Finite Group Databasebeta

← #11876946

Subgroups — #11876946

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#10595173C212yesmaximal, complemented
2#10592851C211yesmaximal, characteristic, complemented
3C3×#5159C211yesmaximal, characteristic
4C3×#5155C211yesmaximal, characteristic, complemented
5#10591502C212yesmaximal, complemented
6#10591478C212yesmaximal, complemented
7#10591446C212yesmaximal, complemented
8#10590871C211yesmaximal, characteristic, complemented
9#10590854C211yesmaximal, characteristic, complemented
10#10590819C211yesmaximal, characteristic, complemented
11Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
12#81812—31nomaximal
13#80852—31nomaximal
14C2×C32×D8C2211yescharacteristic
15D4×C3⋊Dic3C2212yes—
16C3×#938C2212yes—
17C3×#936C2212yes—
18C2×C3×#214C2212yes—
19C2×C3×Dic12C2211yescharacteristic
20C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
21#67⋊Dic3—22no—
22#63969—22no—
23#63957—22no—
24#63956—22no—
25C4×D3×Dic3C2211yescharacteristic
26#63869C2212yes—
27#63856C2212yes—
28#63843C2212yes—
29C2×#3711C2211yescharacteristic
30#63659C2212yes—
31#63644C2211yescharacteristic
32#63642C2211yescharacteristic
33C3×#832C2212yes—
34C3×#817C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36#63575C2212yes—
37#63566C2212yes—
38#63565C2212yes—
39#63555C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5680—32no—
42#5600—32no—
43C3×#495—31no—
44C3×#469—31no—
45#5189—31no—
46#5184—31no—
47#5174—32no—
48#5164—32no—
49#5159D311yescharacteristic
50#5155D311yescharacteristic, complemented
51#5152—31no—
52#5152—31no—
53#5152—61no—
54#5137—31no—
55Dic3×M16—31no—
56#5056—32no—
57#5042—32no—
58#4858—31no—
59#4853—31no—
60#4768—32no—
61#4757—32no—
62C4×ΓL(1,𝔽25)—31no—
63#4683—31no—
64C2×C32×D4C2312yes—
65C22×C3⋊Dic3—22no—
66C2×C3×#67—22no—
67C2×C3×C4×D3C2311yescharacteristic
68C2×C3×Dic6C2312yes—
69C2×D3×Dic3D412yes—
70C32×D8—22no—
71C2×C32×C8C2311yescharacteristic
72#3757—22no—
73C4⋊(C3⋊Dic3)C2312yes—
74C4×C3⋊Dic3C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76C3×#217—22no—
77C3×#217—22no—
78C3×#217—22no—
79C3×#214—24no—
80C3×C4⋊Dic3C2312yes—
81C3×C4×Dic3C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84C3×Dic12—22no—
85C3×ΓL(1,𝔽25)—22no—
86#3724—22no—
87#3724—22no—
88Dic3⋊Dic3—22no—
89Dic3⋊Dic3—22no—
90(C2×D3)⋊Dic3—22no—
91Dic32—22no—
92Dic32D412yes—
93#3711—22no—
94#3183—91noSylow
95C2×C3×Q16—31no—
96C2×C3×SD16—32no—
97C2×C3×D8—21no—
98C2×C3×D8C2×D311yescharacteristic
99C2×C3×D8C2×D311yescharacteristic
100C2×C3×M16—31no—
101C3×#124—32no—
102C3×#121—32no—
103#946—32no—
104Q8×Dic3—32no—
105#938C2×D312yes—
106#936C2×D312yes—
107#935—62no—
108D4×Dic3—32no—
109D4×Dic3—32no—
110D4×Dic3—62no—
111D4×Dic3—62no—
112C2×#214C2×D312yes—
113#924—32no—
114C2×C4×Dic3—31no—
115C2×#208—31no—
116C2×Dic12C2×D311yescharacteristic
117C2×ΓL(1,𝔽25)—31no—
118C2×ΓL(1,𝔽25)C2×D311yescharacteristic
119#890—32no—
120#887—32no—
121#883—62no—
122#67⋊C4—62no—
123#879—62no—
124#879—62no—
125#877—62no—
126#877—62no—
127C42×D3—31no—
128#870—32no—
129C3×#106—31no—
130C3×#102—32no—
131C3×C4×C8—31no—
132#835—32no—
133#835—32no—
134#832—32no—
135#832—32no—
136#832—62no—
137#832C2×D312yes—
138#818—32no—
139#817—31no—
140#817—31no—
141#817—61no—
142#817C2×D311yescharacteristic
143#816—32no—
144#815—31no—
145#815—31no—
146#815—31no—
147#815—31no—
148#815—61no—
149C8×Dic3—31no—
150C8×Dic3C2×D311yescharacteristic
151#810—32no—
152#807—32no—
153C4×C3⋊C8—31no—
154C23×C32—22no—
155C22×C3×D3C2×D411yescharacteristic
156C32×D4—22no—
157C32×D4—22no—
158C2×C32×C4C2411yescharacteristic
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—44no—
161C2×C3⋊Dic3C2×D412yes—
162C3×#67—44no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C2×D411yescharacteristic
166C2×C3×Dic3C2×D412yes—
167C3×C4×D3—21no—
168C3×C4×D3—21no—
169C3×Dic6—22no—
170C3×Dic6—22no—
171D3×Dic3—42no—
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—91no—
181#469—31no—
182#468—92no—
183#442—91no—
184#441—91no—
185#440—92no—
186C4×M16—91no—
187C2×C3×Q8—32no—
188C2×C3×D4—22no—
189C2×C3×D4—62no—
190C2×C3×D4C22×D312yes—
191C2×C3×D4C22×D312yes—
192C22×C3×C4—31no—
193C2×#67—22no—
194C22×Dic3—32no—
195C22×Dic3—62no—
196C22×Dic3—62no—
197C22×Dic3—122no—
198C2×C4×D3—32no—
199C2×C4×D3C22×D311yescharacteristic
200C2×Dic6C22×D312yes—
201C3×Q16—62no—
202C3×SD16—64no—
203C3×D8—24no—
204C3×D8—22no—
205C3×D8—22no—
206C3×M16—62no—
207C2×C3×C8—21no—
208C2×C3×C8—31no—
209C2×C3×C8—31no—
210C2×C3×C8C22×D311yescharacteristic
211C2×C3×C8C22×D311yescharacteristic
212C3×C4⋊C4—32no—
213C3×C22⋊C4—62no—
214C3×C22⋊C4—62no—
215C3×C22⋊C4—62no—
216C3×C42—31no—
217#217—22no—
218#217—22no—
219#217—22no—
220#217—62no—
221#217—62no—
222#217—62no—
223#217—122no—
224#214—24no—
225(C2×D3)⋊C4—62no—
226C4⋊Dic3—32no—
227C4⋊Dic3—32no—
228C4⋊Dic3—62no—
229C4⋊Dic3—62no—
230C4⋊Dic3—62no—
231C4⋊Dic3C22×D312yes—
232Dic3⋊C4—62no—
233Dic3⋊C4—62no—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238C4×Dic3—31no—
239C4×Dic3—31no—
240C4×Dic3—32no—
241C4×Dic3—32no—
242C4×Dic3—61no—
243C4×Dic3—62no—
244C4×Dic3—62no—
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
252Dic12—22no—
253ΓL(1,𝔽25)—22no—
254ΓL(1,𝔽25)—62no—
255C22×C32—42no—
256C22×C32—42no—
257C22×C32—42no—
258C22×C32C22×D411yescharacteristic
259C2×C3×D3—21no—
260C2×C3×D3—22no—
261C32×C4C2×#4111yescharacteristic
262C32×C4C2×#4111yescharacteristic
263C3⋊Dic3—22no—
264C3⋊Dic3—42no—
265C3×Dic3—21no—
266C3×Dic3—22no—
267C3×Dic3—42no—
268C3×Dic3—42no—
269C2×Q16—31no—
270C2×SD16—32no—
271C2×D8D3211yescharacteristic
272C2×M16—31no—
273C2×M16—91no—
274#126—182no—
275#125—92no—
276#124—32no—
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—92no—
286#106—31no—
287#106—91no—
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—22no—
297C23×C3—22no—
298C23×C3—31no—
299C23×C3—42no—
300C22×D3D3×D411yescharacteristic
301C3×Q8—62no—
302C3×Q8—62no—
303C3×D4—24no—
304C3×D4—22no—
305C3×D4—22no—
306C3×D4—22no—
307C3×D4—22no—
308C3×D4—42no—
309C3×D4—124no—
310C2×C3×C4—21no—
311C2×C3×C4—31no—
312C2×C3×C4—32no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4C23×D311yescharacteristic
318C2×C3×C4C23×D311yescharacteristic
319#67—44no—
320C2×Dic3—22no—
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×Dic3—124no—
331C2×Dic3—244no—
332C2×Dic3D3×D411yescharacteristic
333C2×Dic3D3×D412yes—
334C4×D3—21no—
335C4×D3—21no—
336C4×D3—122no—
337Dic6—22no—
338Dic6—22no—
339C3×C8—22no—
340C3×C8—32no—
341C3×C8—61no—
342C3×C8#23712yes—
343C3×C8#23712yes—
344C3⋊C8—21no—
345C3⋊C8—61no—
346C3⋊C8—61no—
347C3⋊C8—121no—
348C3⋊C8#23712yes—
349C2×C32—82no—
350C2×C32#53211yescharacteristic
351C2×C32#57512yes—
352C3×D3—41no—
353C2×Q8—32no—
354C2×D4—62no—
355C2×D4C2×D3212yes—
356C22×C4—31no—
357C22×C4—92no—
358C22×C4—182no—
359Q16—62no—
360SD16—64no—
361D8—22no—
362M16—62no—
363M16—182no—
364C2×C8—31no—
365C2×C8—31no—
366C2×C8—91no—
367C2×C8C2×D3211yescharacteristic
368C4⋊C4—32no—
369C4⋊C4—92no—
370C4⋊C4—182no—
371C4⋊C4—182no—
372C4⋊C4—182no—
373C4⋊C4—182no—
374C22⋊C4—62no—
375C22⋊C4—62no—
376C22⋊C4—62no—
377C22⋊C4—182no—
378C22⋊C4—182no—
379C42—31no—
380C42—92no—
381C42—91no—
382C42—182no—
383C22×C3—21no—
384C22×C3—44no—
385C22×C3—42no—
386C22×C3—42no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—42no—
391C22×C3—61no—
392C22×C3—62no—
393C22×C3—82no—
394C22×C3—82no—
395C22×C3C2×D3×D411yescharacteristic
396C22×C3C2×D3×D411yescharacteristic
397C2×D3—22no—
398C2×D3—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—61no—
402C3×C4—62no—
403C3×C4—122no—
404C3×C4—122no—
405C3×C4C2×#23711yescharacteristic
406C3×C4C2×#23711yescharacteristic
407C3×C4C2×#23711yescharacteristic
408C3×C4D3×#4111yescharacteristic
409Dic3—22no—
410Dic3—21no—
411Dic3—42no—
412Dic3—42no—
413Dic3—62no—
414Dic3—62no—
415Dic3—122no—
416Dic3—122no—
417Dic3—122no—
418Dic3—242no—
419C32#318311yescharacteristic, complemented, Sylow
420C23—22no—
421C23—31no—
422Q8—62no—
423Q8—62no—
424D4—22no—
425D4—22no—
426D4—124no—
427C2×C4—32no—
428C2×C4—31no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—62no—
432C2×C4—62no—
433C2×C4—92no—
434C2×C4—182no—
435C2×C4—362no—
436C2×C4—364no—
437C2×C4C22×D3211yescharacteristic
438C8—32no—
439C8—61no—
440C8—181no—
441C8#380512yes—
442C2×C3—21no—
443C2×C3—22no—
444C2×C3—84no—
445C2×C3—82no—
446C2×C3—82no—
447C2×C3—121no—
448C2×C3#559611yescharacteristic
449C2×C3#571611yescharacteristic
450C2×C3#576812yes—
451C2×C3#577312yes—
452D3—41no—
453C22—42no—
454C22—42no—
455C22—42no—
456C22—61no—
457C22—62no—
458C22D32×D411yescharacteristic
459C4—61no—
460C4—62no—
461C4—122no—
462C4—122no—
463C4—182no—
464C4—362no—
465C4D3×#23711yescharacteristic
466C4C2×#380511yescharacteristic
467C3—21no—
468C3#8085211yescharacteristic, complemented
469C3#8181211yescharacteristic, complemented
470C2—82no—
471C2—121no—
472C2#1059472912yes—
473C2#1059513311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radicalC3×#5159C2
hypercenterC2×D8D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595173C2semidirect
2. #10592851C2semidirect
4. C3×#5155C2semidirect
5. #10591502C2semidirect
6. #10591478C2semidirect
7. #10591446C2semidirect
8. #10590871C2semidirect
9. #10590854C2semidirect
10. #10590819C2semidirect
11. Dic3×ΓL(1,𝔽25)C2semidirect
50. #5155D3semidirect
419. C32#3183semidirect
468. C3#80852semidirect
469. C3#81812semidirect

Maximal subgroups

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

subgroupindex
#105951732
#105928512
C3×#51592
C3×#51552
#105915022
#105914782
#105914462
#105908712
#105908542
#105908192
Dic3×ΓL(1,𝔽25)2
#818123
#808523