Finite Group Databasebeta

← #11866281

Subgroups — #11866281

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64141C211yesmaximal, characteristic
2C3×#5798C211yesmaximal, characteristic, complemented
3C22×C3×#214C211yesmaximal, characteristic, complemented
4#10594866C211yesmaximal, characteristic, complemented
5#10591489C214yesmaximal, complemented
6#10591471C214yesmaximal, complemented
7#10591116C211yesmaximal, characteristic, complemented
8#10591105C211yesmaximal, characteristic, complemented
9#10591099C211yesmaximal, characteristic, complemented
10#83848—31nomaximal
11#82544—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C2×#3828C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×#3754C2212yes—
16#64141—24no—
17C2×#3753C2212yes—
18C2×#3748C2211yescharacteristic
19C2×C3×#217—22no—
20C3×D4×Dic3—22no—
21C3×D4×Dic3C2214yes—
22C2×C3×#214—24no—
23C2×C3×#214C2214yes—
24C3×#926C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27#63966—22no—
28#63871—22no—
29#63866C2212yescomplemented
30#63864C2212yescomplemented
31Dic3⋊(C3⋊C8)C2214yescomplemented
32#63567C2212yescomplemented
33#63565C2214yescomplemented
34#63564C2212yescomplemented
35C22×C3×SD16—31no—
36C3×#518—31no—
37#5816—31no—
38#5798D311yescharacteristic, complemented
39C22×#214D311yescharacteristic, complemented
40C2×#932—31no—
41C2×#932—31no—
42C2×#932—61no—
43#5526—31no—
44#5225—31no—
45#5165—34no—
46#5162—34no—
47#5113—31no—
48#5102—31no—
49#5019—34no—
50#5016—34no—
51#5004—31no—
52#5002—31no—
53#4999—31no—
54C24×C32—21no—
55C2×C32×D4—21no—
56C2×C32×D4—22no—
57C2×C32×D4D414yes—
58C2×C32×D4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C2×#638—21no—
61#3828—22no—
62#3828—22no—
63C2×C4⋊(C3⋊D3)C2311yescharacteristic
64C2×C4×C3⋊D3—21no—
65C2×#634C2311yescharacteristic
66C22×C3×Dic3—21no—
67C22×C3×Dic3—24no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2312yes—
72#3754—24no—
73#3753—24no—
74#3748—22no—
75C2×C3⋊(C3⋊C8)C2312yes—
76C3×#217—21no—
77C3×#217—24no—
78C3×#217D412yes—
79C3×#214—28no—
80C3×C4⋊Dic3D412yes—
81C3×C4⋊Dic3C2312yes—
82C3×C4×Dic3—21no—
83C3×C4×Dic3C2312yes—
84C2×C3×C3⋊C8—22no—
85C2×C3×C3⋊C8C2312yes—
86Dic3⋊Dic3—24no—
87#3722—24no—
88#3042—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—
99C22×C3×C8—31no—
100C3×C4×D4—34no—
101C3×C4×D4—62no—
102C3×#117—31no—
103C3×#117—31no—
104C2×C3×C22⋊C4—62no—
105C2×#217—22no—
106#947—32no—
107#946—62no—
108#944—32no—
109D4×Dic3—22no—
110D4×Dic3C2×D314yes—
111C2×#214—24no—
112C2×#214—32no—
113C2×#214—32no—
114C2×#214—62no—
115C2×#214C2×D314yes—
116#932—68no—
117#932—64no—
118#932—64no—
119C2×#213—32no—
120C2×#213—32no—
121C2×#213—62no—
122#929—62no—
123#926C2×D311yescharacteristic
124#926C2×D311yescharacteristic
125C2×#208—31no—
126C2×#208—31no—
127C2×#208—61no—
128C22×C3⋊C8C2×D311yescharacteristic
129#897—62no—
130#886—62no—
131#875—32no—
132#869—32no—
133#835—34no—
134#821—32no—
135#816—32no—
136Dic3⋊C8—34no—
137#810—34no—
138#810—32no—
139#809—32no—
140C4⋊(C3⋊C8)—34no—
141C23×C32—22no—
142C23×C32—24no—
143C23×C32—82no—
144C23×C32C2×D411yescharacteristic
145C22×C3⋊D3—21no—
146C32×D4—24no—
147C32×D4—22no—
148C32×D4C2×D414yes—
149C2×C32×C4C2×D412yes—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4#4112yes—
152C2×C32×C4C2411yescharacteristic
153#638—42no—
154C2×C3⋊Dic3—21no—
155C4⋊(C3⋊D3)—21no—
156C4⋊(C3⋊D3)—21no—
157C4×C3⋊D3—42no—
158#634—21no—
159#634—21no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—42no—
163C2×C3×Dic3—84no—
164C2×C3×Dic3C2×D414yes—
165C3×Dic6—22no—
166C3×Dic6—22no—
167C3×Dic6—42no—
168C3⋊(C3⋊C8)—22no—
169C3×C3⋊C8—22no—
170C2×AGL(1,ℤ/8)—91no—
171C22×SD16—31no—
172#536—91no—
173#518—31no—
174#463—94no—
175#461—94no—
176#424—91no—
177#419—91no—
178#416—91no—
179C24×C3—21no—
180C24×C3—21no—
181C24×C3—41no—
182C2×C3×Q8—32no—
183C2×C3×Q8—61no—
184C2×C3×Q8—62no—
185C2×C3×Q8—62no—
186C2×C3×D4—22no—
187C2×C3×D4—21no—
188C2×C3×D4—22no—
189C2×C3×D4—21no—
190C2×C3×D4—24no—
191C2×C3×D4—22no—
192C2×C3×D4—42no—
193C2×C3×D4—41no—
194C2×C3×D4D1214yes—
195C2×C3×D4#6714yes—
196C2×C3×D4C22×D312yes—
197C2×C3×D4C22×D312yes—
198C22×C3×C4—21no—
199C22×C3×C4—64no—
200C22×C3×C4—61no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C2×#67—61no—
204C2×#67—61no—
205C2×#67—121no—
206C22×Dic3—21no—
207C22×Dic3—24no—
208#235—64no—
209#235—62no—
210#235—62no—
211#235—62no—
212#235—62no—
213#235—122no—
214C2×D12—31no—
215C2×D12—31no—
216C2×D12—61no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×C4×D3—121no—
220C2×Dic6—22no—
221C2×Dic6—22no—
222C2×Dic6—21no—
223C2×Dic6—31no—
224C2×Dic6—31no—
225C2×Dic6—61no—
226C2×Dic6C22×D312yes—
227C3×SD16—68no—
228C2×C3×C8—32no—
229C2×C3×C8—62no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—32no—
232C3×C22⋊C4—32no—
233C3×C22⋊C4—64no—
234C3×C22⋊C4—61no—
235C3×C42—32no—
236C3×C42—61no—
237#217—21no—
238#217—24no—
239#217#6712yes—
240#214—28no—
241#214—68no—
242#214—64no—
243#214—64no—
244#213—68no—
245#213—64no—
246#213—64no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249C4⋊Dic3—64no—
250C4⋊Dic3#6712yes—
251C4⋊Dic3C22×D312yes—
252Dic3⋊C4—64no—
253C4×Dic3—21no—
254C4×Dic3C22×D312yes—
255#208—64no—
256#208—62no—
257#208—62no—
258C2×C3⋊C8—22no—
259C2×C3⋊C8—32no—
260C2×C3⋊C8—32no—
261C2×C3⋊C8—62no—
262C2×C3⋊C8C22×D312yes—
263C22×C32—22no—
264C22×C32—24no—
265C22×C32—44no—
266C22×C32—84no—
267C22×C32#12112yes—
268C22×C32C22×D411yescharacteristic
269C2×C3⋊D3—41no—
270C2×C3⋊D3—42no—
271C32×C4#12112yes—
272C32×C4C22×D411yescharacteristic
273C32×C4C2×#4111yescharacteristic
274C3⋊Dic3—41no—
275C3×Dic3—24no—
276C3×Dic3—42no—
277C3×Dic3—42no—
278C2×#41—91no—
279C22×Q8—31no—
280C22×D4D3211yescharacteristic
281AGL(1,ℤ/8)—184no—
282C2×SD16—34no—
283C2×SD16—64no—
284C2×SD16—92no—
285C2×D8—92no—
286C2×M16—91no—
287C22×C8—31no—
288C4⋊Q8—92no—
289#124—92no—
290#123—182no—
291C22⋊Q8—182no—
292C4×D4—34no—
293C4×D4—62no—
294#117—31no—
295#117—31no—
296C2×C22⋊C4—62no—
297C4⋊C8—94no—
298#103—92no—
299#103—94no—
300#102—92no—
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—24no—
304C23×C3—24no—
305C23×C3—21no—
306C23×C3—42no—
307C23×C3—44no—
308C23×C3—82no—
309C23×C3—82no—
310C23×C3—84no—
311C23×C3D3×D411yescharacteristic
312C23×C3C2×#6711yescharacteristic
313C22×D3—61no—
314C22×D3—61no—
315C22×D3—121no—
316C3×Q8—62no—
317C3×Q8—62no—
318C3×Q8—122no—
319C3×D4—24no—
320C3×D4—24no—
321C3×D4—22no—
322C3×D4—22no—
323C3×D4—24no—
324C3×D4—42no—
325C3×D4—44no—
326C3×D4C2×D1214yes—
327C3×D4C2×#6714yes—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—34no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—122no—
336C2×C3×C4—244no—
337C2×C3×C4C2×D1212yes—
338C2×C3×C4#23512yes—
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4#23712yes—
341C2×C3×C4C2×#6712yes—
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345#67—124no—
346#67—122no—
347#67—122no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—42no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—84no—
354C2×Dic3—121no—
355C2×Dic3C2×#6714yes—
356D12—62no—
357D12—61no—
358D12—61no—
359D12—61no—
360D12—61no—
361D12—121no—
362C4×D3—124no—
363C4×D3—122no—
364C4×D3—122no—
365Dic6—22no—
366Dic6—22no—
367Dic6—42no—
368Dic6—62no—
369Dic6—61no—
370Dic6—61no—
371Dic6—61no—
372Dic6—61no—
373Dic6—121no—
374C3×C8—62no—
375C3⋊C8—22no—
376C3⋊C8—64no—
377C3⋊C8—62no—
378C3⋊C8—62no—
379C2×C32—22no—
380C2×C32—44no—
381C2×C32C2×#12111yescharacteristic
382C2×C32#57712yes—
383C3⋊D3—81no—
384C24—21no—
385#41—182no—
386#41—182no—
387C2×Q8—32no—
388C2×Q8—61no—
389C2×Q8—62no—
390C2×Q8—62no—
391C2×Q8—91no—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4—91no—
395C2×D4—181no—
396C2×D4#62614yes—
397C2×D4C2×D3212yes—
398C22×C4—64no—
399C22×C4—61no—
400C22×C4—181no—
401C22×C4C2×D3211yescharacteristic
402SD16—68no—
403SD16—184no—
404D8—184no—
405M16—182no—
406C2×C8—32no—
407C2×C8—62no—
408C2×C8—92no—
409C4⋊C4—32no—
410C4⋊C4—32no—
411C4⋊C4—184no—
412C22⋊C4—32no—
413C22⋊C4—64no—
414C22⋊C4—61no—
415C22⋊C4—184no—
416C42—32no—
417C42—61no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—24no—
421C22×C3—24no—
422C22×C3—21no—
423C22×C3—22no—
424C22×C3—42no—
425C22×C3—44no—
426C22×C3—44no—
427C22×C3—44no—
428C22×C3—84no—
429C22×C3—84no—
430C22×C3—84no—
431C22×C3—88no—
432C22×C3#93012yes—
433C22×C3#93912yes—
434C22×C3C2×D3×D411yescharacteristic
435C22×C3C22×#6711yescharacteristic
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—121no—
439C2×D3—121no—
440C2×D3—122no—
441C2×D3—242no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—22no—
445C3×C4—64no—
446C3×C4—122no—
447C3×C4—122no—
448C3×C4#93012yes—
449C3×C4#93912yes—
450C3×C4C22×D1211yescharacteristic
451C3×C4C2×#23511yescharacteristic
452C3×C4C2×#23711yescharacteristic
453C3×C4C22×#6711yescharacteristic
454Dic3—24no—
455Dic3—42no—
456Dic3—42no—
457Dic3—122no—
458Dic3—121no—
459Dic3—121no—
460C32#304211yescharacteristic, complemented, Sylow
461C23—22no—
462C23—24no—
463C23—82no—
464C23—181no—
465C23D3×#6711yescharacteristic
466Q8—62no—
467Q8—62no—
468Q8—122no—
469Q8—181no—
470Q8—181no—
471D4—22no—
472D4—24no—
473D4—181no—
474D4—181no—
475D4—362no—
476D4C2×#62614yes—
477C2×C4—34no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—122no—
481C2×C4—181no—
482C2×C4—244no—
483C2×C4—362no—
484C2×C4#380412yes—
485C2×C4C2×#62612yes—
486C2×C4D3×#6711yescharacteristic
487C2×C4C22×D3211yescharacteristic
488C8—62no—
489C8—182no—
490C2×C3—22no—
491C2×C3—22no—
492C2×C3—22no—
493C2×C3—21no—
494C2×C3—42no—
495C2×C3—44no—
496C2×C3—44no—
497C2×C3—84no—
498C2×C3#576212yes—
499C2×C3C2×#93011yescharacteristic
500C2×C3C2×#93911yescharacteristic
501C2×C3#583612yes—
502D3—242no—
503D3—241no—
504D3—241no—
505C22—22no—
506C22—24no—
507C22—44no—
508C22—84no—
509C22—362no—
510C22—361no—
511C22#6397812yes—
512C22C2×D3×#6711yescharacteristic
513C4—64no—
514C4—122no—
515C4—122no—
516C4—361no—
517C4#6397812yes—
518C4C2×#380411yescharacteristic
519C4C22×#62611yescharacteristic
520C3—21no—
521C3#8254411yescharacteristic, complemented
522C3#8384811yescharacteristic, complemented
523C2—22no—
524C2—44no—
525C2—721no—
526C2#1059510512yes—
527C2C2×#6397811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC2×#64141C2
hypercenterC22×D4D32
hypocenterC32#3042
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. C3×#5798C2semidirect
3. C22×C3×#214C2semidirect
4. #10594866C2semidirect
5. #10591489C2semidirect
6. #10591471C2semidirect
7. #10591116C2semidirect
8. #10591105C2semidirect
9. #10591099C2semidirect
29. #63866C22semidirect
30. #63864C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
32. #63567C22semidirect
33. #63565C22semidirect
34. #63564C22semidirect
38. #5798D3semidirect
39. C22×#214D3semidirect
460. C32#3042semidirect
521. C3#82544semidirect
522. C3#83848semidirect

Maximal subgroups

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

subgroupindex
C2×#641412
C3×#57982
C22×C3×#2142
#105948662
#105914892
#105914712
#105911162
#105911052
#105910992
#838483
#825443