Finite Group Databasebeta

← #11861181

Subgroups — #11861181

Order 1152.

967 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594708C212yesmaximal, complemented
2#10594685C211yesmaximal, characteristic
3#10592592C211yesmaximal, characteristic, complemented
4C3×#4895C211yesmaximal, characteristic, complemented
5C3×#4894C211yesmaximal, characteristic, complemented
6#10591008C212yesmaximal, complemented
7#10590976C212yesmaximal, complemented
8#10590975C212yesmaximal, complemented
9#10590916C211yesmaximal, characteristic, complemented
10#10590915C211yesmaximal, characteristic, complemented
11#10590664C211yesmaximal, characteristic, complemented
12#79898—31nomaximal
13#79889—31nomaximal
14#64306C2212yes—
15M16×C3⋊D3C2212yes—
16C2×#3743C2211yescharacteristic
17C3×#907C2212yescomplemented
18C3×#907C2212yescomplemented
19C3×#904C2211yescharacteristic
20C3×#904C2211yescharacteristic
21C4×#624C2211yescharacteristic
22#63822C2212yes—
23C2×#3712C2211yescharacteristic
24#63814C2212yescomplemented
25#63814C2212yescomplemented
26#63811C412yescomplemented
27#63811C412yescomplemented
28#63805—22no—
29#63803—22no—
30#63798C412yescomplemented
31#63798C412yescomplemented
32D3×ΓL(1,𝔽25)—22no—
33D3×ΓL(1,𝔽25)—22no—
34C32×#108C2211yescharacteristic, complemented
35#63649C2212yescomplemented
36#63646C2211yescharacteristic, complemented
37C3×#825C2212yescomplemented
38C3×#825C2212yescomplemented
39C3×#815C2211yescharacteristic, complemented
40C3×C8×Dic3C2211yescharacteristic, complemented
41#63569C2212yescomplemented
42#63569C2212yescomplemented
43#63554C2211yescharacteristic, complemented
44Dic3×C3⋊C8C2211yescharacteristic, complemented
45#5768—31no—
46#5768—31no—
47#5750—32no—
48#5750—32no—
49C3×#444—31no—
50C3×#443—31no—
51#5197—31no—
52#5196—31no—
53#5145—32no—
54#5144—32no—
55#4895D311yescharacteristic, complemented
56#4894D311yescharacteristic, complemented
57#4893—31no—
58#4893—31no—
59#4893—61no—
60#4824—32no—
61#4823—32no—
62D3×#104—32no—
63D3×#104—32no—
64#4717—31no—
65#4707—31no—
66#4700—31no—
67C4×ΓL(1,𝔽25)—31no—
68C2×C4×C3⋊D3C2311yescharacteristic
69C3×#235C2312yes—
70C3×#235C2312yes—
71#3811—22no—
72C2×#624—21no—
73#3805—22no—
74#3802C2×C412yes—
75C4×D32—22no—
76#3798—22no—
77#3797C2×C412yes—
78#3796C2×C412yes—
79#3796C2×C412yes—
80C32×M16C2312yes—
81C2×C32×C8C2311yescharacteristic
82#3748C2312yes—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84#3743—22no—
85#3743C2×C412yes—
86#3743C2×C412yes—
87C8×C3⋊D3—22no—
88C3×C4×Dic3C2311yescharacteristic
89C3×C4×Dic3C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92C3×Dic12C2×C411yescharacteristic, complemented
93C3×Dic12C2×C411yescharacteristic, complemented
94C3×D24C2×C411yescharacteristic, complemented
95C3×D24C2×C411yescharacteristic, complemented
96C3×#204C2×C412yescomplemented
97C3×#204C2×C412yescomplemented
98C3×ΓL(1,𝔽25)—22no—
99C3×ΓL(1,𝔽25)—22no—
100C3×D3×C8—22no—
101C3×D3×C8—22no—
102Dic32—21no—
103#3718C2×C412yescomplemented
104#3715C2×C412yescomplemented
105#3715C2×C412yescomplemented
106#3713C2×C412yescomplemented
107#3712D412yes—
108#3712D412yes—
109#3711—22no—
110#3711—22no—
111D3×C3⋊C8—22no—
112D3×C3⋊C8—22no—
113#2956—91noSylow
114D3×#41—32no—
115D3×#41—32no—
116C3×#135—31no—
117C3×#135—31no—
118C3×#131—32no—
119C3×#131—32no—
120#950—32no—
121#950—32no—
122#948—32no—
123#948—32no—
124#918—32no—
125#918—32no—
126#915—32no—
127#915—32no—
128#914—32no—
129#914—32no—
130#911—32no—
131#911—32no—
132#907—62no—
133#907—62no—
134#907C2×D312yescomplemented
135#907C2×D312yescomplemented
136D3×M16—32no—
137D3×M16—32no—
138D3×M16—62no—
139D3×M16—62no—
140D3×M16—62no—
141#904C2×D311yescharacteristic
142#904C2×D311yescharacteristic
143#901—32no—
144#901—32no—
145#901—62no—
146#901—62no—
147C2×ΓL(1,𝔽25)—31no—
148C2×ΓL(1,𝔽25)—31no—
149C2×ΓL(1,𝔽25)—31no—
150C2×ΓL(1,𝔽25)—31no—
151C2×ΓL(1,𝔽25)—61no—
152C2×ΓL(1,𝔽25)—62no—
153C2×ΓL(1,𝔽25)—62no—
154C42×D3—31no—
155C42×D3—31no—
156C3×#108—21no—
157C3×#108C2×D311yescharacteristic, complemented
158C3×#108C2×D311yescharacteristic, complemented
159C3×#104—32no—
160C3×#104—32no—
161C3×#97—31no—
162C3×C4×C8—31no—
163#837—32no—
164#837—32no—
165#825C2×D312yescomplemented
166#825C2×D312yescomplemented
167#822—32no—
168#822—32no—
169#822—62no—
170#819—31no—
171#819—31no—
172#819—61no—
173#815—31no—
174#815C2×D311yescharacteristic, complemented
175C8×Dic3—31no—
176C8×Dic3C2×D311yescharacteristic, complemented
177#805—32no—
178#805—32no—
179#803—31no—
180C4×C3⋊C8—31no—
181C22×C3⋊D3#4111yescharacteristic
182C2×D32—22no—
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3#4111yescharacteristic
185C4×C3⋊D3C22×C412yes—
186C4×C3⋊D3C2×D412yes—
187C3×#67—22no—
188C3×#67—22no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C3×D12C22×C412yes—
192C3×D12C22×C412yes—
193C3×C4×D3—22no—
194C3×C4×D3—22no—
195C3×Dic6C22×C412yes—
196C3×Dic6C22×C412yes—
197#627—22no—
198#626—22no—
199#626—22no—
200#625—22no—
201#624—22no—
202#624—42no—
203D3×Dic3—22no—
204D3×Dic3—22no—
205C32×C8—22no—
206C32×C8C22×C411yescharacteristic
207C32×C8C22×C411yescharacteristic
208C3⋊(C3⋊C8)—22no—
209C3⋊(C3⋊C8)C22×C412yes—
210C3×C3⋊C8C2×D411yescharacteristic
211C3×C3⋊C8C2×D412yes—
212C3×C3⋊C8C2×D411yescharacteristic
213#575—91no—
214#568—92no—
215#444—31no—
216#444—91no—
217#444—92no—
218#443—31no—
219#443—91no—
220#443—92no—
221#430—91no—
222C2×#104—92no—
223C4×M16—91no—
224C3×#41—32no—
225C3×#41—32no—
226#239—32no—
227#239—32no—
228D3×Q8—32no—
229D3×Q8—32no—
230#237—32no—
231#237—32no—
232#237—62no—
233#237—62no—
234D3×D4—32no—
235D3×D4—32no—
236D3×D4—62no—
237D3×D4—62no—
238#235—62no—
239#235—62no—
240#235C22×D312yes—
241#235C22×D312yes—
242C2×C4×D3—31no—
243C2×C4×D3—31no—
244C2×C4×D3—61no—
245C2×C4×D3—62no—
246C2×C4×D3—62no—
247C2×C4×D3—61no—
248C2×C4×D3—61no—
249C3×Q16—31no—
250C3×Q16—31no—
251C3×SD16—32no—
252C3×SD16—32no—
253C3×D8—31no—
254C3×D8—31no—
255C3×M16—22no—
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—
268C3×C42—31no—
269#216—32no—
270#216—32no—
271#215—32no—
272#215—32no—
273#214—32no—
274#214—32no—
275#213—32no—
276#213—32no—
277C4×Dic3—61no—
278C4×Dic3—61no—
279C4×Dic3C22×D311yescharacteristic
280C4×Dic3C22×D311yescharacteristic
281#208—32no—
282#208—32no—
283#208—62no—
284#208—62no—
285#208—62no—
286C2×C3⋊C8—31no—
287C2×C3⋊C8—31no—
288C2×C3⋊C8—61no—
289C2×C3⋊C8—62no—
290C2×C3⋊C8—62no—
291C2×C3⋊C8C22×D311yescharacteristic
292C2×C3⋊C8C22×D311yescharacteristic
293Dic12C4×D311yescharacteristic, complemented
294Dic12C4×D311yescharacteristic, complemented
295D24C4×D311yescharacteristic, complemented
296D24C4×D311yescharacteristic, complemented
297#204C4×D312yescomplemented
298#204C4×D312yescomplemented
299ΓL(1,𝔽25)—22no—
300ΓL(1,𝔽25)—22no—
301ΓL(1,𝔽25)—32no—
302ΓL(1,𝔽25)—32no—
303ΓL(1,𝔽25)—32no—
304ΓL(1,𝔽25)—32no—
305ΓL(1,𝔽25)—32no—
306ΓL(1,𝔽25)—32no—
307ΓL(1,𝔽25)—32no—
308ΓL(1,𝔽25)—32no—
309ΓL(1,𝔽25)—62no—
310ΓL(1,𝔽25)—62no—
311ΓL(1,𝔽25)—62no—
312ΓL(1,𝔽25)—62no—
313ΓL(1,𝔽25)—62no—
314ΓL(1,𝔽25)—62no—
315ΓL(1,𝔽25)—122no—
316D3×C8—22no—
317D3×C8—22no—
318D3×C8—62no—
319D3×C8—62no—
320D3×C8—62no—
321D3×C8—62no—
322D3×C8—122no—
323C22×C32C2×#4111yescharacteristic
324C2×C3⋊D3—41no—
325C2×C3⋊D3C4×D412yes—
326C2×C3×D3—22no—
327C2×C3×D3—22no—
328D32—82no—
329C32×C4C23×C411yescharacteristic
330C32×C4C22×D411yescharacteristic
331C3⋊Dic3C4×D412yes—
332C3×Dic3—22no—
333C3×Dic3—22no—
334C3×Dic3—22no—
335C3×Dic3—41no—
336C2×#41—92no—
337#137—92no—
338#137—92no—
339AGL(1,ℤ/8)—92no—
340AGL(1,ℤ/8)—92no—
341#135—31no—
342#135—31no—
343#135—92no—
344#131—32no—
345#131—32no—
346#131—92no—
347#131—92no—
348#131—182no—
349#131—182no—
350C2×M16—91no—
351C2×M16—91no—
352C2×M16—92no—
353C2×M16—182no—
354C2×M16—182no—
355C2×C42—91no—
356#108—92no—
357#108—91no—
358#108D3211yescharacteristic, complemented
359#104—32no—
360#104—32no—
361#104—92no—
362#104—92no—
363#97—31no—
364#97—91no—
365C4×C8—31no—
366C4×C8—91no—
367C22×D3—31no—
368C22×D3—31no—
369C22×D3—61no—
370C22×D3—62no—
371C22×D3—62no—
372C3×Q8—32no—
373C3×Q8—32no—
374C3×D4—32no—
375C3×D4—32no—
376C3×D4—62no—
377C3×D4—62no—
378C2×C3×C4—21no—
379C2×C3×C4—61no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—61no—
383C2×C3×C4C23×D311yescharacteristic
384C2×C3×C4C23×D311yescharacteristic
385#67—22no—
386#67—22no—
387#67—62no—
388#67—62no—
389#67—62no—
390#67—62no—
391C2×Dic3—21no—
392C2×Dic3—21no—
393C2×Dic3—31no—
394C2×Dic3—31no—
395C2×Dic3—61no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398D12—62no—
399D12—62no—
400D12C2×C4×D312yes—
401D12C2×C4×D312yes—
402C4×D3—22no—
403C4×D3—22no—
404C4×D3—32no—
405C4×D3—32no—
406C4×D3—32no—
407C4×D3—32no—
408C4×D3—62no—
409C4×D3—62no—
410C4×D3—62no—
411C4×D3—62no—
412C4×D3—62no—
413C4×D3—62no—
414C4×D3—122no—
415C4×D3—122no—
416Dic6—62no—
417Dic6—62no—
418Dic6C2×C4×D312yes—
419Dic6C2×C4×D312yes—
420C3×C8—22no—
421C3×C8—22no—
422C3×C8—21no—
423C3×C8—21no—
424C3×C8—31no—
425C3×C8—32no—
426C3×C8—31no—
427C3×C8—42no—
428C3×C8C2×C4×D311yescharacteristic
429C3×C8C2×C4×D311yescharacteristic
430C3×C8C2×C4×D311yescharacteristic
431C3×C8C2×C4×D311yescharacteristic
432C3⋊C8—32no—
433C3⋊C8—32no—
434C3⋊C8—62no—
435C3⋊C8—62no—
436C3⋊C8—62no—
437C3⋊C8—122no—
438C3⋊C8D3×D411yescharacteristic
439C3⋊C8D3×D412yes—
440C3⋊C8D3×D411yescharacteristic
441C2×C32—21no—
442C2×C32C2×C4×D411yescharacteristic
443C3⋊D3—22no—
444C3×D3—42no—
445C3×D3—42no—
446#41—32no—
447#41—32no—
448#41—92no—
449#41—92no—
450#41—182no—
451#41—182no—
452C2×Q8—92no—
453C2×D4—92no—
454C2×D4—182no—
455C22×C4—91no—
456C22×C4—182no—
457C22×C4—181no—
458Q16—31no—
459Q16—31no—
460Q16—92no—
461SD16—32no—
462SD16—32no—
463SD16—92no—
464SD16—92no—
465D8—31no—
466D8—31no—
467D8—92no—
468M16—62no—
469M16—62no—
470M16—92no—
471M16—92no—
472M16—92no—
473M16—92no—
474M16—92no—
475M16—182no—
476M16—182no—
477M16—182no—
478M16C2×D3212yes—
479C2×C8—31no—
480C2×C8—31no—
481C2×C8—62no—
482C2×C8—62no—
483C2×C8—91no—
484C2×C8—182no—
485C2×C8—182no—
486C2×C8—182no—
487C2×C8C2×D3211yescharacteristic
488C42—31no—
489C42—31no—
490C42—181no—
491C22×C3—21no—
492C22×C3—62no—
493C22×C3—62no—
494C22×C3D3×#4111yescharacteristic
495C22×C3D3×#4111yescharacteristic
496C2×D3—22no—
497C2×D3—22no—
498C2×D3—32no—
499C2×D3—32no—
500C2×D3—62no—
501C2×D3—121no—
502C2×D3—121no—
503C2×D3—241no—
504C2×D3—242no—
505C2×D3—242no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—62no—
509C3×C4—62no—
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—22no—
518Dic3—22no—
519Dic3—32no—
520Dic3—32no—
521Dic3—41no—
522Dic3—62no—
523C32#295611yescharacteristic, complemented, Sylow
524C23—91no—
525C23—182no—
526Q8—32no—
527Q8—32no—
528Q8—182no—
529D4—32no—
530D4—32no—
531D4—62no—
532D4—62no—
533D4—182no—
534D4—182no—
535D4—182no—
536C2×C4—61no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—61no—
540C2×C4—91no—
541C2×C4—92no—
542C2×C4—92no—
543C2×C4—182no—
544C2×C4—182no—
545C2×C4—182no—
546C2×C4—362no—
547C2×C4C22×D3211yescharacteristic
548C8—22no—
549C8—31no—
550C8—32no—
551C8—31no—
552C8—92no—
553C8—182no—
554C8C4×D3211yescharacteristic
555C8C4×D3211yescharacteristic
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—41no—
560C2×C3—122no—
561C2×C3—122no—
562C2×C3C4×D3×D411yescharacteristic
563C2×C3C4×D3×D411yescharacteristic
564D3—42no—
565D3—42no—
566D3—62no—
567D3—62no—
568D3—122no—
569C22—62no—
570C22—62no—
571C22—92no—
572C22—361no—
573C22—722no—
574C22#6431911yescharacteristic
575C4—62no—
576C4—62no—
577C4—62no—
578C4—92no—
579C4—121no—
580C4C2×C4×D3211yescharacteristic
581C4D32×D411yescharacteristic
582C3—21no—
583C3#7988911yescharacteristic, complemented
584C3#7989811yescharacteristic, complemented
585C2—21no—
586C2—122no—
587C2—122no—
588C2—182no—
589C2#1059460511yescharacteristic
subgroupG/H
centerC4D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#108C22
socleC2×C32C2×C4×D4
prime radical#10594685C2
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. #10594708C2semidirect
3. #10592592C2semidirect
4. C3×#4895C2semidirect
5. C3×#4894C2semidirect
6. #10591008C2semidirect
7. #10590976C2semidirect
8. #10590975C2semidirect
9. #10590916C2semidirect
10. #10590915C2semidirect
11. #10590664C2semidirect
17. C3×#907C22semidirect
18. C3×#907C22semidirect
24. #63814C22semidirect
25. #63814C22semidirect
26. #63811C4semidirect
27. #63811C4semidirect
30. #63798C4semidirect
31. #63798C4semidirect
34. C32×#108C22semidirect
35. #63649C22semidirect
36. #63646C22semidirect
37. C3×#825C22semidirect
38. C3×#825C22semidirect
39. C3×#815C22semidirect
40. C3×C8×Dic3C22semidirect
41. #63569C22semidirect
42. #63569C22semidirect
43. #63554C22semidirect
44. Dic3×C3⋊C8C22semidirect
55. #4895D3semidirect
56. #4894D3semidirect
92. C3×Dic12C2×C4semidirect
93. C3×Dic12C2×C4semidirect
94. C3×D24C2×C4semidirect
95. C3×D24C2×C4semidirect
96. C3×#204C2×C4semidirect
97. C3×#204C2×C4semidirect
103. #3718C2×C4semidirect
104. #3715C2×C4semidirect
105. #3715C2×C4semidirect
106. #3713C2×C4semidirect
134. #907C2×D3semidirect
135. #907C2×D3semidirect
157. C3×#108C2×D3semidirect
158. C3×#108C2×D3semidirect
165. #825C2×D3semidirect
166. #825C2×D3semidirect
174. #815C2×D3semidirect
176. C8×Dic3C2×D3semidirect
293. Dic12C4×D3semidirect
294. Dic12C4×D3semidirect
295. D24C4×D3semidirect
296. D24C4×D3semidirect
297. #204C4×D3semidirect
298. #204C4×D3semidirect
358. #108D32semidirect
523. C32#2956semidirect
583. C3#79889semidirect
584. C3#79898semidirect

Maximal subgroups

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

subgroupindex
#105947082
#105946852
#105925922
C3×#48952
C3×#48942
#105910082
#105909762
#105909752
#105909162
#105909152
#105906642
#798983
#798893