Finite Group Databasebeta

← #11866201

Subgroups — #11866201

Order 1152.

1219 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595996C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5C3×#4999C211yesmaximal, characteristic, complemented
6#10591105C211yesmaximal, characteristic, complemented
7#10591096C211yesmaximal, characteristic, complemented
8#10590366C214yesmaximal, complemented
9#10590349C214yesmaximal, complemented
10#82540—31nomaximal
11#79086—31nomaximal
12C2×#3828C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C32×#117C2211yescharacteristic
16#64104—22no—
17#64091—22no—
18#64084C2212yescomplemented
19#64083C2212yescomplemented
20C3×#926C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C3×#893—22no—
24C3×D3×C22⋊C4—22no—
25C3×C4×D12C2214yescomplemented
26#63830—24no—
27C2×#3716C2212yescomplemented
28C2×#3714—24no—
29C2×#3714C2214yes—
30C2×#3714C2212yescomplemented
31C3×C4⋊(C3⋊C8)C2214yescomplemented
32#63567C2212yescomplemented
33#63564C2214yescomplemented
34#63564C2212yescomplemented
35C3×#518—31no—
36C2×#932—31no—
37C22×#213—31no—
38C2×#908—31no—
39C22×D24—31no—
40#5525—31no—
41#5525—31no—
42#5525—61no—
43#5521D311yescharacteristic, complemented
44C3×#424—31no—
45#5131—31no—
46#5113—31no—
47#5016—34no—
48#5015—34no—
49#5002—31no—
50#5001—31no—
51#4999D311yescharacteristic, complemented
52#4844—34no—
53#4843—34no—
54C23×C3⋊D3—21no—
55C23×C3×D3—21no—
56C22×C32×C4C2311yescharacteristic
57C2×#638—21no—
58#3828—22no—
59#3828—22no—
60C2×C4⋊(C3⋊D3)—22no—
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)—24no—
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×C4⋊(C3⋊D3)C2311yescharacteristic
66C2×C4×C3⋊D3—21no—
67C2×#634C2311yescharacteristic
68C2×C3×D12—21no—
69C2×C3×D12—22no—
70C2×C3×D12D414yescomplemented
71C2×C3×D12C2312yes—
72C2×C3×C4×D3—24no—
73C32×C4⋊C4D412yes—
74C32×C22⋊C4D412yes—
75C32×C42C2312yes—
76#3752—24no—
77C3×#217—21no—
78C3×(C2×D3)⋊C4—24no—
79C3×C4⋊Dic3C2312yes—
80C3×C4×Dic3—21no—
81C3×#208—22no—
82C2×C3×C3⋊C8—22no—
83C2×C3×C3⋊C8C2312yes—
84C2×C3×C3⋊C8C2312yes—
85#3716—24no—
86#3714—28no—
87#3714—24no—
88#3041—91noSylow
89C22×C3×D4—31no—
90C2×#235—31no—
91C2×#235—31no—
92C2×#235—61no—
93C22×D12—31no—
94C22×D12—31no—
95C22×D12—61no—
96C22×D12C2×D311yescharacteristic
97C2×C3×M16—31no—
98C22×C3×C8—31no—
99C3×C4×D4—34no—
100C3×C4×D4—62no—
101C3×#117—21no—
102C3×#117—31no—
103C3×#117C2×D311yescharacteristic
104C3×#117C2×D311yescharacteristic
105C2×C3×C22⋊C4—62no—
106C2×#214—32no—
107#932—64no—
108C2×#213—34no—
109C2×#213—32no—
110C2×#213—64no—
111#926C2×D311yescharacteristic
112C2×#208C2×D311yescharacteristic
113C22×C3⋊C8C2×D311yescharacteristic
114#908—64no—
115C2×D24—34no—
116C2×D24—32no—
117C2×D24—64no—
118C2×#204—32no—
119#895—64no—
120#895—62no—
121#895—62no—
122#893—22no—
123#882—64no—
124#882—62no—
125#882—62no—
126D3×C22⋊C4—22no—
127#875—32no—
128#875—32no—
129#875—62no—
130#874—32no—
131#874—32no—
132#874—62no—
133C4×D12C2×D314yescomplemented
134C3×C4⋊C8—34no—
135#821—34no—
136#821—32no—
137#816—32no—
138#810—32no—
139#809—34no—
140#809—32no—
141C4⋊(C3⋊C8)C2×D314yescomplemented
142C23×C32C2×D411yescharacteristic
143C22×C3⋊D3—22no—
144C22×C3⋊D3—21no—
145C22×C3⋊D3—42no—
146C22×C3⋊D3—82no—
147C22×C3×D3—22no—
148C22×C3×D3—24no—
149C22×C3×D3—82no—
150C2×C32×C4C2×D412yes—
151C2×C32×C4C2×D414yes—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4#4112yes—
154C2×C32×C4C2411yescharacteristic
155#638—42no—
156C2×C3⋊Dic3—21no—
157C4⋊(C3⋊D3)—22no—
158C4⋊(C3⋊D3)—21no—
159C4⋊(C3⋊D3)—22no—
160C4⋊(C3⋊D3)—21no—
161C4⋊(C3⋊D3)—42no—
162C4⋊(C3⋊D3)—84no—
163C4×C3⋊D3—42no—
164#634—21no—
165#634—21no—
166C2×C3×Dic3—22no—
167C3×D12—24no—
168C3×D12—22no—
169C3×D12C2×D414yes—
170C3×C4×D3—84no—
171C3×C3⋊C8—22no—
172C3×C3⋊C8—22no—
173C2×AGL(1,ℤ/8)—91no—
174C22×D8—91no—
175#535—91no—
176#518—31no—
177#463—94no—
178#459—94no—
179#424—31no—
180#418—91no—
181#416—91no—
182C24×C3—61no—
183C23×D3—21no—
184C23×D3—62no—
185C23×D3—61no—
186C23×D3—61no—
187C2×C3×D4—34no—
188C2×C3×D4—32no—
189C2×C3×D4—61no—
190C2×C3×D4—62no—
191C22×C3×C4—21no—
192C22×C3×C4—64no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C2×#67—62no—
196C2×#67—61no—
197C2×#67—61no—
198#235—62no—
199#235—62no—
200#235—62no—
201#235—62no—
202#235—122no—
203#235—122no—
204C2×D12—22no—
205C2×D12—21no—
206C2×D12—31no—
207C2×D12—32no—
208C2×D12—31no—
209C2×D12—32no—
210C2×D12—61no—
211C2×D12—62no—
212C2×D12—62no—
213C2×D12—62no—
214C2×D12—62no—
215C2×D12—62no—
216C2×D12—62no—
217C2×D12—61no—
218C2×D12—61no—
219C2×D12—68no—
220C2×D12—64no—
221C2×D12—64no—
222C2×D12—122no—
223C2×D12—122no—
224C2×D12D1214yescomplemented
225C2×D12C22×D312yes—
226C2×C4×D3—24no—
227C2×C4×D3—62no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×Dic6—31no—
231C2×Dic6—31no—
232C2×Dic6—61no—
233C3×M16—62no—
234C2×C3×C8—32no—
235C2×C3×C8—32no—
236C2×C3×C8—62no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4D1212yes—
240C3×C4⋊C4#6712yes—
241C3×C22⋊C4—22no—
242C3×C22⋊C4—61no—
243C3×C22⋊C4—64no—
244C3×C22⋊C4D1212yes—
245C3×C22⋊C4#6712yes—
246C3×C42—22no—
247C3×C42—61no—
248C3×C42C22×D312yes—
249C3×C42C22×D312yes—
250#217—21no—
251#214—64no—
252#213—68no—
253#213—64no—
254(C2×D3)⋊C4—24no—
255(C2×D3)⋊C4—68no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258C4⋊Dic3C22×D312yes—
259C4×Dic3—21no—
260#208—22no—
261C2×C3⋊C8—22no—
262C2×C3⋊C8C22×D312yes—
263C2×C3⋊C8C22×D312yes—
264D24—68no—
265D24—64no—
266#204—64no—
267C22×C32—22no—
268C22×C32#12112yes—
269C22×C32C22×D411yescharacteristic
270C2×C3⋊D3—41no—
271C2×C3⋊D3—42no—
272C2×C3⋊D3—42no—
273C2×C3⋊D3—44no—
274C2×C3⋊D3—84no—
275C2×C3×D3—24no—
276C2×C3×D3—44no—
277C2×C3×D3—84no—
278C32×C4—24no—
279C32×C4#12112yes—
280C32×C4C22×D411yescharacteristic
281C32×C4C2×#4111yescharacteristic
282C3⋊Dic3—41no—
283C3×Dic3—42no—
284C2×#41—91no—
285C22×D4—31no—
286C22×D4—91no—
287AGL(1,ℤ/8)—184no—
288C2×SD16—92no—
289C2×D8—94no—
290C2×D8—92no—
291C2×D8—184no—
292C2×M16—31no—
293C22×C8—31no—
294#127—92no—
295#124—92no—
296#121—182no—
297#120—182no—
298C4×D4—34no—
299C4×D4—62no—
300#117—31no—
301#117D3211yescharacteristic
302C2×C22⋊C4—62no—
303C4⋊C8—34no—
304#103—92no—
305#102—92no—
306#102—94no—
307C23×C3—21no—
308C23×C3—62no—
309C23×C3—64no—
310C23×C3—242no—
311C23×C3C2×D1211yescharacteristic
312C23×C3C2×#6711yescharacteristic
313C22×D3—22no—
314C22×D3—24no—
315C22×D3—64no—
316C22×D3—62no—
317C22×D3—62no—
318C22×D3—61no—
319C22×D3—62no—
320C22×D3—61no—
321C22×D3—82no—
322C22×D3—124no—
323C22×D3—122no—
324C22×D3—122no—
325C22×D3—242no—
326C22×D3—242no—
327C22×D3—244no—
328C3×D4—34no—
329C3×D4—64no—
330C3×D4—62no—
331C2×C3×C4—21no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—24no—
336C2×C3×C4—62no—
337C2×C3×C4—244no—
338C2×C3×C4C2×D1212yes—
339C2×C3×C4C2×D1214yes—
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4#23512yes—
342C2×C3×C4D3×D412yes—
343C2×C3×C4#23912yes—
344C2×C3×C4C2×#6714yes—
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348#67—124no—
349#67—122no—
350#67—122no—
351C2×Dic3—22no—
352C2×Dic3—62no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355D12—24no—
356D12—22no—
357D12—62no—
358D12—61no—
359D12—62no—
360D12—61no—
361D12—62no—
362D12—61no—
363D12—62no—
364D12—61no—
365D12—122no—
366D12—122no—
367D12—121no—
368D12—121no—
369D12—124no—
370D12—122no—
371D12—122no—
372D12—244no—
373D12—244no—
374D12—248no—
375D12C2×D1214yes—
376C4×D3—84no—
377C4×D3—124no—
378C4×D3—122no—
379C4×D3—122no—
380Dic6—61no—
381Dic6—61no—
382Dic6—61no—
383Dic6—61no—
384Dic6—121no—
385Dic6—121no—
386C3×C8—62no—
387C3×C8—62no—
388C3⋊C8—22no—
389C3⋊C8—22no—
390C2×C32—22no—
391C2×C32C2×#12111yescharacteristic
392C2×C32#57612yes—
393C3⋊D3—81no—
394C3⋊D3—82no—
395C3×D3—44no—
396C24—61no—
397C24—181no—
398#41—182no—
399#41—182no—
400C2×Q8—91no—
401C2×D4—32no—
402C2×D4—34no—
403C2×D4—62no—
404C2×D4—61no—
405C2×D4—92no—
406C2×D4—91no—
407C2×D4—181no—
408C2×D4—182no—
409C2×D4—182no—
410C2×D4—181no—
411C2×D4—184no—
412C22×C4—64no—
413C22×C4—181no—
414C22×C4C2×D3211yescharacteristic
415SD16—184no—
416D8—188no—
417D8—184no—
418M16—62no—
419C2×C8—32no—
420C2×C8—32no—
421C2×C8—62no—
422C4⋊C4—32no—
423C4⋊C4#62612yes—
424C22⋊C4—61no—
425C22⋊C4—64no—
426C22⋊C4—184no—
427C22⋊C4#62612yes—
428C42—61no—
429C42C2×D3212yes—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—21no—
433C22×C3—22no—
434C22×C3—42no—
435C22×C3—64no—
436C22×C3—124no—
437C22×C3—244no—
438C22×C3#89512yes—
439C22×C3#93012yes—
440C22×C3C22×D1211yescharacteristic
441C22×C3C22×#6711yescharacteristic
442C2×D3—24no—
443C2×D3—44no—
444C2×D3—84no—
445C2×D3—122no—
446C2×D3—124no—
447C2×D3—124no—
448C2×D3—128no—
449C2×D3—122no—
450C2×D3—124no—
451C2×D3—121no—
452C2×D3—122no—
453C2×D3—121no—
454C2×D3—122no—
455C2×D3—122no—
456C2×D3—124no—
457C2×D3—244no—
458C2×D3—244no—
459C2×D3—248no—
460C3×C4—24no—
461C3×C4—24no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—22no—
465C3×C4—44no—
466C3×C4—122no—
467C3×C4#89512yes—
468C3×C4#93012yes—
469C3×C4C22×D1211yescharacteristic
470C3×C4C2×#23511yescharacteristic
471C3×C4C2×D3×D411yescharacteristic
472C3×C4C2×#23911yescharacteristic
473Dic3—42no—
474Dic3—122no—
475Dic3—121no—
476Dic3—121no—
477C32#304111yescharacteristic, complemented, Sylow
478C23—62no—
479C23—64no—
480C23—182no—
481C23—181no—
482C23—242no—
483C23—362no—
484C23—722no—
485C23C2×#62611yescharacteristic
486Q8—181no—
487Q8—181no—
488D4—34no—
489D4—62no—
490D4—64no—
491D4—182no—
492D4—181no—
493D4—182no—
494D4—181no—
495D4—362no—
496D4—362no—
497D4—724no—
498C2×C4—62no—
499C2×C4—181no—
500C2×C4—244no—
501C2×C4—362no—
502C2×C4#379912yes—
503C2×C4D3×D1212yes—
504C2×C4C2×#62614yes—
505C2×C4C2×#62611yescharacteristic
506C2×C4C22×D3211yescharacteristic
507C8—62no—
508C8—62no—
509C2×C3—22no—
510C2×C3—22no—
511C2×C3—22no—
512C2×C3—21no—
513C2×C3—42no—
514C2×C3—124no—
515C2×C3C2×#89511yescharacteristic
516C2×C3#575212yes—
517C2×C3C2×#93011yescharacteristic
518C2×C3#583512yes—
519D3—44no—
520D3—244no—
521D3—242no—
522D3—242no—
523D3—241no—
524D3—242no—
525D3—241no—
526C22—22no—
527C22—64no—
528C22—124no—
529C22—244no—
530C22—362no—
531C22—364no—
532C22—361no—
533C22—362no—
534C22—724no—
535C22#6390912yes—
536C22C22×#62611yescharacteristic
537C4—24no—
538C4—122no—
539C4—361no—
540C4#6390912yes—
541C4C2×#379911yescharacteristic
542C4C2×D3×D1211yescharacteristic
543C3—21no—
544C3#7908611yescharacteristic, complemented
545C3#8254011yescharacteristic, complemented
546C2—22no—
547C2—124no—
548C2—722no—
549C2—721no—
550C2C2×#6390911yescharacteristic
551C2#1059544912yes—
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595996C2semidirect
2. C3×#5521C2semidirect
3. C2×#63830C2semidirect
4. C22×#3714C2semidirect
5. C3×#4999C2semidirect
6. #10591105C2semidirect
7. #10591096C2semidirect
8. #10590366C2semidirect
9. #10590349C2semidirect
18. #64084C22semidirect
19. #64083C22semidirect
25. C3×C4×D12C22semidirect
27. C2×#3716C22semidirect
30. C2×#3714C22semidirect
31. C3×C4⋊(C3⋊C8)C22semidirect
32. #63567C22semidirect
33. #63564C22semidirect
34. #63564C22semidirect
43. #5521D3semidirect
51. #4999D3semidirect
70. C2×C3×D12D4semidirect
133. C4×D12C2×D3semidirect
141. C4⋊(C3⋊C8)C2×D3semidirect
224. C2×D12D12semidirect
477. C32#3041semidirect
544. C3#79086semidirect
545. C3#82540semidirect

Maximal subgroups

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

subgroupindex
#105959962
C3×#55212
C2×#638302
C22×#37142
C3×#49992
#105911052
#105910962
#105903662
#105903492
#825403
#790863