Finite Group Databasebeta

← #11866359

Subgroups — #11866359

Order 1152.

1059 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5830C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3#10594818C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5#10592932C211yesmaximal, characteristic, complemented
6#10591578C214yesmaximal, complemented
7#10591438C214yesmaximal, complemented
8#10591117C211yesmaximal, characteristic, complemented
9#10591086C211yesmaximal, characteristic, complemented
10#83969—31nomaximal
11#83391—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15#64135C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#951—24no—
18C3×#947C2212yes—
19C2×C3×#216C2212yescomplemented
20C3×#940C2212yes—
21C3×#937—22no—
22C2×C3×#214C2212yescomplemented
23C3×#930—22no—
24C3×#926C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26#63955—22no—
27#63843—22no—
28Dic3×Dic6C2214yescomplemented
29C2×#3715—24no—
30C2×#3715C2214yes—
31#63662C2212yescomplemented
32#63659C2212yescomplemented
33Dic3⋊(C3⋊C8)C2214yescomplemented
34#63563C2214yes—
35C2×C3×#137—31no—
36C3×#535—31no—
37#5830D311yescharacteristic
38C2×#951D311yescharacteristic, complemented
39#5812—31no—
40C22×#215—31no—
41C22×#214—31no—
42#5516—31no—
43#5233—31no—
44#5233—31no—
45#5233—61no—
46#5215—31no—
47#5185—34no—
48#5163—34no—
49#5131—31no—
50#5119—31no—
51#5075—34no—
52#5054—34no—
53#4999—31no—
54C23×C3×D3—21no—
55C32×#41—22no—
56C32×#41—22no—
57C2×C32×Q8C2311yescharacteristic
58C2×C32×D4—21no—
59C2×C32×D4C2311yescharacteristic
60C22×C32×C4—21no—
61C22×C32×C4C2311yescharacteristic
62C2×C3×#67—24no—
63C22×C3×Dic3—21no—
64C2×C3×D12—22no—
65C2×C3×D12—22no—
66C2×C3×D12—21no—
67C2×C3×D12C2312yes—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6D414yescomplemented
71C2×C3×Dic6C2312yes—
72#3757—21no—
73C4⋊(C3⋊Dic3)C2312yes—
74C4×C3⋊Dic3—21no—
75C2×C3⋊(C3⋊C8)—22no—
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×#217D412yes—
78C3×#216—24no—
79C3×#214—24no—
80C3×(C2×D3)⋊C4—24no—
81C3×C4⋊Dic3D412yes—
82C3×C4×Dic3C2312yes—
83C3×#208—22no—
84C2×C3×C3⋊C8C2312yes—
85Dic3⋊Dic3—24no—
86Dic32—24no—
87#3715—28no—
88#3043—91noSylow
89C2×C3×#41—21no—
90C2×C3×#41C2×D311yescharacteristic
91C2×C3×#41C2×D311yescharacteristic
92C22×C3×Q8—31no—
93C22×C3×D4—31no—
94C22×D12C2×D311yescharacteristic
95C22×Dic6C2×D311yescharacteristic
96C3×#137—64no—
97C2×C3×Q16—32no—
98C2×C3×SD16—32no—
99C2×C3×M16—31no—
100C3×#127—32no—
101C3×#124—32no—
102C3×#121—62no—
103C3×#120—62no—
104C3×#117—31no—
105#951—24no—
106#947C2×D312yes—
107Q8×Dic3—34no—
108Q8×Dic3—62no—
109C2×#216C2×D312yescomplemented
110C2×#215—34no—
111C2×#215—64no—
112#940C2×D312yes—
113#937—22no—
114C2×#214—34no—
115C2×#214—64no—
116C2×#214C2×D312yescomplemented
117#930—22no—
118#926—31no—
119#926—31no—
120#926—61no—
121#926—62no—
122#926C2×D311yescharacteristic
123C2×#208C2×D311yescharacteristic
124C22×C3⋊C8—31no—
125C22×C3⋊C8—31no—
126C22×C3⋊C8—61no—
127#887—62no—
128#877—62no—
129C4×Dic6—34no—
130#835—32no—
131#835—32no—
132#835—62no—
133#832—32no—
134#832—32no—
135#832—34no—
136#832—62no—
137#821—34no—
138Dic3⋊C8—34no—
139C4⋊(C3⋊C8)—34no—
140C23×C32—21no—
141C23×C32C2×D411yescharacteristic
142C22×C3×D3—22no—
143C22×C3×D3—42no—
144C22×C3×D3—82no—
145C32×Q8—21no—
146C32×Q8—21no—
147C32×D4—21no—
148C32×D4—21no—
149C32×D4—42no—
150C2×C32×C4—21no—
151C2×C32×C4—42no—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D412yes—
154C2×C32×C4#4112yes—
155C2×C32×C4C2411yescharacteristic
156C2×C3⋊Dic3—22no—
157C3×#67—84no—
158C2×C3×Dic3—24no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3C2×D414yes—
161C3×D12—22no—
162C3×D12—22no—
163C3×D12—42no—
164C3×Dic6—24no—
165C3×Dic6—22no—
166C3×Dic6C2×D414yes—
167C3⋊(C3⋊C8)—22no—
168C3×C3⋊C8—22no—
169C2×#137—31no—
170C22×SD16—91no—
171#535—31no—
172#519—91no—
173#464—94no—
174#460—94no—
175#424—91no—
176#418—91no—
177#416—91no—
178C24×C3—61no—
179C23×D3—21no—
180C3×#41—24no—
181C3×#41—22no—
182C3×#41—22no—
183C3×#41—22no—
184C3×#41—22no—
185C3×#41—42no—
186C2×C3×Q8—21no—
187C2×C3×Q8—34no—
188C2×C3×Q8—32no—
189C2×C3×Q8—62no—
190C2×C3×Q8—61no—
191C2×C3×Q8C22×D311yescharacteristic
192C2×C3×Q8C22×D311yescharacteristic
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—32no—
197C2×C3×D4—41no—
198C2×C3×D4—64no—
199C2×C3×D4—61no—
200C2×C3×D4—62no—
201C2×C3×D4—62no—
202C2×C3×D4C22×D311yescharacteristic
203C2×C3×D4C22×D311yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—41no—
208C22×C3×C4—61no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C2×#67—24no—
212C22×Dic3—21no—
213C2×D12—22no—
214C2×D12—22no—
215C2×D12—21no—
216C2×D12C22×D312yes—
217C2×Dic6—21no—
218C2×Dic6—22no—
219C2×Dic6#6714yescomplemented
220C2×Dic6C22×D312yes—
221C3×Q16—64no—
222C3×SD16—64no—
223C3×M16—62no—
224C2×C3×C8—32no—
225C3×C4⋊C4—32no—
226C3×C22⋊C4—32no—
227C3×C22⋊C4—64no—
228C3×C42—32no—
229#217—61no—
230#217—61no—
231#217—121no—
232#217#6712yes—
233#216—24no—
234#215—68no—
235#214—24no—
236#214—68no—
237(C2×D3)⋊C4—24no—
238C4⋊Dic3—32no—
239C4⋊Dic3—32no—
240C4⋊Dic3—62no—
241C4⋊Dic3—64no—
242C4⋊Dic3#6712yes—
243Dic3⋊C4—64no—
244C4×Dic3—64no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—64no—
248C4×Dic3—121no—
249C4×Dic3C22×D312yes—
250#208—22no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—62no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8—122no—
257C2×C3⋊C8C22×D312yes—
258C22×C32—22no—
259C22×C32—41no—
260C22×C32—42no—
261C22×C32#12112yes—
262C22×C32C22×D411yescharacteristic
263C2×C3×D3—42no—
264C2×C3×D3—44no—
265C2×C3×D3—84no—
266C32×C4—41no—
267C32×C4#12112yes—
268C32×C4C22×D411yescharacteristic
269C32×C4C2×#4111yescharacteristic
270C3⋊Dic3—42no—
271C3×Dic3—24no—
272C3×Dic3—24no—
273C2×#41D3211yescharacteristic
274C22×Q8—31no—
275C22×D4—31no—
276#137—64no—
277C2×Q16—32no—
278C2×SD16—32no—
279C2×SD16—94no—
280C2×SD16—184no—
281C2×M16—31no—
282C22×C8—91no—
283#127—32no—
284#124—32no—
285#121—62no—
286#120—62no—
287C4×Q8—94no—
288C4×Q8—182no—
289#117—31no—
290#117—91no—
291#117—182no—
292C4⋊C8—94no—
293#103—92no—
294#102—94no—
295#102—92no—
296C23×C3—21no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—41no—
300C23×C3—62no—
301C23×C3—122no—
302C23×C3—242no—
303C23×C3D3×D411yescharacteristic
304C23×C3C2×#6711yescharacteristic
305C22×D3—22no—
306C22×D3—42no—
307C22×D3—82no—
308C3×Q8—22no—
309C3×Q8—21no—
310C3×Q8—21no—
311C3×Q8—21no—
312C3×Q8—21no—
313C3×Q8—34no—
314C3×Q8—41no—
315C3×Q8—64no—
316C3×Q8—62no—
317C3×D4—22no—
318C3×D4—21no—
319C3×D4—21no—
320C3×D4—21no—
321C3×D4—21no—
322C3×D4—41no—
323C3×D4—44no—
324C3×D4—42no—
325C3×D4—42no—
326C3×D4—62no—
327C3×D4—62no—
328C3×D4—122no—
329C3×D4—244no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—34no—
337C2×C3×C4—41no—
338C2×C3×C4—44no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—64no—
342C2×C3×C4—62no—
343C2×C3×C4D3×D412yes—
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4#23712yes—
346C2×C3×C4#23712yes—
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6712yes—
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351#67—84no—
352C2×Dic3—24no—
353C2×Dic3—22no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—122no—
357C2×Dic3C2×#6714yes—
358D12—22no—
359D12—22no—
360D12—42no—
361Dic6—24no—
362Dic6—22no—
363Dic6C2×#6714yes—
364C3×C8—62no—
365C3⋊C8—22no—
366C3⋊C8—62no—
367C3⋊C8—62no—
368C3⋊C8—122no—
369C2×C32—22no—
370C2×C32—81no—
371C2×C32C2×#12111yescharacteristic
372C2×C32#57712yes—
373C3×D3—82no—
374C24—61no—
375#41—22no—
376#41—22no—
377C2×Q8—32no—
378C2×Q8—34no—
379C2×Q8—62no—
380C2×Q8—61no—
381C2×Q8C2×D3211yescharacteristic
382C2×D4—21no—
383C2×D4—32no—
384C2×D4—64no—
385C2×D4—62no—
386C2×D4—62no—
387C2×D4—61no—
388C2×D4C2×D3211yescharacteristic
389C22×C4—21no—
390C22×C4—61no—
391C22×C4C2×D3211yescharacteristic
392Q16—64no—
393SD16—64no—
394SD16—188no—
395M16—62no—
396C2×C8—32no—
397C2×C8—92no—
398C2×C8—182no—
399C4⋊C4—32no—
400C4⋊C4—92no—
401C4⋊C4—184no—
402C22⋊C4—32no—
403C22⋊C4—64no—
404C22⋊C4—181no—
405C42—32no—
406C42—184no—
407C42—181no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—21no—
411C22×C3—22no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—42no—
418C22×C3—82no—
419C22×C3—124no—
420C22×C3—122no—
421C22×C3—244no—
422C22×C3#93812yes—
423C22×C3#93912yes—
424C22×C3C2×D3×D411yescharacteristic
425C22×C3C22×#6711yescharacteristic
426C2×D3—42no—
427C2×D3—44no—
428C2×D3—84no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—42no—
433C3×C4—41no—
434C3×C4—41no—
435C3×C4—64no—
436C3×C4—64no—
437C3×C4#93812yes—
438C3×C4#93912yes—
439C3×C4C2×D3×D411yescharacteristic
440C3×C4C2×#23711yescharacteristic
441C3×C4C2×#23711yescharacteristic
442C3×C4C22×#6711yescharacteristic
443Dic3—24no—
444Dic3—24no—
445Dic3—122no—
446Dic3—122no—
447Dic3—242no—
448C32#304311yescharacteristic, complemented, Sylow
449C23—21no—
450C23—62no—
451C23—122no—
452C23—242no—
453C23D3×#6711yescharacteristic
454Q8—21no—
455Q8—21no—
456Q8—34no—
457Q8—62no—
458Q8—64no—
459D4—21no—
460D4—21no—
461D4—42no—
462D4—62no—
463D4—62no—
464D4—122no—
465D4—244no—
466C2×C4—21no—
467C2×C4—34no—
468C2×C4—42no—
469C2×C4—62no—
470C2×C4—64no—
471C2×C4—182no—
472C2×C4#380512yes—
473C2×C4D3×#6712yes—
474C2×C4D3×#6711yescharacteristic
475C2×C4C22×D3211yescharacteristic
476C8—62no—
477C8—182no—
478C2×C3—22no—
479C2×C3—22no—
480C2×C3—22no—
481C2×C3—21no—
482C2×C3—42no—
483C2×C3—82no—
484C2×C3—81no—
485C2×C3—81no—
486C2×C3—242no—
487C2×C3#577812yes—
488C2×C3C2×#93811yescharacteristic
489C2×C3C2×#93911yescharacteristic
490C2×C3#583612yes—
491D3—82no—
492C22—22no—
493C22—42no—
494C22—41no—
495C22—124no—
496C22—122no—
497C22—244no—
498C22#6397012yes—
499C22C2×D3×#6711yescharacteristic
500C4—41no—
501C4—64no—
502C4—64no—
503C4—362no—
504C4#6397012yes—
505C4C2×#380511yescharacteristic
506C4C2×D3×#6711yescharacteristic
507C3—21no—
508C3#8339111yescharacteristic, complemented
509C3#8396911yescharacteristic, complemented
510C2—22no—
511C2—81no—
512C2—242no—
513C2#1059546412yes—
514C2C2×#6397011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC3×#5830C2
hypercenterC2×#41D32
hypocenterC32#3043
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#951C2semidirect
3. #10594818C2semidirect
4. C22×#3715C2semidirect
5. #10592932C2semidirect
6. #10591578C2semidirect
7. #10591438C2semidirect
8. #10591117C2semidirect
9. #10591086C2semidirect
19. C2×C3×#216C22semidirect
22. C2×C3×#214C22semidirect
28. Dic3×Dic6C22semidirect
31. #63662C22semidirect
32. #63659C22semidirect
33. Dic3⋊(C3⋊C8)C22semidirect
38. C2×#951D3semidirect
70. C2×C3×Dic6D4semidirect
109. C2×#216C2×D3semidirect
116. C2×#214C2×D3semidirect
219. C2×Dic6#67semidirect
448. C32#3043semidirect
508. C3#83391semidirect
509. C3#83969semidirect

Maximal subgroups

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

subgroupindex
C3×#58302
C2×C3×#9512
#105948182
C22×#37152
#105929322
#105915782
#105914382
#105911172
#105910862
#839693
#833913