Finite Group Databasebeta

← #11876952

Subgroups — #11876952

Order 1152.

806 conjugacy classes of subgroups.

The subgroup lattice has 475 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594453C212yesmaximal, complemented
2#10592568C211yesmaximal, characteristic, complemented
3C3×#4867C211yesmaximal, characteristic, complemented
4C3×#4858C211yesmaximal, characteristic, complemented
5#10590865C211yesmaximal, characteristic, complemented
6#10590835C211yesmaximal, characteristic
7#10590819C211yesmaximal, characteristic, complemented
8Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
9#10590585C212yesmaximal, complemented
10#10590537C212yesmaximal, complemented
11#10590484C212yesmaximal, complemented
12#81911—31nomaximal
13#80892—31nomaximal
14C2×#3745C2211yescharacteristic
15#64102C2212yes—
16C2×C3×Dic12C2211yescharacteristic
17C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
18C3×#897C2212yes—
19C3×#890C2212yes—
20#63909C2212yes—
21#63890—22no—
22#63881—22no—
23C4×D3×Dic3C2211yescharacteristic
24#63864C2212yes—
25#63849—22no—
26#63848—22no—
27#63843C2212yes—
28C2×#3717C2212yes—
29C2×#3711C2211yescharacteristic
30C32×#106C2211yescharacteristic
31#63642C2211yescharacteristic
32#63636C2212yes—
33C3×#817C2211yescharacteristic
34C3×C8×Dic3C2211yescharacteristic
35C3×#810C2212yes—
36C3×#807C2212yes—
37#63565C2212yes—
38#63564C2212yes—
39#63555C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5691—32no—
42#5624—32no—
43C3×#499—31no—
44C3×#470—31no—
45#5191—31no—
46#5184—31no—
47#5135—31no—
48Dic3×M16—31no—
49#5068—32no—
50#5049—32no—
51#4889—32no—
52#4886—32no—
53#4869—31no—
54#4869—31no—
55#4869—61no—
56#4867D311yescharacteristic, complemented
57#4865—31no—
58#4858D311yescharacteristic, complemented
59#4853—31no—
60#4817—32no—
61#4800—32no—
62#4696—31no—
63C4×ΓL(1,𝔽25)—31no—
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×C4×C3⋊D3—22no—
66C2×C3×C4×D3C2311yescharacteristic
67C2×C3×Dic6C2312yes—
68C2×#626—22no—
69C2×D3×Dic3D412yes—
70C2×C32×C8C2311yescharacteristic
71C32×C4⋊C4C2312yes—
72#3752—22no—
73C4×C3⋊Dic3C2311yescharacteristic
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75#3745—22no—
76C3×(C2×D3)⋊C4—22no—
77C3×C4⋊Dic3—22no—
78C3×C4⋊Dic3—22no—
79C3×C4⋊Dic3C2312yes—
80C3×Dic3⋊C4—22no—
81C3×C4×Dic3C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84C3×Dic12—22no—
85C3×ΓL(1,𝔽25)—22no—
86Dic3⋊Dic3—22no—
87#3722—22no—
88#3722—22no—
89#3722—22no—
90Dic32—22no—
91Dic32D412yes—
92#3717—24no—
93#3711—22no—
94#3183—91noSylow
95C2×C3×Q16—31no—
96C2×C3×M16—31no—
97C3×#125—32no—
98C3×C22⋊Q8—32no—
99#947—32no—
100Q8×Dic3—32no—
101C2×#215—32no—
102#930—32no—
103C2×C4×Dic3—31no—
104C2×#208—31no—
105C2×Dic12C2×D311yescharacteristic
106C2×D24—31no—
107C2×D24—31no—
108C2×D24—61no—
109C2×#204—32no—
110C2×ΓL(1,𝔽25)—31no—
111C2×ΓL(1,𝔽25)C2×D311yescharacteristic
112#898—62no—
113#898—62no—
114#897C2×D312yes—
115#895—32no—
116#894—62no—
117#893—32no—
118#893—32no—
119#893—62no—
120#893—62no—
121#892—62no—
122#892—62no—
123#890C2×D312yes—
124#887—32no—
125#886—62no—
126#67⋊C4—62no—
127#875—32no—
128C42×D3—31no—
129C3×#107—32no—
130C3×#106—21no—
131C3×#106—31no—
132C3×#106C2×D311yescharacteristic
133C3×#106C2×D311yescharacteristic
134C3×#103—32no—
135C3×C4×C8—31no—
136#835—32no—
137#821—32no—
138#817C2×D311yescharacteristic
139#815—31no—
140#815—31no—
141#815—31no—
142#815—31no—
143#815—61no—
144C8×Dic3—31no—
145C8×Dic3C2×D311yescharacteristic
146#810—32no—
147#810C2×D312yes—
148#809—32no—
149#809—32no—
150#809—32no—
151#809—62no—
152#807C2×D312yes—
153C4×C3⋊C8—31no—
154C22×C3⋊D3—22no—
155C22×C3×D3C2×D411yescharacteristic
156C2×C32×C4—22no—
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3C2×D412yes—
159C4⋊(C3⋊D3)—22no—
160C4⋊(C3⋊D3)—22no—
161C4×C3⋊D3—44no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3C2×D411yescharacteristic
165C2×C3×Dic3C2×D412yes—
166C3×C4×D3—21no—
167C3×C4×D3—21no—
168C3×Dic6—22no—
169C3×Dic6—22no—
170#626—44no—
171D3×Dic3—42no—
172C32×C8#4112yes—
173C3⋊(C3⋊C8)—21no—
174C3×C3⋊C8—21no—
175C3×C3⋊C8#4112yes—
176#529—92no—
177#499—31no—
178#495—91no—
179#488—92no—
180#470—31no—
181#469—91no—
182#468—92no—
183#442—91no—
184#441—91no—
185#440—92no—
186C4×M16—91no—
187C2×C3×Q8—32no—
188C22×C3×C4—31no—
189C2×#67—62no—
190C22×Dic3—32no—
191C2×D12—32no—
192C2×D12—32no—
193C2×D12—62no—
194C2×D12—62no—
195C2×C4×D3—32no—
196C2×C4×D3—62no—
197C2×C4×D3—62no—
198C2×C4×D3—122no—
199C2×C4×D3C22×D311yescharacteristic
200C2×Dic6C22×D312yes—
201C3×Q16—62no—
202C3×M16—62no—
203C2×C3×C8—21no—
204C2×C3×C8—31no—
205C2×C3×C8—31no—
206C2×C3×C8C22×D311yescharacteristic
207C2×C3×C8C22×D311yescharacteristic
208C3×C4⋊C4—22no—
209C3×C4⋊C4—32no—
210C3×C4⋊C4—62no—
211C3×C4⋊C4—62no—
212C3×C4⋊C4—62no—
213C3×C4⋊C4C22×D312yes—
214C3×C4⋊C4C22×D312yes—
215C3×C22⋊C4—62no—
216C3×C42—31no—
217#215—64no—
218(C2×D3)⋊C4—22no—
219(C2×D3)⋊C4—62no—
220(C2×D3)⋊C4—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—122no—
228C4⋊Dic3—22no—
229C4⋊Dic3—22no—
230C4⋊Dic3—62no—
231C4⋊Dic3C22×D312yes—
232Dic3⋊C4—22no—
233Dic3⋊C4—62no—
234C4×Dic3—31no—
235C4×Dic3—31no—
236C4×Dic3—32no—
237C4×Dic3—32no—
238C4×Dic3—61no—
239C4×Dic3—62no—
240C4×Dic3—62no—
241C4×Dic3C22×D311yescharacteristic
242#208—62no—
243C2×C3⋊C8—31no—
244C2×C3⋊C8—31no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8C22×D311yescharacteristic
247C2×C3⋊C8C22×D311yescharacteristic
248Dic12—22no—
249D24—64no—
250D24—62no—
251D24—62no—
252#204—64no—
253ΓL(1,𝔽25)—22no—
254ΓL(1,𝔽25)—62no—
255C22×C32C22×D411yescharacteristic
256C2×C3⋊D3—42no—
257C2×C3⋊D3—42no—
258C2×C3⋊D3—42no—
259C2×C3×D3—21no—
260C2×C3×D3—22no—
261C32×C4—42no—
262C32×C4C2×#4111yescharacteristic
263C32×C4C2×#4111yescharacteristic
264C3⋊Dic3—22no—
265C3×Dic3—21no—
266C3×Dic3—22no—
267C3×Dic3—42no—
268C3×Dic3—42no—
269C2×Q16—31no—
270C2×SD16—92no—
271C2×D8—91no—
272C2×M16—31no—
273C2×M16—91no—
274#126—182no—
275#125—32no—
276#124—92no—
277#123—182no—
278C22⋊Q8—32no—
279#121—92no—
280C4×Q8—92no—
281C4×D4—92no—
282C4×D4—182no—
283#117—182no—
284C2×C42—91no—
285#107—32no—
286#106—31no—
287#106D3211yescharacteristic
288#103—32no—
289#103—92no—
290#102—92no—
291#102—92no—
292#97—91no—
293#97—91no—
294C4×C8—31no—
295C4×C8—91no—
296C23×C3—31no—
297C22×D3—62no—
298C22×D3—62no—
299C22×D3—122no—
300C22×D3D3×D411yescharacteristic
301C3×Q8—62no—
302C3×Q8—62no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—31no—
307C2×C3×C4—32no—
308C2×C3×C4—42no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4C23×D311yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315#67—124no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—32no—
319C2×Dic3—32no—
320C2×Dic3—62no—
321C2×Dic3—122no—
322C2×Dic3D3×D411yescharacteristic
323C2×Dic3D3×D412yes—
324D12—64no—
325D12—62no—
326D12—62no—
327D12—62no—
328D12—62no—
329D12—122no—
330D12—124no—
331C4×D3—21no—
332C4×D3—21no—
333C4×D3—124no—
334C4×D3—124no—
335C4×D3—122no—
336C4×D3—244no—
337Dic6—22no—
338Dic6—22no—
339C3×C8—22no—
340C3×C8—32no—
341C3×C8—61no—
342C3×C8#23712yes—
343C3×C8#23912yes—
344C3⋊C8—21no—
345C3⋊C8—61no—
346C3⋊C8—61no—
347C3⋊C8—121no—
348C3⋊C8#23912yes—
349C2×C32#53211yescharacteristic
350C2×C32#57512yes—
351C3⋊D3—82no—
352C3×D3—41no—
353C2×Q8—32no—
354C2×D4—92no—
355C2×D4—182no—
356C22×C4—31no—
357C22×C4—92no—
358C22×C4—182no—
359Q16—62no—
360SD16—184no—
361D8—182no—
362M16—62no—
363M16—182no—
364C2×C8—31no—
365C2×C8—31no—
366C2×C8—91no—
367C2×C8C2×D3211yescharacteristic
368C4⋊C4—32no—
369C4⋊C4—62no—
370C4⋊C4—62no—
371C4⋊C4—62no—
372C4⋊C4—182no—
373C4⋊C4C2×D3212yes—
374C22⋊C4—62no—
375C22⋊C4—182no—
376C22⋊C4—182no—
377C22⋊C4—182no—
378C22⋊C4—182no—
379C42—31no—
380C42—92no—
381C42—91no—
382C42—182no—
383C22×C3—21no—
384C22×C3—61no—
385C22×C3—62no—
386C22×C3C2×D3×D411yescharacteristic
387C22×C3C2×D3×D411yescharacteristic
388C2×D3—22no—
389C2×D3—21no—
390C2×D3—124no—
391C2×D3—122no—
392C2×D3—122no—
393C2×D3—122no—
394C2×D3—122no—
395C2×D3—122no—
396C2×D3—122no—
397C2×D3—242no—
398C2×D3—242no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—42no—
402C3×C4—42no—
403C3×C4—61no—
404C3×C4—62no—
405C3×C4—82no—
406C3×C4—122no—
407C3×C4—122no—
408C3×C4C2×#23711yescharacteristic
409C3×C4C2×#23911yescharacteristic
410C3×C4C2×#23911yescharacteristic
411C3×C4D3×#4111yescharacteristic
412Dic3—22no—
413Dic3—21no—
414Dic3—42no—
415Dic3—42no—
416Dic3—62no—
417Dic3—62no—
418Dic3—122no—
419C32#318311yescharacteristic, complemented, Sylow
420C23—31no—
421C23—182no—
422Q8—62no—
423Q8—62no—
424D4—182no—
425D4—182no—
426D4—364no—
427C2×C4—22no—
428C2×C4—32no—
429C2×C4—31no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—62no—
433C2×C4—62no—
434C2×C4—92no—
435C2×C4—364no—
436C2×C4—362no—
437C2×C4C22×D3211yescharacteristic
438C8—32no—
439C8—61no—
440C8—181no—
441C8#379612yes—
442C2×C3—21no—
443C2×C3—22no—
444C2×C3—121no—
445C2×C3#559611yescharacteristic
446C2×C3#572511yescharacteristic
447C2×C3#576812yes—
448C2×C3#577712yes—
449D3—41no—
450D3—244no—
451D3—242no—
452D3—242no—
453C22—61no—
454C22—62no—
455C22—362no—
456C22—362no—
457C22—362no—
458C22D32×D411yescharacteristic
459C4—42no—
460C4—61no—
461C4—62no—
462C4—122no—
463C4—122no—
464C4—182no—
465C4C2×#379611yescharacteristic
466C4D3×#23911yescharacteristic
467C3—21no—
468C3#8089211yescharacteristic, complemented
469C3#8191111yescharacteristic, complemented
470C2—121no—
471C2—722no—
472C2#1059436911yescharacteristic
473C2#1059474612yes—
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10590835C2
hypercenter#106D32
hypocenterC32#3183
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. #10594453C2semidirect
2. #10592568C2semidirect
3. C3×#4867C2semidirect
4. C3×#4858C2semidirect
5. #10590865C2semidirect
7. #10590819C2semidirect
8. Dic3×ΓL(1,𝔽25)C2semidirect
9. #10590585C2semidirect
10. #10590537C2semidirect
11. #10590484C2semidirect
56. #4867D3semidirect
58. #4858D3semidirect
419. C32#3183semidirect
468. C3#80892semidirect
469. C3#81911semidirect

Maximal subgroups

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

subgroupindex
#105944532
#105925682
C3×#48672
C3×#48582
#105908652
#105908352
#105908192
Dic3×ΓL(1,𝔽25)2
#105905852
#105905372
#105904842
#819113
#808923