Finite Group Databasebeta

← #11790844

Subgroups — #11790844

Order 1152.

945 conjugacy classes of subgroups.

The subgroup lattice has 527 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2C4×#3757C211yesmaximal, characteristic, complemented
3C3×#5212C211yesmaximal, characteristic, complemented
4C2×#63580C214yesmaximal, complemented
5#71686—31nomaximal
6#69528—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×C3×#67C2212yes—
9C22×C3×D12C411yescharacteristic, complemented
10C2×#3757C2212yes—
11C2×C4×C3⋊Dic3—21no—
12C2×C3×#217C2212yes—
13C3×#930—21no—
14C3×#930—21no—
15C3×#930—21no—
16C3×#930—21no—
17C2×C3×(C2×D3)⋊C4C412yescomplemented
18C2×C3×C4⋊Dic3—21no—
19C2×C3×C4⋊Dic3C411yescharacteristic, complemented
20#63658—21no—
21C3×C3⋊#95—21no—
22#63580—28no—
23C2×C3×#121—31no—
24C2×#930D311yescharacteristic
25C3×#380—31no—
26C2×#834—34no—
27#5212D311yescharacteristic, complemented
28C4×#217—31no—
29C4×#217—31no—
30C4×#217—61no—
31C2×#806—34no—
32C24×C32C2311yescharacteristic
33C23×C3×D3C2×C412yes—
34C22×C32×C4—42no—
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C3⋊Dic3—22no—
42C2×C3×#67—22no—
43C2×C3×#67—22no—
44C2×C3×#67—24no—
45C2×C3×#67—24no—
46C22×C3×Dic3—22no—
47C22×C3×Dic3C2×C412yes—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—42no—
51#3757—22no—
52#3757D414yescomplemented
53C4×C3⋊Dic3—42no—
54C3×#217—24no—
55C3×(C2×D3)⋊C4—22no—
56C3×(C2×D3)⋊C4—22no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—42no—
60#1964—91noSylow
61C22×C3×D4—32no—
62C22×C3×D4—31no—
63C23×C3×C4—21no—
64C23×C3×C4C2×D311yescharacteristic
65C23×C3×C4C2×D311yescharacteristic
66C22×#67C2×D312yes—
67C22×D12Dic311yescharacteristic, complemented
68C3×#121—61no—
69C3×#121—61no—
70C3×#121—61no—
71C3×#121—61no—
72C2×C3×C4⋊C4—31no—
73C2×C3×C4⋊C4—61no—
74C2×C3×C22⋊C4—32no—
75C2×C3×C22⋊C4—32no—
76C2×#217—32no—
77C2×#217—32no—
78C2×#217—62no—
79C2×#217C2×D312yes—
80#930—21no—
81#930—21no—
82#930—21no—
83#930—21no—
84C2×(C2×D3)⋊C4Dic312yescomplemented
85C2×C4⋊Dic3—21no—
86C2×C4⋊Dic3Dic311yescharacteristic, complemented
87C2×C4×Dic3—62no—
88C2×C4×Dic3—61no—
89C2×C4×Dic3—61no—
90C3×#95—61no—
91#834—68no—
92C3⋊#95—21no—
93C3⋊#95—62no—
94C3⋊#95—61no—
95C3⋊#95—61no—
96#806—68no—
97C23×C32—41no—
98C23×C32—41no—
99C23×C32C22×C411yescharacteristic
100C23×C32C2×D411yescharacteristic
101C23×C32C2×D412yes—
102C23×C32C2×D411yescharacteristic
103C23×C32#4112yes—
104C22×C3×D3—22no—
105C22×C3×D3—24no—
106C22×C3×D3—42no—
107C22×C3×D3—42no—
108C2×C32×C4—22no—
109C2×C32×C4—22no—
110C2×C32×C4—22no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4C22⋊C411yescharacteristic
115C2×C32×C4C22⋊C411yescharacteristic
116C2×C32×C4C22⋊C411yescharacteristic
117C2×C32×C4C22⋊C411yescharacteristic
118C2×C3⋊Dic3—24no—
119C2×C3⋊Dic3—42no—
120C2×C3⋊Dic3—42no—
121C3×#67—44no—
122C3×#67—42no—
123C3×#67—42no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—42no—
127C2×C3×Dic3—42no—
128C2×C3×Dic3—42no—
129C3×D12—42no—
130C3×D12—42no—
131C2×#121—31no—
132C2×#99—94no—
133#380—31no—
134C4×C22⋊C4—91no—
135C24×C3—21no—
136C24×C3—32no—
137C24×C3C22×D311yescharacteristic
138C24×C3C22×D311yescharacteristic
139C23×D3C2×Dic312yes—
140C2×C3×D4—62no—
141C2×C3×D4—64no—
142C2×C3×D4—64no—
143C2×C3×D4—62no—
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×C3×D4—122no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—32no—
154C22×C3×C4—42no—
155C22×C3×C4—42no—
156C22×C3×C4—44no—
157C22×C3×C4—62no—
158C22×C3×C4C4×D311yescharacteristic
159C22×C3×C4C4×D311yescharacteristic
160C22×C3×C4D1211yescharacteristic
161C22×C3×C4D1211yescharacteristic
162C22×C3×C4C2×Dic311yescharacteristic
163C22×C3×C4C2×Dic311yescharacteristic
164C22×C3×C4#6711yescharacteristic
165C22×C3×C4#6711yescharacteristic
166C22×C3×C4#6711yescharacteristic
167C22×C3×C4#6711yescharacteristic
168C22×C3×C4#6711yescharacteristic
169C22×C3×C4#6711yescharacteristic
170C2×#67—24no—
171C2×#67—24no—
172C2×#67—22no—
173C2×#67—22no—
174C22×Dic3—22no—
175C22×Dic3—64no—
176C22×Dic3—62no—
177C22×Dic3—62no—
178C22×Dic3C2×Dic312yes—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12—42no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—122no—
185C3×C22⋊C4—62no—
186C3×C22⋊C4—62no—
187C3×C22⋊C4—64no—
188#217—24no—
189#217—34no—
190#217—34no—
191#217—64no—
192#217—64no—
193#217—62no—
194#217—62no—
195(C2×D3)⋊C4—22no—
196(C2×D3)⋊C4—22no—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3—42no—
200C4×Dic3—124no—
201C4×Dic3—122no—
202C4×Dic3—122no—
203C22×C32—21no—
204C22×C32—21no—
205C22×C32—21no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32—42no—
210C22×C32—42no—
211C22×C32C2×C22⋊C411yescharacteristic
212C22×C32C4×D412yes—
213C22×C32#12112yes—
214C22×C32#12411yescharacteristic
215C22×C32#12711yescharacteristic
216C2×C3×D3—42no—
217C2×C3×D3—42no—
218C2×C3×D3—42no—
219C2×C3×D3—84no—
220C32×C4—21no—
221C32×C4—21no—
222C32×C4—21no—
223C32×C4#9912yescomplemented
224C3⋊Dic3—44no—
225C3×Dic3—42no—
226C3×Dic3—82no—
227C22×D4—32no—
228C22×D4—31no—
229C23×C4D3211yescharacteristic
230#121—61no—
231#121—61no—
232#121—61no—
233#121—61no—
234C2×C4⋊C4—31no—
235C2×C4⋊C4—61no—
236C2×C22⋊C4—32no—
237C2×C22⋊C4—32no—
238C2×C22⋊C4—92no—
239C2×C42—181no—
240#99—188no—
241#95—61no—
242#95—181no—
243C23×C3—22no—
244C23×C3—22no—
245C23×C3—21no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—41no—
249C23×C3—41no—
250C23×C3—41no—
251C23×C3—41no—
252C23×C3—42no—
253C23×C3—42no—
254C23×C3—62no—
255C23×C3—64no—
256C23×C3—122no—
257C23×C3—122no—
258C23×C3C2×C4×D311yescharacteristic
259C23×C3C2×D1211yescharacteristic
260C23×C3D3×D412yes—
261C23×C3D3×D412yes—
262C23×C3#23712yes—
263C23×C3#23912yes—
264C23×C3C22×Dic311yescharacteristic
265C23×C3C2×#6711yescharacteristic
266C23×C3C2×#6711yescharacteristic
267C23×C3C2×#6711yescharacteristic
268C22×D3—22no—
269C22×D3—24no—
270C22×D3—42no—
271C22×D3—42no—
272C3×D4—122no—
273C3×D4—124no—
274C3×D4—122no—
275C3×D4—122no—
276C3×D4—122no—
277C2×C3×C4—24no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—42no—
297C2×C3×C4—42no—
298C2×C3×C4—42no—
299C2×C3×C4—64no—
300C2×C3×C4—62no—
301C2×C3×C4—122no—
302C2×C3×C4—122no—
303C2×C3×C4—122no—
304C2×C3×C4(C2×D3)⋊C411yescharacteristic
305C2×C3×C4(C2×D3)⋊C411yescharacteristic
306C2×C3×C4(C2×D3)⋊C411yescharacteristic
307C2×C3×C4(C2×D3)⋊C411yescharacteristic
308C2×C3×C4#21711yescharacteristic
309C2×C3×C4#21711yescharacteristic
310C2×C3×C4#21711yescharacteristic
311C2×C3×C4#21711yescharacteristic
312#67—42no—
313#67—44no—
314#67—42no—
315C2×Dic3—24no—
316C2×Dic3—22no—
317C2×Dic3—42no—
318C2×Dic3—42no—
319C2×Dic3—42no—
320C2×Dic3—68no—
321C2×Dic3—64no—
322C2×Dic3—64no—
323C2×Dic3—124no—
324C2×Dic3—122no—
325C2×Dic3—122no—
326C2×Dic3—124no—
327C2×Dic3—122no—
328C2×Dic3—122no—
329D12—42no—
330D12—42no—
331C2×C32—22no—
332C2×C32—21no—
333C2×C32—22no—
334C2×C32—21no—
335C2×C32#39011yescharacteristic
336C2×C32C2×#9911yescharacteristic
337C2×C32#41011yescharacteristic
338C3×D3—82no—
339C24—32no—
340C24C2×D3211yescharacteristic
341C2×D4—64no—
342C2×D4—64no—
343C2×D4—62no—
344C2×D4—62no—
345C2×D4—61no—
346C2×D4—61no—
347C2×D4—122no—
348C22×C4—32no—
349C22×C4—42no—
350C22×C4—62no—
351C22×C4—182no—
352C22×C4D3×Dic311yescharacteristic
353C22×C4D3×Dic311yescharacteristic
354C22×C4#62511yescharacteristic
355C22×C4#62511yescharacteristic
356C22×C4#62611yescharacteristic
357C22×C4#62611yescharacteristic
358C4⋊C4—61no—
359C4⋊C4—61no—
360C4⋊C4—122no—
361C22⋊C4—62no—
362C22⋊C4—62no—
363C22⋊C4—64no—
364C22⋊C4—94no—
365C22⋊C4—182no—
366C42—362no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—22no—
383C22×C3—21no—
384C22×C3—22no—
385C22×C3—21no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—42no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—42no—
394C22×C3—44no—
395C22×C3—44no—
396C22×C3—122no—
397C22×C3—122no—
398C22×C3—122no—
399C22×C3—244no—
400C22×C3#89312yes—
401C22×C3#89512yes—
402C22×C3C2×(C2×D3)⋊C411yescharacteristic
403C22×C3D4×Dic312yes—
404C22×C3#93611yescharacteristic
405C22×C3#93812yes—
406C22×C3#94011yescharacteristic
407C22×C3#94011yescharacteristic
408C22×C3#94711yescharacteristic
409C22×C3C2×#21711yescharacteristic
410C2×D3—42no—
411C2×D3—42no—
412C2×D3—42no—
413C2×D3—84no—
414C3×C4—22no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—22no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—122no—
425C3×C4—242no—
426C3×C4#80612yescomplemented
427C3×C4#83412yescomplemented
428Dic3—42no—
429Dic3—82no—
430Dic3—128no—
431Dic3—124no—
432Dic3—124no—
433C32#196411yescharacteristic, complemented, Sylow
434C23—41no—
435C23—41no—
436C23—62no—
437C23—64no—
438C23—122no—
439C23—122no—
440C23#379612yes—
441C23#380212yes—
442C23C2×D3×Dic311yescharacteristic
443C23C2×#62511yescharacteristic
444C23C2×#62611yescharacteristic
445D4—122no—
446D4—122no—
447D4—122no—
448D4—124no—
449D4—122no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—64no—
457C2×C4—62no—
458C2×C4—122no—
459C2×C4—122no—
460C2×C4—122no—
461C2×C4—184no—
462C2×C4—362no—
463C2×C4—362no—
464C2×C4(C2×D3)⋊Dic311yescharacteristic
465C2×C4(C2×D3)⋊Dic311yescharacteristic
466C2×C4(C2×D3)⋊Dic311yescharacteristic
467C2×C4(C2×D3)⋊Dic311yescharacteristic
468C2×C3—24no—
469C2×C3—22no—
470C2×C3—21no—
471C2×C3—22no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—22no—
475C2×C3—22no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—41no—
481C2×C3—42no—
482C2×C3—41no—
483C2×C3—242no—
484C2×C3C2×#80611yescharacteristic
485C2×C3#498811yescharacteristic
486C2×C3#500611yescharacteristic
487C2×C3C2×#83411yescharacteristic
488C2×C3#522111yescharacteristic
489C2×C3#524011yescharacteristic
490D3—82no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—42no—
498C22—42no—
499C22—122no—
500C22—122no—
501C22—122no—
502C22—244no—
503C22#6386311yescharacteristic
504C22#6389812yes—
505C22#6391411yescharacteristic
506C22#6391612yes—
507C22C2×(C2×D3)⋊Dic311yescharacteristic
508C4—21no—
509C4—21no—
510C4—21no—
511C4—122no—
512C4—242no—
513C4—364no—
514C4#6358012yescomplemented
515C3—21no—
516C3#6952811yescharacteristic, complemented
517C3#7168611yescharacteristic, complemented
518C2—21no—
519C2—22no—
520C2—22no—
521C2—21no—
522C2—242no—
523C2#1059123111yescharacteristic
524C2#1059132311yescharacteristic
525C2C2×#6358011yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic3
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#930C2
cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1964
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C4×#3757C2semidirect
3. C3×#5212C2semidirect
4. C2×#63580C2semidirect
9. C22×C3×D12C4semidirect
17. C2×C3×(C2×D3)⋊C4C4semidirect
19. C2×C3×C4⋊Dic3C4semidirect
27. #5212D3semidirect
52. #3757D4semidirect
67. C22×D12Dic3semidirect
84. C2×(C2×D3)⋊C4Dic3semidirect
86. C2×C4⋊Dic3Dic3semidirect
223. C32×C4#99semidirect
426. C3×C4#806semidirect
427. C3×C4#834semidirect
433. C32#1964semidirect
514. C4#63580semidirect
516. C3#69528semidirect
517. C3#71686semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9302
C4×#37572
C3×#52122
C2×#635802
#716863
#695283