Finite Group Databasebeta

← #11866366

Subgroups — #11866366

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#909C211yesmaximal, characteristic, complemented
2#10595040C211yesmaximal, characteristic
3#10594818C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5#10592818C211yesmaximal, characteristic, complemented
6C3×#5131C211yesmaximal, characteristic, complemented
7#10591083C211yesmaximal, characteristic, complemented
8#10590876C214yesmaximal, complemented
9#10590797C214yesmaximal, complemented
10#83969—31nomaximal
11#78945—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16#64135C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C3×#909—24no—
20C2×C3×Dic12C2212yescomplemented
21C2×C3×#204C2212yescomplemented
22#63976—22no—
23#63955—22no—
24#63914C2212yes—
25#63908—22no—
26#63863C2212yes—
27#63843C2214yescomplemented
28Dic3×Dic6—22no—
29C2×#3715—24no—
30C2×#3715C2214yes—
31#63641C2214yescomplemented
32C3×#821C2214yes—
33#63565C2212yescomplemented
34#63562C2212yescomplemented
35C2×C3×#137—31no—
36#5830—31no—
37#5812—31no—
38C22×#215—31no—
39#5805—31no—
40C22×#214—31no—
41C2×#909D311yescharacteristic, complemented
42#5516—31no—
43C3×#418—31no—
44#5233—31no—
45#5185—34no—
46#5163—34no—
47#5131D311yescharacteristic, complemented
48#5119—31no—
49#5119—31no—
50#5119—61no—
51#5002—31no—
52#4767—34no—
53#4762—34no—
54C23×C3×D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C3×#67—21no—
57C22×C3×Dic3—21no—
58C3×#235—22no—
59C3×#235—22no—
60C2×C3×D12—22no—
61C2×C3×D12—22no—
62C2×C3×D12—21no—
63C2×C3×D12C2311yescharacteristic
64C2×C3×D12C2312yes—
65C2×C3×C4×D3—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6D414yescomplemented
69C2×C3×Dic6C2311yescharacteristic
70C2×C3×Dic6C2312yes—
71C2×#625—24no—
72C32×M16—22no—
73C2×C32×C8C2312yes—
74#3757D412yes—
75C4⋊(C3⋊Dic3)D412yes—
76C4×C3⋊Dic3C2312yes—
77C2×C3⋊(C3⋊C8)—22no—
78C2×C3⋊(C3⋊C8)C2312yes—
79C3×#217—21no—
80C3×C4⋊Dic3C2312yes—
81C3×C4×Dic3—21no—
82C3×Dic12—24no—
83C3×#204—24no—
84Dic3⋊Dic3—24no—
85(C2×D3)⋊Dic3—24no—
86Dic32—24no—
87#3715—28no—
88#3043—91noSylow
89C2×C3×#41—31no—
90C22×C3×Q8—31no—
91C22×C3×D4—31no—
92C2×#235C2×D311yescharacteristic
93C22×D12C2×D311yescharacteristic
94C22×Dic6C2×D311yescharacteristic
95C3×#137—64no—
96C2×C3×Q16—32no—
97C2×C3×SD16—32no—
98C2×C3×M16—21no—
99C2×C3×M16C2×D311yescharacteristic
100C2×C3×M16C2×D311yescharacteristic
101C3×#117—31no—
102#953—62no—
103#947—32no—
104Q8×Dic3—34no—
105Q8×Dic3—62no—
106C2×#215—34no—
107C2×#215—64no—
108#940—32no—
109#940—32no—
110#938—62no—
111#937—62no—
112#936—32no—
113C2×#214—34no—
114C2×#214—64no—
115#930—62no—
116#926—31no—
117#926—31no—
118#926—61no—
119#926—62no—
120#926C2×D311yescharacteristic
121C22×C3⋊C8—31no—
122C22×C3⋊C8—31no—
123C22×C3⋊C8—61no—
124#909—24no—
125C2×Dic12C2×D312yescomplemented
126C2×#204C2×D312yescomplemented
127#887—34no—
128#877—62no—
129C4×Dic6—62no—
130C3×#102—34no—
131#835—32no—
132#832—32no—
133#821C2×D314yes—
134Dic3⋊C8—34no—
135Dic3⋊C8—34no—
136Dic3⋊C8—64no—
137#810—32no—
138#809—32no—
139C23×C32C2×D411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—21no—
142C22×C3×D3—42no—
143C22×C3×D3—82no—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D412yes—
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3C2×D414yes—
149C3×#67—42no—
150C2×C3×Dic3—24no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—21no—
154C3×D12—22no—
155C3×D12—21no—
156C3×D12—22no—
157C3×D12—21no—
158C3×D12—42no—
159C3×C4×D3—42no—
160C3×Dic6—24no—
161C3×Dic6—22no—
162C3×Dic6—21no—
163C3×Dic6—21no—
164C3×Dic6C2×D414yes—
165#625—84no—
166C32×C8—22no—
167C3⋊(C3⋊C8)—22no—
168C2×#137—31no—
169C22×SD16—91no—
170#535—91no—
171#519—91no—
172#464—94no—
173#460—94no—
174#424—91no—
175#418—31no—
176#416—91no—
177C24×C3—61no—
178C23×D3—21no—
179C3×#41—62no—
180C3×#41—62no—
181C2×C3×Q8—34no—
182C2×C3×Q8—32no—
183C2×C3×Q8—31no—
184C2×C3×Q8—62no—
185C2×C3×Q8—61no—
186C2×C3×D4—31no—
187C2×C3×D4—32no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C2×C3×D4—62no—
191C2×C3×D4—62no—
192C22×C3×C4—21no—
193C22×C3×C4—61no—
194C22×C3×C4—61no—
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C22×D311yescharacteristic
197C2×#67—21no—
198C2×#67—64no—
199C2×#67—64no—
200C22×Dic3—21no—
201#235—22no—
202#235—22no—
203C2×D12—22no—
204C2×D12—22no—
205C2×D12—21no—
206C2×D12C22×D311yescharacteristic
207C2×D12C22×D312yes—
208C2×C4×D3—21no—
209C2×Dic6—21no—
210C2×Dic6—22no—
211C2×Dic6#6714yescomplemented
212C2×Dic6C22×D311yescharacteristic
213C2×Dic6C22×D312yes—
214C3×Q16—64no—
215C3×SD16—64no—
216C3×M16—22no—
217C3×M16—22no—
218C3×M16—42no—
219C2×C3×C8—22no—
220C2×C3×C8C22×D312yes—
221C2×C3×C8C22×D312yes—
222C3×C4⋊C4—32no—
223C3×C22⋊C4—61no—
224C3×C42—61no—
225#217—21no—
226#217—32no—
227#217—32no—
228#217—62no—
229#217—64no—
230#215—68no—
231#214—68no—
232(C2×D3)⋊C4—64no—
233C4⋊Dic3—32no—
234C4⋊Dic3—32no—
235C4⋊Dic3—62no—
236C4⋊Dic3—64no—
237C4⋊Dic3C22×D312yes—
238Dic3⋊C4—64no—
239C4×Dic3—21no—
240C4×Dic3—32no—
241C4×Dic3—32no—
242C4×Dic3—62no—
243C4×Dic3—64no—
244C4×Dic3—64no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—32no—
247C2×C3⋊C8—62no—
248C2×C3⋊C8—62no—
249C2×C3⋊C8—62no—
250C2×C3⋊C8—122no—
251Dic12—24no—
252#204—24no—
253C22×C32—22no—
254C22×C32#12112yes—
255C22×C32C22×D411yescharacteristic
256C2×C3×D3—41no—
257C2×C3×D3—42no—
258C2×C3×D3—42no—
259C2×C3×D3—44no—
260C2×C3×D3—84no—
261C32×C4#12112yes—
262C32×C4C22×D411yescharacteristic
263C32×C4C2×#4111yescharacteristic
264C3⋊Dic3—24no—
265C3×Dic3—24no—
266C3×Dic3—41no—
267C3×Dic3—42no—
268C2×#41—31no—
269C22×Q8—31no—
270C22×D4—31no—
271#137—64no—
272C2×Q16—32no—
273C2×SD16—32no—
274C2×SD16—94no—
275C2×SD16—184no—
276C2×M16D3211yescharacteristic
277C22×C8—91no—
278#127—92no—
279#124—92no—
280#121—182no—
281#120—182no—
282C4×Q8—94no—
283C4×Q8—182no—
284#117—31no—
285#117—91no—
286#117—182no—
287C4⋊C8—94no—
288#103—92no—
289#102—34no—
290#102—92no—
291C23×C3—21no—
292C23×C3—62no—
293C23×C3—61no—
294C23×C3—122no—
295C23×C3—242no—
296C23×C3D3×D411yescharacteristic
297C23×C3D3×D411yescharacteristic
298C22×D3—22no—
299C22×D3—21no—
300C22×D3—42no—
301C22×D3—82no—
302C3×Q8—34no—
303C3×Q8—64no—
304C3×Q8—62no—
305C3×Q8—61no—
306C3×Q8—61no—
307C3×D4—61no—
308C3×D4—61no—
309C3×D4—62no—
310C3×D4—62no—
311C3×D4—122no—
312C3×D4—122no—
313C2×C3×C4—21no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—64no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—61no—
321C2×C3×C4—122no—
322C2×C3×C4#23512yes—
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D412yes—
326C2×C3×C4#23712yes—
327C2×C3×C4C2×#6712yes—
328C2×C3×C4C23×D311yescharacteristic
329C2×C3×C4C23×D311yescharacteristic
330#67—42no—
331#67—244no—
332#67—244no—
333C2×Dic3—24no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—21no—
337C2×Dic3—34no—
338C2×Dic3—34no—
339C2×Dic3—64no—
340D12—22no—
341D12—22no—
342D12—21no—
343D12—21no—
344D12—42no—
345C4×D3—42no—
346Dic6—24no—
347Dic6—22no—
348Dic6—21no—
349Dic6—21no—
350Dic6C2×#6714yes—
351C3×C8—22no—
352C3×C8—22no—
353C3×C8—42no—
354C3⋊C8—62no—
355C3⋊C8—62no—
356C3⋊C8—122no—
357C2×C32—22no—
358C2×C32C2×#12111yescharacteristic
359C2×C32#57712yes—
360C3×D3—81no—
361C3×D3—82no—
362C24—61no—
363#41—62no—
364#41—62no—
365C2×Q8—32no—
366C2×Q8—31no—
367C2×Q8—34no—
368C2×Q8—62no—
369C2×Q8—61no—
370C2×D4—32no—
371C2×D4—31no—
372C2×D4—61no—
373C2×D4—62no—
374C2×D4—61no—
375C2×D4—62no—
376C2×D4—184no—
377C22×C4—61no—
378C22×C4—61no—
379C22×C4C2×D3211yescharacteristic
380Q16—64no—
381SD16—64no—
382SD16—188no—
383M16—22no—
384C2×C8—92no—
385C2×C8—182no—
386C2×C8C2×D3212yes—
387C4⋊C4—32no—
388C4⋊C4—92no—
389C4⋊C4—184no—
390C22⋊C4—61no—
391C22⋊C4—92no—
392C22⋊C4—184no—
393C42—61no—
394C42—92no—
395C42—184no—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—21no—
399C22×C3—22no—
400C22×C3—42no—
401C22×C3—121no—
402C22×C3—122no—
403C22×C3—124no—
404C22×C3—122no—
405C22×C3—244no—
406C22×C3#88412yes—
407C22×C3#93912yes—
408C22×C3C2×D3×D411yescharacteristic
409C22×C3C2×D3×D411yescharacteristic
410C2×D3—42no—
411C2×D3—44no—
412C2×D3—42no—
413C2×D3—41no—
414C2×D3—84no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—22no—
418C3×C4—64no—
419C3×C4—121no—
420C3×C4—122no—
421C3×C4#88412yes—
422C3×C4#93912yes—
423C3×C4C2×#23511yescharacteristic
424C3×C4C2×D3×D411yescharacteristic
425C3×C4C2×#23711yescharacteristic
426C3×C4C22×#6711yescharacteristic
427Dic3—24no—
428Dic3—42no—
429Dic3—41no—
430Dic3—64no—
431Dic3—64no—
432Dic3—124no—
433C32#304311yescharacteristic, complemented, Sylow
434C23—62no—
435C23—61no—
436C23—122no—
437C23—242no—
438C23#380211yescharacteristic
439Q8—34no—
440Q8—62no—
441Q8—64no—
442Q8—61no—
443Q8—61no—
444D4—62no—
445D4—61no—
446D4—61no—
447D4—62no—
448D4—122no—
449D4—122no—
450D4—724no—
451C2×C4—62no—
452C2×C4—64no—
453C2×C4—62no—
454C2×C4—61no—
455C2×C4—94no—
456C2×C4—122no—
457C2×C4#379512yes—
458C2×C4#380211yescharacteristic
459C2×C4D3×#6712yes—
460C2×C4C22×D3211yescharacteristic
461C8—22no—
462C8—182no—
463C2×C3—22no—
464C2×C3—22no—
465C2×C3—21no—
466C2×C3—22no—
467C2×C3—42no—
468C2×C3—242no—
469C2×C3—241no—
470C2×C3C2×#88411yescharacteristic
471C2×C3#577512yes—
472C2×C3#577812yes—
473C2×C3C2×#93911yescharacteristic
474D3—81no—
475D3—82no—
476C22—22no—
477C22—121no—
478C22—122no—
479C22—122no—
480C22—124no—
481C22—244no—
482C22#6388512yes—
483C22C2×#380211yescharacteristic
484C4—64no—
485C4—121no—
486C4—122no—
487C4—184no—
488C4#6388512yes—
489C4C2×#379511yescharacteristic
490C4C2×D3×#6711yescharacteristic
491C3—21no—
492C3#7894511yescharacteristic, complemented
493C3#8396911yescharacteristic, complemented
494C2—22no—
495C2—242no—
496C2—241no—
497C2#1059471912yes—
498C2C2×#6388511yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radical#10595040C2
hypercenterC2×M16D32
hypocenterC32#3043
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#909C2semidirect
3. #10594818C2semidirect
4. C22×#3715C2semidirect
5. #10592818C2semidirect
6. C3×#5131C2semidirect
7. #10591083C2semidirect
8. #10590876C2semidirect
9. #10590797C2semidirect
20. C2×C3×Dic12C22semidirect
21. C2×C3×#204C22semidirect
27. #63843C22semidirect
31. #63641C22semidirect
33. #63565C22semidirect
34. #63562C22semidirect
41. C2×#909D3semidirect
47. #5131D3semidirect
68. C2×C3×Dic6D4semidirect
125. C2×Dic12C2×D3semidirect
126. C2×#204C2×D3semidirect
211. C2×Dic6#67semidirect
433. C32#3043semidirect
492. C3#78945semidirect
493. C3#83969semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9092
#105950402
#105948182
C22×#37152
#105928182
C3×#51312
#105910832
#105908762
#105907972
#839693
#789453