Finite Group Databasebeta

← #11876949

Subgroups — #11876949

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#10595377C212yesmaximal, complemented
2#10592883C211yesmaximal, characteristic, complemented
3C3×#5191C211yesmaximal, characteristic, complemented
4C3×#5189C211yesmaximal, characteristic, complemented
5#10591614C212yesmaximal, complemented
6#10591587C212yesmaximal, complemented
7#10591572C212yesmaximal, complemented
8#10590871C211yesmaximal, characteristic, complemented
9#10590836C211yesmaximal, characteristic
10#10590781C211yesmaximal, characteristic, complemented
11Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
12#81812—31nomaximal
13#80892—31nomaximal
14C2×C32×Q16C2211yescharacteristic
15Q8×C3⋊Dic3C2212yes—
16C3×#947C2212yes—
17C3×#946C2212yes—
18C2×C3×#215C2212yes—
19C2×C3×D24C2211yescharacteristic
20C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
21#63908C2212yes—
22#63902—22no—
23#63898C2212yes—
24#63891—22no—
25#63878—22no—
26C4×D3×Dic3C2211yescharacteristic
27#63869C2212yes—
28#63861—22no—
29C2×#3711C2211yescharacteristic
30#63662C2212yes—
31#63644C2211yescharacteristic
32#63642C2211yescharacteristic
33C3×#835C2212yes—
34C3×#817C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36#63575C2212yes—
37#63563C2212yes—
38#63562C2212yes—
39#63555C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5680—32no—
42#5624—32no—
43C3×#495—31no—
44C3×#470—31no—
45#5191D311yescharacteristic, complemented
46#5189D311yescharacteristic, complemented
47#5184—31no—
48#5184—31no—
49#5184—61no—
50#5174—32no—
51#5164—32no—
52#5159—31no—
53#5152—31no—
54#5135—31no—
55Dic3×M16—31no—
56#5056—32no—
57#5049—32no—
58#4869—31no—
59#4858—31no—
60#4817—32no—
61#4800—32no—
62C4×ΓL(1,𝔽25)—31no—
63#4683—31no—
64C2×C32×Q8C2312yes—
65C2×C3×D12C2312yes—
66C2×C3×C4×D3C2311yescharacteristic
67C2×#625—22no—
68C2×D3×Dic3—22no—
69C2×D3×Dic3D412yes—
70C32×Q16—22no—
71C2×C32×C8C2311yescharacteristic
72C4⋊(C3⋊Dic3)—22no—
73C4⋊(C3⋊Dic3)C2312yes—
74C4×C3⋊Dic3—22no—
75C4×C3⋊Dic3C2311yescharacteristic
76C2×C3⋊(C3⋊C8)C2311yescharacteristic
77C3×#215—24no—
78C3×(C2×D3)⋊C4—22no—
79C3×(C2×D3)⋊C4—22no—
80C3×(C2×D3)⋊C4—22no—
81C3×C4⋊Dic3C2312yes—
82C3×Dic3⋊C4—22no—
83C3×C4×Dic3C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86C3×D24—22no—
87C3×ΓL(1,𝔽25)—22no—
88#3724—22no—
89Dic3⋊Dic3—22no—
90(C2×D3)⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92Dic32D412yes—
93#3711—22no—
94#3183—91noSylow
95C2×C3×Q16—21no—
96C2×C3×Q16C2×D311yescharacteristic
97C2×C3×Q16C2×D311yescharacteristic
98C2×C3×SD16—32no—
99C2×C3×D8—31no—
100C2×C3×M16—31no—
101C3×#124—32no—
102C3×C22⋊Q8—32no—
103#947C2×D312yes—
104#946C2×D312yes—
105Q8×Dic3—32no—
106Q8×Dic3—32no—
107Q8×Dic3—62no—
108C2×#215C2×D312yes—
109#938—32no—
110D4×Dic3—32no—
111#930—32no—
112C2×C4×Dic3—31no—
113C2×#208—31no—
114C2×D24C2×D311yescharacteristic
115C2×ΓL(1,𝔽25)—31no—
116C2×ΓL(1,𝔽25)C2×D311yescharacteristic
117#898—62no—
118#893—32no—
119#892—62no—
120#890—32no—
121#886—62no—
122#883—62no—
123#67⋊C4—62no—
124#67⋊C4—62no—
125#879—62no—
126#877—62no—
127C42×D3—31no—
128#870—32no—
129C3×#106—31no—
130C3×#103—32no—
131C3×C4×C8—31no—
132#835—32no—
133#835—32no—
134#835—62no—
135#835C2×D312yes—
136#832—32no—
137#832—32no—
138#821—32no—
139#818—32no—
140#817—31no—
141#817—31no—
142#817—61no—
143#817C2×D311yescharacteristic
144#815—31no—
145#815—31no—
146#815—31no—
147#815—31no—
148#815—61no—
149C8×Dic3—31no—
150C8×Dic3C2×D311yescharacteristic
151#809—32no—
152#807—32no—
153C4×C3⋊C8—31no—
154C22×C3×D3—22no—
155C22×C3×D3C2×D411yescharacteristic
156C32×Q8—22no—
157C32×Q8—22no—
158C2×C32×C4—22no—
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3C2×D412yes—
162C2×C3×Dic3—22no—
163C2×C3×Dic3C2×D411yescharacteristic
164C2×C3×Dic3C2×D412yes—
165C3×D12—22no—
166C3×D12—22no—
167C3×C4×D3—21no—
168C3×C4×D3—21no—
169#625—44no—
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—91no—
178#495—31no—
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—22no—
188C2×C3×Q8C22×D312yes—
189C2×C3×Q8C22×D312yes—
190C2×C3×D4—32no—
191C22×C3×C4—31no—
192C2×#67—62no—
193C2×#67—62no—
194C22×Dic3—32no—
195C22×Dic3—62no—
196C2×D12C22×D312yes—
197C2×C4×D3—32no—
198C2×C4×D3—62no—
199C2×C4×D3C22×D311yescharacteristic
200C3×Q16—24no—
201C3×Q16—22no—
202C3×Q16—22no—
203C3×SD16—64no—
204C3×D8—62no—
205C3×M16—62no—
206C2×C3×C8—21no—
207C2×C3×C8—31no—
208C2×C3×C8—31no—
209C2×C3×C8C22×D311yescharacteristic
210C2×C3×C8C22×D311yescharacteristic
211C3×C4⋊C4—32no—
212C3×C4⋊C4—62no—
213C3×C22⋊C4—62no—
214C3×C22⋊C4—62no—
215C3×C22⋊C4—62no—
216C3×C42—31no—
217#217—62no—
218#217—62no—
219#215—24no—
220(C2×D3)⋊C4—22no—
221(C2×D3)⋊C4—22no—
222(C2×D3)⋊C4—22no—
223(C2×D3)⋊C4—62no—
224(C2×D3)⋊C4—62no—
225C4⋊Dic3—32no—
226C4⋊Dic3—32no—
227C4⋊Dic3—62no—
228C4⋊Dic3—62no—
229C4⋊Dic3—62no—
230C4⋊Dic3—62no—
231C4⋊Dic3—122no—
232C4⋊Dic3C22×D312yes—
233Dic3⋊C4—22no—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237C4×Dic3—31no—
238C4×Dic3—31no—
239C4×Dic3—32no—
240C4×Dic3—32no—
241C4×Dic3—61no—
242C4×Dic3—62no—
243C4×Dic3—62no—
244C4×Dic3—122no—
245C4×Dic3C22×D311yescharacteristic
246#208—62no—
247C2×C3⋊C8—31no—
248C2×C3⋊C8—31no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8C22×D311yescharacteristic
251C2×C3⋊C8C22×D311yescharacteristic
252D24—22no—
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×Q16D3211yescharacteristic
270C2×SD16—32no—
271C2×D8—31no—
272C2×M16—31no—
273C2×M16—91no—
274#126—182no—
275#125—92no—
276#124—32no—
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—92no—
286#106—31no—
287#106—91no—
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—
297C23×C3—62no—
298C22×D3—22no—
299C22×D3D3×D411yescharacteristic
300C3×Q8—24no—
301C3×Q8—22no—
302C3×Q8—22no—
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—42no—
306C3×D4—62no—
307C3×D4—62no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—31no—
312C2×C3×C4—32no—
313C2×C3×C4—42no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—62no—
317C2×C3×C4C23×D311yescharacteristic
318C2×C3×C4C23×D311yescharacteristic
319#67—124no—
320#67—124no—
321C2×Dic3—22no—
322C2×Dic3—32no—
323C2×Dic3—32no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—122no—
328C2×Dic3—122no—
329C2×Dic3—124no—
330C2×Dic3D3×D411yescharacteristic
331C2×Dic3D3×D412yes—
332D12—22no—
333D12—22no—
334C4×D3—21no—
335C4×D3—21no—
336C4×D3—122no—
337C4×D3—124no—
338C3×C8—22no—
339C3×C8—32no—
340C3×C8—61no—
341C3×C8#23712yes—
342C3×C8#23712yes—
343C3⋊C8—21no—
344C3⋊C8—61no—
345C3⋊C8—61no—
346C3⋊C8—121no—
347C3⋊C8#23712yes—
348C2×C32#53211yescharacteristic
349C2×C32#57512yes—
350C3×D3—41no—
351C3×D3—82no—
352C2×Q8C2×D3212yes—
353C2×D4—32no—
354C2×D4—182no—
355C22×C4—31no—
356C22×C4—92no—
357C22×C4—182no—
358Q16—22no—
359SD16—64no—
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—92no—
370C4⋊C4—182no—
371C4⋊C4—182no—
372C4⋊C4—182no—
373C22⋊C4—62no—
374C22⋊C4—62no—
375C22⋊C4—62no—
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—44no—
398C3×C4—42no—
399C3×C4—42no—
400C3×C4—61no—
401C3×C4—62no—
402C3×C4—122no—
403C3×C4C2×#23711yescharacteristic
404C3×C4C2×#23711yescharacteristic
405C3×C4C2×#23711yescharacteristic
406C3×C4D3×#4111yescharacteristic
407Dic3—22no—
408Dic3—21no—
409Dic3—42no—
410Dic3—62no—
411Dic3—62no—
412Dic3—122no—
413Dic3—122no—
414Dic3—122no—
415Dic3—242no—
416C32#318311yescharacteristic, complemented, Sylow
417C23—31no—
418C23—62no—
419Q8—22no—
420Q8—22no—
421D4—62no—
422D4—62no—
423D4—364no—
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#380512yes—
439C2×C3—21no—
440C2×C3—22no—
441C2×C3—121no—
442C2×C3—242no—
443C2×C3#559611yescharacteristic
444C2×C3#571611yescharacteristic
445C2×C3#576812yes—
446C2×C3#577712yes—
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—
461C4D3×#23711yescharacteristic
462C4C2×#380511yescharacteristic
463C3—21no—
464C3#8089211yescharacteristic, complemented
465C3#8181211yescharacteristic, complemented
466C2—121no—
467C2—242no—
468C2#1059476312yes—
469C2#1059513311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radical#10590836C2
hypercenterC2×Q16D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. #10595377C2semidirect
2. #10592883C2semidirect
3. C3×#5191C2semidirect
4. C3×#5189C2semidirect
5. #10591614C2semidirect
6. #10591587C2semidirect
7. #10591572C2semidirect
8. #10590871C2semidirect
10. #10590781C2semidirect
11. Dic3×ΓL(1,𝔽25)C2semidirect
45. #5191D3semidirect
46. #5189D3semidirect
416. C32#3183semidirect
464. C3#80892semidirect
465. C3#81812semidirect

Maximal subgroups

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

subgroupindex
#105953772
#105928832
C3×#51912
C3×#51892
#105916142
#105915872
#105915722
#105908712
#105908362
#105907812
Dic3×ΓL(1,𝔽25)2
#818123
#808923