Finite Group Databasebeta

← #11866358

Subgroups — #11866358

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64160C211yesmaximal, characteristic, complemented
2C3×#5830C211yesmaximal, characteristic
3#10594828C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6#10591577C214yesmaximal, complemented
7#10591439C214yesmaximal, complemented
8#10591116C211yesmaximal, characteristic, complemented
9#10591085C211yesmaximal, characteristic, complemented
10#83391—31nomaximal
11#78864—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15#64160—24no—
16C2×#3756C2212yescomplemented
17C2×#3754C2212yescomplemented
18C2×#3748C2211yescharacteristic
19C3×#947C2212yes—
20C3×#940C2212yes—
21C3×#937—22no—
22C3×#930—22no—
23C3×#926C2211yescharacteristic
24C3×#926C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26#63957—22no—
27#63844—22no—
28#63844C2214yescomplemented
29C2×#3716—24no—
30C2×#3716C2214yes—
31C3×#835C2212yescomplemented
32C3×#832C2212yescomplemented
33Dic3⋊(C3⋊C8)C2214yescomplemented
34#63562C2214yes—
35C3×#535—31no—
36#5830D311yescharacteristic
37C2×#951—31no—
38C2×#951—31no—
39C2×#951—61no—
40C22×#214—31no—
41C22×#204—31no—
42#5516—31no—
43#5516—31no—
44C3×#416—31no—
45#5233D311yescharacteristic, complemented
46#5215—31no—
47#5102—31no—
48#5075—34no—
49#5054—34no—
50#5001—31no—
51#4999—31no—
52#4798—34no—
53#4762—34no—
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
62C22×C3⋊Dic3—21no—
63C2×#634—21no—
64C2×#634—22no—
65C2×#634D414yescomplemented
66C2×#634C2312yes—
67C2×C3×#67—24no—
68C2×C3×D12—22no—
69C2×C3×D12—22no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72#3756—24no—
73#3754—24no—
74#3748—22no—
75C2×C3⋊(C3⋊C8)C2312yes—
76C3×#217—21no—
77C3×#217D412yes—
78C3×(C2×D3)⋊C4—24no—
79C3×C4⋊Dic3D412yes—
80C3×C4⋊Dic3C2312yes—
81C3×C4×Dic3—21no—
82C3×C4×Dic3C2312yes—
83C2×C3×C3⋊C8—22no—
84C2×C3×C3⋊C8C2312yes—
85#3724—24no—
86Dic32—24no—
87#3716—28no—
88#3043—91noSylow
89C2×C3×#41—21no—
90C2×C3×#41C2×D311yescharacteristic
91C2×C3×#41C2×D311yescharacteristic
92C22×C3×D4—31no—
93C22×D12C2×D311yescharacteristic
94C22×Dic6—31no—
95C22×Dic6—31no—
96C22×Dic6—61no—
97C22×C3×C8—31no—
98C3×#127—32no—
99C3×#124—32no—
100C3×#121—62no—
101C3×#120—62no—
102C3×#117—31no—
103C3×#117—31no—
104#951—64no—
105#951—64no—
106#951—68no—
107#947C2×D312yes—
108C2×#216—32no—
109C2×#216—32no—
110C2×#216—62no—
111#940C2×D312yes—
112#937—22no—
113C2×#214—32no—
114C2×#214—32no—
115C2×#214—34no—
116C2×#214—62no—
117C2×#214—64no—
118#930—22no—
119#926C2×D311yescharacteristic
120#926C2×D311yescharacteristic
121C2×#208—31no—
122C2×#208—31no—
123C2×#208—61no—
124C22×C3⋊C8C2×D311yescharacteristic
125C2×#204—34no—
126C2×#204—64no—
127#887—34no—
128#887—62no—
129#877—62no—
130#877—62no—
131C4×Dic6—34no—
132C4×Dic6—62no—
133C3×#103—32no—
134C3×#102—32no—
135#835C2×D312yescomplemented
136#832—34no—
137#832C2×D312yescomplemented
138Dic3⋊C8—34no—
139#809—34no—
140C4⋊(C3⋊C8)—34no—
141C23×C32—21no—
142C23×C32C2×D411yescharacteristic
143C22×C3×D3—22no—
144C22×C3×D3—42no—
145C22×C3×D3—82no—
146C32×Q8—21no—
147C32×Q8—21no—
148C32×D4—21no—
149C32×D4—21no—
150C32×D4—42no—
151C2×C32×C4—21no—
152C2×C32×C4—42no—
153C2×C32×C4C2×D412yes—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4#4112yes—
156C2×C32×C4C2411yescharacteristic
157C2×C3⋊Dic3—24no—
158C2×C3⋊Dic3—22no—
159#634—24no—
160#634—22no—
161#634C2×D414yes—
162C3×#67—84no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3C2×D414yes—
165C3×D12—22no—
166C3×D12—22no—
167C3×D12—42no—
168C3⋊(C3⋊C8)—22no—
169C3×C3⋊C8—22no—
170C2×#137—91no—
171C22×SD16—91no—
172#535—31no—
173#519—91no—
174#464—94no—
175#460—94no—
176#424—91no—
177#418—91no—
178#416—31no—
179C24×C3—61no—
180C23×D3—21no—
181C3×#41—24no—
182C3×#41—22no—
183C3×#41—22no—
184C3×#41—22no—
185C3×#41—22no—
186C3×#41—42no—
187C2×C3×Q8—21no—
188C2×C3×Q8C22×D311yescharacteristic
189C2×C3×Q8C22×D311yescharacteristic
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—32no—
194C2×C3×D4—41no—
195C2×C3×D4—64no—
196C2×C3×D4—62no—
197C2×C3×D4—62no—
198C2×C3×D4—61no—
199C2×C3×D4C22×D311yescharacteristic
200C2×C3×D4C22×D311yescharacteristic
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—41no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C2×#67—24no—
208C22×Dic3—61no—
209C22×Dic3—61no—
210C22×Dic3—121no—
211C2×D12—22no—
212C2×D12—22no—
213C2×D12—21no—
214C2×D12C22×D312yes—
215C2×Dic6—34no—
216C2×Dic6—34no—
217C2×Dic6—32no—
218C2×Dic6—32no—
219C2×Dic6—62no—
220C2×Dic6—64no—
221C2×Dic6—62no—
222C2×Dic6—61no—
223C2×Dic6—62no—
224C2×Dic6—61no—
225C2×Dic6—122no—
226C2×Dic6—121no—
227C2×C3×C8—32no—
228C2×C3×C8—62no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—32no—
231C3×C22⋊C4—32no—
232C3×C22⋊C4—64no—
233C3×C22⋊C4—61no—
234C3×C42—32no—
235C3×C42—61no—
236#217—21no—
237#217#6712yes—
238#216—64no—
239#216—64no—
240#216—68no—
241#214—68no—
242#214—64no—
243#214—64no—
244#214—68no—
245(C2×D3)⋊C4—24no—
246C4⋊Dic3#6712yes—
247C4⋊Dic3C22×D312yes—
248Dic3⋊C4—64no—
249Dic3⋊C4—64no—
250C4×Dic3—21no—
251C4×Dic3—64no—
252C4×Dic3—64no—
253C4×Dic3C22×D312yes—
254#208—64no—
255#208—62no—
256#208—62no—
257C2×C3⋊C8—22no—
258C2×C3⋊C8—32no—
259C2×C3⋊C8—32no—
260C2×C3⋊C8—62no—
261C2×C3⋊C8C22×D312yes—
262#204—68no—
263C22×C32—22no—
264C22×C32—41no—
265C22×C32—42no—
266C22×C32#12112yes—
267C22×C32C22×D411yescharacteristic
268C2×C3×D3—42no—
269C2×C3×D3—44no—
270C2×C3×D3—84no—
271C32×C4—41no—
272C32×C4#12112yes—
273C32×C4C22×D411yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—24no—
276C3×Dic3—24no—
277C3×Dic3—42no—
278C2×#41D3211yescharacteristic
279C22×Q8—91no—
280C22×D4—31no—
281#137—184no—
282C2×Q16—92no—
283C2×SD16—94no—
284C2×SD16—92no—
285C2×SD16—184no—
286C2×M16—91no—
287C22×C8—31no—
288#127—32no—
289#124—32no—
290#121—62no—
291#120—62no—
292C4×Q8—94no—
293C4×Q8—182no—
294#117—31no—
295#117—31no—
296#117—182no—
297C4⋊C8—94no—
298#103—32no—
299#102—32no—
300#102—94no—
301C23×C3—21no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—41no—
305C23×C3—62no—
306C23×C3—122no—
307C23×C3—242no—
308C23×C3D3×D411yescharacteristic
309C23×C3C2×#6711yescharacteristic
310C22×D3—22no—
311C22×D3—42no—
312C22×D3—82no—
313C3×Q8—22no—
314C3×Q8—21no—
315C3×Q8—21no—
316C3×Q8—21no—
317C3×Q8—21no—
318C3×Q8—41no—
319C3×D4—22no—
320C3×D4—21no—
321C3×D4—21no—
322C3×D4—21no—
323C3×D4—21no—
324C3×D4—41no—
325C3×D4—44no—
326C3×D4—42no—
327C3×D4—42no—
328C3×D4—62no—
329C3×D4—62no—
330C3×D4—122no—
331C3×D4—244no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—34no—
339C2×C3×C4—41no—
340C2×C3×C4—44no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—62no—
344C2×C3×C4#23512yes—
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D412yes—
347C2×C3×C4D3×D412yes—
348C2×C3×C4#23712yes—
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352#67—84no—
353C2×Dic3—22no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—122no—
359C2×Dic3—124no—
360C2×Dic3C2×#6714yes—
361D12—22no—
362D12—22no—
363D12—42no—
364Dic6—34no—
365Dic6—34no—
366Dic6—64no—
367Dic6—64no—
368Dic6—64no—
369Dic6—62no—
370Dic6—62no—
371Dic6—122no—
372Dic6—124no—
373C3×C8—62no—
374C3⋊C8—22no—
375C3⋊C8—64no—
376C3⋊C8—62no—
377C3⋊C8—62no—
378C2×C32—22no—
379C2×C32—81no—
380C2×C32C2×#12111yescharacteristic
381C2×C32#57712yes—
382C3×D3—82no—
383C24—61no—
384#41—22no—
385#41—22no—
386C2×Q8—92no—
387C2×Q8—94no—
388C2×Q8—182no—
389C2×Q8—181no—
390C2×Q8C2×D3211yescharacteristic
391C2×D4—21no—
392C2×D4—32no—
393C2×D4—64no—
394C2×D4—62no—
395C2×D4—61no—
396C2×D4—62no—
397C2×D4C2×D3211yescharacteristic
398C22×C4—21no—
399C22×C4—181no—
400C22×C4C2×D3211yescharacteristic
401Q16—184no—
402SD16—188no—
403SD16—184no—
404M16—182no—
405C2×C8—32no—
406C2×C8—62no—
407C2×C8—92no—
408C4⋊C4—32no—
409C4⋊C4—32no—
410C4⋊C4—184no—
411C22⋊C4—32no—
412C22⋊C4—64no—
413C22⋊C4—61no—
414C42—32no—
415C42—61no—
416C42—184no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—21no—
420C22×C3—22no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—41no—
424C22×C3—42no—
425C22×C3—41no—
426C22×C3—42no—
427C22×C3—82no—
428C22×C3—122no—
429C22×C3—124no—
430C22×C3—244no—
431C22×C3#88412yes—
432C22×C3#93812yes—
433C22×C3C2×D3×D411yescharacteristic
434C22×C3C22×#6711yescharacteristic
435C2×D3—42no—
436C2×D3—44no—
437C2×D3—84no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—42no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4—64no—
445C3×C4—122no—
446C3×C4#88412yes—
447C3×C4#93812yes—
448C3×C4C2×#23511yescharacteristic
449C3×C4C2×D3×D411yescharacteristic
450C3×C4C2×D3×D411yescharacteristic
451C3×C4C2×#23711yescharacteristic
452Dic3—24no—
453Dic3—42no—
454Dic3—64no—
455Dic3—64no—
456Dic3—124no—
457C32#304311yescharacteristic, complemented, Sylow
458C23—21no—
459C23—62no—
460C23—122no—
461C23—242no—
462C23D3×#6711yescharacteristic
463Q8—21no—
464Q8—21no—
465Q8—94no—
466Q8—182no—
467Q8—184no—
468D4—21no—
469D4—21no—
470D4—42no—
471D4—62no—
472D4—62no—
473D4—122no—
474D4—244no—
475C2×C4—21no—
476C2×C4—34no—
477C2×C4—42no—
478C2×C4—62no—
479C2×C4—182no—
480C2×C4—184no—
481C2×C4#380412yes—
482C2×C4D3×#6711yescharacteristic
483C2×C4#381112yes—
484C2×C4C22×D3211yescharacteristic
485C8—62no—
486C8—182no—
487C2×C3—22no—
488C2×C3—22no—
489C2×C3—22no—
490C2×C3—21no—
491C2×C3—42no—
492C2×C3—82no—
493C2×C3—81no—
494C2×C3—81no—
495C2×C3—242no—
496C2×C3C2×#88411yescharacteristic
497C2×C3#577012yes—
498C2×C3C2×#93811yescharacteristic
499C2×C3#583612yes—
500D3—82no—
501C22—22no—
502C22—42no—
503C22—41no—
504C22—124no—
505C22—122no—
506C22—244no—
507C22#6395812yes—
508C22C2×D3×#6711yescharacteristic
509C4—41no—
510C4—64no—
511C4—122no—
512C4—184no—
513C4#6395812yes—
514C4C2×#380411yescharacteristic
515C4C2×#381111yescharacteristic
516C3—21no—
517C3#7886411yescharacteristic, complemented
518C3#8339111yescharacteristic, complemented
519C2—22no—
520C2—81no—
521C2—242no—
522C2#1059546612yes—
523C2C2×#6395811yescharacteristic
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
1. C2×#64160C2semidirect
3. #10594828C2semidirect
4. C22×#3716C2semidirect
5. C3×#5233C2semidirect
6. #10591577C2semidirect
7. #10591439C2semidirect
8. #10591116C2semidirect
9. #10591085C2semidirect
16. C2×#3756C22semidirect
17. C2×#3754C22semidirect
28. #63844C22semidirect
31. C3×#835C22semidirect
32. C3×#832C22semidirect
33. Dic3⋊(C3⋊C8)C22semidirect
45. #5233D3semidirect
65. C2×#634D4semidirect
135. #835C2×D3semidirect
137. #832C2×D3semidirect
457. C32#3043semidirect
517. C3#78864semidirect
518. C3#83391semidirect

Maximal subgroups

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

subgroupindex
C2×#641602
C3×#58302
#105948282
C22×#37162
C3×#52332
#105915772
#105914392
#105911162
#105910852
#833913
#788643