Finite Group Databasebeta

← #11860243

Subgroups — #11860243

Order 1152.

1038 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63807C211yesmaximal, characteristic
2#10594358C212yesmaximal, complemented
3#10592552C211yesmaximal, characteristic, complemented
4C3×#4869C211yesmaximal, characteristic, complemented
5C3×#4860C211yesmaximal, characteristic, complemented
6#10590810C211yesmaximal, characteristic, complemented
7#10590781C211yesmaximal, characteristic, complemented
8D3×#815C211yesmaximal, characteristic, complemented
9#10590608C212yesmaximal, complemented
10#10590590C212yesmaximal, complemented
11#10590461C212yesmaximal, complemented
12#79864—31nomaximal
13#79166—31nomaximal
14C2×#3795C2212yes—
15C2×#3746C2211yescharacteristic
16#64096C2212yes—
17C2×C3×D24C2211yescharacteristic
18C2×C3×D3×C8C2211yescharacteristic
19C3×#893C2212yes—
20C3×#892C2212yes—
21#63902—22no—
22#63898C2212yes—
23#63879—22no—
24#63877—22no—
25C4×D3×Dic3—22no—
26C4×D3×Dic3C2211yescharacteristic
27#63844C2212yes—
28C2×#3716C2212yes—
29C2×D3×C3⋊C8C2211yescharacteristic
30#63807C418yescomplemented
31C32×#106C2211yescharacteristic
32#63642C2211yescharacteristic
33#63637C2212yes—
34C3×#817C2211yescharacteristic
35C3×#815C2211yescharacteristic
36C3×#809C2212yes—
37C3×#807C2212yes—
38#63567C2212yes—
39#63562C2212yes—
40#63555C2211yescharacteristic
41#63554C2211yescharacteristic
42C2×#912—31no—
43C2×#904—31no—
44C4×#237—32no—
45#5522—32no—
46C3×#442—31no—
47C3×#427—31no—
48#5152—31no—
49C2×#815—31no—
50#5018—32no—
51#5002—32no—
52#4889—32no—
53#4889—32no—
54#4869—31no—
55#4869D311yescharacteristic, complemented
56#4860D311yescharacteristic, complemented
57#4853—31no—
58#4853—31no—
59#4853—31no—
60#4853—61no—
61#4772—32no—
62#4757—32no—
63#4716—31no—
64D3×#97—31no—
65C2×#634C2312yes—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3C2311yescharacteristic
69C2×#625—22no—
70C2×D3×Dic3—22no—
71C2×D3×Dic3—22no—
72C2×D3×Dic3D412yes—
73#3795—24no—
74#3795C2×C418yescomplemented
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4C2312yes—
77#3750—22no—
78C4×C3⋊Dic3—22no—
79C4×C3⋊Dic3C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81#3746C2×C414yescomplemented
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3C2312yes—
85C3×C4×Dic3—22no—
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C3×D24C2×C414yescomplemented
90C3×D3×C8C2×C414yescomplemented
91#3724—22no—
92(C2×D3)⋊Dic3—22no—
93Dic32—22no—
94Dic32D412yes—
95#3716C2×C418yescomplemented
96D3×C3⋊C8—22no—
97#2943—91noSylow
98C2×#237—32no—
99C2×#235—32no—
100C2×C3×D8—31no—
101C22×C3×C8—31no—
102C3×C4×D4—32no—
103C3×#117—32no—
104D4×Dic3—32no—
105C2×#214—32no—
106C4×#67—62no—
107C2×C4×Dic3—31no—
108C2×C4×Dic3—62no—
109C22×C3⋊C8—31no—
110#912—38no—
111C2×Dic12—31no—
112C2×Dic12—31no—
113C2×Dic12—61no—
114#904—38no—
115C2×D24C2×D311yescharacteristic
116C2×#204—32no—
117C2×D3×C8—31no—
118C2×D3×C8C2×D311yescharacteristic
119#893—32no—
120#893C2×D312yes—
121#892C2×D312yes—
122#887—32no—
123#887—32no—
124#887—32no—
125#887—62no—
126#67⋊C4—62no—
127#67⋊C4—62no—
128#67⋊C4—62no—
129#877—62no—
130#872—62no—
131C42×D3—31no—
132C42×D3—62no—
133C4×Dic6—32no—
134C3×#107—32no—
135C3×#106—21no—
136C3×#106—31no—
137C3×#106C2×D311yescharacteristic
138C3×#106C2×D311yescharacteristic
139C3×#102—32no—
140C3×#97—31no—
141#832—32no—
142#817C2×D311yescharacteristic
143#816—32no—
144#815—31no—
145#815—31no—
146#815—31no—
147#815—31no—
148#815—31no—
149#815—61no—
150#815C2×D311yescharacteristic
151#810—32no—
152#810—32no—
153#810—32no—
154#810—62no—
155#809—32no—
156#809C2×D312yes—
157#807C2×D312yes—
158#803—31no—
159C22×C3×D3—22no—
160C22×C3×D3C2×D411yescharacteristic
161C2×C32×C4—22no—
162C2×C32×C4C2411yescharacteristic
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3C2×D412yes—
165#634—22no—
166#634C22×C414yes—
167C2×C3×Dic3—22no—
168C2×C3×Dic3C2×D412yes—
169C2×C3×Dic3C2×D411yescharacteristic
170C3×D12—22no—
171C3×D12C22×C414yes—
172C3×C4×D3—44no—
173C3×C4×D3C22×C412yes—
174C3×C4×D3#4112yes—
175#625—28no—
176D3×Dic3—28no—
177D3×Dic3—42no—
178D3×Dic3—44no—
179C32×C8C22×C412yes—
180C3⋊(C3⋊C8)—21no—
181C3×C3⋊C8—21no—
182C3×C3⋊C8C22×C412yes—
183C2×#135—91no—
184C4×#41—92no—
185#442—31no—
186#442—91no—
187#441—91no—
188#441—91no—
189#440—92no—
190#440—92no—
191#427—31no—
192#416—92no—
193C2×#97—91no—
194C2×C3×D4—32no—
195C22×C3×C4—31no—
196C22×C3×C4—62no—
197C2×#67—62no—
198C2×#67—62no—
199C22×Dic3—32no—
200C22×Dic3—62no—
201C22×Dic3—62no—
202#237—38no—
203#237—64no—
204#235—38no—
205#235—64no—
206C2×D12C22×D312yes—
207C2×C4×D3—22no—
208C2×C4×D3—32no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3C22×D311yescharacteristic
212C2×Dic6—32no—
213C2×Dic6—32no—
214C2×Dic6—62no—
215C3×D8—34no—
216C2×C3×C8—21no—
217C2×C3×C8—31no—
218C2×C3×C8—34no—
219C2×C3×C8—31no—
220C2×C3×C8C22×D311yescharacteristic
221C2×C3×C8C22×D311yescharacteristic
222C3×C4⋊C4—22no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4C22×D312yes—
225C3×C4⋊C4C22×D312yes—
226C3×C22⋊C4—62no—
227C3×C22⋊C4—62no—
228C3×C42—31no—
229C3×C42—62no—
230#217—62no—
231#214—38no—
232(C2×D3)⋊C4—22no—
233(C2×D3)⋊C4—22no—
234(C2×D3)⋊C4—62no—
235C4⋊Dic3C22×D312yes—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239Dic3⋊C4—62no—
240Dic3⋊C4—122no—
241C4×Dic3—22no—
242C4×Dic3—31no—
243C4×Dic3—31no—
244C4×Dic3—32no—
245C4×Dic3—32no—
246C4×Dic3—61no—
247C4×Dic3—62no—
248C4×Dic3—62no—
249C4×Dic3—62no—
250C4×Dic3—62no—
251C4×Dic3—122no—
252C4×Dic3C22×D311yescharacteristic
253C2×C3⋊C8—31no—
254C2×C3⋊C8—31no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—62no—
257C2×C3⋊C8C22×D311yescharacteristic
258C2×C3⋊C8C22×D311yescharacteristic
259Dic12—34no—
260Dic12—34no—
261Dic12—64no—
262D24C4×D314yescomplemented
263#204—38no—
264D3×C8—62no—
265D3×C8C4×D314yescomplemented
266C22×C32C22×D411yescharacteristic
267C2×C3×D3—22no—
268C2×C3×D3—24no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3C4×D412yes—
272C32×C4—42no—
273C32×C4C23×C411yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—24no—
276C3⋊Dic3—22no—
277C3×Dic3—22no—
278C3×Dic3—42no—
279C3×Dic3C4×D412yes—
280C2×#41—92no—
281#135—98no—
282C2×Q16—91no—
283C2×SD16—92no—
284C2×D8—31no—
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—32no—
294#117—182no—
295C2×C42—91no—
296C2×C42—182no—
297#107—32no—
298#106—31no—
299#106D3211yescharacteristic
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—31no—
309C23×C3—62no—
310C22×D3—22no—
311C22×D3D3×D411yescharacteristic
312C3×D4—34no—
313C3×D4—62no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—31no—
318C2×C3×C4—32no—
319C2×C3×C4—32no—
320C2×C3×C4—32no—
321C2×C3×C4—42no—
322C2×C3×C4—62no—
323C2×C3×C4—124no—
324C2×C3×C4C23×D311yescharacteristic
325C2×C3×C4C23×D311yescharacteristic
326#67—68no—
327#67—68no—
328C2×Dic3—22no—
329C2×Dic3—32no—
330C2×Dic3—32no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—68no—
335C2×Dic3—122no—
336C2×Dic3—122no—
337C2×Dic3—124no—
338C2×Dic3D3×D412yes—
339C2×Dic3D3×D411yescharacteristic
340D12—22no—
341D12C2×C4×D314yes—
342C4×D3—44no—
343C4×D3—68no—
344C4×D3—122no—
345C4×D3—124no—
346C4×D3C2×C4×D312yes—
347C4×D3#23912yes—
348Dic6—34no—
349Dic6—34no—
350Dic6—64no—
351Dic6—62no—
352Dic6—62no—
353Dic6—122no—
354C3×C8—22no—
355C3×C8—32no—
356C3×C8—61no—
357C3×C8C2×C4×D312yes—
358C3×C8C2×C4×D312yes—
359C3⋊C8—21no—
360C3⋊C8—61no—
361C3⋊C8—61no—
362C3⋊C8—121no—
363C3⋊C8C2×C4×D312yes—
364C2×C32C2×C4×D411yescharacteristic
365C2×C32#57512yes—
366C3×D3—22no—
367C3×D3—44no—
368#41—98no—
369#41—184no—
370C2×Q8—92no—
371C2×D4—32no—
372C2×D4—182no—
373C22×C4—31no—
374C22×C4—62no—
375C22×C4—92no—
376C22×C4—182no—
377C22×C4—182no—
378Q16—94no—
379SD16—98no—
380D8—34no—
381C2×C8—31no—
382C2×C8—34no—
383C2×C8—31no—
384C2×C8—91no—
385C2×C8—182no—
386C2×C8C2×D3211yescharacteristic
387C4⋊C4—32no—
388C4⋊C4—182no—
389C4⋊C4—182no—
390C4⋊C4C2×D3212yes—
391C22⋊C4—62no—
392C22⋊C4—62no—
393C22⋊C4—182no—
394C42—31no—
395C42—62no—
396C42—92no—
397C42—91no—
398C42—182no—
399C42—182no—
400C22×C3—21no—
401C22×C3—32no—
402C22×C3—62no—
403C22×C3—64no—
404C22×C3—122no—
405C22×C3—122no—
406C22×C3C2×D3×D411yescharacteristic
407C22×C3C2×D3×D411yescharacteristic
408C2×D3—22no—
409C2×D3—24no—
410C2×D3—42no—
411C2×D3—42no—
412C2×D3#89312yes—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—32no—
416C3×C4—42no—
417C3×C4—42no—
418C3×C4—62no—
419C3×C4—82no—
420C3×C4—122no—
421C3×C4C22×C4×D311yescharacteristic
422C3×C4C22×C4×D311yescharacteristic
423C3×C4C2×#23911yescharacteristic
424C3×C4D3×#4111yescharacteristic
425Dic3—22no—
426Dic3—42no—
427Dic3—64no—
428Dic3—62no—
429Dic3—62no—
430Dic3—64no—
431Dic3—124no—
432Dic3—122no—
433Dic3#89312yes—
434C32#294311yescharacteristic, complemented, Sylow
435C23—31no—
436C23—62no—
437Q8—94no—
438Q8—182no—
439D4—34no—
440D4—62no—
441D4—188no—
442C2×C4—22no—
443C2×C4—31no—
444C2×C4—32no—
445C2×C4—32no—
446C2×C4—32no—
447C2×C4—62no—
448C2×C4—92no—
449C2×C4—124no—
450C2×C4—188no—
451C2×C4—182no—
452C2×C4—362no—
453C2×C4—364no—
454C2×C4C22×D3211yescharacteristic
455C8—32no—
456C8—61no—
457C8—181no—
458C8C4×D3212yes—
459C2×C3—21no—
460C2×C3—22no—
461C2×C3—62no—
462C2×C3—124no—
463C2×C3C2×#89311yescharacteristic
464C2×C3C4×D3×D411yescharacteristic
465C2×C3#576812yes—
466C2×C3#577312yes—
467D3—22no—
468D3—44no—
469C22—32no—
470C22—62no—
471C22—64no—
472C22—122no—
473C22—122no—
474C22D32×D411yescharacteristic
475C4—32no—
476C4—42no—
477C4—62no—
478C4—122no—
479C4—184no—
480C4—182no—
481C4C2×C4×D3211yescharacteristic
482C4D3×#23911yescharacteristic
483C3—21no—
484C3#7916611yescharacteristic, complemented
485C3#7986411yescharacteristic, complemented
486C2—62no—
487C2—124no—
488C2D3×#89311yescharacteristic
489C2#1059474512yes—
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#63807C2
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32#2943
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. #10594358C2semidirect
3. #10592552C2semidirect
4. C3×#4869C2semidirect
5. C3×#4860C2semidirect
6. #10590810C2semidirect
7. #10590781C2semidirect
8. D3×#815C2semidirect
9. #10590608C2semidirect
10. #10590590C2semidirect
11. #10590461C2semidirect
30. #63807C4semidirect
55. #4869D3semidirect
56. #4860D3semidirect
74. #3795C2×C4semidirect
81. #3746C2×C4semidirect
89. C3×D24C2×C4semidirect
90. C3×D3×C8C2×C4semidirect
95. #3716C2×C4semidirect
262. D24C4×D3semidirect
265. D3×C8C4×D3semidirect
434. C32#2943semidirect
484. C3#79166semidirect
485. C3#79864semidirect

Maximal subgroups

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

subgroupindex
C2×#638072
#105943582
#105925522
C3×#48692
C3×#48602
#105908102
#105907812
D3×#8152
#105906082
#105905902
#105904612
#798643
#791663