Finite Group Databasebeta

← #11787976

Subgroups — #11787976

Order 1152.

941 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596269C211yesmaximal, characteristic
2C2×C3×#935C211yesmaximal, characteristic
3C2×C3×#834C211yesmaximal, characteristic
4#10591696C212yesmaximal, complemented
5#10589187C212yesmaximal, complemented
6#71704—31nomaximal
7#70023—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C23×C3×Dic3C2211yescharacteristic
10C2×#3757—21no—
11C2×#3757C2212yes—
12D4×C3⋊Dic3—24no—
13#64135—21no—
14C2×C3×#217—21no—
15C2×C3×#217C2212yes—
16C2×C3×#217C2211yescharacteristic
17C3×#935—22no—
18C3×#935C414yescomplemented
19C2×C3×Dic3⋊C4—21no—
20C3×#834—22no—
21#63579—24no—
22C2×C3×#123—31no—
23#5798—31no—
24#5798—31no—
25#5798—61no—
26C2×#935D311yescharacteristic
27C2×C3×#99—31no—
28C2×#834D311yescharacteristic
29#5211—32no—
30#4943—32no—
31#4527—32no—
32#4527—32no—
33C24×C32D411yescharacteristic
34C24×C32C2311yescharacteristic
35C2×C32×D4—22no—
36C2×C32×D4—22no—
37C2×C32×D4C2×C412yes—
38C2×C32×D4D412yes—
39C22×C32×C4D411yescharacteristic
40C22×C3⋊Dic3—22no—
41C22×C3⋊Dic3D414yes—
42C22×C3×Dic3—21no—
43C22×C3×Dic3—21no—
44C22×C3×Dic3—21no—
45C22×C3×Dic3—22no—
46C22×C3×Dic3—22no—
47C22×C3×Dic3—22no—
48C22×C3×Dic3C2×C412yescomplemented
49#3757—22no—
50#3757—22no—
51#3757—22no—
52C4⋊(C3⋊Dic3)—22no—
53C4×C3⋊Dic3—22no—
54C3×#217—24no—
55C3×#217—21no—
56C3×#217—22no—
57C3×#217—22no—
58C3×#217C2×C412yescomplemented
59C3×Dic3⋊C4—24no—
60#1890—91noSylow
61C22×C3×D4—21no—
62C22×C3×D4C2×D311yescharacteristic
63C22×C3×D4C2×D311yescharacteristic
64C23×C3×C4—31no—
65C23×Dic3C2×D311yescharacteristic
66C3×#123—34no—
67C3×#123—62no—
68C2×C3×C4⋊C4—61no—
69C2×C3×C22⋊C4—31no—
70C2×C3×C22⋊C4—32no—
71C2×C3×C22⋊C4—61no—
72C2×#217—21no—
73C2×#217—32no—
74C2×#217—32no—
75C2×#217—62no—
76C2×#217—62no—
77C2×#217—61no—
78C2×#217—61no—
79C2×#217C2×D312yes—
80C2×#217C2×D311yescharacteristic
81#935—22no—
82#935Dic314yescomplemented
83D4×Dic3—64no—
84D4×Dic3—64no—
85D4×Dic3—68no—
86#926—62no—
87#926—61no—
88#926—61no—
89C2×Dic3⋊C4—21no—
90C3×#99—62no—
91#834—22no—
92C3⋊#95—64no—
93C3⋊#95—64no—
94C23×C32—21no—
95C23×C32—21no—
96C23×C32—42no—
97C23×C32—42no—
98C23×C32C22⋊C412yes—
99C23×C32C22×C411yescharacteristic
100C23×C32C2×D411yescharacteristic
101C23×C32C2×D412yes—
102C23×C32C2×D411yescharacteristic
103C23×C32#4112yes—
104C32×D4—24no—
105C32×D4—24no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4C22⋊C412yes—
109C2×C3⋊Dic3—24no—
110C2×C3⋊Dic3—44no—
111C2×C3⋊Dic3—82no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—42no—
116C2×C3×Dic3—41no—
117C2×C3×Dic3—42no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—44no—
120C2×C3×Dic3—42no—
121C2×#123—31no—
122#518—91no—
123C2×#99—31no—
124#381—92no—
125#342—92no—
126C24×C3—21no—
127C24×C3—21no—
128C24×C3D1211yescharacteristic
129C24×C3#6711yescharacteristic
130C24×C3C22×D311yescharacteristic
131C24×C3C22×D311yescharacteristic
132C2×C3×D4—24no—
133C2×C3×D4—24no—
134C2×C3×D4—22no—
135C2×C3×D4—22no—
136C2×C3×D4—22no—
137C2×C3×D4—22no—
138C2×C3×D4—22no—
139C2×C3×D4—22no—
140C2×C3×D4C4×D312yes—
141C2×C3×D4C2×Dic312yes—
142C2×C3×D4#6712yes—
143C2×C3×D4#6712yes—
144C22×C3×C4—21no—
145C22×C3×C4—32no—
146C22×C3×C4—61no—
147C22×C3×C4—61no—
148C22×C3×C4—62no—
149C22×C3×C4—62no—
150C22×C3×C4—61no—
151C22×C3×C4—62no—
152C22×C3×C4D1211yescharacteristic
153C22×C3×C4#6711yescharacteristic
154C22×Dic3—22no—
155C22×Dic3—22no—
156C22×Dic3—21no—
157C22×Dic3—21no—
158C22×Dic3—21no—
159C22×Dic3—22no—
160C22×Dic3—34no—
161C22×Dic3—34no—
162C22×Dic3—64no—
163C22×Dic3—64no—
164C22×Dic3—62no—
165C22×Dic3—62no—
166C22×Dic3C2×Dic312yescomplemented
167C3×C4⋊C4—64no—
168C3×C22⋊C4—32no—
169C3×C22⋊C4—64no—
170C3×C22⋊C4—61no—
171C3×C22⋊C4—62no—
172C3×C22⋊C4—62no—
173#217—24no—
174#217—21no—
175#217—22no—
176#217—22no—
177#217—64no—
178#217—64no—
179#217—62no—
180#217—62no—
181#217—64no—
182#217—62no—
183#217—62no—
184#217—62no—
185#217—62no—
186#217C2×Dic312yescomplemented
187C4⋊Dic3—64no—
188C4⋊Dic3—62no—
189C4⋊Dic3—62no—
190Dic3⋊C4—24no—
191C4×Dic3—64no—
192C4×Dic3—62no—
193C4×Dic3—62no—
194C22×C32—22no—
195C22×C32—24no—
196C22×C32—22no—
197C22×C32—42no—
198C22×C32—41no—
199C22×C32—41no—
200C22×C32—42no—
201C22×C32—42no—
202C22×C32—81no—
203C22×C32C2×C22⋊C411yescharacteristic
204C22×C32C4×D412yes—
205C22×C32#12011yescharacteristic
206C22×C32#12112yes—
207C22×C32#12311yescharacteristic
208C32×C4—22no—
209C3⋊Dic3—44no—
210C3×Dic3—42no—
211C3×Dic3—42no—
212C3×Dic3—82no—
213C22×D4D3211yescharacteristic
214C23×C4—31no—
215#123—34no—
216#123—62no—
217C4×D4—184no—
218#117—181no—
219C2×C4⋊C4—61no—
220C2×C22⋊C4—31no—
221C2×C22⋊C4—32no—
222C2×C22⋊C4—61no—
223C2×C22⋊C4—92no—
224C2×C22⋊C4—181no—
225#99—62no—
226#95—184no—
227C23×C3—22no—
228C23×C3—22no—
229C23×C3—21no—
230C23×C3—21no—
231C23×C3—21no—
232C23×C3—21no—
233C23×C3—22no—
234C23×C3—21no—
235C23×C3—22no—
236C23×C3—21no—
237C23×C3—21no—
238C23×C3—22no—
239C23×C3—42no—
240C23×C3—42no—
241C23×C3—42no—
242C23×C3—42no—
243C23×C3—82no—
244C23×C3—82no—
245C23×C3(C2×D3)⋊C412yes—
246C23×C3#21712yes—
247C23×C3C2×C4×D311yescharacteristic
248C23×C3C2×D1211yescharacteristic
249C23×C3D3×D412yes—
250C23×C3D3×D412yes—
251C23×C3#23712yes—
252C23×C3#23712yes—
253C23×C3C22×Dic311yescharacteristic
254C23×C3C2×#6711yescharacteristic
255C23×C3C2×#6711yescharacteristic
256C23×C3C2×#6711yescharacteristic
257C3×D4—28no—
258C3×D4—28no—
259C3×D4—24no—
260C3×D4—24no—
261C3×D4—24no—
262C3×D4—24no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—22no—
270C2×C3×C4—64no—
271C2×C3×C4—62no—
272C2×C3×C4—62no—
273C2×C3×C4—122no—
274C2×C3×C4—121no—
275C2×C3×C4—121no—
276C2×C3×C4—122no—
277C2×C3×C4—124no—
278C2×C3×C4—122no—
279C2×C3×C4(C2×D3)⋊C412yes—
280C2×C3×C4#21712yes—
281C2×Dic3—24no—
282C2×Dic3—22no—
283C2×Dic3—22no—
284C2×Dic3—42no—
285C2×Dic3—41no—
286C2×Dic3—41no—
287C2×Dic3—42no—
288C2×Dic3—44no—
289C2×Dic3—42no—
290C2×Dic3—68no—
291C2×Dic3—64no—
292C2×Dic3—64no—
293C2×Dic3—124no—
294C2×Dic3—124no—
295C2×Dic3—244no—
296C2×Dic3—244no—
297C2×Dic3—242no—
298C2×Dic3—242no—
299C2×C32—21no—
300C2×C32—22no—
301C2×C32—21no—
302C2×C32—22no—
303C2×C32—42no—
304C2×C32#38611yescharacteristic
305C2×C32#45812yes—
306C24#62611yescharacteristic
307C24C2×D3211yescharacteristic
308C2×D4—22no—
309C2×D4—22no—
310C2×D4D3×Dic312yes—
311C2×D4#62512yes—
312C22×C4—32no—
313C22×C4—62no—
314C22×C4—61no—
315C22×C4—61no—
316C22×C4—61no—
317C22×C4—62no—
318C22×C4—62no—
319C22×C4—94no—
320C22×C4—182no—
321C22×C4#62611yescharacteristic
322C4⋊C4—64no—
323C4⋊C4—182no—
324C22⋊C4—32no—
325C22⋊C4—64no—
326C22⋊C4—61no—
327C22⋊C4—62no—
328C22⋊C4—62no—
329C22⋊C4—182no—
330C22⋊C4—182no—
331C22⋊C4—182no—
332C42—182no—
333C22×C3—24no—
334C22×C3—22no—
335C22×C3—22no—
336C22×C3—24no—
337C22×C3—24no—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—22no—
343C22×C3—22no—
344C22×C3—21no—
345C22×C3—44no—
346C22×C3—42no—
347C22×C3—41no—
348C22×C3—42no—
349C22×C3—42no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—42no—
354C22×C3—42no—
355C22×C3—44no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3—81no—
359C22×C3—82no—
360C22×C3—81no—
361C22×C3—82no—
362C22×C3—81no—
363C22×C3—81no—
364C22×C3—82no—
365C22×C3#67⋊C412yes—
366C22×C3#88211yescharacteristic
367C22×C3#88611yescharacteristic
368C22×C3C2×(C2×D3)⋊C411yescharacteristic
369C22×C3D4×Dic312yes—
370C22×C3#93511yescharacteristic
371C22×C3#93711yescharacteristic
372C22×C3#93912yes—
373C22×C3#93912yes—
374C22×C3C2×#21711yescharacteristic
375C3×C4—24no—
376C3×C4—22no—
377C3×C4—22no—
378C3×C4—122no—
379C3×C4—122no—
380C3×C4—242no—
381Dic3—42no—
382Dic3—42no—
383Dic3—82no—
384Dic3—128no—
385Dic3—124no—
386Dic3—124no—
387C32#189011yescharacteristic, complemented, Sylow
388C23—21no—
389C23—21no—
390C23—42no—
391C23—42no—
392C23(C2×D3)⋊Dic312yes—
393C23C2×D3×Dic311yescharacteristic
394C23#380512yes—
395C23C2×#62511yescharacteristic
396C23C2×#62611yescharacteristic
397C23#381112yes—
398D4—24no—
399D4—24no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—64no—
405C2×C4—122no—
406C2×C4—121no—
407C2×C4—122no—
408C2×C4—121no—
409C2×C4—124no—
410C2×C4—122no—
411C2×C4—184no—
412C2×C4—364no—
413C2×C4—722no—
414C2×C4(C2×D3)⋊Dic312yes—
415C2×C3—21no—
416C2×C3—22no—
417C2×C3—21no—
418C2×C3—22no—
419C2×C3—22no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—22no—
423C2×C3—22no—
424C2×C3—21no—
425C2×C3—41no—
426C2×C3—41no—
427C2×C3—42no—
428C2×C3—42no—
429C2×C3—44no—
430C2×C3—42no—
431C2×C3—42no—
432C2×C3#474212yes—
433C2×C3#495811yescharacteristic
434C2×C3#505312yes—
435C2×C3#522011yescharacteristic
436C22—24no—
437C22—22no—
438C22—22no—
439C22—41no—
440C22—42no—
441C22—41no—
442C22—42no—
443C22—42no—
444C22—81no—
445C22C2×(C2×D3)⋊Dic311yescharacteristic
446C22#6396211yescharacteristic
447C22#67⋊Dic312yes—
448C22#6398012yes—
449C22#6398111yescharacteristic
450C4—22no—
451C4—122no—
452C4—122no—
453C4—242no—
454C4—364no—
455C3—21no—
456C3#7002311yescharacteristic, complemented
457C3#7170411yescharacteristic, complemented
458C2—21no—
459C2—22no—
460C2—21no—
461C2—22no—
462C2—42no—
463C2#1059153512yes—
464C2#1059171311yescharacteristic
subgroupG/H
centerC22#63981
commutatorC23×C32C22×C4
FrattiniC24C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32#120
cosocleC24×C32C23
hypercenterC22×D4D32
hypocenterC32#1890
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591696C2semidirect
5. #10589187C2semidirect
18. C3×#935C4semidirect
48. C22×C3×Dic3C2×C4semidirect
58. C3×#217C2×C4semidirect
82. #935Dic3semidirect
166. C22×Dic3C2×Dic3semidirect
186. #217C2×Dic3semidirect
387. C32#1890semidirect
456. C3#70023semidirect
457. C3#71704semidirect

Maximal subgroups

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

subgroupindex
#105962692
C2×C3×#9352
C2×C3×#8342
#105916962
#105891872
#717043
#700233