Finite Group Databasebeta

← #11863660

Subgroups — #11863660

Order 1152.

1641 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic
2C3⋊D3×C22⋊Q8C211yesmaximal, characteristic
3C2×#63944C212yesmaximal, complemented
4C3×#5050C212yesmaximal, complemented
5#10591654C212yesmaximal, complemented
6#10591186C212yesmaximal, complemented
7#10591152C211yesmaximal, characteristic
8#10590605C212yesmaximal, complemented
9#10590601C212yesmaximal, complemented
10D3×#451—32nomaximal
11C2×Q8×C3⋊D3C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C3×Dic6C2212yes—
14C22×#627—21no—
15C22×#624—21no—
16C2×#3797—21no—
17C2×#3797—21no—
18C2×#3797—28no—
19C2×#3797C2212yes—
20C2×#3797C2212yes—
21C32×C22⋊Q8C2211yescharacteristic
22#64155C2211yescharacteristic
23#64133C2211yescharacteristic
24#64106C2211yescharacteristic
25#64105—21no—
26C4⋊C4×C3⋊D3—21no—
27C4⋊C4×C3⋊D3C2211yescharacteristic
28C22⋊C4×C3⋊D3—21no—
29#64087—21no—
30C2×C3×#216C2214yescomplemented
31#63944—28no—
32C2×#3719C2214yescomplemented
33C2×#3710C2212yes—
34C3×#830C2212yes—
35C3×#810C2214yescomplemented
36#63566C2214yescomplemented
37#63557C2212yes—
38C22×D3×Q8—32no—
39C2×D3×Q16—34no—
40D3×C22⋊Q8—32no—
41D3×C22⋊Q8—61no—
42C3×#451—32no—
43#5228—32no—
44#5186—34no—
45#5050D312yescomplemented
46#4809—34no—
47D3×#103—34no—
48#4739—32no—
49D3×C22⋊C8—32no—
50C23×C3⋊D3D411yescharacteristic
51C2×C32×Q8C2311yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54Q8×C3⋊D3—24no—
55C2×C4×C3⋊D3—24no—
56C2×C4×C3⋊D3—21no—
57C2×C4×C3⋊D3—21no—
58C2×C4×C3⋊D3D411yescharacteristic
59C2×C4×C3⋊D3D411yescharacteristic
60C2×C4×C3⋊D3C2311yescharacteristic
61C2×C4×C3⋊D3C2311yescharacteristic
62C2×#634—21no—
63C2×#634C2311yescharacteristic
64C22×C3×Dic3—22no—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—28no—
67C2×C3×Dic6C2314yes—
68C2×#627—28no—
69C2×#627—22no—
70C2×#627—22no—
71C2×#624—28no—
72C2×#624—22no—
73C2×#624—22no—
74#3797—28no—
75#3797—28no—
76#3797—24no—
77#3797—28no—
78#3797D418yes—
79C32×C4⋊C4—21no—
80C32×C4⋊C4C2311yescharacteristic
81C32×C22⋊C4—21no—
82#3757—21no—
83#3752—21no—
84#3752—21no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87#3750—21no—
88#3750—21no—
89#3750—21no—
90C3×#216—28no—
91C2×C3×C3⋊C8C2314yes—
92#3719—28no—
93#3710—24no—
94C2×#451—91noSylow
95C22×C3×Q8—32no—
96C2×D3×Q8—32no—
97C2×D3×Q8—34no—
98C2×D3×Q8—34no—
99C2×D3×Q8—61no—
100C2×D3×Q8—62no—
101C2×D3×Q8—62no—
102C2×D3×Q8—616no—
103C22×C4×D3—32no—
104C22×C4×D3—61no—
105C22×C4×D3—62no—
106C22×Dic6—62no—
107C22×Dic6C2×D312yes—
108C2×C3×Q16—34no—
109C3×C22⋊Q8—21no—
110C3×C22⋊Q8C2×D312yes—
111#946—32no—
112#946—61no—
113C2×#216—34no—
114C2×#216C2×D314yescomplemented
115#924—32no—
116#924—61no—
117D3×Q16—616no—
118C2×Dic12—34no—
119C2×D3×C8—34no—
120#897—32no—
121#897—61no—
122#896—62no—
123#896—62no—
124D3×C4⋊C4—32no—
125D3×C4⋊C4—61no—
126D3×C4⋊C4—62no—
127D3×C4⋊C4—62no—
128D3×C22⋊C4—62no—
129D3×C22⋊C4—62no—
130#878—62no—
131#878—62no—
132C3×#103—34no—
133C3×C22⋊C8—32no—
134#835—34no—
135#830C2×D312yes—
136(C2×D3)⋊C8—34no—
137#816—34no—
138#810C2×D314yescomplemented
139C23×C32C2×D411yescharacteristic
140C22×C3⋊D3—22no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3Q1614yescomplemented
143C22×C3⋊D3C2×D411yescharacteristic
144C22×C3⋊D3C2×D411yescharacteristic
145C32×Q8—22no—
146C2×C32×C4—21no—
147C2×C32×C4—21no—
148C2×C32×C4—22no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2411yescharacteristic
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3C2×D411yescharacteristic
155C2×C3⋊Dic3C2×D411yescharacteristic
156C4×C3⋊D3—22no—
157C4×C3⋊D3—22no—
158C4×C3⋊D3—22no—
159C4×C3⋊D3—42no—
160C4×C3⋊D3—42no—
161C4×C3⋊D3C2×D414yes—
162#634—22no—
163#634—42no—
164C2×C3×Dic3—28no—
165C2×C3×Dic3—24no—
166C3×Dic6—28no—
167C3×Dic6—24no—
168C3×Dic6C2×D418yes—
169#627—28no—
170#627—28no—
171#624—28no—
172#624—28no—
173C3×C3⋊C8—24no—
174C23×Q8—91no—
175C22×Q16—92no—
176C2×C22⋊Q8—91no—
177#451—32no—
178#451—92no—
179#451—92no—
180#451—92no—
181C2×#103—92no—
182C2×C22⋊C8—91no—
183C23×D3—32no—
184C23×D3—61no—
185C2×C3×Q8—21no—
186C2×C3×Q8—34no—
187C2×C3×Q8—68no—
188C2×C3×Q8—62no—
189C2×C3×Q8C22×D312yes—
190C22×C3×C4—21no—
191C22×C3×C4—62no—
192C22×C3×C4C22×D312yes—
193C22×Dic3—22no—
194C22×Dic3—32no—
195C22×Dic3—61no—
196D3×Q8—316no—
197D3×Q8—68no—
198D3×Q8—68no—
199D3×Q8—616no—
200D3×Q8—616no—
201D3×Q8—68no—
202D3×Q8—68no—
203D3×Q8—124no—
204C2×C4×D3—32no—
205C2×C4×D3—32no—
206C2×C4×D3—32no—
207C2×C4×D3—32no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C4×D3—61no—
212C2×C4×D3—68no—
213C2×C4×D3—64no—
214C2×C4×D3—64no—
215C2×C4×D3—616no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×C4×D3—62no—
220C2×C4×D3—124no—
221C2×Dic6—22no—
222C2×Dic6—28no—
223C2×Dic6—32no—
224C2×Dic6—61no—
225C2×Dic6—64no—
226C2×Dic6—64no—
227C2×Dic6—616no—
228C2×Dic6—62no—
229C2×Dic6—62no—
230C2×Dic6C22×D314yes—
231C3×Q16—68no—
232C2×C3×C8—34no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4C22×D312yes—
237C3×C22⋊C4—22no—
238C3×C22⋊C4—22no—
239#217—62no—
240#217—62no—
241#216—28no—
242#216—68no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247C4⋊Dic3—32no—
248C4⋊Dic3—61no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251Dic3⋊C4—62no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257C2×C3⋊C8C22×D314yes—
258Dic12—68no—
259D3×C8—68no—
260C22×C32—21no—
261C22×C32—21no—
262C22×C32C2×Q1612yescomplemented
263C22×C32C22×D411yescharacteristic
264C2×C3⋊D3—21no—
265C2×C3⋊D3—21no—
266C2×C3⋊D3—28no—
267C2×C3⋊D3#12012yes—
268C2×C3⋊D3C2×Q1612yes—
269C2×C3⋊D3C2×Q1612yescomplemented
270C2×C3⋊D3#13712yes—
271C32×C4—21no—
272C32×C4—41no—
273C32×C4—41no—
274C32×C4C22×D412yes—
275C3⋊Dic3—21no—
276C3⋊Dic3—41no—
277C3⋊Dic3—41no—
278C3⋊Dic3#12012yes—
279C3×Dic3—28no—
280C22×Q8—32no—
281C22×Q8—92no—
282C22×Q8—92no—
283C22×Q8—91no—
284C22×Q8—181no—
285C22×Q8—181no—
286C22×Q8—181no—
287C22×Q8—188no—
288C23×C4—91no—
289C23×C4—181no—
290C2×Q16—34no—
291C2×Q16—94no—
292C2×Q16—188no—
293C22×C8—92no—
294C22⋊Q8—91no—
295C22⋊Q8—91no—
296C22⋊Q8—91no—
297C22⋊Q8—181no—
298C22⋊Q8—181no—
299C22⋊Q8D3211yescharacteristic
300C2×C4⋊C4—91no—
301C2×C4⋊C4—181no—
302C2×C22⋊C4—181no—
303#103—34no—
304#103—94no—
305C22⋊C8—32no—
306C22⋊C8—92no—
307C23×C3—21no—
308C23×C3D3×D412yes—
309C22×D3—32no—
310C22×D3—38no—
311C22×D3—32no—
312C22×D3—61no—
313C22×D3—64no—
314C22×D3—61no—
315C22×D3—64no—
316C22×D3—64no—
317C22×D3—122no—
318C22×D3—122no—
319C3×Q8—24no—
320C3×Q8—38no—
321C3×Q8—42no—
322C3×Q8—68no—
323C3×Q8—64no—
324C2×C3×C4—24no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—42no—
332C2×C3×C4—68no—
333C2×C3×C4—64no—
334C2×C3×C4D3×D412yes—
335C2×C3×C4C23×D312yes—
336C2×Dic3—28no—
337C2×Dic3—24no—
338C2×Dic3—32no—
339C2×Dic3—32no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—64no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—122no—
348C4×D3—38no—
349C4×D3—64no—
350C4×D3—616no—
351C4×D3—616no—
352C4×D3—64no—
353C4×D3—64no—
354C4×D3—64no—
355C4×D3—122no—
356C4×D3—122no—
357C4×D3—122no—
358C4×D3—124no—
359C4×D3—124no—
360C4×D3—124no—
361C4×D3—124no—
362Dic6—28no—
363Dic6—24no—
364Dic6—616no—
365Dic6—616no—
366Dic6—64no—
367Dic6—122no—
368Dic6—124no—
369Dic6—124no—
370Dic6D3×D418yes—
371C3×C8—64no—
372C3⋊C8—24no—
373C2×C32—22no—
374C2×C32C2×#12011yescharacteristic
375C2×C32C22×Q1611yescharacteristic
376C2×C32C2×#13711yescharacteristic
377C3⋊D3—22no—
378C3⋊D3#45114yescomplemented
379C24—91no—
380C2×Q8—34no—
381C2×Q8—68no—
382C2×Q8—62no—
383C2×Q8—98no—
384C2×Q8—91no—
385C2×Q8—181no—
386C2×Q8—182no—
387C2×Q8—182no—
388C2×Q8—188no—
389C2×Q8—184no—
390C2×Q8—184no—
391C2×Q8—188no—
392C2×Q8—188no—
393C2×Q8—188no—
394C2×Q8C2×D3211yescharacteristic
395C22×C4—62no—
396C22×C4—91no—
397C22×C4—91no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—184no—
402C22×C4—181no—
403C22×C4—181no—
404C22×C4—182no—
405C22×C4—182no—
406C22×C4—188no—
407C22×C4C2×D3211yescharacteristic
408Q16—68no—
409Q16—188no—
410C2×C8—34no—
411C2×C8—184no—
412C4⋊C4—21no—
413C4⋊C4—91no—
414C4⋊C4—181no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4C2×D3211yescharacteristic
419C22⋊C4—21no—
420C22⋊C4—181no—
421C22⋊C4—181no—
422C22⋊C4—181no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—21no—
426C22×C3—22no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3D3×Q1614yescomplemented
430C22×C3C2×D3×D412yes—
431C2×D3—34no—
432C2×D3—34no—
433C2×D3—34no—
434C2×D3—34no—
435C2×D3—62no—
436C2×D3—62no—
437C2×D3—62no—
438C2×D3—62no—
439C2×D3—616no—
440C2×D3—62no—
441C2×D3—62no—
442C2×D3—128no—
443C2×D3—121no—
444C2×D3—121no—
445C3×C4—22no—
446C3×C4—22no—
447C3×C4—41no—
448C3×C4—42no—
449C3×C4—42no—
450C3×C4—42no—
451C3×C4—42no—
452C3×C4—68no—
453C3×C4C2×D3×D414yes—
454Dic3—28no—
455Dic3—34no—
456Dic3—62no—
457Dic3—62no—
458Dic3—121no—
459Dic3—122no—
460Dic3—122no—
461Dic3—122no—
462Dic3—122no—
463C32C2×#45111yescharacteristic, complemented, Sylow
464C23—91no—
465C23—91no—
466C23—94no—
467C23—182no—
468C23—182no—
469C23#381111yescharacteristic
470Q8—22no—
471Q8—38no—
472Q8—68no—
473Q8—64no—
474Q8—188no—
475Q8—188no—
476Q8—182no—
477Q8—362no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—68no—
482C2×C4—64no—
483C2×C4—91no—
484C2×C4—94no—
485C2×C4—91no—
486C2×C4—182no—
487C2×C4—182no—
488C2×C4—188no—
489C2×C4—188no—
490C2×C4—182no—
491C2×C4—182no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—362no—
495C2×C4—362no—
496C2×C4#381111yescharacteristic
497C2×C4C22×D3211yescharacteristic
498C8—64no—
499C2×C3—24no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—42no—
504C2×C3D3×#12012yes—
505C2×C3C2×D3×Q1612yes—
506C2×C3D3×#13712yes—
507D3—38no—
508D3—64no—
509D3—64no—
510D3—122no—
511C22—21no—
512C22—21no—
513C22—92no—
514C22—92no—
515C22—92no—
516C22—92no—
517C22—188no—
518C22—181no—
519C22—181no—
520C22#6394412yescomplemented
521C22C2×#381111yescharacteristic
522C4—21no—
523C4—41no—
524C4—41no—
525C4—68no—
526C4—92no—
527C4—181no—
528C4—361no—
529C4—361no—
530C4D32×D412yes—
531C3—21no—
532C3D3×#45112yescomplemented
533C2—22no—
534C2—94no—
535C2—182no—
536C2#1059527811yescharacteristic
537C2C2×#6394411yescharacteristic
538C2#1059546811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
hypercenterC22⋊Q8D32
hypocenterC32C2×#451
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
3. C2×#63944C2semidirect
4. C3×#5050C2semidirect
5. #10591654C2semidirect
6. #10591186C2semidirect
8. #10590605C2semidirect
9. #10590601C2semidirect
30. C2×C3×#216C22semidirect
32. C2×#3719C22semidirect
35. C3×#810C22semidirect
36. #63566C22semidirect
45. #5050D3semidirect
114. C2×#216C2×D3semidirect
138. #810C2×D3semidirect
142. C22×C3⋊D3Q16semidirect
262. C22×C32C2×Q16semidirect
269. C2×C3⋊D3C2×Q16semidirect
378. C3⋊D3#451semidirect
429. C22×C3D3×Q16semidirect
463. C32C2×#451semidirect
520. C22#63944semidirect
532. C3D3×#451semidirect

Maximal subgroups

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

subgroupindex
C22×#37972
C3⋊D3×C22⋊Q82
C2×#639442
C3×#50502
#105916542
#105911862
#105911522
#105906052
#105906012
D3×#4513