Finite Group Databasebeta

← #11876988

Subgroups — #11876988

Order 1152.

958 conjugacy classes of subgroups.

The subgroup lattice has 511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594369C212yesmaximal, complemented
2#10592568C211yesmaximal, characteristic, complemented
3C3×#4865C211yesmaximal, characteristic, complemented
4C3×#4855C211yesmaximal, characteristic, complemented
5#10590880C211yesmaximal, characteristic, complemented
6#10590835C211yesmaximal, characteristic, complemented
7#10590781C211yesmaximal, characteristic, complemented
8Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
9#10590586C212yesmaximal, complemented
10#10590548C212yesmaximal, complemented
11#10590462C212yesmaximal, complemented
12#81888—31nomaximal
13#80853—31nomaximal
14C2×#3796—22no—
15C2×#3745C2211yescharacteristic
16#64102C2212yes—
17C2×C3×D24C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
19C3×#895C2212yes—
20C3×#888C2212yes—
21#63911C2212yes—
22#63909C2212yes—
23#63907—22no—
24#63898C2212yes—
25#63886—22no—
26#63881—22no—
27C4×D3×Dic3C2211yescharacteristic
28C2×#3714C2212yes—
29C2×#3711C2211yescharacteristic
30C32×#106C2211yescharacteristic
31#63642C2211yescharacteristic
32#63636C2212yes—
33C3×#817C2211yescharacteristic
34C3×C8×Dic3C2211yescharacteristic
35C3×#809C2212yes—
36C3×#808C2212yes—
37#63564C2212yes—
38#63562C2212yes—
39#63555C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5725—32no—
42#5596—32no—
43C3×#498—31no—
44C3×#469—31no—
45#5152—31no—
46#5151—31no—
47#5135—31no—
48Dic3×M16—31no—
49#5088—32no—
50#5039—32no—
51#4869—31no—
52#4869—31no—
53#4869—31no—
54#4869—32no—
55#4869—61no—
56#4865—31no—
57#4865—32no—
58#4865D311yescharacteristic, complemented
59#4855D311yescharacteristic, complemented
60#4785—32no—
61#4760—32no—
62#4695—31no—
63C4×ΓL(1,𝔽25)—31no—
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×C4×C3⋊D3—22no—
66C2×C3×D12—22no—
67C2×C3×D12C2312yes—
68C2×C3×C4×D3C2311yescharacteristic
69C2×C3×Dic6—22no—
70C2×#626—22no—
71C2×#626—22no—
72C2×#626—22no—
73C2×D3×Dic3—22no—
74C2×D3×Dic3D412yes—
75#3796—48no—
76C2×C32×C8C2311yescharacteristic
77C32×C4⋊C4C2312yes—
78#3752—22no—
79C4×C3⋊Dic3C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81#3745—22no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3C2312yes—
84C3×Dic3⋊C4—22no—
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C3×D24—22no—
89C3×ΓL(1,𝔽25)—22no—
90#3722—22no—
91(C2×D3)⋊Dic3—22no—
92Dic32D412yes—
93#3714—24no—
94#3711—22no—
95#3184—91noSylow
96C2×#239—62no—
97C2×#237—62no—
98C2×C3×D8—31no—
99C2×C3×M16—31no—
100C3×C4⋊Q8—32no—
101C3×#121—32no—
102#947—62no—
103#940—32no—
104#939—62no—
105D4×Dic3—32no—
106C2×#213—32no—
107#930—32no—
108C2×C4×Dic3—31no—
109C2×#208—31no—
110C2×D24—32no—
111C2×D24—31no—
112C2×D24—31no—
113C2×D24—61no—
114C2×D24C2×D311yescharacteristic
115C2×ΓL(1,𝔽25)—31no—
116C2×ΓL(1,𝔽25)C2×D311yescharacteristic
117#895—32no—
118#895—62no—
119#895C2×D312yes—
120#893—32no—
121#893—32no—
122#893—32no—
123#893—62no—
124#893—62no—
125#888C2×D312yes—
126#885—62no—
127#67⋊C4—62no—
128#874—32no—
129C42×D3—31no—
130C3×#106—21no—
131C3×#106—31no—
132C3×#106—32no—
133C3×#106C2×D311yescharacteristic
134C3×#106C2×D311yescharacteristic
135C3×#102—32no—
136C3×C4×C8—31no—
137#832—32no—
138#821—32no—
139#817C2×D311yescharacteristic
140#815—31no—
141#815—31no—
142#815—31no—
143#815—31no—
144#815—61no—
145C8×Dic3—31no—
146C8×Dic3C2×D311yescharacteristic
147#809—32no—
148#809—32no—
149#809—32no—
150#809—32no—
151#809—62no—
152#809C2×D312yes—
153#808C2×D312yes—
154C4×C3⋊C8—31no—
155C22×C3⋊D3—22no—
156C22×C3×D3—22no—
157C22×C3×D3C2×D411yescharacteristic
158C2×C32×C4—22no—
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3C2×D412yes—
161C4⋊(C3⋊D3)—22no—
162C4⋊(C3⋊D3)—22no—
163C4×C3⋊D3—44no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C2×D411yescharacteristic
166C2×C3×Dic3C2×D412yes—
167C3×D12—22no—
168C3×D12—22no—
169C3×D12—44no—
170C3×C4×D3—21no—
171C3×C4×D3—21no—
172C3×Dic6—44no—
173#626—44no—
174#626—44no—
175#626—44no—
176D3×Dic3—24no—
177D3×Dic3—44no—
178C32×C8#4112yescomplemented
179C3⋊(C3⋊C8)—21no—
180C3×C3⋊C8—21no—
181C3×C3⋊C8#4112yescomplemented
182#532—92no—
183#498—31no—
184#493—91no—
185#486—92no—
186#469—31no—
187#469—92no—
188#469—91no—
189#442—92no—
190#442—91no—
191#442—91no—
192C4×M16—91no—
193C2×C3×Q8—62no—
194C2×C3×D4—32no—
195C2×C3×D4—62no—
196C22×C3×C4—31no—
197C2×#67—62no—
198C2×#67—62no—
199C2×#67—62no—
200C22×Dic3—32no—
201C22×Dic3—62no—
202#239—128no—
203#237—128no—
204C2×D12—22no—
205C2×D12—32no—
206C2×D12—32no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—62no—
210C2×D12—62no—
211C2×D12C22×D312yes—
212C2×C4×D3—32no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—122no—
217C2×C4×D3C22×D311yescharacteristic
218C2×Dic6—22no—
219C3×D8—62no—
220C3×M16—62no—
221C2×C3×C8—21no—
222C2×C3×C8—31no—
223C2×C3×C8—31no—
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C22×D311yescharacteristic
226C3×C4⋊C4—22no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4C22×D312yes—
230C3×C4⋊C4C22×D312yes—
231C3×C22⋊C4—62no—
232C3×C42—31no—
233#217—62no—
234#213—64no—
235(C2×D3)⋊C4—22no—
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—
241(C2×D3)⋊C4—122no—
242C4⋊Dic3C22×D312yes—
243Dic3⋊C4—22no—
244C4×Dic3—31no—
245C4×Dic3—31no—
246C4×Dic3—32no—
247C4×Dic3—32no—
248C4×Dic3—61no—
249C4×Dic3C22×D311yescharacteristic
250#208—62no—
251C2×C3⋊C8—31no—
252C2×C3⋊C8—31no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8C22×D311yescharacteristic
255C2×C3⋊C8C22×D311yescharacteristic
256D24—22no—
257D24—64no—
258D24—64no—
259D24—62no—
260D24—62no—
261ΓL(1,𝔽25)—22no—
262ΓL(1,𝔽25)—62no—
263C22×C32C22×D411yescharacteristic
264C2×C3⋊D3—42no—
265C2×C3⋊D3—42no—
266C2×C3⋊D3—42no—
267C2×C3×D3—21no—
268C2×C3×D3—22no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C32×C4—42no—
273C32×C4C2×#4111yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—22no—
276C3×Dic3—21no—
277C3×Dic3—42no—
278C3×Dic3AGL(1,ℤ/8)14yes—
279C2×#41—182no—
280C2×D8—31no—
281C2×D8—92no—
282C2×D8—91no—
283C2×M16—31no—
284C2×M16—91no—
285C4⋊Q8—32no—
286#127—92no—
287#124—182no—
288#121—32no—
289#121—92no—
290#121—182no—
291C4×D4—92no—
292C4×D4—92no—
293C4×D4—182no—
294C2×C42—91no—
295#106—31no—
296#106—32no—
297#106D3211yescharacteristic
298#102—32no—
299#102—92no—
300#102—92no—
301#102—92no—
302#97—91no—
303#97—91no—
304C4×C8—31no—
305C4×C8—91no—
306C23×C3—31no—
307C23×C3—62no—
308C22×D3—22no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—122no—
312C22×D3D3×D411yescharacteristic
313C3×Q8—124no—
314C3×D4—62no—
315C3×D4—62no—
316C3×D4—124no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—32no—
321C2×C3×C4—31no—
322C2×C3×C4—42no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—62no—
326C2×C3×C4C23×D311yescharacteristic
327C2×C3×C4C23×D311yescharacteristic
328#67—124no—
329#67—124no—
330#67—124no—
331C2×Dic3—22no—
332C2×Dic3—32no—
333C2×Dic3—32no—
334C2×Dic3—62no—
335C2×Dic3—64no—
336C2×Dic3—124no—
337C2×Dic3D3×D411yescharacteristic
338C2×Dic3D3×D412yes—
339D12—22no—
340D12—22no—
341D12—44no—
342D12—64no—
343D12—62no—
344D12—62no—
345D12—62no—
346D12—62no—
347D12—122no—
348D12—124no—
349D12—124no—
350D12—124no—
351C4×D3—21no—
352C4×D3—21no—
353C4×D3—64no—
354C4×D3—124no—
355C4×D3—124no—
356C4×D3—124no—
357C4×D3—244no—
358Dic6—44no—
359C3×C8—22no—
360C3×C8—32no—
361C3×C8—61no—
362C3×C8#23712yescomplemented
363C3×C8#23912yescomplemented
364C3⋊C8—21no—
365C3⋊C8—61no—
366C3⋊C8—61no—
367C3⋊C8—121no—
368C3⋊C8#23912yescomplemented
369C2×C32#53211yescharacteristic
370C2×C32C2×AGL(1,ℤ/8)12yes—
371C3⋊D3—82no—
372C3×D3—41no—
373C3×D3—82no—
374#41—368no—
375C2×Q8—62no—
376C2×D4—32no—
377C2×D4—62no—
378C2×D4—92no—
379C2×D4—182no—
380C2×D4—182no—
381C2×D4—182no—
382C22×C4—31no—
383C22×C4—92no—
384C22×C4—182no—
385C22×C4—182no—
386D8—62no—
387D8—184no—
388D8—182no—
389M16—62no—
390M16—182no—
391C2×C8—31no—
392C2×C8—31no—
393C2×C8—91no—
394C2×C8C2×D3211yescharacteristic
395C4⋊C4—32no—
396C4⋊C4—62no—
397C4⋊C4C2×D3212yes—
398C22⋊C4—62no—
399C22⋊C4—182no—
400C22⋊C4—182no—
401C22⋊C4—182no—
402C42—31no—
403C42—92no—
404C42—91no—
405C22×C3—21no—
406C22×C3—61no—
407C22×C3—62no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3C2×D3×D411yescharacteristic
412C22×C3C2×D3×D411yescharacteristic
413C2×D3—22no—
414C2×D3—21no—
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—42no—
418C2×D3—124no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—122no—
425C2×D3—242no—
426C2×D3—242no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—34no—
430C3×C4—42no—
431C3×C4—42no—
432C3×C4—61no—
433C3×C4—82no—
434C3×C4—122no—
435C3×C4C2×#23711yescharacteristic
436C3×C4C2×#23911yescharacteristic
437C3×C4C2×#23911yescharacteristic
438C3×C4D3×#4111yescharacteristic
439Dic3—21no—
440Dic3—42no—
441Dic3—62no—
442Dic3—62no—
443Dic3—122no—
444Dic3#91414yes—
445C32#318411yescharacteristic, complemented, Sylow
446C23—31no—
447C23—62no—
448C23—182no—
449Q8—124no—
450D4—62no—
451D4—62no—
452D4—124no—
453D4—182no—
454D4—182no—
455D4—364no—
456D4—364no—
457D4—364no—
458C2×C4—22no—
459C2×C4—32no—
460C2×C4—31no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—62no—
464C2×C4—92no—
465C2×C4—184no—
466C2×C4—364no—
467C2×C4—364no—
468C2×C4C22×D3211yescharacteristic
469C8—32no—
470C8—61no—
471C8—181no—
472C8#379612yescomplemented
473C2×C3—21no—
474C2×C3—22no—
475C2×C3—121no—
476C2×C3—242no—
477C2×C3#559611yescharacteristic
478C2×C3#572511yescharacteristic
479C2×C3C2×#91412yes—
480C2×C3D3×AGL(1,ℤ/8)12yes—
481D3—41no—
482D3—82no—
483D3—244no—
484D3—242no—
485D3—242no—
486C22—61no—
487C22—62no—
488C22—122no—
489C22—122no—
490C22—122no—
491C22—362no—
492C22—362no—
493C22—362no—
494C22D32×D411yescharacteristic
495C4—34no—
496C4—42no—
497C4—61no—
498C4—122no—
499C4—182no—
500C4C2×#379611yescharacteristic
501C4D3×#23911yescharacteristic
502C3—21no—
503C3#8085311yescharacteristic, complemented
504C3#8188811yescharacteristic, complemented
505C2—121no—
506C2—242no—
507C2—722no—
508C2#1059436911yescharacteristic
509C2D3×#91412yes—
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
hypercenter#106D32
hypocenterC32#3184
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. #10594369C2semidirect
2. #10592568C2semidirect
3. C3×#4865C2semidirect
4. C3×#4855C2semidirect
5. #10590880C2semidirect
6. #10590835C2semidirect
7. #10590781C2semidirect
8. Dic3×ΓL(1,𝔽25)C2semidirect
9. #10590586C2semidirect
10. #10590548C2semidirect
11. #10590462C2semidirect
58. #4865D3semidirect
59. #4855D3semidirect
178. C32×C8#41semidirect
181. C3×C3⋊C8#41semidirect
362. C3×C8#237semidirect
363. C3×C8#239semidirect
368. C3⋊C8#239semidirect
445. C32#3184semidirect
472. C8#3796semidirect
503. C3#80853semidirect
504. C3#81888semidirect

Maximal subgroups

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

subgroupindex
#105943692
#105925682
C3×#48652
C3×#48552
#105908802
#105908352
#105907812
Dic3×ΓL(1,𝔽25)2
#105905862
#105905482
#105904622
#818883
#808533