Finite Group Databasebeta

← #11860954

Subgroups — #11860954

Order 1152.

1034 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63808C211yesmaximal, characteristic
2#10593890C212yesmaximal, complemented
3#10592410C211yesmaximal, characteristic, complemented
4C3×#4716C211yesmaximal, characteristic, complemented
5C3×#4708C211yesmaximal, characteristic, complemented
6#10590812C211yesmaximal, characteristic, complemented
7#10590792C212yesmaximal, complemented
8#10590768C211yesmaximal, characteristic, complemented
9D3×#817C211yesmaximal, characteristic, complemented
10#10590671C212yesmaximal, complemented
11C4×#3717C212yesmaximal, complemented
12#79832—31nomaximal
13#78574—31nomaximal
14C2×#3799C2212yes—
15C2×#3745C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2212yes—
17C2×C3×Dic12C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
19C2×C3×D3×C8C2211yescharacteristic
20C3×#872C2211yescharacteristic
21C3×C4×Dic6C2212yes—
22#63894C2212yes—
23D3×C4⋊Dic3C2212yes—
24#63883—22no—
25#63881—22no—
26#63880—22no—
27Dic3×Dic6C2212yes—
28#63836—22no—
29C2×#3717C2212yes—
30#63808C418yescomplemented
31C32×#97C2211yescharacteristic
32#63648C2212yes—
33#63644C2211yescharacteristic
34C3×#817C2211yescharacteristic
35C3×#816C2212yes—
36C3×#815C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38C3×C4×C3⋊C8C2211yescharacteristic
39#63573C2212yes—
40#63566C2212yes—
41#63564C2212yes—
42C2×#919—31no—
43C2×#904—31no—
44#5574—32no—
45#5523—32no—
46C3×#441—31no—
47C3×#405—31no—
48#5184—31no—
49#5133—32no—
50C2×#817—31no—
51C4×#215—32no—
52#4869—31no—
53D3×#106—31no—
54#4803—32no—
55#4788—32no—
56#4716—31no—
57#4716D311yescharacteristic, complemented
58#4711—31no—
59#4711—31no—
60#4711—31no—
61#4711—61no—
62#4708D311yescharacteristic, complemented
63C4×#204—32no—
64C4×#204—32no—
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×C4×C3⋊D3—22no—
67C2×C3×C4×D3C2311yescharacteristic
68C2×C3×Dic6C2312yes—
69C2×#626—22no—
70C2×#624—22no—
71C2×#624—22no—
72C2×D3×Dic3—22no—
73#3799—24no—
74#3799C2×C418yescomplemented
75C2×C32×C8C2311yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C32×C42C2311yescharacteristic
78#3752—22no—
79C4⋊(C3⋊Dic3)C2312yes—
80#3745C2×C414yescomplemented
81C3×(C2×D3)⋊C4D412yes—
82C3×C4⋊Dic3C2312yes—
83C3×Dic3⋊C4—22no—
84C3×Dic3⋊C4D412yes—
85C3×C4×Dic3—22no—
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C3×Dic12C2×C414yescomplemented
90C3×ΓL(1,𝔽25)—22no—
91C3×D3×C8C2×C414yescomplemented
92Dic3⋊Dic3—22no—
93Dic3⋊Dic3—22no—
94#3722—22no—
95Dic32—22no—
96#3717C2×C418yescomplemented
97#2952—91noSylow
98C2×#239—32no—
99C2×#235—32no—
100C2×C3×Q16—31no—
101C2×C3×M16—31no—
102C22×C3×C8—31no—
103C3×C4×Q8—32no—
104C3×#117—31no—
105Q8×Dic3—32no—
106C2×#215—32no—
107C2×C4⋊Dic3—32no—
108#919—38no—
109C2×Dic12C2×D311yescharacteristic
110#904—38no—
111C2×D24—31no—
112C2×D24—31no—
113C2×D24—61no—
114C2×#204—32no—
115C2×ΓL(1,𝔽25)C2×D311yescharacteristic
116C2×D3×C8C2×D311yescharacteristic
117#893—32no—
118#893—62no—
119#892—62no—
120D3×C4⋊C4—32no—
121D3×C4⋊C4—62no—
122D3×C4⋊C4—62no—
123#67⋊C4—62no—
124#67⋊C4—62no—
125C4×D12—32no—
126C4×D12—32no—
127C4×D12—32no—
128C4×D12—62no—
129C4×D12—62no—
130#872—62no—
131#872C2×D311yescharacteristic
132C4×Dic6—32no—
133C4×Dic6C2×D312yes—
134C3×#106—31no—
135C3×#103—32no—
136C3×#97—21no—
137C3×#97—31no—
138C3×#97C2×D311yescharacteristic
139C3×#97C2×D311yescharacteristic
140C3×C4×C8—31no—
141C3×C4×C8—31no—
142#835—32no—
143#821—32no—
144#821—32no—
145#821—32no—
146#821—62no—
147#817—31no—
148#817—31no—
149#817—32no—
150#817—61no—
151#817C2×D311yescharacteristic
152#816—32no—
153#816C2×D312yes—
154#815C2×D311yescharacteristic
155C8×Dic3C2×D311yescharacteristic
156#809—32no—
157#808—32no—
158C4×C3⋊C8C2×D311yescharacteristic
159C22×C3⋊D3—22no—
160C22×C3×D3C2×D411yescharacteristic
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2411yescharacteristic
163C2×C3⋊Dic3—22no—
164C4⋊(C3⋊D3)—22no—
165C4⋊(C3⋊D3)C22×C414yes—
166C4×C3⋊D3—82no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3C2×D412yes—
170C2×C3×Dic3C2×D411yescharacteristic
171C3×C4×D3C22×C412yes—
172C3×C4×D3#4112yes—
173C3×Dic6—22no—
174C3×Dic6C22×C414yes—
175#626—28no—
176#624—28no—
177#624—82no—
178D3×Dic3—82no—
179C32×C8—21no—
180C32×C8C22×C412yes—
181C3×C3⋊C8—21no—
182C3×C3⋊C8C22×C412yes—
183C2×#135—91no—
184#520—92no—
185#442—91no—
186#442—91no—
187#441—31no—
188#441—91no—
189C4×SD16—92no—
190C4×SD16—92no—
191C2×#106—91no—
192#417—92no—
193#405—31no—
194C2×C3×Q8—32no—
195C22×C3×C4—31no—
196C2×#67—62no—
197C22×Dic3—62no—
198#239—38no—
199#239—64no—
200#235—38no—
201#235—64no—
202C2×D12—32no—
203C2×D12—32no—
204C2×D12—62no—
205C2×D12—62no—
206C2×C4×D3—62no—
207C2×C4×D3—62no—
208C2×C4×D3—62no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—122no—
214C2×C4×D3C22×D311yescharacteristic
215C2×Dic6C22×D312yes—
216C3×Q16—34no—
217C3×M16—62no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—31no—
221C2×C3×C8—34no—
222C2×C3×C8—31no—
223C2×C3×C8C22×D311yescharacteristic
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C22×D311yescharacteristic
227C3×C4⋊C4—32no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—62no—
230C3×C22⋊C4—32no—
231C3×C42—21no—
232C3×C42—31no—
233C3×C42—62no—
234C3×C42C22×D311yescharacteristic
235C3×C42C22×D311yescharacteristic
236#215—38no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—122no—
242(C2×D3)⋊C4D1212yes—
243C4⋊Dic3—32no—
244C4⋊Dic3—32no—
245C4⋊Dic3—62no—
246C4⋊Dic3—62no—
247C4⋊Dic3—62no—
248C4⋊Dic3C22×D312yes—
249Dic3⋊C4—22no—
250Dic3⋊C4—62no—
251Dic3⋊C4—62no—
252Dic3⋊C4D1212yes—
253C4×Dic3—22no—
254C4×Dic3—62no—
255C4×Dic3—62no—
256C4×Dic3C22×D311yescharacteristic
257C2×C3⋊C8C22×D311yescharacteristic
258C2×C3⋊C8C22×D311yescharacteristic
259Dic12C4×D314yescomplemented
260D24—34no—
261D24—34no—
262D24—64no—
263#204—38no—
264ΓL(1,𝔽25)—22no—
265D3×C8C4×D314yescomplemented
266C22×C32C22×D411yescharacteristic
267C2×C3⋊D3—24no—
268C2×C3⋊D3—42no—
269C2×C3⋊D3—42no—
270C2×C3×D3—22no—
271C2×C3×D3C4×D412yes—
272C32×C4—22no—
273C32×C4C23×C411yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—42no—
276C3×Dic3—24no—
277C3×Dic3—22no—
278C3×Dic3—42no—
279C3×Dic3C4×D412yes—
280C2×#41—92no—
281#135—98no—
282C2×Q16—31no—
283C2×SD16—92no—
284C2×D8—91no—
285C2×M16—31no—
286C22×C8—31no—
287C4×Q8—32no—
288C4×Q8—92no—
289C4×D4—92no—
290C4×D4—92no—
291C4×D4—182no—
292C4×D4—182no—
293#117—31no—
294#117—182no—
295C2×C4⋊C4—92no—
296C2×C4⋊C4—182no—
297#106—31no—
298#106—92no—
299#106—91no—
300#103—32no—
301#103—92no—
302#102—92no—
303#102—92no—
304#97—31no—
305#97D3211yescharacteristic
306C4×C8—31no—
307C4×C8—31no—
308C23×C3—31no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—122no—
312C22×D3C2×D1211yescharacteristic
313C3×Q8—34no—
314C3×Q8—62no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—31no—
318C2×C3×C4—32no—
319C2×C3×C4—32no—
320C2×C3×C4—32no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4C2×D1212yes—
324C2×C3×C4D3×D412yes—
325C2×C3×C4C23×D311yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327#67—68no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—122no—
333C2×Dic3—242no—
334C2×Dic3C2×D1212yes—
335C2×Dic3C2×D1211yescharacteristic
336D12—34no—
337D12—34no—
338D12—64no—
339D12—68no—
340D12—62no—
341D12—62no—
342D12—122no—
343C4×D3—68no—
344C4×D3—68no—
345C4×D3—242no—
346C4×D3—242no—
347C4×D3—242no—
348C4×D3—242no—
349C4×D3—242no—
350C4×D3—244no—
351C4×D3C2×C4×D312yes—
352C4×D3#23512yes—
353Dic6—22no—
354Dic6C2×C4×D314yes—
355C3×C8—21no—
356C3×C8—21no—
357C3×C8—22no—
358C3×C8—32no—
359C3×C8—41no—
360C3×C8—61no—
361C3×C8C2×C4×D312yes—
362C3×C8C2×C4×D312yes—
363C3⋊C8—21no—
364C3⋊C8C2×C4×D312yes—
365C2×C32C2×C4×D411yescharacteristic
366C2×C32#57712yes—
367C3⋊D3—44no—
368C3×D3—22no—
369#41—98no—
370#41—184no—
371C2×Q8—32no—
372C2×D4—92no—
373C2×D4—182no—
374C22×C4—31no—
375C22×C4—182no—
376C22×C4—182no—
377C22×C4—182no—
378C22×C4—182no—
379Q16—34no—
380SD16—98no—
381D8—94no—
382M16—62no—
383C2×C8—31no—
384C2×C8—34no—
385C2×C8—31no—
386C2×C8C2×D3211yescharacteristic
387C2×C8C2×D3211yescharacteristic
388C4⋊C4—32no—
389C4⋊C4—32no—
390C4⋊C4—62no—
391C4⋊C4—92no—
392C4⋊C4—182no—
393C4⋊C4—182no—
394C22⋊C4—32no—
395C22⋊C4—182no—
396C22⋊C4—182no—
397C42—31no—
398C42—62no—
399C42—182no—
400C42C2×D3211yescharacteristic
401C22×C3—21no—
402C22×C3—32no—
403C22×C3—62no—
404C22×C3C22×D1211yescharacteristic
405C22×C3C2×D3×D411yescharacteristic
406C2×D3—22no—
407C2×D3—64no—
408C2×D3—64no—
409C2×D3—124no—
410C2×D3—122no—
411C2×D3—122no—
412C2×D3—122no—
413C2×D3—122no—
414C2×D3—242no—
415C2×D3—242no—
416C2×D3C4×D1212yes—
417C3×C4—22no—
418C3×C4—22no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—32no—
422C3×C4—42no—
423C3×C4—64no—
424C3×C4—62no—
425C3×C4—122no—
426C3×C4C22×C4×D311yescharacteristic
427C3×C4C22×C4×D311yescharacteristic
428C3×C4C2×#23511yescharacteristic
429C3×C4D3×#4111yescharacteristic
430Dic3—22no—
431Dic3—24no—
432Dic3—42no—
433Dic3—122no—
434Dic3—122no—
435Dic3—242no—
436Dic3C4×D1212yes—
437C32#295211yescharacteristic, complemented, Sylow
438C23—31no—
439C23—182no—
440Q8—34no—
441Q8—62no—
442D4—94no—
443D4—188no—
444D4—182no—
445C2×C4—31no—
446C2×C4—32no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—188no—
452C2×C4—182no—
453C2×C4—722no—
454C2×C4—722no—
455C2×C4—722no—
456C2×C4D3×D1212yes—
457C2×C4C22×D3211yescharacteristic
458C8—21no—
459C8—32no—
460C8—61no—
461C8C4×D3212yes—
462C2×C3—22no—
463C2×C3—21no—
464C2×C3—62no—
465C2×C3C2×C4×D1211yescharacteristic
466C2×C3C4×D3×D411yescharacteristic
467C2×C3#575112yes—
468C2×C3#577812yes—
469D3—22no—
470D3—124no—
471D3—124no—
472D3—244no—
473C22—32no—
474C22—62no—
475C22—184no—
476C22—362no—
477C22—362no—
478C22C2×D3×D1211yescharacteristic
479C4—22no—
480C4—32no—
481C4—62no—
482C4—64no—
483C4—122no—
484C4—362no—
485C4C2×C4×D3211yescharacteristic
486C4D3×#23511yescharacteristic
487C3—21no—
488C3#7857411yescharacteristic, complemented
489C3#7983211yescharacteristic, complemented
490C2—62no—
491C2—364no—
492C2C4×D3×D1211yescharacteristic
493C2#1059471512yes—
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#63808C2
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. #10593890C2semidirect
3. #10592410C2semidirect
4. C3×#4716C2semidirect
5. C3×#4708C2semidirect
6. #10590812C2semidirect
7. #10590792C2semidirect
8. #10590768C2semidirect
9. D3×#817C2semidirect
10. #10590671C2semidirect
11. C4×#3717C2semidirect
30. #63808C4semidirect
57. #4716D3semidirect
62. #4708D3semidirect
74. #3799C2×C4semidirect
80. #3745C2×C4semidirect
89. C3×Dic12C2×C4semidirect
91. C3×D3×C8C2×C4semidirect
96. #3717C2×C4semidirect
259. Dic12C4×D3semidirect
265. D3×C8C4×D3semidirect
437. C32#2952semidirect
488. C3#78574semidirect
489. C3#79832semidirect

Maximal subgroups

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

subgroupindex
C2×#638082
#105938902
#105924102
C3×#47162
C3×#47082
#105908122
#105907922
#105907682
D3×#8172
#105906712
C4×#37172
#798323
#785743