Finite Group Databasebeta

← #11786470

Subgroups — #11786470

Order 1152.

785 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊Dic3C211yesmaximal, characteristic
2C2×#63644C211yesmaximal, characteristic, complemented
3C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
4#10591313C211yesmaximal, characteristic
5C2×#63573C211yesmaximal, characteristic, complemented
6C3×#4551C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#69928—31nomaximal
9#68875—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×D3×Dic3—21no—
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×Dic3⋊Dic3—21no—
19C2×(C2×D3)⋊Dic3—21no—
20D3×C4⋊Dic3—22no—
21D3×C4⋊Dic3—22no—
22#63644—22no—
23C3×(C2×D3)⋊C8C414yescomplemented
24#63579—21no—
25#63573—22no—
26C22×C4⋊Dic3—31no—
27C2×D3×C4⋊C4—31no—
28C2×C3×C22⋊C8—31no—
29#5212—31no—
30C2×(C2×D3)⋊C8D311yescharacteristic
31C2×#817—31no—
32C2×#817—31no—
33C2×#817—31no—
34C2×#817—61no—
35#4987—31no—
36C2×#808—31no—
37C3×#340—31no—
38#4551—31no—
39#4551D311yescharacteristic, complemented
40#4529—31no—
41C23×C3×D3D411yescharacteristic
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3D411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3C2×C412yes—
53C2×C3×C4×D3Q812yes—
54C2×D3×Dic3—24no—
55C2×D3×Dic3—42no—
56C2×D3×Dic3—42no—
57C2×C32×C8—21no—
58C2×C32×C8—21no—
59C2×C32×C8C2×C412yescomplemented
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)D412yes—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3D412yes—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8C2×C412yescomplemented
71Dic3⋊Dic3—24no—
72(C2×D3)⋊Dic3—42no—
73#1853—91noSylow
74C23×C3×C4—31no—
75C23×Dic3—61no—
76C22×C4×D3—61no—
77C22×C4×D3C2×D311yescharacteristic
78C22×C3×C8—21no—
79C22×C3×C8—31no—
80C22×C3×C8C2×D311yescharacteristic
81C22×C3×C8C2×D311yescharacteristic
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84C2×#217—61no—
85C2×(C2×D3)⋊C4—61no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—61no—
91C2×C4⋊Dic3—61no—
92C2×C4⋊Dic3—62no—
93C2×C4⋊Dic3—61no—
94C2×C4⋊Dic3—62no—
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×Dic3⋊C4—61no—
98C22×C3⋊C8C2×D311yescharacteristic
99D3×C4⋊C4—62no—
100D3×C4⋊C4—62no—
101C3×C22⋊C8—34no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104(C2×D3)⋊C8Dic314yescomplemented
105#817—62no—
106#817—62no—
107#817—64no—
108#817—62no—
109#808—62no—
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—21no—
112C22×C3×D3—21no—
113C22×C3×D3—21no—
114C22×C3×D3—21no—
115C22×C3×D3C4⋊C412yes—
116C22×C3×D3SD1612yes—
117C22×C3×D3SD1612yes—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×Q811yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3C4⋊C412yes—
139C3×C4×D3—22no—
140C3×C4×D3—22no—
141C3×C4×D3—22no—
142C3×C4×D3—22no—
143D3×Dic3—48no—
144C32×C8—22no—
145C3×C3⋊C8—22no—
146C22×C4⋊C4—91no—
147C2×#106—91no—
148C2×#106—91no—
149C2×C22⋊C8—31no—
150#380—91no—
151#340—31no—
152#340—91no—
153C24×C3—31no—
154C23×D3D1211yescharacteristic
155C22×C3×C4—21no—
156C22×C3×C4—31no—
157C22×C3×C4—32no—
158C22×C3×C4—32no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C22×Dic3—21no—
168C22×Dic3—21no—
169C22×Dic3—64no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—61no—
173C22×Dic3—61no—
174C22×Dic3—121no—
175C22×Dic3—121no—
176C22×Dic3—122no—
177C22×Dic3—122no—
178C22×Dic3D1211yescharacteristic
179C2×C4×D3—21no—
180C2×C4×D3—21no—
181C2×C4×D3—21no—
182C2×C4×D3—21no—
183C2×C4×D3—64no—
184C2×C4×D3—122no—
185C2×C4×D3—122no—
186C2×C4×D3Dic612yes—
187C2×C4×D3C2×Dic312yes—
188C2×C3×C8—22no—
189C2×C3×C8—22no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—22no—
195C2×C3×C8—32no—
196C2×C3×C8—61no—
197C2×C3×C8—61no—
198C2×C3×C8C4×D312yescomplemented
199C2×C3×C8C2×Dic312yescomplemented
200C3×C4⋊C4—32no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204#217—122no—
205(C2×D3)⋊C4—122no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C4⋊Dic3—21no—
209C4⋊Dic3—32no—
210C4⋊Dic3—32no—
211C4⋊Dic3—62no—
212C4⋊Dic3—64no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3—62no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3—61no—
220C4⋊Dic3—121no—
221C4⋊Dic3—121no—
222C4⋊Dic3D1212yes—
223Dic3⋊C4—64no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8C2×Dic312yescomplemented
227C22×C32C2×C4⋊C411yescharacteristic
228C22×C32#12011yescharacteristic
229C22×C32#12311yescharacteristic
230C22×C32C2×SD1611yescharacteristic
231C22×C32C2×SD1611yescharacteristic
232C22×C32AGL(1,ℤ/8)11yescharacteristic
233C22×C32#13711yescharacteristic
234C2×C3×D3—22no—
235C2×C3×D3—22no—
236C2×C3×D3—22no—
237C2×C3×D3—22no—
238C2×C3×D3—22no—
239C2×C3×D3—22no—
240C2×C3×D3#10614yescomplemented
241C32×C4C4×D411yescharacteristic
242C32×C4C4×D411yescharacteristic
243C32×C4C22⋊Q811yescharacteristic
244C32×C4C22⋊Q811yescharacteristic
245C3⋊Dic3—42no—
246C3⋊Dic3—81no—
247C3×Dic3—22no—
248C3×Dic3—42no—
249C3×Dic3—81no—
250C23×C4—31no—
251C23×C4—181no—
252C22×C8—31no—
253C22×C8D3211yescharacteristic
254C2×C4⋊C4—31no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—182no—
259C2×C4⋊C4—182no—
260C2×C4⋊C4—181no—
261C2×C22⋊C4—181no—
262#106—182no—
263#106—182no—
264C22⋊C8—34no—
265#95—181no—
266C23×C3—21no—
267C23×C3—32no—
268C23×C3—32no—
269C23×C3—32no—
270C23×C3—61no—
271C23×C3—61no—
272C23×C3—61no—
273C23×C3—61no—
274C23×C3C2×D1211yescharacteristic
275C23×C3D3×D411yescharacteristic
276C22×D3—21no—
277C22×D3—21no—
278C22×D3—21no—
279C22×D3—21no—
280C22×D3#20412yes—
281C22×D3#20412yes—
282C22×D3C4⋊Dic312yes—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—32no—
290C2×C3×C4—61no—
291C2×C3×C4—61no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4C2×Dic611yescharacteristic
303C2×C3×C4C2×C4×D311yescharacteristic
304C2×C3×C4C2×D1211yescharacteristic
305C2×C3×C4#23511yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4#23711yescharacteristic
310C2×C3×C4#23711yescharacteristic
311C2×C3×C4#23711yescharacteristic
312C2×C3×C4D3×Q811yescharacteristic
313C2×C3×C4C22×Dic311yescharacteristic
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—22no—
317C2×Dic3—41no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—41no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—122no—
325C2×Dic3—128no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3—121no—
329C2×Dic3—121no—
330C2×Dic3—122no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—121no—
337C2×Dic3—241no—
338C2×Dic3—241no—
339C2×Dic3—241no—
340C2×Dic3—241no—
341C2×Dic3C4⋊Dic312yes—
342C4×D3—22no—
343C4×D3—22no—
344C4×D3—22no—
345C4×D3—22no—
346C4×D3—128no—
347C3×C8—24no—
348C3×C8—22no—
349C3×C8—22no—
350C3×C8—62no—
351C3⋊C8—22no—
352C2×C32#38511yescharacteristic
353C2×C32C2×#10611yescharacteristic
354C2×C32#42811yescharacteristic
355C2×C32#44811yescharacteristic
356C2×C32#45011yescharacteristic
357C2×C32#48111yescharacteristic
358C2×C32#48311yescharacteristic
359C3×D3—24no—
360C24—31no—
361C22×C4—31no—
362C22×C4—32no—
363C22×C4—32no—
364C22×C4—61no—
365C22×C4—61no—
366C22×C4—61no—
367C22×C4—61no—
368C22×C4—61no—
369C22×C4—61no—
370C22×C4—184no—
371C22×C4—181no—
372C22×C4—181no—
373C22×C4—362no—
374C22×C4—362no—
375C22×C4C2×D3211yescharacteristic
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—32no—
379C2×C8—61no—
380C2×C8—61no—
381C2×C8D3×Dic312yescomplemented
382C4⋊C4—32no—
383C4⋊C4—61no—
384C4⋊C4—61no—
385C4⋊C4—61no—
386C4⋊C4—92no—
387C4⋊C4—184no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C22⋊C4—362no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—34no—
400C22×C3—62no—
401C22×C3—62no—
402C22×C3—62no—
403C22×C3—62no—
404C22×C3—62no—
405C22×C3—62no—
406C22×C3#88211yescharacteristic
407C22×C3#88211yescharacteristic
408C22×C3#88311yescharacteristic
409C22×C3#88611yescharacteristic
410C22×C3D3×C4⋊C411yescharacteristic
411C22×C3C2×#20411yescharacteristic
412C22×C3C2×#20411yescharacteristic
413C22×C3#90811yescharacteristic
414C22×C3#90911yescharacteristic
415C22×C3#91111yescharacteristic
416C22×C3D3×SD1611yescharacteristic
417C22×C3D3×SD1611yescharacteristic
418C22×C3#91811yescharacteristic
419C22×C3C2×C4⋊Dic311yescharacteristic
420C2×D3—22no—
421C2×D3—22no—
422C2×D3—22no—
423C2×D3—22no—
424C2×D3—22no—
425C2×D3—22no—
426C2×D3#81714yescomplemented
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—62no—
432C3×C4—122no—
433C3×C4—241no—
434C3×C4C4×D1211yescharacteristic
435C3×C4#87811yescharacteristic
436C3×C4#87811yescharacteristic
437C3×C4#67⋊C411yescharacteristic
438C3×C4#89611yescharacteristic
439C3×C4#89711yescharacteristic
440C3×C4D4×Dic311yescharacteristic
441C3×C4D4×Dic311yescharacteristic
442Dic3—22no—
443Dic3—42no—
444Dic3—81no—
445Dic3—122no—
446Dic3—122no—
447Dic3—242no—
448Dic3—242no—
449Dic3—241no—
450Dic3—241no—
451C32#185311yescharacteristic, complemented, Sylow
452C23—32no—
453C23—32no—
454C23—32no—
455C23—61no—
456C23—61no—
457C23—61no—
458C23—61no—
459C23D3×D1211yescharacteristic
460C2×C4—32no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—121no—
469C2×C4—121no—
470C2×C4—121no—
471C2×C4—121no—
472C2×C4—121no—
473C2×C4—182no—
474C2×C4—368no—
475C2×C4—361no—
476C2×C4—361no—
477C2×C4—361no—
478C2×C4—361no—
479C2×C4—361no—
480C2×C4D3×Dic611yescharacteristic
481C2×C4#379511yescharacteristic
482C2×C4D3×D1211yescharacteristic
483C2×C4C2×D3×Dic311yescharacteristic
484C2×C4#380511yescharacteristic
485C2×C4#381111yescharacteristic
486C8—22no—
487C8—62no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—64no—
496C2×C3#466811yescharacteristic
497C2×C3#472111yescharacteristic
498C2×C3#473111yescharacteristic
499C2×C3#473511yescharacteristic
500C2×C3#473811yescharacteristic
501C2×C3#477611yescharacteristic
502C2×C3#477711yescharacteristic
503C2×C3#480511yescharacteristic
504C2×C3#480611yescharacteristic
505C2×C3D3×#10611yescharacteristic
506C2×C3#488111yescharacteristic
507C2×C3#495011yescharacteristic
508C2×C3C2×#81711yescharacteristic
509C2×C3#512111yescharacteristic
510D3—24no—
511C22—34no—
512C22—62no—
513C22—62no—
514C22—62no—
515C22—62no—
516C22—62no—
517C22—62no—
518C22D3×#20411yescharacteristic
519C22D3×#20411yescharacteristic
520C22#6379511yescharacteristic
521C22#6380111yescharacteristic
522C22D3×C4⋊Dic311yescharacteristic
523C22#6389111yescharacteristic
524C22#6392311yescharacteristic
525C4—62no—
526C4—122no—
527C4—241no—
528C4—362no—
529C4—721no—
530C4Dic3×D1211yescharacteristic
531C4#6389311yescharacteristic
532C4#6389611yescharacteristic
533C4#67⋊Dic311yescharacteristic
534C3—21no—
535C3#6887511yescharacteristic, complemented
536C3#6992811yescharacteristic, complemented
537C2—64no—
538C2D3×#81711yescharacteristic
539C2#1059067511yescharacteristic
540C2#1059067611yescharacteristic
541C2#1059068311yescharacteristic
542C2#1059094611yescharacteristic
543C2#1059095111yescharacteristic
544C2#1059137911yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1853
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63644C2semidirect
5. C2×#63573C2semidirect
6. C3×#4551C2semidirect
7. #10589164C2semidirect
23. C3×(C2×D3)⋊C8C4semidirect
39. #4551D3semidirect
59. C2×C32×C8C2×C4semidirect
70. C2×C3×C3⋊C8C2×C4semidirect
104. (C2×D3)⋊C8Dic3semidirect
198. C2×C3×C8C4×D3semidirect
199. C2×C3×C8C2×Dic3semidirect
226. C2×C3⋊C8C2×Dic3semidirect
240. C2×C3×D3#106semidirect
381. C2×C8D3×Dic3semidirect
426. C2×D3#817semidirect
451. C32#1853semidirect
535. C3#68875semidirect
536. C3#69928semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊Dic32
C2×#636442
C2×C3×(C2×D3)⋊C82
#105913132
C2×#635732
C3×#45512
#105891642
#699283
#688753