Finite Group Databasebeta

← #11860953

Subgroups — #11860953

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63810C211yesmaximal, characteristic
2#10593889C212yesmaximal, complemented
3#10592407C211yesmaximal, characteristic, complemented
4C3×#4716C211yesmaximal, characteristic, complemented
5C3×#4711C211yesmaximal, characteristic, complemented
6#10590957C212yesmaximal, complemented
7#10590819C211yesmaximal, characteristic, complemented
8#10590781C211yesmaximal, characteristic, complemented
9#10590742C212yesmaximal, complemented
10#10590685C211yesmaximal, characteristic, complemented
11C4×#3715C212yesmaximal, complemented
12#79868—31nomaximal
13#79832—31nomaximal
14C2×#3796C2212yes—
15C2×#3743C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17#64081C2211yescharacteristic
18C2×C3×Dic12C2211yescharacteristic
19C2×C3×D24C2211yescharacteristic
20C3×C4×D12C2212yes—
21C3×C4×Dic6C2212yes—
22#63904—22no—
23#63900C2212yes—
24#63898C2212yes—
25#63880—22no—
26#63877—22no—
27D3×Dic3⋊C4—22no—
28#63843C2212yes—
29C2×#3715C2212yes—
30#63810C418yescomplemented
31C32×#97C2211yescharacteristic
32#63642C2211yescharacteristic
33C8×C3⋊Dic3C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#821C2212yes—
36C3×#817C2211yescharacteristic
37C3×#817C2211yescharacteristic
38C3×#816C2212yes—
39#63574C2212yes—
40#63565C2212yes—
41#63562C2212yes—
42C2×#919—31no—
43C2×#912—31no—
44#5574—32no—
45#5546—32no—
46C3×#442—31no—
47C3×#441—31no—
48#5184—31no—
49#5152—31no—
50C4×#215—32no—
51C4×#214—32no—
52#4869—31no—
53D3×#106—31no—
54D3×#106—31no—
55#4853—31no—
56#4803—32no—
57#4788—32no—
58#4771—32no—
59#4758—32no—
60#4716D311yescharacteristic, complemented
61#4711D311yescharacteristic, complemented
62#4708—31no—
63#4708—31no—
64#4708—61no—
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×Dic6C2312yes—
69C2×#626—22no—
70C2×#624—22no—
71C2×D3×Dic3—22no—
72C2×D3×Dic3—22no—
73#3796—24no—
74#3796C2×C418yescomplemented
75C2×C32×C8C2311yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C32×C42C2311yescharacteristic
78#3752D412yes—
79#3750D412yes—
80C4×C3⋊Dic3C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83#3743—22no—
84C8×C3⋊D3C2×C414yescomplemented
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3C2312yes—
87C3×C4⋊Dic3C2312yes—
88C3×Dic3⋊C4—22no—
89C3×C4×Dic3—22no—
90C3×Dic12C2×C414yescomplemented
91C3×D24C2×C414yescomplemented
92#3724—22no—
93Dic3⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95Dic32—22no—
96#3715C2×C418yescomplemented
97#2952—91noSylow
98C2×#239—32no—
99C2×#237—32no—
100C2×C3×Q16—31no—
101C2×C3×D8—31no—
102C3×C4×Q8—32no—
103C3×C4×D4—32no—
104Q8×Dic3—32no—
105C2×#215—32no—
106D4×Dic3—32no—
107C2×#214—32no—
108C4×#67—62no—
109C2×Dic3⋊C4—62no—
110#919—38no—
111#912—38no—
112C2×Dic12C2×D311yescharacteristic
113C2×D24C2×D311yescharacteristic
114C2×ΓL(1,𝔽25)—31no—
115C2×ΓL(1,𝔽25)—31no—
116C2×ΓL(1,𝔽25)—61no—
117C2×D3×C8—31no—
118C2×D3×C8—31no—
119C2×D3×C8—61no—
120#893—32no—
121#893—62no—
122D3×C4⋊C4—32no—
123D3×C4⋊C4—32no—
124D3×C4⋊C4—62no—
125#887—32no—
126#67⋊C4—62no—
127#877—62no—
128C4×D12—62no—
129C4×D12C2×D312yes—
130#872—31no—
131#872—31no—
132#872—61no—
133#872—62no—
134C4×Dic6C2×D312yes—
135C3×#106—31no—
136C3×#106—31no—
137C3×#103—32no—
138C3×#102—32no—
139C3×#97—21no—
140C3×#97C2×D311yescharacteristic
141C3×#97C2×D311yescharacteristic
142#835—32no—
143#832—32no—
144#821C2×D312yes—
145#817C2×D311yescharacteristic
146#817C2×D311yescharacteristic
147#816C2×D312yes—
148#815—31no—
149#815—31no—
150#815—61no—
151C8×Dic3—31no—
152C8×Dic3—31no—
153C8×Dic3—61no—
154#810—32no—
155#809—32no—
156#808—32no—
157#808—32no—
158C4×C3⋊C8—31no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—61no—
161C22×C3⋊D3C2×D411yescharacteristic
162C22×C3×D3—22no—
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2411yescharacteristic
165C2×C3⋊Dic3C2×D412yes—
166C2×C3⋊Dic3C2×D411yescharacteristic
167C4×C3⋊D3C22×C412yes—
168C4×C3⋊D3#4112yes—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C3×D12—22no—
173C3×D12C22×C414yes—
174C3×C4×D3—82no—
175C3×Dic6—22no—
176C3×Dic6C22×C414yes—
177#626—28no—
178#624—82no—
179D3×Dic3—28no—
180D3×Dic3—82no—
181C32×C8—21no—
182C32×C8C22×C412yes—
183C3⋊(C3⋊C8)—21no—
184C3⋊(C3⋊C8)C22×C412yes—
185C2×#135—91no—
186#520—92no—
187#442—31no—
188#442—91no—
189#441—31no—
190#441—91no—
191C4×SD16—92no—
192C4×SD16—92no—
193C2×#106—91no—
194#417—92no—
195#405—91no—
196C2×C3×Q8—32no—
197C2×C3×D4—32no—
198C22×C3×C4—62no—
199C2×#67—62no—
200C22×Dic3—62no—
201C22×Dic3—62no—
202#239—38no—
203#239—64no—
204#237—38no—
205#237—64no—
206C2×D12—62no—
207C2×D12C22×D312yes—
208C2×C4×D3—22no—
209C2×C4×D3—31no—
210C2×C4×D3—31no—
211C2×C4×D3—61no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×Dic6C22×D312yes—
217C3×Q16—34no—
218C3×D8—34no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8C22×D311yescharacteristic
222C2×C3×C8C22×D311yescharacteristic
223C2×C3×C8C22×D311yescharacteristic
224C2×C3×C8C22×D311yescharacteristic
225C3×C4⋊C4—32no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—62no—
228C3×C22⋊C4—62no—
229C3×C42—21no—
230C3×C42—62no—
231C3×C42C22×D311yescharacteristic
232C3×C42C22×D311yescharacteristic
233#217—62no—
234#215—38no—
235#214—38no—
236(C2×D3)⋊C4—22no—
237(C2×D3)⋊C4—32no—
238(C2×D3)⋊C4—32no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241C4⋊Dic3—62no—
242C4⋊Dic3C22×D312yes—
243C4⋊Dic3C22×D312yes—
244Dic3⋊C4—22no—
245Dic3⋊C4—32no—
246Dic3⋊C4—32no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249Dic3⋊C4—62no—
250Dic3⋊C4—62no—
251C4×Dic3—22no—
252C4×Dic3—31no—
253C4×Dic3—31no—
254C4×Dic3—61no—
255C4×Dic3—62no—
256C4×Dic3—62no—
257C2×C3⋊C8—31no—
258C2×C3⋊C8—31no—
259C2×C3⋊C8—31no—
260C2×C3⋊C8—31no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—61no—
263Dic12C4×D314yescomplemented
264D24C4×D314yescomplemented
265ΓL(1,𝔽25)—62no—
266ΓL(1,𝔽25)—62no—
267ΓL(1,𝔽25)—64no—
268D3×C8—34no—
269D3×C8—34no—
270D3×C8—64no—
271C22×C32C22×D411yescharacteristic
272C2×C3⋊D3—22no—
273C2×C3⋊D3C4×D412yes—
274C2×C3×D3—24no—
275C2×C3×D3—42no—
276C2×C3×D3—42no—
277C32×C4—22no—
278C32×C4C23×C411yescharacteristic
279C32×C4C2×#4111yescharacteristic
280C3⋊Dic3—22no—
281C3⋊Dic3C4×D412yes—
282C3×Dic3—24no—
283C3×Dic3—42no—
284C3×Dic3—42no—
285C2×#41—92no—
286#135—98no—
287C2×Q16—31no—
288C2×SD16—92no—
289C2×D8—31no—
290C2×M16—91no—
291C22×C8—91no—
292C4×Q8—32no—
293C4×Q8—92no—
294C4×D4—32no—
295C4×D4—92no—
296C4×D4—182no—
297C4×D4—182no—
298#117—91no—
299#117—182no—
300C2×C4⋊C4—92no—
301C2×C4⋊C4—182no—
302#106—31no—
303#106—31no—
304#106—92no—
305#103—32no—
306#103—92no—
307#102—32no—
308#102—92no—
309#97—91no—
310#97D3211yescharacteristic
311C4×C8—91no—
312C4×C8—91no—
313C23×C3—62no—
314C22×D3—22no—
315C22×D3—31no—
316C22×D3—31no—
317C22×D3—61no—
318C3×Q8—34no—
319C3×Q8—62no—
320C3×D4—34no—
321C3×D4—62no—
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—242no—
328C2×C3×C4D3×D412yes—
329C2×C3×C4D3×D412yes—
330C2×C3×C4C23×D311yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332#67—68no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—31no—
337C2×Dic3—31no—
338C2×Dic3—32no—
339C2×Dic3—32no—
340C2×Dic3—61no—
341C2×Dic3—62no—
342C2×Dic3—68no—
343C2×Dic3—242no—
344D12—22no—
345D12—68no—
346D12C2×C4×D314yes—
347C4×D3—32no—
348C4×D3—32no—
349C4×D3—32no—
350C4×D3—32no—
351C4×D3—62no—
352C4×D3—62no—
353C4×D3—68no—
354C4×D3—82no—
355C4×D3—242no—
356C4×D3—242no—
357C4×D3—242no—
358Dic6—22no—
359Dic6C2×C4×D314yes—
360C3×C8—22no—
361C3×C8—21no—
362C3×C8—21no—
363C3×C8—22no—
364C3×C8C2×C4×D312yes—
365C3×C8C2×C4×D312yes—
366C3⋊C8—32no—
367C3⋊C8—32no—
368C3⋊C8—62no—
369C3⋊C8—62no—
370C3⋊C8—61no—
371C3⋊C8—61no—
372C2×C32C2×C4×D411yescharacteristic
373C2×C32#57712yes—
374C3⋊D3—22no—
375C3×D3—44no—
376#41—98no—
377#41—184no—
378C2×Q8—32no—
379C2×D4—32no—
380C2×D4—182no—
381C22×C4—62no—
382C22×C4—91no—
383C22×C4—182no—
384C22×C4—182no—
385C22×C4—182no—
386Q16—34no—
387SD16—98no—
388D8—34no—
389M16—182no—
390C2×C8—91no—
391C2×C8—94no—
392C2×C8—91no—
393C2×C8C2×D3211yescharacteristic
394C2×C8C2×D3211yescharacteristic
395C4⋊C4—32no—
396C4⋊C4—32no—
397C4⋊C4—62no—
398C4⋊C4—92no—
399C4⋊C4—182no—
400C4⋊C4—182no—
401C22⋊C4—62no—
402C22⋊C4—92no—
403C22⋊C4—182no—
404C42—62no—
405C42—91no—
406C42—182no—
407C42C2×D3211yescharacteristic
408C22×C3—21no—
409C22×C3—64no—
410C22×C3—122no—
411C22×C3—122no—
412C22×C3C2×D3×D411yescharacteristic
413C22×C3C2×D3×D411yescharacteristic
414C2×D3—24no—
415C2×D3—32no—
416C2×D3—32no—
417C2×D3—42no—
418C2×D3—42no—
419C2×D3—62no—
420C2×D3—62no—
421C2×D3—62no—
422C2×D3—122no—
423C3×C4—22no—
424C3×C4—22no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—42no—
428C3×C4—64no—
429C3×C4—122no—
430C3×C4—122no—
431C3×C4C22×C4×D311yescharacteristic
432C3×C4C22×C4×D311yescharacteristic
433C3×C4D3×#4111yescharacteristic
434C3×C4D3×#4111yescharacteristic
435Dic3—24no—
436Dic3—32no—
437Dic3—32no—
438Dic3—42no—
439Dic3—42no—
440Dic3—62no—
441Dic3—62no—
442Dic3—62no—
443Dic3—122no—
444C32#295211yescharacteristic, complemented, Sylow
445C23—62no—
446C23—91no—
447Q8—34no—
448Q8—62no—
449D4—34no—
450D4—62no—
451D4—188no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—62no—
455C2×C4—91no—
456C2×C4—92no—
457C2×C4—92no—
458C2×C4—92no—
459C2×C4—188no—
460C2×C4—242no—
461C2×C4—722no—
462C2×C4—722no—
463C2×C4#380212yes—
464C2×C4C22×D3211yescharacteristic
465C8—21no—
466C8—92no—
467C8—181no—
468C8C4×D3212yes—
469C2×C3—22no—
470C2×C3—21no—
471C2×C3—124no—
472C2×C3C4×D3×D411yescharacteristic
473C2×C3C4×D3×D411yescharacteristic
474C2×C3#577512yes—
475C2×C3#577812yes—
476D3—44no—
477D3—62no—
478D3—62no—
479D3—122no—
480C22—64no—
481C22—92no—
482C22—122no—
483C22—122no—
484C22—182no—
485C22C2×#380211yescharacteristic
486C4—22no—
487C4—64no—
488C4—92no—
489C4—122no—
490C4—122no—
491C4—182no—
492C4C2×C4×D3211yescharacteristic
493C4#6430611yescharacteristic
494C3—21no—
495C3#7983211yescharacteristic, complemented
496C3#7986811yescharacteristic, complemented
497C2—124no—
498C2—182no—
499C2C4×#380211yescharacteristic
500C2#1059471912yes—
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#63810C2
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #10593889C2semidirect
3. #10592407C2semidirect
4. C3×#4716C2semidirect
5. C3×#4711C2semidirect
6. #10590957C2semidirect
7. #10590819C2semidirect
8. #10590781C2semidirect
9. #10590742C2semidirect
10. #10590685C2semidirect
11. C4×#3715C2semidirect
30. #63810C4semidirect
60. #4716D3semidirect
61. #4711D3semidirect
74. #3796C2×C4semidirect
84. C8×C3⋊D3C2×C4semidirect
90. C3×Dic12C2×C4semidirect
91. C3×D24C2×C4semidirect
96. #3715C2×C4semidirect
263. Dic12C4×D3semidirect
264. D24C4×D3semidirect
444. C32#2952semidirect
495. C3#79832semidirect
496. C3#79868semidirect

Maximal subgroups

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

subgroupindex
C2×#638102
#105938892
#105924072
C3×#47162
C3×#47112
#105909572
#105908192
#105907812
#105907422
#105906852
C4×#37152
#798683
#798323