Finite Group Databasebeta

← #11876908

Subgroups — #11876908

Order 1152.

783 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593921C212yesmaximal, complemented
2#10592382C211yesmaximal, characteristic, complemented
3C3×#4696C211yesmaximal, characteristic, complemented
4C3×C4×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
5#10590854C211yesmaximal, characteristic, complemented
6#10590836C211yesmaximal, characteristic
7#10590833C212yesmaximal, complemented
8#10590812C211yesmaximal, characteristic, complemented
9#10590771C211yesmaximal, characteristic, complemented
10#10590766C212yesmaximal, complemented
11#10590274C212yesmaximal, complemented
12#81812—31nomaximal
13#78534—31nomaximal
14#64079C2212yes—
15C2×C3×Dic12C2211yescharacteristic
16C2×C3×D24C2211yescharacteristic
17C2×C3×#204C2212yes—
18C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
19C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
20C3×#875C2212yes—
21C3×C42×D3C2211yescharacteristic
22#63908C2212yes—
23#63905—22no—
24Dic3×D12C2212yes—
25#63879—22no—
26#63877—22no—
27#63859—22no—
28#63856C2212yes—
29Dic3×Dic6C2212yes—
30C32×C4×C8C2211yescharacteristic
31#63645C2212yes—
32#63644C2211yescharacteristic
33#63644C2211yescharacteristic
34C3×#815C2211yescharacteristic
35C3×#815C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63566C2212yes—
38#63566C2212yes—
39#63563C2212yes—
40#63563C2212yes—
41#5680—32no—
42#5479—32no—
43C3×#495—31no—
44C3×C4×M16—31no—
45#5189—31no—
46#5184—31no—
47#5174—32no—
48#5164—32no—
49#5159—31no—
50#5152—31no—
51#5137—31no—
52#5135—31no—
53#5134—32no—
54#5056—32no—
55#4716—31no—
56#4711—31no—
57#4710—32no—
58#4697—32no—
59#4696D311yescharacteristic, complemented
60C4×ΓL(1,𝔽25)D311yescharacteristic, complemented
61#4683—31no—
62#4683—31no—
63#4683—61no—
64C2×C3×D12C2312yes—
65C2×C3×C4×D3D412yes—
66C2×C3×C4×D3C2311yescharacteristic
67C2×C3×Dic6C2312yes—
68C2×#625—22no—
69C2×D3×Dic3—22no—
70C2×C32×C8C2311yescharacteristic
71C2×C32×C8C2311yescharacteristic
72C32×C42C2311yescharacteristic
73C4⋊(C3⋊Dic3)C2312yes—
74C4⋊(C3⋊Dic3)C2312yes—
75#3750—22no—
76#3750—22no—
77C3×(C2×D3)⋊C4—22no—
78C3×(C2×D3)⋊C4—22no—
79C3×C4×Dic3D412yes—
80C3×C4×Dic3C2311yescharacteristic
81C2×C3×C3⋊C8C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83C3×Dic12—22no—
84C3×D24—22no—
85C3×#204—24no—
86C3×ΓL(1,𝔽25)—22no—
87C3×ΓL(1,𝔽25)—22no—
88#3724—22no—
89Dic3⋊Dic3—22no—
90(C2×D3)⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92(C2×D3)⋊Dic3—22no—
93Dic32—22no—
94#3183—91noSylow
95C2×C3×Q16—31no—
96C2×C3×SD16—32no—
97C2×C3×D8—31no—
98C2×C3×M16—31no—
99C2×C3×M16—31no—
100C3×#124—32no—
101C2×C3×C42—31no—
102#946—32no—
103Q8×Dic3—32no—
104#938—32no—
105D4×Dic3—32no—
106#930—32no—
107#929—62no—
108C4×#67—62no—
109#924—32no—
110C2×Dic12C2×D311yescharacteristic
111C2×D24C2×D311yescharacteristic
112C2×#204C2×D312yes—
113C2×ΓL(1,𝔽25)C2×D311yescharacteristic
114C2×ΓL(1,𝔽25)C2×D311yescharacteristic
115#883—62no—
116#67⋊C4—62no—
117#879—62no—
118#877—62no—
119#876—62no—
120#875C2×D312yes—
121C4×D12—32no—
122#872—62no—
123C42×D3C2×D311yescharacteristic
124#870—32no—
125#870—32no—
126#870—62no—
127C4×Dic6—32no—
128C3×#97—31no—
129C3×#97—31no—
130C3×C4×C8—21no—
131C3×C4×C8—31no—
132C3×C4×C8C2×D311yescharacteristic
133C3×C4×C8C2×D311yescharacteristic
134#835—32no—
135#835—32no—
136#832—32no—
137#832—32no—
138#821—32no—
139#821—32no—
140#818—32no—
141#818—32no—
142#818—62no—
143#817—31no—
144#817—31no—
145#817—31no—
146#817—31no—
147#817—61no—
148#817—61no—
149#816—32no—
150#816—32no—
151#815C2×D311yescharacteristic
152#815C2×D311yescharacteristic
153C4×C3⋊C8C2×D311yescharacteristic
154C22×C3×D3—22no—
155C22×C3×D3C2×D411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3C2×D412yes—
162C2×C3×Dic3C2×D411yescharacteristic
163C3×D12—22no—
164C3×D12—22no—
165C3×C4×D3—21no—
166C3×C4×D3—21no—
167C3×C4×D3—42no—
168C3×Dic6—22no—
169C3×Dic6—22no—
170#625—44no—
171D3×Dic3—44no—
172C32×C8#4112yes—
173C32×C8#4112yes—
174C3×C3⋊C8—21no—
175C3×C3⋊C8—21no—
176#529—92no—
177#499—91no—
178#495—31no—
179#488—92no—
180#470—91no—
181#469—91no—
182#468—92no—
183#442—91no—
184#441—91no—
185#440—92no—
186C4×M16—31no—
187C2×C3×Q8—32no—
188C2×C3×D4—32no—
189C22×C3×C4—31no—
190C22×C3×C4—32no—
191C2×#67—62no—
192C2×#67—62no—
193C22×Dic3—62no—
194C2×D12C22×D312yes—
195C2×C4×D3—62no—
196C2×C4×D3D1212yes—
197C2×C4×D3C22×D311yescharacteristic
198C2×Dic6C22×D312yes—
199C3×Q16—62no—
200C3×SD16—64no—
201C3×D8—62no—
202C3×M16—62no—
203C3×M16—62no—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—31no—
207C2×C3×C8—31no—
208C2×C3×C8C22×D311yescharacteristic
209C2×C3×C8C22×D311yescharacteristic
210C2×C3×C8C22×D311yescharacteristic
211C2×C3×C8C22×D311yescharacteristic
212C3×C22⋊C4—62no—
213C3×C22⋊C4—62no—
214C3×C42—21no—
215C3×C42—32no—
216C3×C42—31no—
217C3×C42C22×D311yescharacteristic
218C3×C42C22×D311yescharacteristic
219#217—62no—
220#217—62no—
221#217—62no—
222(C2×D3)⋊C4—22no—
223(C2×D3)⋊C4—22no—
224(C2×D3)⋊C4—62no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—62no—
227C4⋊Dic3—32no—
228C4⋊Dic3—32no—
229C4⋊Dic3—32no—
230C4⋊Dic3—32no—
231C4⋊Dic3—62no—
232C4⋊Dic3—62no—
233C4⋊Dic3—62no—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241Dic3⋊C4—122no—
242Dic3⋊C4—122no—
243C4×Dic3—62no—
244C4×Dic3—62no—
245C4×Dic3D1212yes—
246C4×Dic3C22×D311yescharacteristic
247C2×C3⋊C8C22×D311yescharacteristic
248C2×C3⋊C8C22×D311yescharacteristic
249Dic12—22no—
250D24—22no—
251#204—24no—
252ΓL(1,𝔽25)—22no—
253ΓL(1,𝔽25)—22no—
254C22×C32C22×D411yescharacteristic
255C2×C3×D3—21no—
256C2×C3×D3—22no—
257C2×C3×D3—42no—
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C32×C4—22no—
261C32×C4C2×#4111yescharacteristic
262C32×C4C2×#4111yescharacteristic
263C3⋊Dic3—42no—
264C3⋊Dic3—42no—
265C3×Dic3—21no—
266C3×Dic3—22no—
267C3×Dic3—42no—
268C2×Q16—31no—
269C2×SD16—32no—
270C2×D8—31no—
271C2×M16—31no—
272C2×M16—31no—
273#126—182no—
274#125—92no—
275#124—32no—
276#123—182no—
277C22⋊Q8—92no—
278#121—92no—
279C4×Q8—92no—
280C4×D4—92no—
281C4×D4—182no—
282#117—182no—
283C2×C42—31no—
284#107—92no—
285#106—91no—
286#106—91no—
287#103—92no—
288#103—92no—
289#102—92no—
290#102—92no—
291#97—31no—
292#97—31no—
293C4×C8—31no—
294C4×C8D3211yescharacteristic
295C23×C3—31no—
296C23×C3—62no—
297C22×D3—22no—
298C22×D3C2×D1211yescharacteristic
299C3×Q8—62no—
300C3×Q8—62no—
301C3×D4—62no—
302C3×D4—62no—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—32no—
306C2×C3×C4—31no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309C2×C3×C4—62no—
310C2×C3×C4—122no—
311C2×C3×C4C2×D1212yes—
312C2×C3×C4D3×D412yes—
313C2×C3×C4C23×D311yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315#67—124no—
316#67—124no—
317C2×Dic3—22no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—122no—
323C2×Dic3—122no—
324C2×Dic3—124no—
325C2×Dic3C2×D1212yes—
326C2×Dic3C2×D1211yescharacteristic
327D12—22no—
328D12—22no—
329C4×D3—21no—
330C4×D3—21no—
331C4×D3—42no—
332C4×D3—124no—
333Dic6—22no—
334Dic6—22no—
335C3×C8—22no—
336C3×C8—22no—
337C3×C8—61no—
338C3×C8—61no—
339C3×C8#23512yes—
340C3×C8#23512yes—
341C3×C8#23712yes—
342C3×C8#23712yes—
343C3⋊C8—21no—
344C3⋊C8—21no—
345C2×C32#53211yescharacteristic
346C2×C32#57512yes—
347C3×D3—41no—
348C3×D3—82no—
349C2×Q8—32no—
350C2×D4—32no—
351C2×D4—182no—
352C22×C4—31no—
353C22×C4—32no—
354C22×C4—182no—
355Q16—62no—
356SD16—64no—
357D8—62no—
358M16—62no—
359M16—62no—
360C2×C8—31no—
361C2×C8—31no—
362C2×C8C2×D3211yescharacteristic
363C2×C8C2×D3211yescharacteristic
364C4⋊C4—92no—
365C4⋊C4—92no—
366C4⋊C4—182no—
367C4⋊C4—182no—
368C4⋊C4—182no—
369C4⋊C4—182no—
370C22⋊C4—62no—
371C22⋊C4—62no—
372C22⋊C4—182no—
373C22⋊C4—182no—
374C22⋊C4—182no—
375C42—31no—
376C42—32no—
377C42—182no—
378C42C2×D3211yescharacteristic
379C22×C3—21no—
380C22×C3—61no—
381C22×C3—62no—
382C22×C3—122no—
383C22×C3—122no—
384C22×C3—122no—
385C22×C3C22×D1211yescharacteristic
386C22×C3C2×D3×D411yescharacteristic
387C2×D3—21no—
388C2×D3—22no—
389C2×D3—42no—
390C2×D3—42no—
391C2×D3—42no—
392C3×C4—22no—
393C3×C4—22no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—42no—
397C3×C4—61no—
398C3×C4—62no—
399C3×C4—122no—
400C3×C4C2×#23511yescharacteristic
401C3×C4C2×#23511yescharacteristic
402C3×C4C2×#23711yescharacteristic
403C3×C4C2×#23711yescharacteristic
404Dic3—21no—
405Dic3—22no—
406Dic3—42no—
407Dic3—122no—
408Dic3—122no—
409Dic3—122no—
410Dic3—122no—
411Dic3—242no—
412Dic3—242no—
413C32#318311yescharacteristic, complemented, Sylow
414C23—31no—
415C23—62no—
416Q8—62no—
417Q8—62no—
418D4—62no—
419D4—62no—
420D4—364no—
421C2×C4—32no—
422C2×C4—31no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—62no—
426C2×C4—122no—
427C2×C4—182no—
428C2×C4—182no—
429C2×C4—364no—
430C2×C4D3×D1212yes—
431C2×C4C22×D3211yescharacteristic
432C8—61no—
433C8—61no—
434C8#379512yes—
435C8#379512yes—
436C2×C3—21no—
437C2×C3—22no—
438C2×C3—121no—
439C2×C3—242no—
440C2×C3#547711yescharacteristic
441C2×C3#571611yescharacteristic
442C2×C3#574812yes—
443C2×C3#576812yes—
444D3—41no—
445D3—82no—
446C22—61no—
447C22—62no—
448C22—122no—
449C22—122no—
450C22—122no—
451C22C2×D3×D1211yescharacteristic
452C4—22no—
453C4—61no—
454C4—62no—
455C4—122no—
456C4—362no—
457C4—362no—
458C4C2×#379511yescharacteristic
459C4C2×#379511yescharacteristic
460C3—21no—
461C3#7853411yescharacteristic, complemented
462C3#8181211yescharacteristic, complemented
463C2—121no—
464C2—242no—
465C2#1059389711yescharacteristic
466C2#1059467612yes—
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10590836C2
hypercenterC4×C8D32
hypocenterC32#3183
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. #10593921C2semidirect
2. #10592382C2semidirect
3. C3×#4696C2semidirect
4. C3×C4×ΓL(1,𝔽25)C2semidirect
5. #10590854C2semidirect
7. #10590833C2semidirect
8. #10590812C2semidirect
9. #10590771C2semidirect
10. #10590766C2semidirect
11. #10590274C2semidirect
59. #4696D3semidirect
60. C4×ΓL(1,𝔽25)D3semidirect
413. C32#3183semidirect
461. C3#78534semidirect
462. C3#81812semidirect

Maximal subgroups

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

subgroupindex
#105939212
#105923822
C3×#46962
C3×C4×ΓL(1,𝔽25)2
#105908542
#105908362
#105908332
#105908122
#105907712
#105907662
#105902742
#818123
#785343