Finite Group Databasebeta

← #11876906

Subgroups — #11876906

Order 1152.

805 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593976C212yesmaximal, complemented
2#10592395C211yesmaximal, characteristic, complemented
3C3×C4×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
4C3×#4683C211yesmaximal, characteristic, complemented
5#10590853C211yesmaximal, characteristic, complemented
6#10590838C212yesmaximal, complemented
7#10590835C211yesmaximal, characteristic
8#10590810C211yesmaximal, characteristic, complemented
9#10590773C212yesmaximal, complemented
10#10590768C211yesmaximal, characteristic, complemented
11#10590293C212yesmaximal, complemented
12#81911—31nomaximal
13#78534—31nomaximal
14C2×#3746C2211yescharacteristic
15C2×#3745C2211yescharacteristic
16C2×#3744C2212yes—
17#64084C2212yes—
18C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
19C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C3×#870C2212yes—
22#63909C2212yes—
23#63904—22no—
24#63894C2212yes—
25#63868—22no—
26#63857C2212yes—
27#63850—22no—
28#63844C2212yes—
29#63836—22no—
30C32×C4×C8C2211yescharacteristic
31C3×#818C2212yes—
32C3×#817C2211yescharacteristic
33C3×#817C2211yescharacteristic
34C3×#815C2211yescharacteristic
35C3×#815C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63567C2212yes—
38#63567C2212yes—
39#63564C2212yes—
40#63564C2212yes—
41#5691—32no—
42#5479—32no—
43C3×#499—31no—
44C3×C4×M16—31no—
45#5137—31no—
46#5135—31no—
47#5134—32no—
48#5068—32no—
49#4889—32no—
50#4886—32no—
51#4869—31no—
52#4867—31no—
53#4865—31no—
54#4853—31no—
55#4716—31no—
56#4711—31no—
57#4710—32no—
58#4697—32no—
59#4696—31no—
60#4696—31no—
61#4696—61no—
62C4×ΓL(1,𝔽25)D311yescharacteristic, complemented
63#4683D311yescharacteristic, complemented
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×#634C2312yes—
66C2×C3×C4×D3D412yes—
67C2×C3×C4×D3C2311yescharacteristic
68C2×#626—22no—
69C2×#624—22no—
70C2×C32×C8C2311yescharacteristic
71C2×C32×C8C2311yescharacteristic
72C32×C42C2311yescharacteristic
73#3752—22no—
74#3752—22no—
75#3746—22no—
76#3745—22no—
77#3744—24no—
78C3×C4⋊Dic3C2312yes—
79C3×C4⋊Dic3C2312yes—
80C3×Dic3⋊C4—22no—
81C3×Dic3⋊C4—22no—
82C3×C4×Dic3D412yes—
83C3×C4×Dic3C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86C3×ΓL(1,𝔽25)—22no—
87C3×ΓL(1,𝔽25)—22no—
88#3724—22no—
89Dic3⋊Dic3—22no—
90#3722—22no—
91#3722—22no—
92(C2×D3)⋊Dic3—22no—
93Dic32—22no—
94#3183—91noSylow
95C2×C3×M16—31no—
96C2×C3×M16—31no—
97C3×#125—32no—
98C2×C3×C42—31no—
99#930—32no—
100#929—62no—
101C4×#67—62no—
102#924—32no—
103C2×Dic12—31no—
104C2×Dic12—31no—
105C2×Dic12—61no—
106C2×D24—31no—
107C2×D24—31no—
108C2×D24—61no—
109C2×#204—32no—
110C2×#204—32no—
111C2×#204—62no—
112C2×ΓL(1,𝔽25)C2×D311yescharacteristic
113C2×ΓL(1,𝔽25)C2×D311yescharacteristic
114#898—62no—
115#897—32no—
116#895—32no—
117#894—62no—
118#893—32no—
119#893—62no—
120#892—62no—
121#887—32no—
122#876—62no—
123#875—32no—
124#875—32no—
125#875—62no—
126C4×D12—32no—
127#872—62no—
128C42×D3C2×D311yescharacteristic
129#870C2×D312yes—
130C4×Dic6—32no—
131C3×#107—32no—
132C3×#106—31no—
133C3×#106—31no—
134C3×#97—31no—
135C3×#97—31no—
136C3×C4×C8—21no—
137C3×C4×C8—31no—
138C3×C4×C8C2×D311yescharacteristic
139C3×C4×C8C2×D311yescharacteristic
140#821—32no—
141#821—32no—
142#818C2×D312yes—
143#817C2×D311yescharacteristic
144#817C2×D311yescharacteristic
145#816—32no—
146#816—32no—
147#815C2×D311yescharacteristic
148#815C2×D311yescharacteristic
149#810—32no—
150#810—32no—
151#809—32no—
152#809—32no—
153C4×C3⋊C8C2×D311yescharacteristic
154C22×C3⋊D3—22no—
155C22×C3×D3C2×D411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3—22no—
159C4⋊(C3⋊D3)—22no—
160C4⋊(C3⋊D3)—22no—
161#634—22no—
162#634—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C2×D412yes—
166C2×C3×Dic3C2×D411yescharacteristic
167C3×C4×D3—21no—
168C3×C4×D3—21no—
169C3×C4×D3—42no—
170#626—44no—
171#624—44no—
172C32×C8#4112yes—
173C32×C8#4112yes—
174C3×C3⋊C8—21no—
175C3×C3⋊C8—21no—
176#529—92no—
177#499—31no—
178#495—91no—
179#488—92no—
180#470—91no—
181#469—91no—
182#468—92no—
183#442—91no—
184#441—91no—
185#440—92no—
186C4×M16—31no—
187C22×C3×C4—31no—
188C22×C3×C4—32no—
189C2×#67—62no—
190C2×D12—32no—
191C2×D12—32no—
192C2×D12—62no—
193C2×D12—62no—
194C2×C4×D3—62no—
195C2×C4×D3—62no—
196C2×C4×D3D1212yes—
197C2×C4×D3C22×D311yescharacteristic
198C2×Dic6—32no—
199C2×Dic6—32no—
200C2×Dic6—62no—
201C3×M16—62no—
202C3×M16—62no—
203C2×C3×C8—21no—
204C2×C3×C8—21no—
205C2×C3×C8—31no—
206C2×C3×C8—31no—
207C2×C3×C8C22×D311yescharacteristic
208C2×C3×C8C22×D311yescharacteristic
209C2×C3×C8C22×D311yescharacteristic
210C2×C3×C8C22×D311yescharacteristic
211C3×C4⋊C4—32no—
212C3×C4⋊C4—32no—
213C3×C4⋊C4—62no—
214C3×C4⋊C4—62no—
215C3×C42—21no—
216C3×C42—32no—
217C3×C42—31no—
218C3×C42C22×D311yescharacteristic
219C3×C42C22×D311yescharacteristic
220#217—62no—
221(C2×D3)⋊C4—62no—
222(C2×D3)⋊C4—62no—
223(C2×D3)⋊C4—62no—
224(C2×D3)⋊C4—62no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—62no—
228(C2×D3)⋊C4—62no—
229(C2×D3)⋊C4—62no—
230(C2×D3)⋊C4—122no—
231(C2×D3)⋊C4—122no—
232C4⋊Dic3—62no—
233C4⋊Dic3C22×D312yes—
234C4⋊Dic3C22×D312yes—
235Dic3⋊C4—22no—
236Dic3⋊C4—22no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239Dic3⋊C4—62no—
240C4×Dic3—62no—
241C4×Dic3—62no—
242C4×Dic3D1212yes—
243C4×Dic3C22×D311yescharacteristic
244C2×C3⋊C8C22×D311yescharacteristic
245C2×C3⋊C8C22×D311yescharacteristic
246Dic12—62no—
247Dic12—62no—
248Dic12—122no—
249D24—62no—
250D24—62no—
251D24—122no—
252#204—64no—
253#204—64no—
254#204—124no—
255ΓL(1,𝔽25)—22no—
256ΓL(1,𝔽25)—22no—
257C22×C32C22×D411yescharacteristic
258C2×C3⋊D3—42no—
259C2×C3⋊D3—42no—
260C2×C3⋊D3—42no—
261C2×C3×D3—21no—
262C2×C3×D3—22no—
263C32×C4—22no—
264C32×C4C2×#4111yescharacteristic
265C32×C4C2×#4111yescharacteristic
266C3⋊Dic3—42no—
267C3×Dic3—21no—
268C3×Dic3—22no—
269C3×Dic3—42no—
270C3×Dic3—42no—
271C2×Q16—91no—
272C2×SD16—92no—
273C2×D8—91no—
274C2×M16—31no—
275C2×M16—31no—
276#126—182no—
277#125—32no—
278#124—92no—
279#123—182no—
280C22⋊Q8—92no—
281#121—92no—
282C4×Q8—92no—
283C4×D4—92no—
284C4×D4—182no—
285#117—182no—
286C2×C42—31no—
287#107—32no—
288#106—31no—
289#106—31no—
290#103—92no—
291#103—92no—
292#102—92no—
293#102—92no—
294#97—31no—
295#97—31no—
296C4×C8—31no—
297C4×C8D3211yescharacteristic
298C23×C3—31no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—122no—
302C22×D3C2×D1211yescharacteristic
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—62no—
311C2×C3×C4—122no—
312C2×C3×C4C2×D1212yes—
313C2×C3×C4D3×D412yes—
314C2×C3×C4C23×D311yescharacteristic
315C2×C3×C4C23×D311yescharacteristic
316#67—124no—
317C2×Dic3—22no—
318C2×Dic3—22no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—122no—
322C2×Dic3C2×D1212yes—
323C2×Dic3C2×D1211yescharacteristic
324D12—62no—
325D12—62no—
326D12—62no—
327D12—62no—
328D12—122no—
329D12—122no—
330D12—124no—
331C4×D3—21no—
332C4×D3—21no—
333C4×D3—42no—
334C4×D3—124no—
335C4×D3—124no—
336Dic6—62no—
337Dic6—62no—
338Dic6—62no—
339Dic6—62no—
340Dic6—122no—
341Dic6—122no—
342C3×C8—22no—
343C3×C8—22no—
344C3×C8—61no—
345C3×C8—61no—
346C3×C8#23512yes—
347C3×C8#23512yes—
348C3×C8#23912yes—
349C3×C8#23912yes—
350C3⋊C8—21no—
351C3⋊C8—21no—
352C2×C32#53211yescharacteristic
353C2×C32#57512yes—
354C3⋊D3—82no—
355C3×D3—41no—
356C2×Q8—92no—
357C2×D4—92no—
358C2×D4—182no—
359C22×C4—31no—
360C22×C4—32no—
361C22×C4—182no—
362Q16—182no—
363SD16—184no—
364D8—182no—
365M16—62no—
366M16—62no—
367C2×C8—31no—
368C2×C8—31no—
369C2×C8C2×D3211yescharacteristic
370C2×C8C2×D3211yescharacteristic
371C4⋊C4—32no—
372C4⋊C4—32no—
373C4⋊C4—62no—
374C4⋊C4—62no—
375C4⋊C4—182no—
376C4⋊C4—182no—
377C22⋊C4—182no—
378C22⋊C4—182no—
379C22⋊C4—182no—
380C22⋊C4—182no—
381C22⋊C4—182no—
382C42—31no—
383C42—32no—
384C42—182no—
385C42C2×D3211yescharacteristic
386C22×C3—21no—
387C22×C3—61no—
388C22×C3—62no—
389C22×C3C22×D1211yescharacteristic
390C22×C3C2×D3×D411yescharacteristic
391C2×D3—21no—
392C2×D3—22no—
393C2×D3—122no—
394C2×D3—122no—
395C2×D3—122no—
396C2×D3—122no—
397C2×D3—122no—
398C2×D3—122no—
399C2×D3—242no—
400C2×D3—242no—
401C2×D3—242no—
402C3×C4—22no—
403C3×C4—22no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—42no—
407C3×C4—61no—
408C3×C4—62no—
409C3×C4—122no—
410C3×C4—122no—
411C3×C4C2×#23511yescharacteristic
412C3×C4C2×#23511yescharacteristic
413C3×C4C2×#23911yescharacteristic
414C3×C4C2×#23911yescharacteristic
415Dic3—21no—
416Dic3—22no—
417Dic3—42no—
418Dic3—42no—
419Dic3—122no—
420Dic3—122no—
421Dic3—242no—
422C32#318311yescharacteristic, complemented, Sylow
423C23—31no—
424C23—182no—
425Q8—182no—
426Q8—182no—
427D4—182no—
428D4—182no—
429D4—364no—
430C2×C4—32no—
431C2×C4—31no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—122no—
437C2×C4—182no—
438C2×C4—364no—
439C2×C4D3×D1212yes—
440C2×C4C22×D3211yescharacteristic
441C8—61no—
442C8—61no—
443C8#379912yes—
444C8#379912yes—
445C2×C3—22no—
446C2×C3—21no—
447C2×C3—121no—
448C2×C3#547711yescharacteristic
449C2×C3#572511yescharacteristic
450C2×C3#574812yes—
451C2×C3#576812yes—
452D3—41no—
453D3—242no—
454D3—242no—
455D3—482no—
456C22—62no—
457C22—61no—
458C22—362no—
459C22—362no—
460C22—362no—
461C22C2×D3×D1211yescharacteristic
462C4—22no—
463C4—62no—
464C4—61no—
465C4—122no—
466C4—122no—
467C4—362no—
468C4C2×#379911yescharacteristic
469C4C2×#379911yescharacteristic
470C3—21no—
471C3#7853411yescharacteristic, complemented
472C3#8191111yescharacteristic, complemented
473C2—121no—
474C2—722no—
475C2#1059397011yescharacteristic
476C2#1059467612yes—
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10590835C2
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. #10593976C2semidirect
2. #10592395C2semidirect
3. C3×C4×ΓL(1,𝔽25)C2semidirect
4. C3×#4683C2semidirect
5. #10590853C2semidirect
6. #10590838C2semidirect
8. #10590810C2semidirect
9. #10590773C2semidirect
10. #10590768C2semidirect
11. #10590293C2semidirect
62. C4×ΓL(1,𝔽25)D3semidirect
63. #4683D3semidirect
422. C32#3183semidirect
471. C3#78534semidirect
472. C3#81911semidirect

Maximal subgroups

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

subgroupindex
#105939762
#105923952
C3×C4×ΓL(1,𝔽25)2
C3×#46832
#105908532
#105908382
#105908352
#105908102
#105907732
#105907682
#105902932
#819113
#785343