Finite Group Databasebeta

← #11866355

Subgroups — #11866355

Order 1152.

1113 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596283C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic, complemented
3C22×C3×#215C211yesmaximal, characteristic, complemented
4#10595040C211yesmaximal, characteristic
5#10591622C214yesmaximal, complemented
6#10591612C214yesmaximal, complemented
7#10591119C211yesmaximal, characteristic, complemented
8#10591086C211yesmaximal, characteristic, complemented
9#10591084C211yesmaximal, characteristic, complemented
10#83969—31nomaximal
11#83849—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15Q8×C3⋊Dic3—22no—
16Q8×C3⋊Dic3C2214yescomplemented
17#64135—22no—
18#64135C2211yescharacteristic
19#64135C2211yescharacteristic
20C2×C3×#216C2212yescomplemented
21C3×#942—24no—
22C2×C3×#215—24no—
23C2×C3×#215C2214yes—
24C2×C3×#215C2212yescomplemented
25C2×C3×#208C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27#63976—22no—
28#63914C2212yes—
29#63908—22no—
30#63863C2212yes—
31#63572C2214yescomplemented
32#63566C2212yescomplemented
33#63563C2214yes—
34#63563C2212yescomplemented
35C2×C3×#137—31no—
36C22×C3×SD16—31no—
37#5830—31no—
38#5812—31no—
39#5812—31no—
40#5812—61no—
41C2×#942D311yescharacteristic, complemented
42C22×#215D311yescharacteristic, complemented
43#5805—31no—
44#5233—31no—
45#5215—31no—
46#5185—34no—
47#5166—34no—
48#5163—34no—
49#5163—34no—
50#5131—31no—
51#5119—31no—
52#5113—31no—
53#5102—31no—
54C23×C3×D3—21no—
55C2×C32×Q8—21no—
56C2×C32×Q8—22no—
57C2×C32×Q8D414yescomplemented
58C2×C32×Q8C2312yes—
59C22×C32×C4—21no—
60C22×C32×C4C2311yescharacteristic
61C2×C3×#67—21no—
62C3×#235—22no—
63C3×#235—22no—
64C2×C3×D12—22no—
65C2×C3×D12—22no—
66C2×C3×D12—21no—
67C2×C3×D12C2312yes—
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6C2311yescharacteristic
71C2×#625—24no—
72#3757—21no—
73#3757D412yes—
74C4⋊(C3⋊Dic3)—24no—
75C4⋊(C3⋊Dic3)D412yes—
76C4⋊(C3⋊Dic3)C2312yes—
77C4×C3⋊Dic3—21no—
78C4×C3⋊Dic3—24no—
79C4×C3⋊Dic3C2312yes—
80C3×#216—24no—
81C3×#215—28no—
82C3×#215—24no—
83C3×#208—22no—
84C2×C3×C3⋊C8—22no—
85C2×C3×C3⋊C8C2312yes—
86C2×C3×C3⋊C8C2312yes—
87(C2×D3)⋊Dic3—24no—
88#3043—91noSylow
89C2×C3×#41—31no—
90C22×C3×Q8—21no—
91C22×C3×Q8C2×D311yescharacteristic
92C22×C3×Q8C2×D311yescharacteristic
93C22×C3×D4—31no—
94C2×#235C2×D311yescharacteristic
95C22×D12C2×D311yescharacteristic
96C3×#137—64no—
97C2×C3×Q16—32no—
98C2×C3×SD16—34no—
99C2×C3×SD16—32no—
100C2×C3×SD16—64no—
101C2×C3×M16—31no—
102C22×C3×C8—31no—
103#953—62no—
104#947—32no—
105Q8×Dic3—34no—
106Q8×Dic3—34no—
107Q8×Dic3—64no—
108Q8×Dic3—62no—
109Q8×Dic3—62no—
110Q8×Dic3—64no—
111C2×#216C2×D312yescomplemented
112#942—24no—
113C2×#215—24no—
114C2×#215C2×D314yes—
115C2×#215C2×D312yescomplemented
116#940—32no—
117#940—32no—
118#938—62no—
119#937—62no—
120#936—32no—
121#930—62no—
122#926—31no—
123#926—31no—
124#926—31no—
125#926—31no—
126#926—61no—
127#926—61no—
128#926—62no—
129#926—62no—
130#926—64no—
131C2×#208C2×D311yescharacteristic
132C22×C3⋊C8C2×D311yescharacteristic
133#835—32no—
134#832—32no—
135#832—34no—
136#821—34no—
137#821—32no—
138#816—32no—
139Dic3⋊C8—34no—
140Dic3⋊C8—34no—
141C23×C32C2×D411yescharacteristic
142C22×C3×D3—22no—
143C22×C3×D3—21no—
144C22×C3×D3—42no—
145C22×C3×D3—82no—
146C32×Q8—24no—
147C32×Q8—22no—
148C32×Q8C2×D414yes—
149C2×C32×C4—24no—
150C2×C32×C4—22no—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D412yes—
153C2×C32×C4#4112yes—
154C2×C32×C4C2411yescharacteristic
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3C2×D414yes—
157C3×#67—42no—
158C2×C3×Dic3—21no—
159C3×D12—22no—
160C3×D12—21no—
161C3×D12—22no—
162C3×D12—21no—
163C3×D12—42no—
164C3×C4×D3—42no—
165C3×Dic6—21no—
166C3×Dic6—21no—
167#625—84no—
168C3×C3⋊C8—22no—
169C3×C3⋊C8—22no—
170C2×#137—31no—
171C22×SD16—31no—
172#535—91no—
173#519—91no—
174#464—94no—
175#460—94no—
176#424—91no—
177#418—91no—
178#416—91no—
179C24×C3—61no—
180C23×D3—21no—
181C3×#41—62no—
182C3×#41—62no—
183C2×C3×Q8—22no—
184C2×C3×Q8—24no—
185C2×C3×Q8—21no—
186C2×C3×Q8—21no—
187C2×C3×Q8—22no—
188C2×C3×Q8—22no—
189C2×C3×Q8—24no—
190C2×C3×Q8—22no—
191C2×C3×Q8—31no—
192C2×C3×Q8#6714yescomplemented
193C2×C3×Q8#6714yescomplemented
194C2×C3×Q8C22×D312yes—
195C2×C3×Q8C22×D312yes—
196C2×C3×D4—32no—
197C2×C3×D4—31no—
198C2×C3×D4—61no—
199C2×C3×D4—61no—
200C2×C3×D4—62no—
201C2×C3×D4—62no—
202C22×C3×C4—22no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—61no—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C2×#67—21no—
210C2×#67—64no—
211C2×#67—64no—
212#235—22no—
213#235—22no—
214C2×D12—22no—
215C2×D12—22no—
216C2×D12—21no—
217C2×D12C22×D311yescharacteristic
218C2×D12C22×D312yes—
219C2×C4×D3—21no—
220C2×Dic6C22×D311yescharacteristic
221C3×Q16—64no—
222C3×SD16—68no—
223C3×SD16—64no—
224C3×M16—62no—
225C2×C3×C8—32no—
226C2×C3×C8—32no—
227C2×C3×C8—62no—
228#217—32no—
229#217—32no—
230#217—62no—
231#217—64no—
232#217—62no—
233#217—61no—
234#217—61no—
235#216—24no—
236#215—28no—
237#215—24no—
238(C2×D3)⋊C4—64no—
239C4⋊Dic3—32no—
240C4⋊Dic3—32no—
241C4⋊Dic3—32no—
242C4⋊Dic3—32no—
243C4⋊Dic3—62no—
244C4⋊Dic3—62no—
245C4⋊Dic3—64no—
246C4⋊Dic3—64no—
247C4⋊Dic3—68no—
248C4×Dic3—32no—
249C4×Dic3—32no—
250C4×Dic3—62no—
251C4×Dic3—64no—
252C4×Dic3—64no—
253C4×Dic3—68no—
254C4×Dic3—62no—
255C4×Dic3—61no—
256C4×Dic3—61no—
257#208—22no—
258C2×C3⋊C8—22no—
259C2×C3⋊C8C22×D312yes—
260C2×C3⋊C8C22×D312yes—
261C22×C32—22no—
262C22×C32#12112yes—
263C22×C32C22×D411yescharacteristic
264C2×C3×D3—41no—
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C2×C3×D3—44no—
268C2×C3×D3—84no—
269C32×C4—24no—
270C32×C4#12112yes—
271C32×C4C22×D411yescharacteristic
272C32×C4C2×#4111yescharacteristic
273C3⋊Dic3—24no—
274C3⋊Dic3—42no—
275C3×Dic3—41no—
276C2×#41—31no—
277C22×Q8D3211yescharacteristic
278C22×D4—31no—
279#137—64no—
280C2×Q16—32no—
281C2×SD16—34no—
282C2×SD16—32no—
283C2×SD16—64no—
284C2×M16—31no—
285C22×C8—31no—
286#127—92no—
287#124—92no—
288#121—182no—
289#120—182no—
290C4×Q8—94no—
291C4×Q8—182no—
292#117—91no—
293#117—91no—
294#117—182no—
295C4⋊C8—94no—
296#103—92no—
297#102—92no—
298#102—94no—
299C23×C3—21no—
300C23×C3—62no—
301C23×C3—61no—
302C23×C3—122no—
303C23×C3—242no—
304C23×C3D3×D411yescharacteristic
305C23×C3D3×D411yescharacteristic
306C22×D3—22no—
307C22×D3—21no—
308C22×D3—42no—
309C22×D3—82no—
310C3×Q8—24no—
311C3×Q8—28no—
312C3×Q8—24no—
313C3×Q8—24no—
314C3×Q8—22no—
315C3×Q8—22no—
316C3×Q8—24no—
317C3×Q8—61no—
318C3×Q8—61no—
319C3×Q8C2×#6714yes—
320C3×Q8C2×#6714yes—
321C3×D4—62no—
322C3×D4—61no—
323C3×D4—62no—
324C3×D4—61no—
325C3×D4—122no—
326C3×D4—122no—
327C2×C3×C4—24no—
328C2×C3×C4—28no—
329C2×C3×C4—24no—
330C2×C3×C4—24no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—61no—
338C2×C3×C4—122no—
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4#23712yes—
342C2×C3×C4#23712yes—
343C2×C3×C4C2×#6712yes—
344C2×C3×C4C2×#6712yes—
345C2×C3×C4C23×D311yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347#67—42no—
348#67—244no—
349#67—244no—
350C2×Dic3—21no—
351C2×Dic3—34no—
352C2×Dic3—34no—
353C2×Dic3—64no—
354C2×Dic3—64no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357D12—22no—
358D12—21no—
359D12—22no—
360D12—21no—
361D12—42no—
362C4×D3—42no—
363Dic6—21no—
364Dic6—21no—
365C3×C8—62no—
366C3×C8—62no—
367C3⋊C8—22no—
368C3⋊C8—22no—
369C2×C32—22no—
370C2×C32C2×#12111yescharacteristic
371C2×C32#57712yes—
372C3×D3—81no—
373C3×D3—82no—
374C24—61no—
375#41—62no—
376#41—62no—
377C2×Q8—22no—
378C2×Q8—21no—
379C2×Q8—31no—
380C2×Q8#62514yescomplemented
381C2×Q8C2×D3212yes—
382C2×D4—32no—
383C2×D4—31no—
384C2×D4—61no—
385C2×D4—62no—
386C2×D4—62no—
387C2×D4—61no—
388C2×D4—184no—
389C22×C4—21no—
390C22×C4—61no—
391C22×C4C2×D3211yescharacteristic
392Q16—64no—
393SD16—68no—
394SD16—64no—
395M16—62no—
396C2×C8—32no—
397C2×C8—32no—
398C2×C8—62no—
399C4⋊C4—92no—
400C4⋊C4—92no—
401C4⋊C4—184no—
402C22⋊C4—92no—
403C22⋊C4—184no—
404C22⋊C4—181no—
405C42—92no—
406C42—184no—
407C42—181no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—21no—
411C22×C3—22no—
412C22×C3—42no—
413C22×C3—122no—
414C22×C3—124no—
415C22×C3—121no—
416C22×C3—122no—
417C22×C3—244no—
418C22×C3#93912yes—
419C22×C3#93912yes—
420C22×C3C2×D3×D411yescharacteristic
421C22×C3C2×D3×D411yescharacteristic
422C2×D3—44no—
423C2×D3—42no—
424C2×D3—41no—
425C2×D3—42no—
426C2×D3—84no—
427C3×C4—28no—
428C3×C4—24no—
429C3×C4—24no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—22no—
433C3×C4—121no—
434C3×C4#93912yes—
435C3×C4#93912yes—
436C3×C4C2×#23711yescharacteristic
437C3×C4C2×#23711yescharacteristic
438C3×C4C22×#6711yescharacteristic
439C3×C4C22×#6711yescharacteristic
440Dic3—41no—
441Dic3—64no—
442Dic3—64no—
443Dic3—124no—
444Dic3—124no—
445Dic3—122no—
446Dic3—122no—
447C32#304311yescharacteristic, complemented, Sylow
448C23—62no—
449C23—61no—
450C23—122no—
451C23—242no—
452C23#381111yescharacteristic
453Q8—22no—
454Q8—24no—
455Q8—61no—
456Q8—61no—
457Q8C2×#62514yes—
458D4—62no—
459D4—61no—
460D4—62no—
461D4—61no—
462D4—122no—
463D4—122no—
464D4—724no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—61no—
468C2×C4—94no—
469C2×C4—122no—
470C2×C4—182no—
471C2×C4#380512yes—
472C2×C4C2×#62512yes—
473C2×C4#381111yescharacteristic
474C2×C4C22×D3211yescharacteristic
475C8—62no—
476C8—62no—
477C2×C3—22no—
478C2×C3—22no—
479C2×C3—21no—
480C2×C3—22no—
481C2×C3—42no—
482C2×C3—242no—
483C2×C3—241no—
484C2×C3#576212yes—
485C2×C3#577812yes—
486C2×C3C2×#93911yescharacteristic
487C2×C3C2×#93911yescharacteristic
488D3—81no—
489D3—82no—
490C22—22no—
491C22—121no—
492C22—122no—
493C22—122no—
494C22—124no—
495C22—244no—
496C22#6398012yes—
497C22C2×#381111yescharacteristic
498C4—24no—
499C4—121no—
500C4—184no—
501C4—362no—
502C4#6398012yes—
503C4C2×#380511yescharacteristic
504C4C22×#62511yescharacteristic
505C3—21no—
506C3#8384911yescharacteristic, complemented
507C3#8396911yescharacteristic, complemented
508C2—22no—
509C2—242no—
510C2—241no—
511C2#1059532412yes—
512C2C2×#6398011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radical#10595040C2
hypercenterC22×Q8D32
hypocenterC32#3043
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. #10596283C2semidirect
2. C2×C3×#942C2semidirect
3. C22×C3×#215C2semidirect
5. #10591622C2semidirect
6. #10591612C2semidirect
7. #10591119C2semidirect
8. #10591086C2semidirect
9. #10591084C2semidirect
16. Q8×C3⋊Dic3C22semidirect
20. C2×C3×#216C22semidirect
24. C2×C3×#215C22semidirect
31. #63572C22semidirect
32. #63566C22semidirect
34. #63563C22semidirect
41. C2×#942D3semidirect
42. C22×#215D3semidirect
57. C2×C32×Q8D4semidirect
111. C2×#216C2×D3semidirect
115. C2×#215C2×D3semidirect
192. C2×C3×Q8#67semidirect
193. C2×C3×Q8#67semidirect
380. C2×Q8#625semidirect
447. C32#3043semidirect
506. C3#83849semidirect
507. C3#83969semidirect

Maximal subgroups

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

subgroupindex
#105962832
C2×C3×#9422
C22×C3×#2152
#105950402
#105916222
#105916122
#105911192
#105910862
#105910842
#839693
#838493