#131—92no—
347#131—92no—
348#131—92no—
349#131—182no—
350#131—182no—
351C2×M16—31no—
352C2×M16—32no—
353C2×M16—91no—
354C2×M16—182no—
355C2×M16—182no—
356C2×C42—91no—
357#108—32no—
358#108—31no—
359#108D3211yescharacteristic, complemented
360#104—32no—
361#104—92no—
362#104—92no—
363#104—92no—
364#97—31no—
365#97—91no—
366C4×C8—91no—
367C4×C8—91no—
368C23×C3—31no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3#23911yescharacteristic
372C3×Q8—32no—
373C3×D4—32no—
374C3×D4—62no—
375C2×C3×C4—21no—
376C2×C3×C4—31no—
377C2×C3×C4—32no—
378C2×C3×C4—32no—
379C2×C3×C4—62no—
380C2×C3×C4—61no—
381C2×C3×C4C23×D311yescharacteristic
382C2×C3×C4C23×D311yescharacteristic
383#67—22no—
384#67—62no—
385#67—62no—
386#67—62no—
387#67—62no—
388#67—62no—
389#67—62no—
390#67—122no—
391C2×Dic3—21no—
392C2×Dic3—62no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—62no—
396C2×Dic3—121no—
397C2×Dic3—122no—
398C2×Dic3#23911yescharacteristic
399D12—32no—
400D12—32no—
401D12—62no—
402D12—62no—
403D12—62no—
404D12C2×C4×D312yes—
405C4×D3—22no—
406C4×D3—62no—
407C4×D3—62no—
408C4×D3—62no—
409C4×D3—62no—
410C4×D3—62no—
411C4×D3—62no—
412C4×D3—122no—
413C4×D3—122no—
414C4×D3C2×C4×D312yes—
415C4×D3D3×D412yes—
416Dic6—32no—
417Dic6—32no—
418Dic6—62no—
419Dic6—62no—
420Dic6—62no—
421Dic6C2×C4×D312yes—
422C3×C8—22no—
423C3×C8—22no—
424C3×C8—21no—
425C3×C8—21no—
426C3×C8—32no—
427C3×C8—32no—
428C3×C8—42no—
429C3×C8—62no—
430C3×C8C2×C4×D311yescharacteristic
431C3×C8C2×C4×D311yescharacteristic
432C3×C8C2×C4×D311yescharacteristic
433C3×C8C2×C4×D311yescharacteristic
434C3⋊C8—22no—
435C3⋊C8—31no—
436C3⋊C8—31no—
437C3⋊C8—31no—
438C3⋊C8—31no—
439C3⋊C8—61no—
440C3⋊C8—61no—
441C3⋊C8C2×C4×D312yes—
442C3⋊C8D3×D412yes—
443C2×C32—21no—
444C2×C32C2×C4×D411yescharacteristic
445C3⋊D3—42no—
446C3×D3—22no—
447C3×D3—42no—
448#41—32no—
449#41—92no—
450#41—92no—
451#41—92no—
452#41—182no—
453#41—182no—
454C2×Q8—92no—
455C2×D4—92no—
456C2×D4—182no—
457C22×C4—31no—
458C22×C4—182no—
459C22×C4—181no—
460Q16—31no—
461Q16—92no—
462Q16—91no—
463SD16—32no—
464SD16—92no—
465SD16—92no—
466SD16—92no—
467D8—31no—
468D8—92no—
469D8—91no—
470M16—32no—
471M16—32no—
472M16—32no—
473M16—62no—
474M16—62no—
475M16—92no—
476M16—92no—
477M16—182no—
478M16—182no—
479M16—182no—
480M16C2×D3212yes—
481C2×C8—31no—
482C2×C8—31no—
483C2×C8—62no—
484C2×C8—62no—
485C2×C8—91no—
486C2×C8—182no—
487C2×C8—182no—
488C2×C8—182no—
489C2×C8C2×D3211yescharacteristic
490C42—31no—
491C42—91no—
492C42—181no—
493C22×C3—21no—
494C22×C3—32no—
495C22×C3—62no—
496C22×C3—121no—
497C22×C3C2×#23911yescharacteristic
498C22×C3D3×#4111yescharacteristic
499C2×D3—22no—
500C2×D3—41no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—122no—
504C2×D3—242no—
505C2×D3—242no—
506C2×D3#89312yes—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—32no—
510C3×C4—62no—
511C3×C4—121no—
512C3×C4C22×C4×D311yescharacteristic
513C3×C4C22×C4×D311yescharacteristic
514C3×C4C2×D3×D411yescharacteristic
515C3×C4C2×D3×D411yescharacteristic
516Dic3—22no—
517Dic3—41no—
518Dic3—62no—
519Dic3—62no—
520Dic3—62no—
521Dic3—62no—
522Dic3—122no—
523Dic3—122no—
524Dic3#89312yes—
525C32#295611yescharacteristic, complemented, Sylow
526C23—31no—
527C23—182no—
528Q8—32no—
529Q8—92no—
530Q8—182no—
531D4—32no—
532D4—62no—
533D4—92no—
534D4—182no—
535D4—182no—
536D4—182no—
537D4—182no—
538C2×C4—31no—
539C2×C4—32no—
540C2×C4—32no—
541C2×C4—62no—
542C2×C4—61no—
543C2×C4—182no—
544C2×C4—182no—
545C2×C4—182no—
546C2×C4—181no—
547C2×C4—182no—
548C2×C4—362no—
549C2×C4C22×D3211yescharacteristic
550C8—22no—
551C8—32no—
552C8—32no—
553C8—62no—
554C8—91no—
555C8—91no—
556C8C4×D3211yescharacteristic
557C8C4×D3211yescharacteristic
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—41no—
562C2×C3—62no—
563C2×C3—122no—
564C2×C3C2×#89311yescharacteristic
565C2×C3C4×D3×D411yescharacteristic
566D3—22no—
567D3—42no—
568D3—122no—
569D3—122no—
570D3—242no—
571C22—32no—
572C22—62no—
573C22—121no—
574C22—182no—
575C22—722no—
576C22D3×#23911yescharacteristic
577C4—32no—
578C4—62no—
579C4—121no—
580C4—182no—
581C4—182no—
582C4C2×C4×D3211yescharacteristic
583C4D32×D411yescharacteristic
584C3—21no—
585C3#7925811yescharacteristic, complemented
586C3#7989811yescharacteristic, complemented
587C2—21no—
588C2—62no—
589C2—122no—
590C2—362no—
591C2D3×#89311yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#108C22
socleC2×C32C2×C4×D4
prime radical#10594676C2
cosocleC2×C32×C4C24
hypercenter#108D32
hypocenterC32#2956
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
1. #10594706C2semidirect
3. #10592594C2semidirect
4. C3×#4894C2semidirect
5. C3×#4893C2semidirect
6. D3×#825C2semidirect
7. #10590995C2semidirect
8. #10590978C2semidirect
9. #10590919C2semidirect
10. #10590918C2semidirect
11. #10590667C2semidirect
15. #64116C22semidirect
17. C3×#907C22semidirect
24. #63817C22semidirect
25. #63815C22semidirect
28. #63801C4semidirect
29. #63800C4semidirect
30. #63795C4semidirect
31. #63794C4semidirect
34. C32×#108C22semidirect
35. #63652C22semidirect
36. C8×C3⋊Dic3C22semidirect
37. C3×#825C22semidirect
38. C3×#822C22semidirect
39. C3×#819C22semidirect
40. C3×#815C22semidirect
41. #63570C22semidirect
42. #63568C22semidirect
43. #63554C22semidirect
44. #63553C22semidirect
62. #4894D3semidirect
63. #4893D3semidirect
84. #3746C2×C4semidirect
85. #3745C2×C4semidirect
86. #3744C2×C4semidirect
93. C3×Dic12C2×C4semidirect
94. C3×D24C2×C4semidirect
95. C3×#204C2×C4semidirect
103. #3719C2×C4semidirect
104. #3717C2×C4semidirect
105. #3716C2×C4semidirect
106. #3714C2×C4semidirect
138. #907C2×D3semidirect
159. C3×#108C2×D3semidirect
160. C3×#108C2×D3semidirect
169. #825C2×D3semidirect
170. #822C2×D3semidirect
171. #819C2×D3semidirect
173. #815C2×D3semidirect
292. Dic12C4×D3semidirect
297. D24C4×D3semidirect
303. #204C4×D3semidirect
359. #108D32semidirect
525. C32#2956semidirect
585. C3#79258semidirect
586. C3#79898semidirect

Maximal subgroups

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

subgroupindex
#105947062
#105946762
#105925942
C3×#48942
C3×#48932
D3×#8252
#105909952
#105909782
#105909192
#105909182
#105906672
#798983
#792583