Finite Group Databasebeta

← #11788855

Subgroups — #11788855

Order 1152.

865 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5804C211yesmaximal, characteristic
2C3×#5798C211yesmaximal, characteristic, complemented
3C2×#63661C211yesmaximal, characteristic, complemented
4C2×#63580C212yesmaximal, complemented
5#10589187C212yesmaximal, complemented
6#71848—31nomaximal
7#71656—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C22×C3×#67C2211yescharacteristic
10C2×#3757C2212yes—
11C3×#953—21no—
12C2×C3×#217—21no—
13C2×C3×#217C2211yescharacteristic
14C2×C3×#217C2212yes—
15C3×#939—22no—
16C3×#937C412yescomplemented
17C3×#935C412yescomplemented
18C3×D4×Dic3—24no—
19C3×#929—21no—
20C3×#926—21no—
21#63661—22no—
22#63580—24no—
23C3×#534—31no—
24C3×#518—31no—
25#5804D311yescharacteristic
26#5798D311yescharacteristic, complemented
27C2×#834—31no—
28C2×#834—31no—
29C2×#834—32no—
30C2×#834—61no—
31C2×#806—32no—
32#4527—32no—
33#4527—32no—
34C24×C32D411yescharacteristic
35C24×C32C2311yescharacteristic
36C23×C3×D3C2×C411yescharacteristic, complemented
37C2×C32×D4—22no—
38C2×C32×D4—22no—
39C2×C32×D4C2×C412yes—
40C2×C32×D4D412yes—
41C22×C32×C4D411yescharacteristic
42C22×C3⋊Dic3—22no—
43C2×C3×#67—21no—
44C2×C3×#67—21no—
45C2×C3×#67—22no—
46C2×C3×#67—22no—
47C2×C3×#67—22no—
48C22×C3×Dic3—22no—
49C22×C3×Dic3—22no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3C2×C411yescharacteristic, complemented
52#3757—22no—
53#3757—22no—
54C3×#217—22no—
55C3×#217—22no—
56C3×#217—22no—
57C3×#217—21no—
58C3×#217C2×C412yescomplemented
59C3×#217D414yescomplemented
60C3×(C2×D3)⋊C4—22no—
61C3×C4⋊Dic3—22no—
62C3×Dic3⋊C4—22no—
63C3×C4×Dic3—22no—
64#1913—91noSylow
65C22×C3×D4—21no—
66C22×C3×D4—31no—
67C22×C3×D4C2×D311yescharacteristic
68C22×C3×D4C2×D311yescharacteristic
69C22×#67C2×D311yescharacteristic
70C3×#123—32no—
71C3×#123—61no—
72C3×#121—62no—
73C3×#120—32no—
74C3×#120—61no—
75C3×C4×D4—64no—
76C3×#117—61no—
77C2×C3×C22⋊C4—32no—
78C2×C3×C22⋊C4—31no—
79C2×C3×C22⋊C4—61no—
80#953—21no—
81C2×#217—21no—
82C2×#217—32no—
83C2×#217—32no—
84C2×#217—62no—
85C2×#217C2×D311yescharacteristic
86C2×#217C2×D312yes—
87#939—22no—
88#937Dic312yescomplemented
89#935Dic312yescomplemented
90D4×Dic3—24no—
91#929—21no—
92#926—21no—
93#834—64no—
94#834—62no—
95#834—62no—
96#834—64no—
97#806—64no—
98C23×C32—21no—
99C23×C32—21no—
100C23×C32—81no—
101C23×C32—81no—
102C23×C32C22⋊C412yes—
103C23×C32C22×C411yescharacteristic
104C23×C32C2×D411yescharacteristic
105C23×C32C2×D412yes—
106C23×C32C2×D411yescharacteristic
107C23×C32#4112yes—
108C22×C3×D3—21no—
109C22×C3×D3—22no—
110C22×C3×D3—81no—
111C32×D4—24no—
112C32×D4—24no—
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4C22⋊C412yes—
116C2×C3⋊Dic3—42no—
117C2×C3⋊Dic3—82no—
118C3×#67—41no—
119C3×#67—42no—
120C3×#67—41no—
121C3×#67—82no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—82no—
127C2×C3×Dic3—82no—
128C2×C3×Dic3—81no—
129#534—31no—
130#518—31no—
131C2×#99—92no—
132C2×#99—91no—
133#342—92no—
134C24×C3—21no—
135C24×C3—21no—
136C24×C3—31no—
137C24×C3#6711yescharacteristic
138C24×C3#6711yescharacteristic
139C24×C3C22×D311yescharacteristic
140C24×C3C22×D311yescharacteristic
141C23×D3C2×Dic311yescharacteristic, complemented
142C2×C3×D4—22no—
143C2×C3×D4—22no—
144C2×C3×D4—22no—
145C2×C3×D4—22no—
146C2×C3×D4—22no—
147C2×C3×D4—22no—
148C2×C3×D4—42no—
149C2×C3×D4—42no—
150C2×C3×D4—61no—
151C2×C3×D4—62no—
152C2×C3×D4—62no—
153C2×C3×D4—61no—
154C2×C3×D4—62no—
155C2×C3×D4C4×D312yes—
156C2×C3×D4D1212yes—
157C2×C3×D4C2×Dic312yes—
158C2×C3×D4#6712yes—
159C22×C3×C4—21no—
160C22×C3×C4—31no—
161C22×C3×C4—62no—
162C22×C3×C4—61no—
163C22×C3×C4—62no—
164C22×C3×C4#6711yescharacteristic
165C22×C3×C4#6711yescharacteristic
166C2×#67—22no—
167C2×#67—22no—
168C2×#67—21no—
169C2×#67—21no—
170C2×#67—22no—
171C22×Dic3—22no—
172C22×Dic3—22no—
173C22×Dic3—21no—
174C22×Dic3—62no—
175C22×Dic3—62no—
176C22×Dic3—122no—
177C22×Dic3C2×Dic311yescharacteristic, complemented
178C3×C4⋊C4—62no—
179C3×C4⋊C4—62no—
180C3×C22⋊C4—32no—
181C3×C22⋊C4—34no—
182C3×C22⋊C4—62no—
183C3×C22⋊C4—62no—
184C3×C22⋊C4—62no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—62no—
187C3×C42—62no—
188#217—22no—
189#217—22no—
190#217—22no—
191#217—21no—
192#217—64no—
193#217—62no—
194#217—62no—
195#217—62no—
196#217—62no—
197#217—122no—
198#217C2×Dic312yescomplemented
199#217#6714yescomplemented
200(C2×D3)⋊C4—22no—
201C4⋊Dic3—22no—
202Dic3⋊C4—22no—
203C4×Dic3—22no—
204C22×C32—22no—
205C22×C32—42no—
206C22×C32—41no—
207C22×C32—41no—
208C22×C32—42no—
209C22×C32—41no—
210C22×C32—42no—
211C22×C32—42no—
212C22×C32—81no—
213C22×C32C2×C22⋊C411yescharacteristic
214C22×C32C4×D412yes—
215C22×C32#12011yescharacteristic
216C22×C32#12112yes—
217C22×C32#12311yescharacteristic
218C2×C3×D3—42no—
219C2×C3×D3—41no—
220C2×C3×D3—82no—
221C32×C4—22no—
222C3⋊Dic3—82no—
223C3×Dic3—44no—
224C3×Dic3—42no—
225C3×Dic3—41no—
226C22×D4—31no—
227C22×D4D3211yescharacteristic
228#123—32no—
229#123—61no—
230#121—62no—
231#120—32no—
232#120—61no—
233C4×D4—64no—
234#117—61no—
235C2×C22⋊C4—32no—
236C2×C22⋊C4—31no—
237C2×C22⋊C4—61no—
238C2×C22⋊C4—92no—
239#99—184no—
240#99—182no—
241C23×C3—21no—
242C23×C3—21no—
243C23×C3—21no—
244C23×C3—21no—
245C23×C3—22no—
246C23×C3—21no—
247C23×C3—22no—
248C23×C3—21no—
249C23×C3—21no—
250C23×C3—22no—
251C23×C3—41no—
252C23×C3—41no—
253C23×C3—61no—
254C23×C3—62no—
255C23×C3—81no—
256C23×C3—81no—
257C23×C3—81no—
258C23×C3—81no—
259C23×C3—82no—
260C23×C3—82no—
261C23×C3—241no—
262C23×C3(C2×D3)⋊C412yes—
263C23×C3#21712yes—
264C23×C3C2×C4×D311yescharacteristic
265C23×C3C2×D1211yescharacteristic
266C23×C3#23512yes—
267C23×C3D3×D412yes—
268C23×C3#23712yes—
269C23×C3C22×Dic311yescharacteristic
270C23×C3C2×#6711yescharacteristic
271C23×C3C2×#6711yescharacteristic
272C23×C3C2×#6711yescharacteristic
273C23×C3C2×#6712yes—
274C22×D3—21no—
275C22×D3—22no—
276C22×D3—81no—
277C3×D4—24no—
278C3×D4—24no—
279C3×D4—24no—
280C3×D4—24no—
281C3×D4—44no—
282C3×D4—44no—
283C3×D4—121no—
284C3×D4—122no—
285C3×D4—121no—
286C3×D4—242no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—62no—
295C2×C3×C4—61no—
296C2×C3×C4—62no—
297C2×C3×C4—64no—
298C2×C3×C4—242no—
299C2×C3×C4—242no—
300C2×C3×C4—241no—
301C2×C3×C4(C2×D3)⋊C412yes—
302C2×C3×C4#21712yes—
303#67—41no—
304#67—41no—
305#67—42no—
306#67—82no—
307C2×Dic3—22no—
308C2×Dic3—21no—
309C2×Dic3—22no—
310C2×Dic3—24no—
311C2×Dic3—82no—
312C2×Dic3—82no—
313C2×Dic3—81no—
314C2×Dic3—124no—
315C2×Dic3—122no—
316C2×Dic3—122no—
317C2×Dic3—244no—
318C2×Dic3—242no—
319C2×Dic3—242no—
320C2×C32—21no—
321C2×C32—21no—
322C2×C32—21no—
323C2×C32—22no—
324C2×C32—22no—
325C2×C32—42no—
326C2×C32#38611yescharacteristic
327C3×D3—81no—
328C24—31no—
329C24#62511yescharacteristic
330C24C2×D3211yescharacteristic
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—62no—
334C2×D4—61no—
335C2×D4—61no—
336C2×D4—62no—
337C2×D4—62no—
338C2×D4D3×Dic312yes—
339C2×D4#62612yes—
340C22×C4—31no—
341C22×C4—62no—
342C22×C4—61no—
343C22×C4—62no—
344C22×C4—182no—
345C22×C4#62511yescharacteristic
346C4⋊C4—62no—
347C4⋊C4—62no—
348C22⋊C4—32no—
349C22⋊C4—34no—
350C22⋊C4—62no—
351C22⋊C4—62no—
352C22⋊C4—62no—
353C22⋊C4—61no—
354C22⋊C4—62no—
355C22⋊C4—182no—
356C22⋊C4—182no—
357C42—62no—
358C22×C3—22no—
359C22×C3—22no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—22no—
363C22×C3—21no—
364C22×C3—22no—
365C22×C3—42no—
366C22×C3—41no—
367C22×C3—42no—
368C22×C3—42no—
369C22×C3—42no—
370C22×C3—41no—
371C22×C3—42no—
372C22×C3—41no—
373C22×C3—41no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—42no—
377C22×C3—42no—
378C22×C3—42no—
379C22×C3—44no—
380C22×C3—42no—
381C22×C3—42no—
382C22×C3—81no—
383C22×C3—82no—
384C22×C3—81no—
385C22×C3—82no—
386C22×C3—82no—
387C22×C3—81no—
388C22×C3—81no—
389C22×C3—82no—
390C22×C3—122no—
391C22×C3—121no—
392C22×C3—242no—
393C22×C3C2×(C2×D3)⋊C411yescharacteristic
394C22×C3C4×#6712yes—
395C22×C3#92911yescharacteristic
396C22×C3#93012yes—
397C22×C3D4×Dic312yes—
398C22×C3#93511yescharacteristic
399C22×C3#93711yescharacteristic
400C22×C3#93912yes—
401C22×C3C2×#21711yescharacteristic
402C22×C3#95311yescharacteristic
403C2×D3—42no—
404C2×D3—41no—
405C2×D3—82no—
406C3×C4—22no—
407C3×C4—22no—
408C3×C4—42no—
409C3×C4—124no—
410C3×C4—122no—
411C3×C4—121no—
412Dic3—44no—
413Dic3—42no—
414Dic3—41no—
415Dic3—242no—
416Dic3—242no—
417Dic3—244no—
418C32#191311yescharacteristic, complemented, Sylow
419C23—21no—
420C23—21no—
421C23—61no—
422C23—62no—
423C23—81no—
424C23—81no—
425C23—241no—
426C23(C2×D3)⋊Dic312yes—
427C23C2×D3×Dic311yescharacteristic
428C23#380412yes—
429C23C2×#62511yescharacteristic
430C23C2×#62611yescharacteristic
431C23D3×#6712yes—
432D4—24no—
433D4—24no—
434D4—121no—
435D4—121no—
436D4—122no—
437D4—242no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—62no—
441C2×C4—61no—
442C2×C4—62no—
443C2×C4—64no—
444C2×C4—242no—
445C2×C4—242no—
446C2×C4—241no—
447C2×C4—362no—
448C2×C4—722no—
449C2×C4(C2×D3)⋊Dic312yes—
450C2×C3—22no—
451C2×C3—21no—
452C2×C3—22no—
453C2×C3—21no—
454C2×C3—22no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—22no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—22no—
461C2×C3—21no—
462C2×C3—42no—
463C2×C3—41no—
464C2×C3—41no—
465C2×C3—42no—
466C2×C3—42no—
467C2×C3—42no—
468C2×C3—82no—
469C2×C3—241no—
470C2×C3#521311yescharacteristic
471C2×C3#522011yescharacteristic
472D3—81no—
473C22—22no—
474C22—41no—
475C22—42no—
476C22—42no—
477C22—41no—
478C22—41no—
479C22—42no—
480C22—42no—
481C22—81no—
482C22—122no—
483C22—121no—
484C22—242no—
485C22C2×(C2×D3)⋊Dic311yescharacteristic
486C22#6396111yescharacteristic
487C22Dic3×#6712yes—
488C22#6397611yescharacteristic
489C22#6397812yes—
490C4—22no—
491C4—124no—
492C4—122no—
493C4—121no—
494C4—722no—
495C3—21no—
496C3#7165611yescharacteristic, complemented
497C3#7184811yescharacteristic, complemented
498C2—21no—
499C2—21no—
500C2—22no—
501C2—21no—
502C2—22no—
503C2—42no—
504C2—241no—
505C2#1059171011yescharacteristic
subgroupG/H
centerC2#10591710
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC22×C32×D4C22
socleC2×C32#386
prime radicalC3×#5804C2
cosocleC24×C32C23
hypercenterC22×D4D32
hypocenterC32#1913
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5798C2semidirect
3. C2×#63661C2semidirect
4. C2×#63580C2semidirect
5. #10589187C2semidirect
16. C3×#937C4semidirect
17. C3×#935C4semidirect
26. #5798D3semidirect
36. C23×C3×D3C2×C4semidirect
51. C22×C3×Dic3C2×C4semidirect
58. C3×#217C2×C4semidirect
59. C3×#217D4semidirect
88. #937Dic3semidirect
89. #935Dic3semidirect
141. C23×D3C2×Dic3semidirect
177. C22×Dic3C2×Dic3semidirect
198. #217C2×Dic3semidirect
199. #217#67semidirect
418. C32#1913semidirect
496. C3#71656semidirect
497. C3#71848semidirect

Maximal subgroups

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

subgroupindex
C3×#58042
C3×#57982
C2×#636612
C2×#635802
#105891872
#718483
#716563