Finite Group Databasebeta

← #11786847

Subgroups — #11786847

Order 1152.

783 conjugacy classes of subgroups.

The subgroup lattice has 547 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63898C211yesmaximal, characteristic
2C2×C3×#821C211yesmaximal, characteristic
3#10591357C211yesmaximal, characteristic, complemented
4C2×#63576C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic
6#10589416C211yesmaximal, characteristic, complemented
7C3×#4551C211yesmaximal, characteristic, complemented
8#70167—31nomaximal
9#68894—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×D3×Dic3—21no—
12C22×C32×C8C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×Dic3⋊Dic3—21no—
19C2×(C2×D3)⋊Dic3—21no—
20#63898—22no—
21#63898—22no—
22C3×#821—22no—
23#63579—21no—
24#63576—22no—
25#63562C414yescomplemented
26C2×D4×Dic3—31no—
27C2×#893—31no—
28C2×C3×#102—31no—
29C2×#832—31no—
30C2×#821D311yescharacteristic
31#4984—31no—
32#4972—31no—
33C2×#809—31no—
34C2×#807—31no—
35C2×#807—31no—
36C3×#340—31no—
37#4551D311yescharacteristic, complemented
38#4550—31no—
39#4550—31no—
40#4550—61no—
41C23×C3×D3—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3D411yescharacteristic
44C22×C3⋊Dic3D411yescharacteristic
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12C2×C412yes—
52C2×C3×D12D412yes—
53C2×C3×D12Q812yes—
54C2×D3×Dic3—24no—
55C2×D3×Dic3—42no—
56C2×D3×Dic3—42no—
57C2×C32×C8—21no—
58C2×C32×C8—21no—
59C2×C32×C8—21no—
60C4×C3⋊Dic3—21no—
61C4×C3⋊Dic3—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)C2×C412yescomplemented
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3C2×C412yescomplemented
70C3×C4⋊Dic3D412yes—
71Dic3⋊Dic3—42no—
72(C2×D3)⋊Dic3—24no—
73#1862—91noSylow
74C22×C3×D4—31no—
75C23×Dic3—61no—
76C22×D12C2×D311yescharacteristic
77C22×C4×D3—61no—
78C22×C3×C8—21no—
79C22×C3×C8C2×D311yescharacteristic
80C22×C3×C8C2×D311yescharacteristic
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84C2×#217—61no—
85D4×Dic3—62no—
86D4×Dic3—62no—
87C2×(C2×D3)⋊C4—61no—
88C2×C4⋊Dic3—61no—
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×Dic3⋊C4—61no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—31no—
95C2×C4×Dic3—61no—
96C22×C3⋊C8—31no—
97C22×C3⋊C8—31no—
98C22×C3⋊C8—61no—
99#893—62no—
100#893—62no—
101C3×#102—62no—
102#832—34no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105#821—22no—
106#809—34no—
107#807—62no—
108#807—62no—
109C23×C32C2×D411yescharacteristic
110C22×C3×D3—22no—
111C22×C3×D3—22no—
112C22×C3×D3—22no—
113C22×C3×D3—41no—
114C22×C3×D3—41no—
115C22×C3×D3—41no—
116C22×C3×D3—41no—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×Q811yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3D812yes—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C3×D12—22no—
139C3×D12—22no—
140C3×D12—22no—
141C3×D12C4⋊C414yescomplemented
142D3×Dic3—48no—
143C32×C8—41no—
144C3⋊(C3⋊C8)—22no—
145C2×C4×D4—91no—
146C2×#107—91no—
147C2×#102—31no—
148C2×#102—91no—
149#389—91no—
150#340—31no—
151#336—91no—
152C24×C3—61no—
153C23×D3—21no—
154C2×C3×D4—32no—
155C2×C3×D4—32no—
156C2×C3×D4—32no—
157C2×C3×D4—61no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—61no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C22×Dic3—21no—
167C22×Dic3—21no—
168C22×Dic3—21no—
169C22×Dic3—31no—
170C22×Dic3—31no—
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—64no—
176C22×Dic3—122no—
177C22×Dic3—122no—
178C2×D12—21no—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12Dic612yes—
182C2×D12C4×D312yes—
183C2×D12#6712yes—
184C2×C4×D3—64no—
185C2×C4×D3—122no—
186C2×C4×D3—122no—
187C2×C3×C8—22no—
188C2×C3×C8—21no—
189C2×C3×C8—21no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—41no—
195C2×C3×C8—41no—
196C3×C4⋊C4—32no—
197C3×C4⋊C4—32no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—61no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202#217—64no—
203(C2×D3)⋊C4—64no—
204C4⋊Dic3—21no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C4⋊Dic3—122no—
209C4⋊Dic3C4×D312yescomplemented
210C4⋊Dic3D1212yes—
211Dic3⋊C4—122no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C4×Dic3—121no—
217C4×Dic3—121no—
218C2×C3⋊C8—32no—
219C2×C3⋊C8—32no—
220C2×C3⋊C8—62no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—121no—
226C2×C3⋊C8—121no—
227C22×C32C4×D411yescharacteristic
228C22×C32#12011yescharacteristic
229C22×C32C22⋊Q811yescharacteristic
230C22×C32C2×D811yescharacteristic
231C22×C32#13511yescharacteristic
232C22×C32AGL(1,ℤ/8)11yescharacteristic
233C22×C32#13711yescharacteristic
234C2×C3×D3—24no—
235C2×C3×D3—42no—
236C2×C3×D3—42no—
237C2×C3×D3—42no—
238C2×C3×D3—42no—
239C2×C3×D3—42no—
240C2×C3×D3—42no—
241C32×C4C2×C4⋊C411yescharacteristic
242C32×C4C4×D411yescharacteristic
243C32×C4C22⋊Q811yescharacteristic
244C32×C4#12311yescharacteristic
245C3⋊Dic3—22no—
246C3⋊Dic3—41no—
247C3×Dic3—42no—
248C3×Dic3—42no—
249C3×Dic3—81no—
250C22×D4—31no—
251C23×C4—181no—
252C22×C8—91no—
253C22×C8D3211yescharacteristic
254C4×D4—182no—
255C4×D4—182no—
256C2×C4⋊C4—31no—
257C2×C4⋊C4—31no—
258C2×C4⋊C4—31no—
259C2×C4⋊C4—181no—
260C2×C22⋊C4—181no—
261C2×C42—91no—
262#107—182no—
263#102—62no—
264#102—94no—
265#95—181no—
266C23×C3—21no—
267C23×C3—62no—
268C23×C3—62no—
269C23×C3—62no—
270C23×C3—121no—
271C23×C3—121no—
272C23×C3—121no—
273C23×C3—121no—
274C23×C3D3×D411yescharacteristic
275C23×C3D3×D411yescharacteristic
276C22×D3—22no—
277C22×D3—22no—
278C22×D3—22no—
279C22×D3—41no—
280C22×D3—41no—
281C22×D3—41no—
282C22×D3—41no—
283C3×D4—34no—
284C3×D4—62no—
285C3×D4—62no—
286C3×D4—62no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
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×C4×D311yescharacteristic
305C2×C3×C4C2×D1211yescharacteristic
306C2×C3×C4#23511yescharacteristic
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×C4C2×#6711yescharacteristic
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—32no—
317C2×Dic3—32no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—41no—
322C2×Dic3—41no—
323C2×Dic3—41no—
324C2×Dic3—41no—
325C2×Dic3—62no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—62no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—121no—
338C2×Dic3—121no—
339C2×Dic3—121no—
340C2×Dic3—121no—
341C2×Dic3—128no—
342D12—22no—
343D12—22no—
344D12—22no—
345D12Dic3⋊C414yescomplemented
346C4×D3—128no—
347C3×C8—42no—
348C3×C8—41no—
349C3×C8—41no—
350C3⋊C8—62no—
351C3⋊C8—62no—
352C3⋊C8—122no—
353C2×C32#38511yescharacteristic
354C2×C32C4×D811yescharacteristic
355C2×C32#44011yescharacteristic
356C2×C32#44711yescharacteristic
357C2×C32#45211yescharacteristic
358C2×C32#47411yescharacteristic
359C2×C32#47811yescharacteristic
360C3×D3—44no—
361C24—61no—
362C2×D4—32no—
363C2×D4—32no—
364C2×D4—32no—
365C2×D4—61no—
366C2×D4—61no—
367C2×D4—61no—
368C22×C4—61no—
369C22×C4—61no—
370C22×C4—61no—
371C22×C4—91no—
372C22×C4—91no—
373C22×C4—184no—
374C22×C4—362no—
375C22×C4—362no—
376C22×C4C2×D3211yescharacteristic
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—92no—
381C2×C8—181no—
382C2×C8—181no—
383C4⋊C4—32no—
384C4⋊C4—32no—
385C4⋊C4—61no—
386C4⋊C4—61no—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C4⋊C4—362no—
390C22⋊C4—184no—
391C42—181no—
392C42—181no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—64no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3—122no—
404C22×C3—122no—
405C22×C3—122no—
406C22×C3—122no—
407C22×C3#87811yescharacteristic
408C22×C3#67⋊C411yescharacteristic
409C22×C3#67⋊C411yescharacteristic
410C22×C3#88211yescharacteristic
411C22×C3#89611yescharacteristic
412C22×C3D3×D811yescharacteristic
413C22×C3D3×D811yescharacteristic
414C22×C3#91111yescharacteristic
415C22×C3#91411yescharacteristic
416C22×C3#91511yescharacteristic
417C22×C3#91611yescharacteristic
418C22×C3#91611yescharacteristic
419C22×C3#91811yescharacteristic
420C22×C3#93711yescharacteristic
421C2×D3—24no—
422C2×D3—42no—
423C2×D3—42no—
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—42no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—122no—
433C3×C4—122no—
434C3×C4—241no—
435C3×C4C4×D1211yescharacteristic
436C3×C4#87811yescharacteristic
437C3×C4#67⋊C411yescharacteristic
438C3×C4#88311yescharacteristic
439C3×C4D3×C4⋊C411yescharacteristic
440C3×C4#89711yescharacteristic
441C3×C4C2×Dic3⋊C411yescharacteristic
442C3×C4#93511yescharacteristic
443Dic3—42no—
444Dic3—42no—
445Dic3—62no—
446Dic3—62no—
447Dic3—81no—
448Dic3—122no—
449Dic3—122no—
450Dic3—121no—
451Dic3—121no—
452C32#186211yescharacteristic, complemented, Sylow
453C23—62no—
454C23—62no—
455C23—62no—
456C23—121no—
457C23—121no—
458C23—121no—
459C23—121no—
460C23#380211yescharacteristic
461D4—34no—
462D4—62no—
463D4—62no—
464D4—62no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—92no—
468C2×C4—121no—
469C2×C4—121no—
470C2×C4—121no—
471C2×C4—121no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—368no—
481C2×C4D3×Dic611yescharacteristic
482C2×C4C4×D3211yescharacteristic
483C2×C4D3×D1211yescharacteristic
484C2×C4#380411yescharacteristic
485C2×C4#380511yescharacteristic
486C2×C4D3×#6711yescharacteristic
487C8—41no—
488C8—182no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—124no—
497C2×C3#466811yescharacteristic
498C2×C3#475611yescharacteristic
499C2×C3#475611yescharacteristic
500C2×C3#475711yescharacteristic
501C2×C3#475911yescharacteristic
502C2×C3#476311yescharacteristic
503C2×C3#477311yescharacteristic
504C2×C3#480811yescharacteristic
505C2×C3#481711yescharacteristic
506C2×C3#487111yescharacteristic
507C2×C3#489011yescharacteristic
508C2×C3#494611yescharacteristic
509C2×C3#515611yescharacteristic
510C2×C3#517311yescharacteristic
511D3—44no—
512C22—64no—
513C22—122no—
514C22—122no—
515C22—122no—
516C22—122no—
517C22—122no—
518C22—122no—
519C22#6379711yescharacteristic
520C22#6379811yescharacteristic
521C22#6380911yescharacteristic
522C22#6381111yescharacteristic
523C22#6389911yescharacteristic
524C22#6390211yescharacteristic
525C22#6392211yescharacteristic
526C4—122no—
527C4—122no—
528C4—182no—
529C4—241no—
530C4—361no—
531C4D3×Dic3⋊C411yescharacteristic
532C4#6388011yescharacteristic
533C4#6389311yescharacteristic
534C4#6396911yescharacteristic
535C3—21no—
536C3#6889411yescharacteristic, complemented
537C3#7016711yescharacteristic, complemented
538C2—124no—
539C2#1059074011yescharacteristic
540C2#1059074311yescharacteristic
541C2#1059077811yescharacteristic
542C2#1059078211yescharacteristic
543C2#1059094511yescharacteristic
544C2#1059096111yescharacteristic
545C2#1059137311yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1862
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
3. #10591357C2semidirect
4. C2×#63576C2semidirect
6. #10589416C2semidirect
7. C3×#4551C2semidirect
25. #63562C4semidirect
37. #4551D3semidirect
64. C2×C3⋊(C3⋊C8)C2×C4semidirect
69. C3×C4⋊Dic3C2×C4semidirect
141. C3×D12C4⋊C4semidirect
209. C4⋊Dic3C4×D3semidirect
345. D12Dic3⋊C4semidirect
452. C32#1862semidirect
536. C3#68894semidirect
537. C3#70167semidirect

Maximal subgroups

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

subgroupindex
C2×#638982
C2×C3×#8212
#105913572
C2×#635762
C2×#635622
#105894162
C3×#45512
#701673
#688943