Finite Group Databasebeta

← #11866348

Subgroups — #11866348

Order 1152.

1147 conjugacy classes of subgroups.

The subgroup lattice has 533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596276C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3#10594818C211yesmaximal, characteristic, complemented
4C2×#63833C211yesmaximal, characteristic, complemented
5C3×#5215C211yesmaximal, characteristic, complemented
6#10591444C214yesmaximal, complemented
7#10591443C214yesmaximal, complemented
8#10591119C211yesmaximal, characteristic, complemented
9#10591105C211yesmaximal, characteristic, complemented
10#83849—31nomaximal
11#78945—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C2×#3828C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15#64162—22no—
16#64149C2212yes—
17#64147—22no—
18#64145C2212yes—
19#64135C2211yescharacteristic
20C2×C3×#214—24no—
21C2×C3×#214C2214yes—
22C3×#926C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25#63955—22no—
26#63843C2214yescomplemented
27Dic3×Dic6—22no—
28C2×#3719C2212yescomplemented
29#63833—24no—
30C2×#3717C2212yescomplemented
31C3×#832C2214yes—
32#63572C2214yescomplemented
33#63567C2212yescomplemented
34#63564C2212yescomplemented
35C22×C3×SD16—31no—
36#5812—31no—
37C2×#942—31no—
38#5805—31no—
39#5805—31no—
40#5805—61no—
41C22×#214D311yescharacteristic, complemented
42C2×#909—31no—
43#5516—31no—
44C3×#418—31no—
45#5215D311yescharacteristic, complemented
46#5166—34no—
47#5163—34no—
48#5119—31no—
49#5113—31no—
50#5102—31no—
51#5002—31no—
52#4767—34no—
53#4762—34no—
54C24×C32—21no—
55C2×C32×D4—22no—
56C2×C32×D4—21no—
57C2×C32×D4—22no—
58C2×C32×D4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C2×#638—21no—
61C2×#638—24no—
62#3828—22no—
63#3828—22no—
64C2×C4⋊(C3⋊D3)C2311yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×#634C2311yescharacteristic
67C22×C3×Dic3—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6D414yescomplemented
71C2×C3×Dic6C2312yes—
72#3757—24no—
73#3757D412yes—
74C4⋊(C3⋊Dic3)D412yes—
75C4×C3⋊Dic3C2312yes—
76C3×#217—21no—
77C3×#214—28no—
78C3×C4⋊Dic3C2312yes—
79C3×C4×Dic3—21no—
80C3×#208—22no—
81C2×C3×C3⋊C8—22no—
82C2×C3×C3⋊C8C2312yes—
83C2×C3×C3⋊C8C2312yes—
84Dic3⋊Dic3—24no—
85Dic32—24no—
86#3719—24no—
87#3717—24no—
88#3043—91noSylow
89C22×C3×Q8—31no—
90C22×C3×D4—21no—
91C22×C3×D4C2×D311yescharacteristic
92C22×C3×D4C2×D311yescharacteristic
93C2×#235—31no—
94C2×#235—31no—
95C2×#235—61no—
96C22×Dic6C2×D311yescharacteristic
97C2×C3×SD16—34no—
98C2×C3×SD16—64no—
99C2×C3×M16—31no—
100C22×C3×C8—31no—
101C3×#117—31no—
102#953—62no—
103#953—62no—
104#953—64no—
105Q8×Dic3—34no—
106Q8×Dic3—62no—
107C2×#216—32no—
108#942—64no—
109C2×#215—32no—
110#940—32no—
111#940—32no—
112#940—62no—
113#938—62no—
114#938—62no—
115#938—64no—
116#936—32no—
117#936—32no—
118#936—62no—
119C2×#214—24no—
120C2×#214C2×D314yes—
121#926—31no—
122#926—31no—
123#926—61no—
124#926—62no—
125#926C2×D311yescharacteristic
126C2×#208C2×D311yescharacteristic
127C22×C3⋊C8C2×D311yescharacteristic
128#909—64no—
129C2×Dic12—32no—
130C2×#204—32no—
131#887—34no—
132#877—62no—
133C4×Dic6—62no—
134C3×#102—34no—
135#832C2×D314yes—
136#821—32no—
137#816—32no—
138Dic3⋊C8—34no—
139Dic3⋊C8—34no—
140#810—32no—
141#809—32no—
142C23×C32—22no—
143C23×C32—42no—
144C23×C32—82no—
145C23×C32C2×D411yescharacteristic
146C22×C3⋊D3—21no—
147C32×D4—22no—
148C32×D4—22no—
149C32×D4—42no—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D412yes—
152C2×C32×C4#4112yes—
153C2×C32×C4C2411yescharacteristic
154#638—42no—
155#638—84no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3C2×D414yes—
158C4⋊(C3⋊D3)—21no—
159C4⋊(C3⋊D3)—21no—
160C4×C3⋊D3—42no—
161#634—21no—
162#634—21no—
163C2×C3×Dic3—24no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C3×Dic6—24no—
167C3×Dic6—22no—
168C3×Dic6C2×D414yes—
169C3×C3⋊C8—22no—
170C3×C3⋊C8—22no—
171C2×#137—91no—
172C22×SD16—31no—
173#535—91no—
174#519—91no—
175#464—94no—
176#460—94no—
177#424—91no—
178#418—31no—
179#416—91no—
180C24×C3—22no—
181C24×C3—21no—
182C24×C3—21no—
183C2×C3×Q8—34no—
184C2×C3×Q8—32no—
185C2×C3×Q8—62no—
186C2×C3×Q8—61no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—22no—
193C2×C3×D4—22no—
194C2×C3×D4—22no—
195C2×C3×D4—42no—
196C2×C3×D4—42no—
197C2×C3×D4C22×D312yes—
198C2×C3×D4C22×D312yes—
199C22×C3×C4—21no—
200C22×C3×C4—61no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C2×#67—64no—
204C2×#67—64no—
205C2×#67—62no—
206C2×#67—61no—
207C2×#67—61no—
208C2×#67—68no—
209C22×Dic3—21no—
210#235—62no—
211#235—62no—
212#235—62no—
213#235—62no—
214#235—122no—
215#235—122no—
216C2×D12—31no—
217C2×D12—31no—
218C2×D12—61no—
219C2×C4×D3—62no—
220C2×C4×D3—61no—
221C2×C4×D3—61no—
222C2×Dic6—21no—
223C2×Dic6—22no—
224C2×Dic6—31no—
225C2×Dic6—31no—
226C2×Dic6—61no—
227C2×Dic6#6714yescomplemented
228C2×Dic6C22×D312yes—
229C3×SD16—68no—
230C3×M16—62no—
231C2×C3×C8—32no—
232C2×C3×C8—32no—
233C2×C3×C8—62no—
234C3×C4⋊C4—32no—
235C3×C22⋊C4—61no—
236C3×C42—61no—
237#217—21no—
238#217—32no—
239#217—32no—
240#217—62no—
241#217—64no—
242#217—64no—
243#217—68no—
244#216—64no—
245#215—64no—
246#214—28no—
247C4⋊Dic3—32no—
248C4⋊Dic3—32no—
249C4⋊Dic3—62no—
250C4⋊Dic3—64no—
251C4⋊Dic3C22×D312yes—
252Dic3⋊C4—64no—
253C4×Dic3—21no—
254C4×Dic3—32no—
255C4×Dic3—32no—
256C4×Dic3—62no—
257C4×Dic3—64no—
258C4×Dic3—64no—
259#208—22no—
260C2×C3⋊C8—22no—
261C2×C3⋊C8C22×D312yes—
262C2×C3⋊C8C22×D312yes—
263Dic12—64no—
264#204—64no—
265C22×C32—22no—
266C22×C32—42no—
267C22×C32—44no—
268C22×C32—84no—
269C22×C32#12112yes—
270C22×C32C22×D411yescharacteristic
271C2×C3⋊D3—41no—
272C2×C3⋊D3—42no—
273C32×C4#12112yes—
274C32×C4C22×D411yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3⋊Dic3—24no—
277C3⋊Dic3—41no—
278C3×Dic3—24no—
279C3×Dic3—42no—
280C2×#41—91no—
281C22×Q8—31no—
282C22×D4D3211yescharacteristic
283#137—184no—
284C2×Q16—92no—
285C2×SD16—34no—
286C2×SD16—64no—
287C2×SD16—92no—
288C2×M16—31no—
289C22×C8—31no—
290#127—92no—
291#124—92no—
292#121—182no—
293#120—182no—
294C4×Q8—94no—
295C4×Q8—182no—
296#117—31no—
297#117—91no—
298#117—182no—
299C4⋊C8—94no—
300#103—92no—
301#102—34no—
302#102—92no—
303C23×C3—24no—
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—21no—
307C23×C3—44no—
308C23×C3—42no—
309C23×C3—42no—
310C23×C3—82no—
311C23×C3—82no—
312C23×C3—84no—
313C23×C3D3×D411yescharacteristic
314C23×C3D3×D411yescharacteristic
315C22×D3—62no—
316C22×D3—61no—
317C22×D3—61no—
318C3×Q8—34no—
319C3×Q8—64no—
320C3×Q8—62no—
321C3×D4—22no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—42no—
326C3×D4—42no—
327C3×D4—44no—
328C3×D4—42no—
329C3×D4—42no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—64no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4#23512yes—
338C2×C3×C4D3×D412yes—
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4#23712yes—
342C2×C3×C4C2×#6712yes—
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345#67—124no—
346#67—122no—
347#67—122no—
348#67—244no—
349#67—244no—
350#67—248no—
351C2×Dic3—24no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—34no—
355C2×Dic3—34no—
356C2×Dic3—64no—
357C2×Dic3—62no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360D12—61no—
361D12—61no—
362D12—61no—
363D12—61no—
364D12—121no—
365D12—121no—
366C4×D3—124no—
367C4×D3—122no—
368C4×D3—122no—
369Dic6—24no—
370Dic6—22no—
371Dic6—61no—
372Dic6—61no—
373Dic6—61no—
374Dic6—61no—
375Dic6—121no—
376Dic6—121no—
377Dic6C2×#6714yes—
378C3×C8—62no—
379C3×C8—62no—
380C3⋊C8—22no—
381C3⋊C8—22no—
382C2×C32—22no—
383C2×C32—82no—
384C2×C32C2×#12111yescharacteristic
385C2×C32#57712yes—
386C3⋊D3—81no—
387C24—21no—
388#41—182no—
389#41—182no—
390C2×Q8—32no—
391C2×Q8—34no—
392C2×Q8—62no—
393C2×Q8—61no—
394C2×Q8—91no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—21no—
398C2×D4—91no—
399C2×D4—184no—
400C2×D4—181no—
401C2×D4C2×D3212yes—
402C22×C4—61no—
403C22×C4—181no—
404C22×C4C2×D3211yescharacteristic
405Q16—184no—
406SD16—68no—
407SD16—184no—
408M16—62no—
409C2×C8—32no—
410C2×C8—32no—
411C2×C8—62no—
412C4⋊C4—32no—
413C4⋊C4—92no—
414C4⋊C4—184no—
415C22⋊C4—61no—
416C22⋊C4—92no—
417C22⋊C4—184no—
418C42—61no—
419C42—92no—
420C42—184no—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—21no—
424C22×C3—22no—
425C22×C3—42no—
426C22×C3—48no—
427C22×C3—44no—
428C22×C3—42no—
429C22×C3—44no—
430C22×C3—44no—
431C22×C3—42no—
432C22×C3—84no—
433C22×C3—84no—
434C22×C3—88no—
435C22×C3#88412yes—
436C22×C3#93912yes—
437C22×C3C2×D3×D411yescharacteristic
438C22×C3C2×D3×D411yescharacteristic
439C2×D3—122no—
440C2×D3—124no—
441C2×D3—121no—
442C2×D3—122no—
443C2×D3—122no—
444C2×D3—121no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—22no—
448C3×C4—64no—
449C3×C4—122no—
450C3×C4#88412yes—
451C3×C4#93912yes—
452C3×C4C2×#23511yescharacteristic
453C3×C4C2×D3×D411yescharacteristic
454C3×C4C2×#23711yescharacteristic
455C3×C4C22×#6711yescharacteristic
456Dic3—24no—
457Dic3—42no—
458Dic3—64no—
459Dic3—64no—
460Dic3—124no—
461Dic3—122no—
462Dic3—121no—
463Dic3—121no—
464C32#304311yescharacteristic, complemented, Sylow
465C23—22no—
466C23—42no—
467C23—82no—
468C23—181no—
469C23#381111yescharacteristic
470Q8—34no—
471Q8—62no—
472Q8—64no—
473Q8—181no—
474Q8—181no—
475D4—22no—
476D4—22no—
477D4—42no—
478D4—181no—
479D4—181no—
480D4—362no—
481D4—724no—
482C2×C4—62no—
483C2×C4—64no—
484C2×C4—62no—
485C2×C4—94no—
486C2×C4—181no—
487C2×C4—362no—
488C2×C4#380412yes—
489C2×C4D3×#6712yes—
490C2×C4#381111yescharacteristic
491C2×C4C22×D3211yescharacteristic
492C8—62no—
493C8—62no—
494C2×C3—22no—
495C2×C3—22no—
496C2×C3—22no—
497C2×C3—21no—
498C2×C3—42no—
499C2×C3—84no—
500C2×C3—82no—
501C2×C3—82no—
502C2×C3C2×#88411yescharacteristic
503C2×C3#576212yes—
504C2×C3#577512yes—
505C2×C3C2×#93911yescharacteristic
506D3—242no—
507D3—241no—
508D3—241no—
509C22—22no—
510C22—44no—
511C22—42no—
512C22—84no—
513C22—362no—
514C22—361no—
515C22#6397112yes—
516C22C2×#381111yescharacteristic
517C4—64no—
518C4—122no—
519C4—184no—
520C4—361no—
521C4#6397112yes—
522C4C2×#380411yescharacteristic
523C4C2×D3×#6711yescharacteristic
524C3—21no—
525C3#7894511yescharacteristic, complemented
526C3#8384911yescharacteristic, complemented
527C2—22no—
528C2—82no—
529C2—721no—
530C2#1059511512yes—
531C2C2×#6397111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radical#10596276C2
hypercenterC22×D4D32
hypocenterC32#3043
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#214C2semidirect
3. #10594818C2semidirect
4. C2×#63833C2semidirect
5. C3×#5215C2semidirect
6. #10591444C2semidirect
7. #10591443C2semidirect
8. #10591119C2semidirect
9. #10591105C2semidirect
26. #63843C22semidirect
28. C2×#3719C22semidirect
30. C2×#3717C22semidirect
32. #63572C22semidirect
33. #63567C22semidirect
34. #63564C22semidirect
41. C22×#214D3semidirect
45. #5215D3semidirect
70. C2×C3×Dic6D4semidirect
227. C2×Dic6#67semidirect
464. C32#3043semidirect
525. C3#78945semidirect
526. C3#83849semidirect

Maximal subgroups

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

subgroupindex
#105962762
C22×C3×#2142
#105948182
C2×#638332
C3×#52152
#105914442
#105914432
#105911192
#105911052
#838493
#789453