Finite Group Databasebeta

← #11877008

Subgroups — #11877008

Order 1152.

951 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593970C211yesmaximal, characteristic, complemented
2#10593897C211yesmaximal, characteristic, complemented
3#10592393C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C3×C4×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
6#10590827C214yesmaximal, complemented
7#10590746C214yesmaximal, complemented
8#10590350C211yesmaximal, characteristic, complemented
9#10590303C211yesmaximal, characteristic, complemented
10#81560—31nomaximal
11#78535—31nomaximal
12C2×#3799—21no—
13C2×#3795—21no—
14#64083C2211yescharacteristic
15#64078C2211yescharacteristic
16C2×C3×ΓL(1,𝔽25)C2212yes—
17C3×#874C2211yescharacteristic
18C3×C42×D3C2211yescharacteristic
19C3×#869C2211yescharacteristic
20#63909—21no—
21#63909C2212yes—
22#63908—21no—
23#63908C2212yes—
24#63894—21no—
25#63894C2212yes—
26Dic3×D12—21no—
27Dic3×D12C2212yes—
28#63864—21no—
29#63860—21no—
30C2×#3714C2214yes—
31C32×C4×C8C2211yescharacteristic
32#63648C2214yes—
33C3×#821C2214yes—
34C3×#815C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36#63573C2214yes—
37#5725—31no—
38#5716—31no—
39#5477—31no—
40#5477—31no—
41C3×#486—31no—
42C3×C4×M16—31no—
43#5135—34no—
44#5080—31no—
45#5073—31no—
46#4785—34no—
47#4782—34no—
48#4711—34no—
49#4695—31no—
50#4694—31no—
51#4694—31no—
52#4694—61no—
53#4694D311yescharacteristic, complemented
54C4×ΓL(1,𝔽25)D311yescharacteristic, complemented
55#4680—31no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×#634—21no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12C2312yes—
63C2×C3×C4×D3D411yescharacteristic
64C2×C3×C4×D3D411yescharacteristic
65C2×C3×C4×D3C2311yescharacteristic
66C2×C3×Dic6—21no—
67C2×#626—22no—
68C2×#625—22no—
69C2×#624—22no—
70C2×D3×Dic3—22no—
71#3799—44no—
72#3795—44no—
73C2×C32×C8C2312yes—
74C32×C42C2311yescharacteristic
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)C2312yes—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3C2312yes—
79C3×C4×Dic3D411yescharacteristic
80C3×C4×Dic3D411yescharacteristic
81C3×C4×Dic3C2311yescharacteristic
82C2×C3×C3⋊C8C2312yes—
83C3×ΓL(1,𝔽25)—24no—
84#3722—22no—
85#3722—22no—
86(C2×D3)⋊Dic3—22no—
87(C2×D3)⋊Dic3—22no—
88#3714—28no—
89#3184—91noSylow
90C2×#239—61no—
91C2×#237—61no—
92C2×#235—61no—
93C2×#235—61no—
94C2×C3×M16—32no—
95C3×C4⋊Q8—31no—
96C3×#127—31no—
97C2×C3×C42—31no—
98#947—61no—
99#938—32no—
100#938—61no—
101#936—61no—
102D4×Dic3—32no—
103D4×Dic3—61no—
104C2×#213—34no—
105#930—32no—
106#930—32no—
107#930—61no—
108#930—61no—
109C2×D24—34no—
110C2×ΓL(1,𝔽25)C2×D312yes—
111#895—32no—
112#895—61no—
113#893—32no—
114#893—61no—
115#875—61no—
116#875—61no—
117#874—31no—
118#874—31no—
119#874—61no—
120#874C2×D311yescharacteristic
121C4×D12—32no—
122C4×D12—32no—
123C4×D12—61no—
124C4×D12—61no—
125C42×D3C2×D311yescharacteristic
126#869—31no—
127#869—31no—
128#869—61no—
129#869C2×D311yescharacteristic
130C3×#102—34no—
131C3×#97—32no—
132C3×C4×C8—21no—
133C3×C4×C8—31no—
134C3×C4×C8C2×D311yescharacteristic
135C3×C4×C8C2×D311yescharacteristic
136#821—34no—
137#821—34no—
138#821—64no—
139#821C2×D314yes—
140#817—34no—
141#815C2×D312yes—
142#808—34no—
143C4×C3⋊C8C2×D311yescharacteristic
144C22×C3⋊D3—22no—
145C22×C3×D3—22no—
146C22×C3×D3C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2411yescharacteristic
150C2×C3⋊Dic3—22no—
151C4⋊(C3⋊D3)—24no—
152C4⋊(C3⋊D3)—42no—
153C4⋊(C3⋊D3)—42no—
154#634—42no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3C2×D411yescharacteristic
157C2×C3×Dic3C2×D411yescharacteristic
158C2×C3×Dic3C2×D411yescharacteristic
159C3×D12—24no—
160C3×D12—42no—
161C3×D12—42no—
162C3×C4×D3—22no—
163C3×C4×D3—22no—
164C3×C4×D3—22no—
165C3×Dic6—42no—
166#626—44no—
167#625—44no—
168#624—44no—
169D3×Dic3—44no—
170C32×C8—22no—
171C3×C3⋊C8#4114yescomplemented
172#532—91no—
173#532—91no—
174#498—91no—
175#493—91no—
176#486—31no—
177#486—91no—
178#469—94no—
179#442—94no—
180C4×M16—31no—
181C2×C3×Q8—61no—
182C2×C3×D4—32no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C22×C3×C4—31no—
186C22×C3×C4—31no—
187C22×C3×C4—31no—
188C2×#67—62no—
189C2×#67—62no—
190C2×#67—62no—
191C22×Dic3—62no—
192#239—124no—
193#237—124no—
194#235—124no—
195#235—124no—
196C2×D12—21no—
197C2×D12—21no—
198C2×D12—32no—
199C2×D12—32no—
200C2×D12—62no—
201C2×D12—62no—
202C2×D12—61no—
203C2×D12—61no—
204C2×D12—61no—
205C2×D12—61no—
206C2×D12—121no—
207C2×D12—121no—
208C2×D12C22×D312yes—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3D1211yescharacteristic
213C2×C4×D3D1211yescharacteristic
214C2×C4×D3C22×D311yescharacteristic
215C2×Dic6—21no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×Dic6—121no—
219C3×M16—64no—
220C2×C3×C8—22no—
221C2×C3×C8—32no—
222C2×C3×C8C22×D312yes—
223C2×C3×C8C22×D312yes—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—61no—
226C3×C42—21no—
227C3×C42—31no—
228C3×C42—31no—
229C3×C42—31no—
230C3×C42C22×D311yescharacteristic
231C3×C42C22×D311yescharacteristic
232#217—62no—
233#217—62no—
234#213—68no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241C4⋊Dic3—21no—
242C4⋊Dic3—32no—
243C4⋊Dic3—32no—
244C4⋊Dic3—62no—
245C4⋊Dic3—61no—
246C4⋊Dic3—61no—
247C4⋊Dic3—121no—
248C4⋊Dic3C22×D312yes—
249C4×Dic3D1211yescharacteristic
250C4×Dic3D1211yescharacteristic
251C4×Dic3C22×D311yescharacteristic
252C2×C3⋊C8C22×D312yes—
253D24—68no—
254ΓL(1,𝔽25)—24no—
255C22×C32C22×D411yescharacteristic
256C2×C3⋊D3—42no—
257C2×C3⋊D3—42no—
258C2×C3⋊D3—42no—
259C2×C3×D3—21no—
260C2×C3×D3—21no—
261C2×C3×D3—21no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C32×C4AGL(1,ℤ/8)12yes—
266C32×C4AGL(1,ℤ/8)12yes—
267C32×C4C2×#4112yes—
268C3⋊Dic3—42no—
269C3×Dic3—21no—
270C3×Dic3—21no—
271C3×Dic3—21no—
272C3×Dic3—42no—
273C2×#41—181no—
274C2×#41—181no—
275C2×D8—94no—
276C2×M16—32no—
277C4⋊Q8—31no—
278C4⋊Q8—91no—
279#127—31no—
280#127—91no—
281#124—181no—
282#124—181no—
283#121—92no—
284#121—92no—
285#121—181no—
286#121—181no—
287C4×D4—92no—
288C4×D4—92no—
289C4×D4—181no—
290C4×D4—181no—
291C2×C42—31no—
292#106—94no—
293#102—34no—
294#102—94no—
295#97—32no—
296C4×C8—31no—
297C4×C8D3211yescharacteristic
298C23×C3—31no—
299C23×C3—62no—
300C22×D3—22no—
301C22×D3—62no—
302C22×D3—62no—
303C22×D3—122no—
304C22×D3C2×D1211yescharacteristic
305C3×Q8—122no—
306C3×D4—64no—
307C3×D4—122no—
308C3×D4—122no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—31no—
313C2×C3×C4—31no—
314C2×C3×C4—31no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4C2×D1211yescharacteristic
320C2×C3×C4C2×D1211yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4C23×D311yescharacteristic
324C2×C3×C4C23×D311yescharacteristic
325#67—124no—
326#67—124no—
327#67—124no—
328C2×Dic3—22no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—122no—
332C2×Dic3—124no—
333C2×Dic3C2×D1211yescharacteristic
334C2×Dic3C2×D1211yescharacteristic
335C2×Dic3C2×D1211yescharacteristic
336D12—24no—
337D12—42no—
338D12—42no—
339D12—64no—
340D12—64no—
341D12—124no—
342D12—124no—
343D12—122no—
344D12—122no—
345D12—122no—
346D12—122no—
347D12—242no—
348D12—242no—
349C4×D3—22no—
350C4×D3—22no—
351C4×D3—22no—
352C4×D3—124no—
353C4×D3—124no—
354C4×D3—124no—
355Dic6—42no—
356Dic6—122no—
357Dic6—122no—
358Dic6—242no—
359C3×C8—22no—
360C3×C8—22no—
361C3×C8—34no—
362C3×C8—42no—
363C3⋊C8#23514yescomplemented
364C2×C32#53211yescharacteristic
365C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
366C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
367C3⋊D3—82no—
368C3×D3—41no—
369C3×D3—82no—
370#41—364no—
371#41—364no—
372C2×Q8—61no—
373C2×Q8—181no—
374C2×D4—32no—
375C2×D4—61no—
376C2×D4—61no—
377C2×D4—92no—
378C2×D4—182no—
379C2×D4—182no—
380C2×D4—181no—
381C2×D4—181no—
382C22×C4—31no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—182no—
386C22×C4—182no—
387D8—188no—
388M16—64no—
389C2×C8—32no—
390C2×C8C2×D3212yes—
391C4⋊C4—32no—
392C4⋊C4—61no—
393C4⋊C4—92no—
394C4⋊C4—181no—
395C22⋊C4—182no—
396C22⋊C4—182no—
397C22⋊C4—182no—
398C22⋊C4—182no—
399C42—31no—
400C42—31no—
401C42—31no—
402C42C2×D3211yescharacteristic
403C22×C3—21no—
404C22×C3—61no—
405C22×C3—61no—
406C22×C3—61no—
407C22×C3—122no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3C22×D1211yescharacteristic
411C22×C3C2×D3×D411yescharacteristic
412C2×D3—21no—
413C2×D3—21no—
414C2×D3—21no—
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—42no—
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—242no—
425C2×D3—242no—
426C2×D3—242no—
427C3×C4—22no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—61no—
431C3×C4—61no—
432C3×C4—61no—
433C3×C4—122no—
434C3×C4#90812yes—
435C3×C4#90812yes—
436C3×C4#91112yes—
437C3×C4#91412yes—
438C3×C4C2×#23512yes—
439C3×C4D3×#4112yes—
440Dic3—21no—
441Dic3—21no—
442Dic3—21no—
443Dic3—42no—
444Dic3—122no—
445Dic3—122no—
446Dic3—242no—
447C32#318411yescharacteristic, complemented, Sylow
448C23—31no—
449C23—62no—
450C23—182no—
451Q8—122no—
452Q8—362no—
453D4—64no—
454D4—122no—
455D4—122no—
456D4—184no—
457D4—364no—
458D4—364no—
459D4—362no—
460D4—362no—
461C2×C4—31no—
462C2×C4—31no—
463C2×C4—31no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—182no—
469C2×C4—364no—
470C2×C4—364no—
471C2×C4D3×D1211yescharacteristic
472C2×C4D3×D1211yescharacteristic
473C2×C4C22×D3211yescharacteristic
474C8—22no—
475C8—34no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—121no—
480C2×C3—242no—
481C2×C3#547711yescharacteristic
482C2×C3#566811yescharacteristic
483C2×C3C2×#90811yescharacteristic
484C2×C3C2×#90811yescharacteristic
485C2×C3C2×#91111yescharacteristic
486C2×C3C2×#91411yescharacteristic
487D3—41no—
488D3—82no—
489D3—242no—
490D3—242no—
491D3—482no—
492C22—61no—
493C22—61no—
494C22—61no—
495C22—122no—
496C22—122no—
497C22—122no—
498C22—362no—
499C22—362no—
500C22—362no—
501C22C2×D3×D1211yescharacteristic
502C4—61no—
503C4—61no—
504C4—61no—
505C4—122no—
506C4—362no—
507C4#6379412yes—
508C4#6379512yes—
509C4D3×#23512yes—
510C3—21no—
511C3#7853511yescharacteristic, complemented
512C3#8156011yescharacteristic, complemented
513C2—121no—
514C2—242no—
515C2—722no—
516C2#1059396911yescharacteristic
517C2C2×#6379411yescharacteristic
518C2C2×#6379511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
hypercenterC4×C8D32
hypocenterC32#3184
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. #10593970C2semidirect
2. #10593897C2semidirect
3. #10592393C2semidirect
4. C3×#4694C2semidirect
5. C3×C4×ΓL(1,𝔽25)C2semidirect
6. #10590827C2semidirect
7. #10590746C2semidirect
8. #10590350C2semidirect
9. #10590303C2semidirect
53. #4694D3semidirect
54. C4×ΓL(1,𝔽25)D3semidirect
171. C3×C3⋊C8#41semidirect
363. C3⋊C8#235semidirect
447. C32#3184semidirect
511. C3#78535semidirect
512. C3#81560semidirect

Maximal subgroups

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

subgroupindex
#105939702
#105938972
#105923932
C3×#46942
C3×C4×ΓL(1,𝔽25)2
#105908272
#105907462
#105903502
#105903032
#815603
#785353