Finite Group Databasebeta

← #11860210

Subgroups — #11860210

Order 1152.

1050 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×C3×#912C211yesmaximal, characteristic
2Dic3×#237C212yesmaximal, complemented
3#10592851C211yesmaximal, characteristic, complemented
4C3×#5152C211yesmaximal, characteristic, complemented
5#10591446C212yesmaximal, complemented
6#10591440C212yesmaximal, complemented
7#10591420C212yesmaximal, complemented
8#10590819C211yesmaximal, characteristic, complemented
9#10590812C211yesmaximal, characteristic, complemented
10#10590706C211yesmaximal, characteristic, complemented
11D3×#815C211yesmaximal, characteristic, complemented
12#83897—31nomaximal
13#79864—31nomaximal
14C2×C3×#237C2212yes—
15C2×C32×D8C2211yescharacteristic
16D4×C3⋊Dic3C2212yes—
17C3×D4×Dic3C2212yes—
18C2×C3×#214C2212yes—
19C3×#912C418yescomplemented
20C2×C3×Dic12C2211yescharacteristic
21C2×C3×D3×C8C2211yescharacteristic
22#67⋊Dic3—22no—
23Dic3×#67—22no—
24#63955—22no—
25C2×Dic32—22no—
26C4×D3×Dic3C2211yescharacteristic
27#63843C2212yes—
28Dic3×Dic6C2212yes—
29#63841C2212yes—
30C2×D3×C3⋊C8C2211yescharacteristic
31#63659C2212yes—
32#63644C2211yescharacteristic
33#63642C2211yescharacteristic
34C3×#832C2212yes—
35C3×#817C2211yescharacteristic
36C3×#815C2211yescharacteristic
37#63575C2212yes—
38#63566C2212yes—
39#63565C2212yes—
40#63555C2211yescharacteristic
41#63554C2211yescharacteristic
42C2×C3×#135—31no—
43Dic3×#41—32no—
44C2×#912D311yescharacteristic
45C4×#237—32no—
46C3×#442—31no—
47#5233—32no—
48#5184—31no—
49#5184—31no—
50#5164—32no—
51#5164—32no—
52#5152—31no—
53#5152—31no—
54#5152—61no—
55#5152D311yescharacteristic, complemented
56#5106—31no—
57C2×#815—31no—
58#5018—32no—
59#4860—31no—
60#4853—31no—
61#4772—32no—
62#4757—32no—
63#4716—31no—
64D3×#97—31no—
65C2×C32×D4C2312yes—
66C22×C3⋊Dic3—22no—
67C2×C3×#67—22no—
68C22×C3×Dic3—22no—
69C22×C3×Dic3—22no—
70C3×#237—24no—
71C3×#237C2×C418yescomplemented
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×Dic6C2312yes—
74C2×D3×Dic3D412yes—
75C32×D8C2×C414yescomplemented
76C2×C32×C8C2311yescharacteristic
77#3757—22no—
78C4⋊(C3⋊Dic3)C2312yes—
79C4×C3⋊Dic3C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C3×#217—22no—
82C3×#214C2×C418yescomplemented
83C3×C4⋊Dic3C2312yes—
84C3×C4×Dic3C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C3×Dic12C2×C414yescomplemented
88C3×D3×C8C2×C414yescomplemented
89Dic3⋊Dic3—22no—
90Dic3⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92Dic32—22no—
93Dic32—22no—
94Dic32—22no—
95Dic32D412yes—
96D3×C3⋊C8—22no—
97#2943—91noSylow
98C2×C3×#41—32no—
99C2×#237C2×D312yes—
100C3×#135—38no—
101C2×C3×Q16—31no—
102C2×C3×SD16—32no—
103C2×C3×D8—21no—
104C2×C3×D8C2×D311yescharacteristic
105C2×C3×D8C2×D311yescharacteristic
106C22×C3×C8—31no—
107C3×C4×D4—32no—
108Q8×Dic3—32no—
109Q8×Dic3—32no—
110D4×Dic3—32no—
111D4×Dic3—32no—
112D4×Dic3—62no—
113D4×Dic3—62no—
114D4×Dic3—62no—
115D4×Dic3C2×D312yes—
116C2×#214C2×D312yes—
117C4×#67—62no—
118#926—32no—
119#926—62no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—62no—
122C2×C4×Dic3—62no—
123C22×C3⋊C8—31no—
124#912Dic318yescomplemented
125C2×Dic12C2×D311yescharacteristic
126C2×D3×C8—31no—
127C2×D3×C8C2×D311yescharacteristic
128#892—32no—
129#887—32no—
130#67⋊C4—62no—
131#877—62no—
132C42×D3—31no—
133C4×Dic6—32no—
134C3×#106—31no—
135C3×#102—32no—
136C3×#97—31no—
137#835—32no—
138#835—32no—
139#832—32no—
140#832—32no—
141#832—62no—
142#832C2×D312yes—
143#818—32no—
144#817—31no—
145#817—31no—
146#817—61no—
147#817C2×D311yescharacteristic
148#816—32no—
149#815—31no—
150#815—31no—
151#815—31no—
152#815—31no—
153#815—31no—
154#815—61no—
155#815C2×D311yescharacteristic
156#810—32no—
157#807—32no—
158#803—31no—
159C23×C32—22no—
160C22×C3×D3C2×D411yescharacteristic
161C32×D4—22no—
162C32×D4C22×C414yes—
163C2×C32×C4C2411yescharacteristic
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—44no—
166C2×C3⋊Dic3C2×D412yes—
167C3×#67—28no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—28no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—44no—
172C2×C3×Dic3C2×D412yes—
173C2×C3×Dic3C2×D411yescharacteristic
174C3×C4×D3C22×C412yes—
175C3×C4×D3#4112yes—
176C3×Dic6—22no—
177C3×Dic6C22×C414yes—
178D3×Dic3—42no—
179C32×C8C22×C412yes—
180C3⋊(C3⋊C8)—21no—
181C3×C3⋊C8—21no—
182C3×C3⋊C8C22×C412yes—
183C2×#135—31no—
184C4×#41—92no—
185#442—31no—
186#442—91no—
187#441—91no—
188#441—91no—
189#440—92no—
190#440—92no—
191#427—91no—
192#416—92no—
193C2×#97—91no—
194C3×#41—38no—
195C3×#41—64no—
196C2×C3×Q8—32no—
197C2×C3×D4—22no—
198C2×C3×D4—62no—
199C2×C3×D4C22×D312yes—
200C2×C3×D4C22×D312yes—
201C22×C3×C4—31no—
202C22×C3×C4—62no—
203C22×C3×C4—62no—
204C2×#67—22no—
205C22×Dic3—22no—
206C22×Dic3—22no—
207C22×Dic3—32no—
208C22×Dic3—62no—
209C22×Dic3—62no—
210C22×Dic3—122no—
211#237—24no—
212#237C2×Dic318yescomplemented
213C2×C4×D3—32no—
214C2×C4×D3C22×D311yescharacteristic
215C2×Dic6C22×D312yes—
216C3×Q16—34no—
217C3×SD16—38no—
218C3×D8—24no—
219C3×D8C4×D314yescomplemented
220C3×D8C2×Dic314yescomplemented
221C2×C3×C8—21no—
222C2×C3×C8—31no—
223C2×C3×C8—34no—
224C2×C3×C8—31no—
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C22×D311yescharacteristic
227C3×C4⋊C4—32no—
228C3×C22⋊C4—62no—
229C3×C42—31no—
230#217—22no—
231#217—62no—
232#217—62no—
233#217—62no—
234#217—122no—
235#214C2×Dic318yescomplemented
236(C2×D3)⋊C4—62no—
237C4⋊Dic3—32no—
238C4⋊Dic3—32no—
239C4⋊Dic3—62no—
240C4⋊Dic3—62no—
241C4⋊Dic3—62no—
242C4⋊Dic3C22×D312yes—
243Dic3⋊C4—62no—
244Dic3⋊C4—62no—
245C4×Dic3—31no—
246C4×Dic3—31no—
247C4×Dic3—32no—
248C4×Dic3—32no—
249C4×Dic3—61no—
250C4×Dic3—62no—
251C4×Dic3—62no—
252C4×Dic3—62no—
253C4×Dic3—62no—
254C4×Dic3—62no—
255C4×Dic3—62no—
256C4×Dic3C22×D311yescharacteristic
257C2×C3⋊C8—31no—
258C2×C3⋊C8—31no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8—62no—
261C2×C3⋊C8C22×D311yescharacteristic
262C2×C3⋊C8C22×D311yescharacteristic
263Dic12C2×Dic314yescomplemented
264D3×C8—62no—
265D3×C8C2×Dic314yescomplemented
266C22×C32—24no—
267C22×C32—42no—
268C22×C32—42no—
269C22×C32C22×D411yescharacteristic
270C2×C3×D3—22no—
271C2×C3×D3C4×D412yes—
272C32×C4C23×C411yescharacteristic
273C32×C4C2×#4111yescharacteristic
274C3⋊Dic3—22no—
275C3⋊Dic3—42no—
276C3×Dic3—24no—
277C3×Dic3—22no—
278C3×Dic3—42no—
279C3×Dic3C4×D412yes—
280C2×#41—32no—
281#135—38no—
282C2×Q16—31no—
283C2×SD16—32no—
284C2×D8D3211yescharacteristic
285C22×C8—31no—
286C22×C8—91no—
287C4×Q8—92no—
288C4×Q8—92no—
289C4×D4—32no—
290C4×D4—92no—
291C4×D4—182no—
292C4×D4—182no—
293#117—92no—
294#117—182no—
295C2×C42—91no—
296C2×C42—182no—
297#107—92no—
298#106—31no—
299#106—91no—
300#103—92no—
301#103—92no—
302#102—32no—
303#102—92no—
304#97—31no—
305#97—91no—
306#97—91no—
307#97—91no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—31no—
311C23×C3—42no—
312C22×D3D3×D411yescharacteristic
313C3×Q8—34no—
314C3×Q8—62no—
315C3×D4—22no—
316C3×D4—22no—
317C3×D4—24no—
318C3×D4—42no—
319C3×D4—68no—
320C3×D4C2×C4×D314yes—
321C3×D4C22×Dic314yes—
322C2×C3×C4—21no—
323C2×C3×C4—31no—
324C2×C3×C4—32no—
325C2×C3×C4—32no—
326C2×C3×C4—32no—
327C2×C3×C4—68no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—124no—
331C2×C3×C4C23×D311yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333#67—28no—
334C2×Dic3—22no—
335C2×Dic3—28no—
336C2×Dic3—22no—
337C2×Dic3—32no—
338C2×Dic3—32no—
339C2×Dic3—44no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—122no—
344C2×Dic3—122no—
345C2×Dic3—124no—
346C2×Dic3—124no—
347C2×Dic3—244no—
348C2×Dic3D3×D412yes—
349C2×Dic3D3×D411yescharacteristic
350C4×D3—122no—
351C4×D3#23712yes—
352C4×D3C22×Dic312yes—
353Dic6—22no—
354Dic6C22×Dic314yes—
355C3×C8—22no—
356C3×C8—32no—
357C3×C8—61no—
358C3×C8C2×C4×D312yes—
359C3×C8C22×Dic312yes—
360C3⋊C8—21no—
361C3⋊C8—61no—
362C3⋊C8—61no—
363C3⋊C8—121no—
364C3⋊C8C22×Dic312yes—
365C2×C32—44no—
366C2×C32C2×C4×D411yescharacteristic
367C2×C32#57512yes—
368C3×D3—22no—
369#41—38no—
370#41—64no—
371C2×Q8—32no—
372C2×D4—62no—
373C2×D4C2×D3212yes—
374C22×C4—31no—
375C22×C4—62no—
376C22×C4—62no—
377C22×C4—92no—
378C22×C4—182no—
379Q16—34no—
380SD16—38no—
381D8D3×Dic314yescomplemented
382C2×C8—31no—
383C2×C8—34no—
384C2×C8—31no—
385C2×C8—91no—
386C2×C8—182no—
387C2×C8C2×D3211yescharacteristic
388C4⋊C4—32no—
389C4⋊C4—92no—
390C4⋊C4—182no—
391C4⋊C4—182no—
392C22⋊C4—62no—
393C22⋊C4—182no—
394C22⋊C4—182no—
395C42—31no—
396C42—92no—
397C42—91no—
398C42—182no—
399C42—182no—
400C42—182no—
401C22×C3—24no—
402C22×C3—24no—
403C22×C3—21no—
404C22×C3—32no—
405C22×C3—44no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—42no—
410C22×C3—62no—
411C22×C3—82no—
412C22×C3—82no—
413C22×C3C2×D3×D411yescharacteristic
414C22×C3C2×D3×D411yescharacteristic
415C2×D3—22no—
416C2×D3D4×Dic312yes—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—32no—
420C3×C4—62no—
421C3×C4—64no—
422C3×C4—122no—
423C3×C4C22×C4×D311yescharacteristic
424C3×C4C2×#23711yescharacteristic
425C3×C4D3×#4111yescharacteristic
426C3×C4C23×Dic311yescharacteristic
427Dic3—22no—
428Dic3—24no—
429Dic3—42no—
430Dic3—62no—
431Dic3—62no—
432Dic3—122no—
433Dic3—122no—
434Dic3—122no—
435Dic3—242no—
436Dic3D4×Dic312yes—
437C32#294311yescharacteristic, complemented, Sylow
438C23—22no—
439C23—31no—
440Q8—34no—
441Q8—62no—
442D4—22no—
443D4—68no—
444D4C2×D3×Dic314yes—
445C2×C4—31no—
446C2×C4—32no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—68no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—92no—
453C2×C4—124no—
454C2×C4—182no—
455C2×C4—362no—
456C2×C4—364no—
457C2×C4C22×D3211yescharacteristic
458C8—32no—
459C8—61no—
460C8—181no—
461C8C2×D3×Dic312yes—
462C2×C3—21no—
463C2×C3—22no—
464C2×C3—44no—
465C2×C3—44no—
466C2×C3—62no—
467C2×C3—84no—
468C2×C3C4×D3×D411yescharacteristic
469C2×C3#576812yes—
470C2×C3#577312yes—
471C2×C3C2×D4×Dic311yescharacteristic
472D3—22no—
473C22—24no—
474C22—32no—
475C22—42no—
476C22—42no—
477C22—62no—
478C22D32×D411yescharacteristic
479C4—32no—
480C4—64no—
481C4—62no—
482C4—122no—
483C4—182no—
484C4—362no—
485C4D3×#23711yescharacteristic
486C4C22×D3×Dic311yescharacteristic
487C3—21no—
488C3#7986411yescharacteristic, complemented
489C3#8389711yescharacteristic, complemented
490C2—44no—
491C2—62no—
492C2#1059472912yes—
493C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radicalC2×C3×#912C2
cosocleC2×C32×C4C24
hypercenterC2×D8D32
hypocenterC32#2943
LCSG ▷ 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
2. Dic3×#237C2semidirect
3. #10592851C2semidirect
4. C3×#5152C2semidirect
5. #10591446C2semidirect
6. #10591440C2semidirect
7. #10591420C2semidirect
8. #10590819C2semidirect
9. #10590812C2semidirect
10. #10590706C2semidirect
11. D3×#815C2semidirect
19. C3×#912C4semidirect
55. #5152D3semidirect
71. C3×#237C2×C4semidirect
75. C32×D8C2×C4semidirect
82. C3×#214C2×C4semidirect
87. C3×Dic12C2×C4semidirect
88. C3×D3×C8C2×C4semidirect
124. #912Dic3semidirect
212. #237C2×Dic3semidirect
219. C3×D8C4×D3semidirect
220. C3×D8C2×Dic3semidirect
235. #214C2×Dic3semidirect
263. Dic12C2×Dic3semidirect
265. D3×C8C2×Dic3semidirect
381. D8D3×Dic3semidirect
437. C32#2943semidirect
488. C3#79864semidirect
489. C3#83897semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9122
Dic3×#2372
#105928512
C3×#51522
#105914462
#105914402
#105914202
#105908192
#105908122
#105907062
D3×#8152
#838973
#798643