Finite Group Databasebeta

← #11860974

Subgroups — #11860974

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63810C211yesmaximal, characteristic
2#10594361C212yesmaximal, complemented
3C3⋊D3×#106C211yesmaximal, characteristic, complemented
4C3×#4869C211yesmaximal, characteristic, complemented
5C3×#4853C211yesmaximal, characteristic, complemented
6#10590812C211yesmaximal, characteristic, complemented
7#10590771C211yesmaximal, characteristic, complemented
8#10590703C211yesmaximal, characteristic, complemented
9#10590612C212yesmaximal, complemented
10#10590475C212yesmaximal, complemented
11#10590453C212yesmaximal, complemented
12#79868—31nomaximal
13#79832—31nomaximal
14C2×#3796C2212yes—
15C2×C8×C3⋊D3C2211yescharacteristic
16C4⋊C4×C3⋊D3C2212yes—
17C2×C3×Dic12C2211yescharacteristic
18C2×C3×D24C2211yescharacteristic
19C3×#893C2212yes—
20C3×#887C2212yes—
21C4×#626—22no—
22Dic3×D12C2212yes—
23#63881—22no—
24#63877—22no—
25D3×Dic3⋊C4—22no—
26#63874C2211yescharacteristic
27Dic3×Dic6C2212yes—
28C2×#3715C2212yes—
29C2×#3712C2211yescharacteristic
30#63810C418yescomplemented
31C32×#106C2211yescharacteristic
32#63644C2211yescharacteristic
33#63635C2212yes—
34C3×#815C2211yescharacteristic
35C3×#815C2211yescharacteristic
36C3×#810C2212yes—
37C3×#809C2212yes—
38#63566C2212yes—
39#63563C2212yes—
40Dic3×C3⋊C8C2211yescharacteristic
41Dic3×C3⋊C8C2211yescharacteristic
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#4869D311yescharacteristic, complemented
53D3×#106—31no—
54D3×#106—31no—
55D3×#106—61no—
56#4853D311yescharacteristic, complemented
57#4803—32no—
58#4788—32no—
59#4771—32no—
60#4758—32no—
61#4716—31no—
62#4711—31no—
63#4708—31no—
64#4708—31no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×C3×D12C2312yes—
68C2×C3×C4×D3—22no—
69C2×C3×Dic6C2312yes—
70C2×#626—22no—
71C2×D3×Dic3—22no—
72C2×D3×Dic3—22no—
73#3796—24no—
74#3796C2×C418yescomplemented
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4C2312yes—
77C4⋊(C3⋊Dic3)C2312yes—
78#3750—22no—
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C8×C3⋊D3C2×C414yescomplemented
81C3×(C2×D3)⋊C4—22no—
82C3×Dic3⋊C4—22no—
83C3×C4×Dic3—22no—
84C3×C4×Dic3C2311yescharacteristic
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C3×Dic12C2×C414yescomplemented
89C3×D24C2×C414yescomplemented
90#3724D412yes—
91Dic3⋊Dic3—22no—
92#3722D412yes—
93(C2×D3)⋊Dic3—22no—
94Dic32—22no—
95#3715C2×C418yescomplemented
96#3712—22no—
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×D3×C8—31no—
117C2×D3×C8—31no—
118C2×D3×C8—61no—
119#893—62no—
120#893C2×D312yes—
121D3×C4⋊C4—32no—
122D3×C4⋊C4—32no—
123D3×C4⋊C4—62no—
124D3×C4⋊C4—62no—
125#887C2×D312yes—
126#67⋊C4—62no—
127#877—62no—
128C4×D12—32no—
129C4×D12—62no—
130#872—31no—
131#872—31no—
132#872—62no—
133C4×Dic6—32no—
134C3×#106—21no—
135C3×#106C2×D311yescharacteristic
136C3×#106C2×D311yescharacteristic
137C3×#103—32no—
138C3×#102—32no—
139C3×#97—31no—
140C3×#97—31no—
141#835—32no—
142#832—32no—
143#821—32no—
144#817—31no—
145#817—31no—
146#817—61no—
147#816—32no—
148#815C2×D311yescharacteristic
149#815C2×D311yescharacteristic
150C8×Dic3—31no—
151C8×Dic3—31no—
152#810C2×D312yes—
153#809C2×D312yes—
154#808—32no—
155#808—32no—
156#808—62no—
157C4×C3⋊C8—31no—
158C4×C3⋊C8—31no—
159C22×C3⋊D3C2×D411yescharacteristic
160C22×C3×D3—22no—
161C2×C32×C4—22no—
162C2×C32×C4C2411yescharacteristic
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3C2×D411yescharacteristic
165C4×C3⋊D3—82no—
166C4×C3⋊D3C22×C412yes—
167C4×C3⋊D3#4112yes—
168C2×C3×Dic3—22no—
169C2×C3×Dic3C2×D412yes—
170C2×C3×Dic3C2×D412yes—
171C3×D12—22no—
172C3×D12C22×C414yes—
173C3×C4×D3—82no—
174C3×Dic6—22no—
175C3×Dic6C22×C414yes—
176#626—28no—
177D3×Dic3—28no—
178D3×Dic3—82no—
179C32×C8C22×C412yes—
180C3⋊(C3⋊C8)C22×C412yes—
181C3×C3⋊C8—21no—
182C3×C3⋊C8—21no—
183C2×#135—91no—
184#520—92no—
185#442—31no—
186#442—91no—
187#441—31no—
188#441—91no—
189C4×SD16—92no—
190C4×SD16—92no—
191C2×#106—91no—
192#417—92no—
193#405—91no—
194C2×C3×Q8—32no—
195C2×C3×D4—32no—
196C22×C3×C4—62no—
197C2×#67—62no—
198C22×Dic3—62no—
199C22×Dic3—62no—
200#239—38no—
201#239—64no—
202#237—38no—
203#237—64no—
204C2×D12—62no—
205C2×D12C22×D312yes—
206C2×C4×D3—22no—
207C2×C4×D3—31no—
208C2×C4×D3—31no—
209C2×C4×D3—61no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—122no—
215C2×Dic6C22×D312yes—
216C3×Q16—34no—
217C3×D8—34no—
218C2×C3×C8—21no—
219C2×C3×C8—31no—
220C2×C3×C8—31no—
221C2×C3×C8C22×D311yescharacteristic
222C2×C3×C8C22×D311yescharacteristic
223C3×C4⋊C4—22no—
224C3×C4⋊C4—62no—
225C3×C4⋊C4C22×D312yes—
226C3×C4⋊C4C22×D312yes—
227C3×C22⋊C4—62no—
228C3×C42—31no—
229C3×C42—31no—
230C3×C42—62no—
231#217—62no—
232#215—38no—
233#214—38no—
234(C2×D3)⋊C4—22no—
235(C2×D3)⋊C4—32no—
236(C2×D3)⋊C4—32no—
237(C2×D3)⋊C4—62no—
238C4⋊Dic3—32no—
239C4⋊Dic3—32no—
240C4⋊Dic3—62no—
241C4⋊Dic3—62no—
242Dic3⋊C4—22no—
243Dic3⋊C4—32no—
244Dic3⋊C4—32no—
245Dic3⋊C4—62no—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248Dic3⋊C4—122no—
249C4×Dic3—22no—
250C4×Dic3—62no—
251C4×Dic3—62no—
252C4×Dic3C22×D311yescharacteristic
253C4×Dic3C22×D311yescharacteristic
254C2×C3⋊C8—31no—
255C2×C3⋊C8—31no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8C22×D311yescharacteristic
258C2×C3⋊C8C22×D311yescharacteristic
259Dic12C4×D314yescomplemented
260D24C4×D314yescomplemented
261ΓL(1,𝔽25)—62no—
262ΓL(1,𝔽25)—62no—
263D3×C8—34no—
264D3×C8—34no—
265D3×C8—64no—
266C22×C32C22×D411yescharacteristic
267C2×C3⋊D3—22no—
268C2×C3⋊D3C4×D412yes—
269C2×C3×D3—24no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C32×C4—42no—
273C32×C4C23×C411yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—42no—
276C3⋊Dic3C4×D412yes—
277C3×Dic3—24no—
278C3×Dic3—22no—
279C3×Dic3—22no—
280C2×#41—92no—
281#135—98no—
282C2×Q16—31no—
283C2×SD16—92no—
284C2×D8—31no—
285C2×M16—91no—
286C22×C8—91no—
287C4×Q8—32no—
288C4×Q8—92no—
289C4×D4—32no—
290C4×D4—92no—
291C4×D4—182no—
292C4×D4—182no—
293#117—91no—
294#117—182no—
295C2×C4⋊C4—92no—
296C2×C4⋊C4—182no—
297#106—91no—
298#106—92no—
299#106D3211yescharacteristic
300#103—32no—
301#103—92no—
302#102—32no—
303#102—92no—
304#97—31no—
305#97—31no—
306C4×C8—91no—
307C4×C8—91no—
308C23×C3—62no—
309C22×D3—22no—
310C22×D3—31no—
311C22×D3—31no—
312C22×D3—61no—
313C3×Q8—34no—
314C3×Q8—62no—
315C3×D4—34no—
316C3×D4—62no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—32no—
321C2×C3×C4—32no—
322C2×C3×C4—42no—
323C2×C3×C4—62no—
324C2×C3×C4—242no—
325C2×C3×C4C23×D311yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327#67—68no—
328C2×Dic3—22no—
329C2×Dic3—31no—
330C2×Dic3—31no—
331C2×Dic3—61no—
332C2×Dic3—68no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—122no—
336C2×Dic3—242no—
337C2×Dic3D3×D412yes—
338C2×Dic3D3×D412yes—
339D12—22no—
340D12—68no—
341D12C2×C4×D314yes—
342C4×D3—32no—
343C4×D3—32no—
344C4×D3—32no—
345C4×D3—32no—
346C4×D3—62no—
347C4×D3—62no—
348C4×D3—68no—
349C4×D3—82no—
350C4×D3—242no—
351C4×D3—242no—
352C4×D3—242no—
353C4×D3—244no—
354Dic6—22no—
355Dic6C2×C4×D314yes—
356C3×C8—22no—
357C3×C8—61no—
358C3×C8—61no—
359C3×C8C2×C4×D312yes—
360C3×C8C2×C4×D312yes—
361C3⋊C8—21no—
362C3⋊C8—21no—
363C3⋊C8—32no—
364C3⋊C8—32no—
365C3⋊C8—62no—
366C2×C32C2×C4×D411yescharacteristic
367C2×C32#57712yes—
368C3⋊D3—22no—
369C3×D3—44no—
370#41—98no—
371#41—184no—
372C2×Q8—32no—
373C2×D4—32no—
374C2×D4—182no—
375C22×C4—62no—
376C22×C4—91no—
377C22×C4—182no—
378C22×C4—182no—
379C22×C4—182no—
380Q16—34no—
381SD16—98no—
382D8—34no—
383M16—182no—
384C2×C8—31no—
385C2×C8—31no—
386C2×C8—91no—
387C2×C8—94no—
388C2×C8C2×D3211yescharacteristic
389C4⋊C4—62no—
390C4⋊C4—92no—
391C4⋊C4—92no—
392C4⋊C4—182no—
393C4⋊C4—182no—
394C4⋊C4C2×D3212yes—
395C22⋊C4—62no—
396C22⋊C4—92no—
397C22⋊C4—182no—
398C42—31no—
399C42—31no—
400C42—62no—
401C42—182no—
402C22×C3—21no—
403C22×C3—64no—
404C22×C3—122no—
405C22×C3—122no—
406C22×C3C2×D3×D411yescharacteristic
407C22×C3C2×D3×D411yescharacteristic
408C2×D3—24no—
409C2×D3—32no—
410C2×D3—32no—
411C2×D3—42no—
412C2×D3—42no—
413C2×D3—62no—
414C2×D3—64no—
415C2×D3—62no—
416C2×D3—62no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—42no—
420C3×C4—42no—
421C3×C4—62no—
422C3×C4—62no—
423C3×C4—64no—
424C3×C4—82no—
425C3×C4C22×C4×D311yescharacteristic
426C3×C4C22×C4×D311yescharacteristic
427C3×C4D3×#4111yescharacteristic
428C3×C4D3×#4111yescharacteristic
429Dic3—22no—
430Dic3—22no—
431Dic3—24no—
432Dic3—32no—
433Dic3—32no—
434Dic3—62no—
435Dic3—122no—
436Dic3—122no—
437Dic3—242no—
438C32#295211yescharacteristic, complemented, Sylow
439C23—62no—
440C23—91no—
441Q8—34no—
442Q8—62no—
443D4—34no—
444D4—62no—
445D4—188no—
446C2×C4—22no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—62no—
450C2×C4—91no—
451C2×C4—92no—
452C2×C4—92no—
453C2×C4—188no—
454C2×C4—182no—
455C2×C4—242no—
456C2×C4—722no—
457C2×C4—722no—
458C2×C4C22×D3211yescharacteristic
459C8—61no—
460C8—61no—
461C8—92no—
462C8C4×D3212yes—
463C2×C3—21no—
464C2×C3—22no—
465C2×C3—124no—
466C2×C3C4×D3×D411yescharacteristic
467C2×C3C4×D3×D411yescharacteristic
468C2×C3#577512yes—
469C2×C3#577812yes—
470D3—44no—
471D3—64no—
472D3—62no—
473D3—62no—
474C22—64no—
475C22—92no—
476C22—122no—
477C22—122no—
478C22—182no—
479C22D32×D411yescharacteristic
480C4—42no—
481C4—64no—
482C4—62no—
483C4—62no—
484C4—92no—
485C4—362no—
486C4C2×C4×D3211yescharacteristic
487C4#6431911yescharacteristic
488C3—21no—
489C3#7983211yescharacteristic, complemented
490C3#7986811yescharacteristic, complemented
491C2—124no—
492C2—182no—
493C2#1059460511yescharacteristic
494C2#1059475412yes—
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#63810C2
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594361C2semidirect
3. C3⋊D3×#106C2semidirect
4. C3×#4869C2semidirect
5. C3×#4853C2semidirect
6. #10590812C2semidirect
7. #10590771C2semidirect
8. #10590703C2semidirect
9. #10590612C2semidirect
10. #10590475C2semidirect
11. #10590453C2semidirect
30. #63810C4semidirect
52. #4869D3semidirect
56. #4853D3semidirect
74. #3796C2×C4semidirect
80. C8×C3⋊D3C2×C4semidirect
88. C3×Dic12C2×C4semidirect
89. C3×D24C2×C4semidirect
95. #3715C2×C4semidirect
259. Dic12C4×D3semidirect
260. D24C4×D3semidirect
438. C32#2952semidirect
489. C3#79832semidirect
490. C3#79868semidirect

Maximal subgroups

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

subgroupindex
C2×#638102
#105943612
C3⋊D3×#1062
C3×#48692
C3×#48532
#105908122
#105907712
#105907032
#105906122
#105904752
#105904532
#798683
#798323