Finite Group Databasebeta

← #11787356

Subgroups — #11787356

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64139C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C2×C3×#830C211yesmaximal, characteristic, complemented
4C2×#63564C212yesmaximal, complemented
5#10589164C212yesmaximal, complemented
6#71586—31nomaximal
7#69933—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C22×#638—21no—
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11#64139—22no—
12#64139C414yescomplemented
13C2×#3752—21no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×#217—21no—
16C3×#926—24no—
17C2×C3×C4⋊Dic3C2212yes—
18C2×C3×C4×Dic3—21no—
19C22×C3×C3⋊C8C2212yes—
20C3×#830—22no—
21#63564—24no—
22C2×C3×#117—31no—
23C2×#930—31no—
24C2×#930—31no—
25C2×#930—61no—
26C2×#926D311yescharacteristic, complemented
27C2×C3×C22⋊C8—31no—
28C2×#830D311yescharacteristic, complemented
29C2×#821—32no—
30C2×#809—32no—
31#4551—32no—
32#4529—32no—
33C24×C32D411yescharacteristic
34C23×C3⋊D3—21no—
35C22×C32×C4—22no—
36C22×C32×C4—22no—
37C22×C32×C4C2×C412yes—
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D412yes—
40C22×C32×C4C2311yescharacteristic
41C2×#638—24no—
42C2×#638—44no—
43C22×C3⋊Dic3—21no—
44C2×C4⋊(C3⋊D3)—22no—
45C2×C4⋊(C3⋊D3)—22no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)C2×C412yes—
48C22×C3×Dic3—22no—
49#3752—24no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)C2×C412yes—
52C3×#217—24no—
53C3×C4⋊Dic3—22no—
54C3×C4⋊Dic3D414yescomplemented
55C3×C4×Dic3—24no—
56C2×C3×C3⋊C8—22no—
57C2×C3×C3⋊C8—22no—
58C2×C3×C3⋊C8—22no—
59#1875—91noSylow
60C23×C3×C4—21no—
61C23×C3×C4C2×D311yescharacteristic
62C23×C3×C4C2×D311yescharacteristic
63C22×#67—62no—
64C22×#67—61no—
65C22×#67—61no—
66C22×D12—31no—
67C22×D12—31no—
68C22×D12—61no—
69C22×C3×C8—32no—
70C3×#117—64no—
71C2×C3×C4⋊C4—32no—
72C2×C3×C22⋊C4—61no—
73C2×C3×C42—61no—
74C2×#217—21no—
75#930—34no—
76#930—34no—
77#930—64no—
78#930—64no—
79#930—62no—
80#930—62no—
81C2×(C2×D3)⋊C4—62no—
82C2×(C2×D3)⋊C4—61no—
83C2×(C2×D3)⋊C4—61no—
84#926—24no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—61no—
88C2×C4⋊Dic3C2×D312yes—
89C2×C4×Dic3—21no—
90C22×C3⋊C8C2×D312yes—
91C3×C22⋊C8—62no—
92#830—22no—
93#821—64no—
94#809—64no—
95C23×C32—22no—
96C23×C32—21no—
97C23×C32—21no—
98C23×C32—22no—
99C23×C32C22⋊C412yes—
100C23×C32C2×D411yescharacteristic
101C22×C3⋊D3—22no—
102C22×C3⋊D3—41no—
103C22×C3⋊D3—41no—
104C22×C3⋊D3—42no—
105C22×C3⋊D3—42no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4—24no—
109C2×C32×C4—24no—
110C2×C32×C4C22⋊C412yes—
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D412yes—
114C2×C32×C4#4112yes—
115#638—48no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—42no—
118C4⋊(C3⋊D3)—24no—
119C4⋊(C3⋊D3)—42no—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—42no—
122C2×C3×Dic3—42no—
123C3×C3⋊C8—42no—
124C2×#121—91no—
125C2×#117—31no—
126C2×#102—92no—
127C2×C22⋊C8—31no—
128#340—92no—
129C24×C3—21no—
130C24×C3D1211yescharacteristic
131C24×C3#6711yescharacteristic
132C23×D3—62no—
133C23×D3—61no—
134C23×D3—61no—
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—21no—
141C22×C3×C4—22no—
142C22×C3×C4—21no—
143C22×C3×C4—42no—
144C22×C3×C4—42no—
145C22×C3×C4—62no—
146C22×C3×C4C4×D312yes—
147C22×C3×C4C4×D312yes—
148C22×C3×C4D1211yescharacteristic
149C22×C3×C4D1212yes—
150C22×C3×C4#6711yescharacteristic
151C22×C3×C4#6712yes—
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C2×#67—68no—
155C2×#67—64no—
156C2×#67—64no—
157C2×#67—128no—
158C2×#67—124no—
159C2×#67—124no—
160C22×Dic3—22no—
161C22×Dic3—62no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C2×D12—32no—
165C2×D12—32no—
166C2×D12—62no—
167C2×D12—62no—
168C2×D12—62no—
169C2×D12—62no—
170C2×D12—62no—
171C2×D12—62no—
172C2×D12—61no—
173C2×D12—61no—
174C2×D12—122no—
175C2×D12—122no—
176C2×C3×C8—62no—
177C2×C3×C8—62no—
178C2×C3×C8—62no—
179C3×C4⋊C4—34no—
180C3×C4⋊C4—62no—
181C3×C22⋊C4—64no—
182C3×C42—64no—
183#217—24no—
184(C2×D3)⋊C4—68no—
185(C2×D3)⋊C4—64no—
186(C2×D3)⋊C4—64no—
187C4⋊Dic3—22no—
188C4⋊Dic3—32no—
189C4⋊Dic3—32no—
190C4⋊Dic3—62no—
191C4⋊Dic3—62no—
192C4⋊Dic3—61no—
193C4⋊Dic3—61no—
194C4⋊Dic3#6714yescomplemented
195C4×Dic3—24no—
196C2×C3⋊C8—22no—
197C2×C3⋊C8—22no—
198C2×C3⋊C8—22no—
199C22×C32—22no—
200C22×C32—22no—
201C22×C32—22no—
202C22×C32—42no—
203C22×C32—42no—
204C22×C32C2×C22⋊C411yescharacteristic
205C22×C32#12011yescharacteristic
206C22×C32#12311yescharacteristic
207C22×C32#13512yes—
208C22×C32AGL(1,ℤ/8)12yes—
209C2×C3⋊D3—42no—
210C2×C3⋊D3—42no—
211C2×C3⋊D3—42no—
212C2×C3⋊D3—82no—
213C2×C3⋊D3—82no—
214C32×C4—22no—
215C32×C4C4×D412yes—
216C32×C4#12112yes—
217C3⋊Dic3—42no—
218C3×Dic3—44no—
219C22×D4—91no—
220C22×D4—181no—
221C23×C4D3211yescharacteristic
222C22×C8—32no—
223#121—94no—
224#121—182no—
225#117—64no—
226C2×C4⋊C4—32no—
227C2×C4⋊C4—91no—
228C2×C22⋊C4—61no—
229C2×C22⋊C4—181no—
230C2×C42—61no—
231#102—184no—
232C22⋊C8—62no—
233C23×C3—24no—
234C23×C3—21no—
235C23×C3—21no—
236C23×C3—22no—
237C23×C3—22no—
238C23×C3—21no—
239C23×C3—22no—
240C23×C3—22no—
241C23×C3—21no—
242C23×C3—22no—
243C23×C3—21no—
244C23×C3—41no—
245C23×C3—41no—
246C23×C3—42no—
247C23×C3(C2×D3)⋊C412yes—
248C23×C3(C2×D3)⋊C412yes—
249C23×C3C2×D1211yescharacteristic
250C23×C3C2×#6711yescharacteristic
251C22×D3—64no—
252C22×D3—62no—
253C22×D3—62no—
254C22×D3—122no—
255C22×D3—122no—
256C22×D3—124no—
257C22×D3—124no—
258C22×D3—121no—
259C22×D3—121no—
260C22×D3—122no—
261C22×D3—122no—
262C22×D3—121no—
263C22×D3—122no—
264C22×D3—122no—
265C22×D3—121no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—24no—
271C2×C3×C4—24no—
272C2×C3×C4—24no—
273C2×C3×C4—24no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—22no—
279C2×C3×C4—44no—
280C2×C3×C4—44no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—64no—
284C2×C3×C4—122no—
285C2×C3×C4—122no—
286C2×C3×C4(C2×D3)⋊C412yes—
287C2×C3×C4(C2×D3)⋊C412yes—
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4C2×D1211yescharacteristic
291C2×C3×C4#23512yes—
292C2×C3×C4D3×D412yes—
293C2×C3×C4#23712yes—
294C2×C3×C4C2×#6711yescharacteristic
295C2×C3×C4C2×#6712yes—
296#67—1216no—
297#67—128no—
298#67—128no—
299C2×Dic3—24no—
300C2×Dic3—42no—
301C2×Dic3—42no—
302C2×Dic3—64no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—124no—
306C2×Dic3—122no—
307C2×Dic3—122no—
308D12—64no—
309D12—64no—
310D12—124no—
311D12—124no—
312D12—122no—
313D12—122no—
314C3×C8—122no—
315C3⋊C8—42no—
316C2×C32—42no—
317C2×C32#38611yescharacteristic
318C2×C32#41611yescharacteristic
319C2×C32#41811yescharacteristic
320C2×C32#44912yes—
321C2×C32#48212yes—
322C3⋊D3—82no—
323C24—181no—
324C24#62611yescharacteristic
325C2×D4—92no—
326C2×D4—184no—
327C2×D4—182no—
328C2×D4—181no—
329C2×D4—182no—
330C2×D4—364no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—62no—
334C22×C4—181no—
335C22×C4#62412yes—
336C22×C4#62611yescharacteristic
337C22×C4#62612yes—
338C22×C4C2×D3211yescharacteristic
339C2×C8—62no—
340C2×C8—62no—
341C2×C8—62no—
342C4⋊C4—34no—
343C4⋊C4—62no—
344C4⋊C4—92no—
345C4⋊C4—181no—
346C22⋊C4—64no—
347C22⋊C4—184no—
348C42—64no—
349C22×C3—24no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—22no—
355C22×C3—22no—
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—42no—
362C22×C3—42no—
363C22×C3—44no—
364C22×C3—44no—
365C22×C3—42no—
366C22×C3—42no—
367C22×C3—42no—
368C22×C3—42no—
369C22×C3#88211yescharacteristic
370C22×C3#88611yescharacteristic
371C22×C3#90412yes—
372C22×C3#90812yes—
373C22×C3C2×(C2×D3)⋊C411yescharacteristic
374C22×C3C2×(C2×D3)⋊C411yescharacteristic
375C22×C3#92911yescharacteristic
376C22×C3#94912yes—
377C22×C3#95012yes—
378C22×C3#95311yescharacteristic
379C2×D3—124no—
380C2×D3—124no—
381C2×D3—124no—
382C2×D3—122no—
383C2×D3—122no—
384C2×D3—122no—
385C2×D3—122no—
386C2×D3—122no—
387C2×D3—122no—
388C2×D3—244no—
389C2×D3—244no—
390C2×D3—242no—
391C2×D3—242no—
392C2×D3—242no—
393C2×D3—242no—
394C3×C4—22no—
395C3×C4—22no—
396C3×C4—22no—
397C3×C4—22no—
398C3×C4—42no—
399C3×C4—124no—
400C3×C4#67⋊C412yes—
401C3×C4C4×#6712yes—
402C3×C4#93012yes—
403C3×C4#93912yes—
404Dic3—44no—
405Dic3—124no—
406Dic3—122no—
407Dic3—122no—
408C32#187511yescharacteristic, complemented, Sylow
409C23—22no—
410C23—22no—
411C23—21no—
412C23—21no—
413C23—182no—
414C23—362no—
415C23—362no—
416C23—361no—
417C23—361no—
418C23#372212yes—
419C23C2×#62611yescharacteristic
420D4—184no—
421D4—368no—
422D4—362no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—64no—
428C2×C4—122no—
429C2×C4—122no—
430C2×C4—182no—
431C2×C4—362no—
432C2×C4#372212yes—
433C2×C4#380412yes—
434C2×C4C2×#62411yescharacteristic
435C2×C4C2×#62611yescharacteristic
436C2×C4D3×#6712yes—
437C8—122no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—22no—
441C2×C3—22no—
442C2×C3—21no—
443C2×C3—44no—
444C2×C3—42no—
445C2×C3—42no—
446C2×C3#473412yes—
447C2×C3#473712yes—
448C2×C3#495811yescharacteristic
449C2×C3#500111yescharacteristic
450C2×C3#500211yescharacteristic
451C2×C3#500312yes—
452C2×C3#511311yescharacteristic
453C2×C3#513111yescharacteristic
454C2×C3#521311yescharacteristic
455C2×C3#523812yes—
456D3—244no—
457D3—242no—
458D3—242no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—42no—
463C22—42no—
464C22—362no—
465C22—362no—
466C22—362no—
467C22—722no—
468C22—722no—
469C22#6382512yes—
470C22#6382912yes—
471C22C2×#372211yescharacteristic
472C22#6396611yescharacteristic
473C22#6397711yescharacteristic
474C4—22no—
475C4—124no—
476C4—362no—
477C4#6395212yes—
478C4#6397812yes—
479C3—21no—
480C3#6993311yescharacteristic, complemented
481C3#7158611yescharacteristic, complemented
482C2—42no—
483C2—722no—
484C2#1059109611yescharacteristic
485C2#1059110511yescharacteristic
486C2#1059113612yes—
487C2#1059116312yes—
488C2#1059171111yescharacteristic
subgroupG/H
centerC23C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC2×#64139C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1875
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C2×C3×#830C2semidirect
4. C2×#63564C2semidirect
5. #10589164C2semidirect
12. #64139C4semidirect
26. C2×#926D3semidirect
28. C2×#830D3semidirect
54. C3×C4⋊Dic3D4semidirect
194. C4⋊Dic3#67semidirect
408. C32#1875semidirect
480. C3#69933semidirect
481. C3#71586semidirect

Maximal subgroups

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

subgroupindex
C2×#641392
C2×C3×#9262
C2×C3×#8302
C2×#635642
#105891642
#715863
#699333