Finite Group Databasebeta

← #11876955

Subgroups — #11876955

Order 1152.

794 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594427C212yesmaximal, complemented
2#10592552C211yesmaximal, characteristic, complemented
3C3×#4865C211yesmaximal, characteristic
4C3×#4858C211yesmaximal, characteristic, complemented
5#10590864C211yesmaximal, characteristic, complemented
6#10590853C211yesmaximal, characteristic, complemented
7#10590781C211yesmaximal, characteristic, complemented
8Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
9#10590588C212yesmaximal, complemented
10#10590533C212yesmaximal, complemented
11#10590461C212yesmaximal, complemented
12#81911—31nomaximal
13#80852—31nomaximal
14C2×#3746C2211yescharacteristic
15#64096C2212yes—
16C2×C3×D24C2211yescharacteristic
17C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
18C3×#895C2212yes—
19C3×#890C2212yes—
20#63898—22no—
21#63898C2212yes—
22#63884—22no—
23#63878—22no—
24C4×D3×Dic3C2211yescharacteristic
25#63860C2212yes—
26#63858—22no—
27#63857C2212yes—
28C2×#3716C2212yes—
29C2×#3711C2211yescharacteristic
30C32×#106C2211yescharacteristic
31#63642C2211yescharacteristic
32#63637C2212yes—
33C3×#817C2211yescharacteristic
34C3×C8×Dic3C2211yescharacteristic
35C3×#809C2212yes—
36C3×#807C2212yes—
37#63567C2212yes—
38#63562C2212yes—
39#63555C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5691—32no—
42#5600—32no—
43C3×#499—31no—
44C3×#469—31no—
45#5155—31no—
46#5152—31no—
47#5137—31no—
48Dic3×M16—31no—
49#5068—32no—
50#5042—32no—
51#4889—32no—
52#4886—32no—
53#4869—31no—
54#4867—31no—
55#4865D311yescharacteristic
56#4858D311yescharacteristic, complemented
57#4853—31no—
58#4853—31no—
59#4853—61no—
60#4768—32no—
61#4757—32no—
62#4696—31no—
63C4×ΓL(1,𝔽25)—31no—
64C2×#634C2312yes—
65C2×C3×D12—22no—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3C2311yescharacteristic
68C2×D3×Dic3—22no—
69C2×D3×Dic3D412yes—
70C2×C32×C8C2311yescharacteristic
71C32×C4⋊C4C2312yes—
72#3750—22no—
73C4×C3⋊Dic3—22no—
74C4×C3⋊Dic3C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76#3746—22no—
77C3×(C2×D3)⋊C4—22no—
78C3×C4⋊Dic3—22no—
79C3×C4⋊Dic3C2312yes—
80C3×Dic3⋊C4—22no—
81C3×C4×Dic3C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84C3×D24—22no—
85C3×ΓL(1,𝔽25)—22no—
86Dic3⋊Dic3—22no—
87(C2×D3)⋊Dic3—22no—
88(C2×D3)⋊Dic3—22no—
89(C2×D3)⋊Dic3—22no—
90(C2×D3)⋊Dic3—22no—
91Dic32D412yes—
92#3716—24no—
93#3711—22no—
94#3183—91noSylow
95C2×C3×D8—31no—
96C2×C3×M16—31no—
97C3×#125—32no—
98C3×#121—32no—
99#936—32no—
100#935—62no—
101D4×Dic3—32no—
102D4×Dic3—62no—
103C2×#214—32no—
104#924—32no—
105C2×C4×Dic3—31no—
106C2×#208—31no—
107C2×Dic12—31no—
108C2×Dic12—31no—
109C2×Dic12—61no—
110C2×D24C2×D311yescharacteristic
111C2×#204—32no—
112C2×ΓL(1,𝔽25)—31no—
113C2×ΓL(1,𝔽25)C2×D311yescharacteristic
114#898—62no—
115#897—32no—
116#895C2×D312yes—
117#894—62no—
118#893—32no—
119#893—62no—
120#892—62no—
121#890C2×D312yes—
122#887—32no—
123#887—32no—
124#887—62no—
125#879—62no—
126#877—62no—
127#875—32no—
128C42×D3—31no—
129C3×#107—32no—
130C3×#106—21no—
131C3×#106—31no—
132C3×#106C2×D311yescharacteristic
133C3×#106C2×D311yescharacteristic
134C3×#102—32no—
135C3×C4×C8—31no—
136#832—32no—
137#817C2×D311yescharacteristic
138#816—32no—
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#810—32no—
148#810—32no—
149#810—62no—
150#809—32no—
151#809C2×D312yes—
152#807C2×D312yes—
153C4×C3⋊C8—31no—
154C22×C3×D3—22no—
155C22×C3×D3C2×D411yescharacteristic
156C2×C32×C4—22no—
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3C2×D412yes—
160#634—22no—
161#634—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3C2×D411yescharacteristic
164C2×C3×Dic3C2×D412yes—
165C3×D12—22no—
166C3×D12—22no—
167C3×D12—44no—
168C3×C4×D3—21no—
169C3×C4×D3—21no—
170D3×Dic3—42no—
171D3×Dic3—44no—
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—91no—
181#469—31no—
182#468—92no—
183#442—91no—
184#441—91no—
185#440—92no—
186C4×M16—91no—
187C2×C3×D4—32no—
188C2×C3×D4—62no—
189C22×C3×C4—31no—
190C22×Dic3—32no—
191C22×Dic3—62no—
192C2×D12—22no—
193C2×D12C22×D312yes—
194C2×C4×D3—32no—
195C2×C4×D3—62no—
196C2×C4×D3C22×D311yescharacteristic
197C2×Dic6—32no—
198C2×Dic6—32no—
199C2×Dic6—62no—
200C3×D8—62no—
201C3×M16—62no—
202C2×C3×C8—21no—
203C2×C3×C8—31no—
204C2×C3×C8—31no—
205C2×C3×C8C22×D311yescharacteristic
206C2×C3×C8C22×D311yescharacteristic
207C3×C4⋊C4—22no—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—62no—
210C3×C4⋊C4—62no—
211C3×C4⋊C4C22×D312yes—
212C3×C4⋊C4C22×D312yes—
213C3×C22⋊C4—62no—
214C3×C42—31no—
215#217—62no—
216#217—62no—
217#217—62no—
218#217—62no—
219#214—64no—
220(C2×D3)⋊C4—22no—
221(C2×D3)⋊C4—62no—
222(C2×D3)⋊C4—62no—
223(C2×D3)⋊C4—62no—
224(C2×D3)⋊C4—62no—
225C4⋊Dic3—22no—
226C4⋊Dic3—62no—
227C4⋊Dic3C22×D312yes—
228Dic3⋊C4—22no—
229Dic3⋊C4—62no—
230Dic3⋊C4—62no—
231Dic3⋊C4—62no—
232Dic3⋊C4—122no—
233C4×Dic3—31no—
234C4×Dic3—31no—
235C4×Dic3—32no—
236C4×Dic3—32no—
237C4×Dic3—61no—
238C4×Dic3—62no—
239C4×Dic3—62no—
240C4×Dic3—122no—
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—64no—
249Dic12—62no—
250Dic12—62no—
251D24—22no—
252#204—64no—
253ΓL(1,𝔽25)—22no—
254ΓL(1,𝔽25)—62no—
255C22×C32C22×D411yescharacteristic
256C2×C3×D3—21no—
257C2×C3×D3—22no—
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C32×C4—42no—
262C32×C4C2×#4111yescharacteristic
263C32×C4C2×#4111yescharacteristic
264C3⋊Dic3—22no—
265C3⋊Dic3—42no—
266C3×Dic3—21no—
267C3×Dic3—22no—
268C3×Dic3—42no—
269C2×Q16—91no—
270C2×SD16—92no—
271C2×D8—31no—
272C2×M16—31no—
273C2×M16—91no—
274#126—182no—
275#125—32no—
276#124—92no—
277#123—182no—
278C22⋊Q8—92no—
279#121—32no—
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—92no—
289#103—92no—
290#102—32no—
291#102—92no—
292#97—91no—
293#97—91no—
294C4×C8—31no—
295C4×C8—91no—
296C23×C3—31no—
297C23×C3—62no—
298C22×D3—22no—
299C22×D3D3×D411yescharacteristic
300C3×D4—62no—
301C3×D4—62no—
302C3×D4—124no—
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×C4C23×D311yescharacteristic
313C2×C3×C4C23×D311yescharacteristic
314C2×Dic3—22no—
315C2×Dic3—32no—
316C2×Dic3—32no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—122no—
321C2×Dic3—122no—
322C2×Dic3—124no—
323C2×Dic3D3×D411yescharacteristic
324C2×Dic3D3×D412yes—
325D12—22no—
326D12—22no—
327D12—44no—
328C4×D3—21no—
329C4×D3—21no—
330C4×D3—122no—
331C4×D3—124no—
332Dic6—64no—
333Dic6—62no—
334Dic6—62no—
335Dic6—62no—
336Dic6—62no—
337Dic6—122no—
338C3×C8—22no—
339C3×C8—32no—
340C3×C8—61no—
341C3×C8#23712yes—
342C3×C8#23912yes—
343C3⋊C8—21no—
344C3⋊C8—61no—
345C3⋊C8—61no—
346C3⋊C8—121no—
347C3⋊C8#23912yes—
348C2×C32#53211yescharacteristic
349C2×C32#57512yes—
350C3×D3—41no—
351C3×D3—82no—
352C2×Q8—92no—
353C2×D4—32no—
354C2×D4—62no—
355C22×C4—31no—
356C22×C4—92no—
357C22×C4—182no—
358Q16—182no—
359SD16—184no—
360D8—62no—
361M16—62no—
362M16—182no—
363C2×C8—31no—
364C2×C8—31no—
365C2×C8—91no—
366C2×C8C2×D3211yescharacteristic
367C4⋊C4—32no—
368C4⋊C4—62no—
369C4⋊C4—62no—
370C4⋊C4—182no—
371C4⋊C4—182no—
372C4⋊C4C2×D3212yes—
373C22⋊C4—62no—
374C22⋊C4—182no—
375C22⋊C4—182no—
376C22⋊C4—182no—
377C22⋊C4—182no—
378C42—31no—
379C42—92no—
380C42—91no—
381C42—182no—
382C22×C3—21no—
383C22×C3—61no—
384C22×C3—62no—
385C22×C3—122no—
386C22×C3—122no—
387C22×C3—122no—
388C22×C3C2×D3×D411yescharacteristic
389C22×C3C2×D3×D411yescharacteristic
390C2×D3—22no—
391C2×D3—21no—
392C2×D3—42no—
393C2×D3—42no—
394C2×D3—42no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—42no—
398C3×C4—42no—
399C3×C4—61no—
400C3×C4—62no—
401C3×C4—82no—
402C3×C4—122no—
403C3×C4C2×#23711yescharacteristic
404C3×C4C2×#23911yescharacteristic
405C3×C4C2×#23911yescharacteristic
406C3×C4D3×#4111yescharacteristic
407Dic3—22no—
408Dic3—21no—
409Dic3—42no—
410Dic3—62no—
411Dic3—62no—
412Dic3—122no—
413Dic3—124no—
414Dic3—122no—
415Dic3—122no—
416C32#318311yescharacteristic, complemented, Sylow
417C23—31no—
418C23—62no—
419Q8—182no—
420Q8—182no—
421D4—62no—
422D4—62no—
423D4—124no—
424C2×C4—22no—
425C2×C4—32no—
426C2×C4—31no—
427C2×C4—61no—
428C2×C4—61no—
429C2×C4—62no—
430C2×C4—92no—
431C2×C4—182no—
432C2×C4—362no—
433C2×C4—364no—
434C2×C4C22×D3211yescharacteristic
435C8—32no—
436C8—61no—
437C8—181no—
438C8#379612yes—
439C2×C3—21no—
440C2×C3—22no—
441C2×C3—121no—
442C2×C3—242no—
443C2×C3#559611yescharacteristic
444C2×C3#572511yescharacteristic
445C2×C3#576812yes—
446C2×C3#577312yes—
447D3—41no—
448D3—82no—
449C22—61no—
450C22—62no—
451C22—122no—
452C22—122no—
453C22—122no—
454C22D32×D411yescharacteristic
455C4—42no—
456C4—61no—
457C4—62no—
458C4—122no—
459C4—182no—
460C4—362no—
461C4C2×#379611yescharacteristic
462C4D3×#23911yescharacteristic
463C3—21no—
464C3#8085211yescharacteristic, complemented
465C3#8191111yescharacteristic, complemented
466C2—121no—
467C2—242no—
468C2#1059436911yescharacteristic
469C2#1059474512yes—
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC3×#4865C2
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. #10594427C2semidirect
2. #10592552C2semidirect
4. C3×#4858C2semidirect
5. #10590864C2semidirect
6. #10590853C2semidirect
7. #10590781C2semidirect
8. Dic3×ΓL(1,𝔽25)C2semidirect
9. #10590588C2semidirect
10. #10590533C2semidirect
11. #10590461C2semidirect
56. #4858D3semidirect
416. C32#3183semidirect
464. C3#80852semidirect
465. C3#81911semidirect

Maximal subgroups

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

subgroupindex
#105944272
#105925522
C3×#48652
C3×#48582
#105908642
#105908532
#105907812
Dic3×ΓL(1,𝔽25)2
#105905882
#105905332
#105904612
#819113
#808523