Finite Group Databasebeta

← #11783944

Subgroups — #11783944

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63898C211yesmaximal, characteristic
2C2×C8×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#821C211yesmaximal, characteristic
4#10591274C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic
6C3×#4551C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8Dic3×#102—31nomaximal
9#68780—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×(C2×D3)⋊Dic3—21no—
19C2×Dic32—21no—
20#63898—22no—
21#63898C414yescomplemented
22C8×C3⋊Dic3—22no—
23C3×#821C414yescomplemented
24#63579—21no—
25#63562C414yescomplemented
26C2×D4×Dic3—31no—
27C2×#893—31no—
28C2×C3×#102—31no—
29C2×#832—31no—
30C2×#821D311yescharacteristic
31C2×C8×Dic3—31no—
32C2×C8×Dic3—31no—
33C2×C8×Dic3—61no—
34Dic3×C4⋊C4—31no—
35Dic3×C4⋊C4—31no—
36C2×#809—31no—
37C3×#340—31no—
38#4551D311yescharacteristic, complemented
39#4529—31no—
40#4529—31no—
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×D12C2×C412yes—
53C2×C3×D12C2×C412yes—
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⋊Dic3C2×C412yes—
61C4×C3⋊Dic3D412yes—
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⋊Dic3C2×C412yes—
69C3×C4⋊Dic3C2×C412yescomplemented
70C3×C4⋊Dic3C2×C412yescomplemented
71(C2×D3)⋊Dic3—24no—
72Dic32—42no—
73C4×#102—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—34no—
86D4×Dic3—62no—
87C2×(C2×D3)⋊C4—61no—
88C2×C4⋊Dic3C2×D311yescharacteristic
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×C4×Dic3—31no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—61no—
94C2×C4×Dic3—61no—
95C2×C4×Dic3—61no—
96C22×C3⋊C8—31no—
97C22×C3⋊C8—31no—
98C22×C3⋊C8—61no—
99#893—34no—
100#893—62no—
101C3×#102—34no—
102#832—34no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105#821Dic314yescomplemented
106C8×Dic3—62no—
107C8×Dic3—62no—
108C8×Dic3—64no—
109#809—34no—
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—22no—
112C22×C3×D3—22no—
113C22×C3×D3—22no—
114C22×C3×D3—41no—
115C22×C3×D3—41no—
116C22×C3×D3—41no—
117C22×C3×D3—41no—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3C22⋊C412yes—
127C2×C3⋊Dic3C22⋊C412yes—
128C2×C3⋊Dic3D812yes—
129C2×C3⋊Dic3SD1612yes—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
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×Dic3—41no—
139C3×D12—22no—
140C3×D12—22no—
141C3×D12—22no—
142C3×D12C4214yescomplemented
143D3×Dic3—48no—
144C32×C8—22no—
145C3⋊(C3⋊C8)—22no—
146C2×C4×D4—91no—
147C2×#102—31no—
148C2×#102—91no—
149C2×C4×C8—91no—
150C4×C4⋊C4—91no—
151#340—31no—
152#340—91no—
153C24×C3—61no—
154C23×D3—21no—
155C2×C3×D4—32no—
156C2×C3×D4—32no—
157C2×C3×D4—32no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C22×C3×C4—21no—
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—21no—
170C22×Dic3—31no—
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—31no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—64no—
177C22×Dic3—122no—
178C22×Dic3—122no—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12C4×D312yes—
183C2×D12C4×D312yes—
184C2×D12C2×Dic312yes—
185C2×C4×D3—64no—
186C2×C4×D3—122no—
187C2×C4×D3—122no—
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×C8C4×D312yescomplemented
196C2×C3×C8C2×Dic312yescomplemented
197C3×C4⋊C4—32no—
198C3×C4⋊C4—32no—
199C3×C4⋊C4—32no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203#217—64no—
204(C2×D3)⋊C4—64no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C4⋊Dic3C4×D312yes—
209C4⋊Dic3C4×D312yescomplemented
210C4⋊Dic3C2×Dic312yescomplemented
211C4×Dic3—32no—
212C4×Dic3—32no—
213C4×Dic3—32no—
214C4×Dic3—32no—
215C4×Dic3—62no—
216C4×Dic3—62no—
217C4×Dic3—122no—
218C4×Dic3—122no—
219C2×C3⋊C8—32no—
220C2×C3⋊C8—32no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—62no—
223C2×C3⋊C8—62no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C22×C32C2×C22⋊C411yescharacteristic
229C22×C32C4×D411yescharacteristic
230C22×C32C4×D411yescharacteristic
231C22×C32C2×D811yescharacteristic
232C22×C32C2×SD1611yescharacteristic
233C22×C32#13511yescharacteristic
234C22×C32#13511yescharacteristic
235C2×C3×D3—24no—
236C2×C3×D3—42no—
237C2×C3×D3—42no—
238C2×C3×D3—42no—
239C2×C3×D3—42no—
240C2×C3×D3—42no—
241C2×C3×D3—42no—
242C32×C4C2×C4211yescharacteristic
243C32×C4#11711yescharacteristic
244C32×C4C4×D411yescharacteristic
245C32×C4C4×D411yescharacteristic
246C3⋊Dic3—22no—
247C3⋊Dic3#10214yescomplemented
248C3×Dic3—42no—
249C3×Dic3—42no—
250C3×Dic3—42no—
251C22×D4—31no—
252C23×C4—181no—
253C22×C8—91no—
254C22×C8D3211yescharacteristic
255C4×D4—94no—
256C4×D4—182no—
257C2×C4⋊C4—31no—
258C2×C4⋊C4—31no—
259C2×C4⋊C4—31no—
260C2×C22⋊C4—181no—
261C2×C42—91no—
262C2×C42—181no—
263#102—34no—
264#102—94no—
265C4×C8—182no—
266#95—181no—
267C23×C3—21no—
268C23×C3—62no—
269C23×C3—62no—
270C23×C3—62no—
271C23×C3—121no—
272C23×C3—121no—
273C23×C3—121no—
274C23×C3—121no—
275C23×C3D3×D411yescharacteristic
276C23×C3D3×D411yescharacteristic
277C22×D3—22no—
278C22×D3—22no—
279C22×D3—22no—
280C22×D3—41no—
281C22×D3—41no—
282C22×D3—41no—
283C22×D3—41no—
284C3×D4—34no—
285C3×D4—62no—
286C3×D4—62no—
287C3×D4—62no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
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×C4—121no—
303C2×C3×C4C2×C4×D311yescharacteristic
304C2×C3×C4C2×C4×D311yescharacteristic
305C2×C3×C4C2×C4×D311yescharacteristic
306C2×C3×C4C2×C4×D311yescharacteristic
307C2×C3×C4C2×C4×D311yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4#23711yescharacteristic
311C2×C3×C4#23711yescharacteristic
312C2×C3×C4#23711yescharacteristic
313C2×C3×C4#23911yescharacteristic
314C2×C3×C4C22×Dic311yescharacteristic
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—32no—
319C2×Dic3—32no—
320C2×Dic3—32no—
321C2×Dic3—32no—
322C2×Dic3—32no—
323C2×Dic3—32no—
324C2×Dic3—32no—
325C2×Dic3—32no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—128no—
343D12—22no—
344D12—22no—
345D12—22no—
346D12C4×Dic314yescomplemented
347C4×D3—128no—
348C3×C8—24no—
349C3×C8—22no—
350C3×C8—22no—
351C3⋊C8—64no—
352C3⋊C8—62no—
353C3⋊C8—62no—
354C2×C32C4×C22⋊C411yescharacteristic
355C2×C32C2×#10211yescharacteristic
356C2×C32#41611yescharacteristic
357C2×C32C4×D811yescharacteristic
358C2×C32C4×D811yescharacteristic
359C2×C32C4×SD1611yescharacteristic
360C2×C32C4×SD1611yescharacteristic
361C3×D3—44no—
362C24—61no—
363C2×D4—32no—
364C2×D4—32no—
365C2×D4—32no—
366C2×D4—61no—
367C2×D4—61no—
368C2×D4—61no—
369C22×C4—61no—
370C22×C4—61no—
371C22×C4—61no—
372C22×C4—91no—
373C22×C4—91no—
374C22×C4—184no—
375C22×C4—362no—
376C22×C4—362no—
377C22×C4C2×D3211yescharacteristic
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—92no—
381C2×C8—181no—
382C2×C8—181no—
383C2×C8D3×Dic312yescomplemented
384C4⋊C4—32no—
385C4⋊C4—32no—
386C4⋊C4—32no—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C22⋊C4—184no—
391C42—92no—
392C42—92no—
393C42—362no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—64no—
402C22×C3—122no—
403C22×C3—122no—
404C22×C3—122no—
405C22×C3—122no—
406C22×C3—122no—
407C22×C3—122no—
408C22×C3D3×C22⋊C411yescharacteristic
409C22×C3D3×C22⋊C411yescharacteristic
410C22×C3#67⋊C411yescharacteristic
411C22×C3#67⋊C411yescharacteristic
412C22×C3#89311yescharacteristic
413C22×C3D3×D811yescharacteristic
414C22×C3D3×D811yescharacteristic
415C22×C3#91211yescharacteristic
416C22×C3D3×SD1611yescharacteristic
417C22×C3D3×SD1611yescharacteristic
418C22×C3#91611yescharacteristic
419C22×C3#91611yescharacteristic
420C22×C3#91911yescharacteristic
421C22×C3D4×Dic311yescharacteristic
422C2×D3—24no—
423C2×D3—42no—
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—42no—
428C2×D3—42no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—122no—
434C3×C4—122no—
435C3×C4—122no—
436C3×C4C42×D311yescharacteristic
437C3×C4#87711yescharacteristic
438C3×C4#67⋊C411yescharacteristic
439C3×C4#67⋊C411yescharacteristic
440C3×C4#89211yescharacteristic
441C3×C4#89311yescharacteristic
442C3×C4C2×C4×Dic311yescharacteristic
443C3×C4D4×Dic311yescharacteristic
444Dic3—34no—
445Dic3—34no—
446Dic3—42no—
447Dic3—42no—
448Dic3—42no—
449Dic3—64no—
450Dic3—64no—
451Dic3—62no—
452Dic3—62no—
453C32C4×#10211yescharacteristic, complemented, Sylow
454C23—62no—
455C23—62no—
456C23—62no—
457C23—121no—
458C23—121no—
459C23—121no—
460C23—121no—
461C23#380211yescharacteristic
462D4—34no—
463D4—62no—
464D4—62no—
465D4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—92no—
470C2×C4—92no—
471C2×C4—92no—
472C2×C4—92no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—368no—
482C2×C4#379611yescharacteristic
483C2×C4C4×D3211yescharacteristic
484C2×C4C4×D3211yescharacteristic
485C2×C4C2×D3×Dic311yescharacteristic
486C2×C4#380511yescharacteristic
487C2×C4#381111yescharacteristic
488C8—22no—
489C8—182no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—124no—
498C2×C3#466611yescharacteristic
499C2×C3#475611yescharacteristic
500C2×C3#475611yescharacteristic
501C2×C3#475811yescharacteristic
502C2×C3D3×#10211yescharacteristic
503C2×C3D3×#10211yescharacteristic
504C2×C3#477211yescharacteristic
505C2×C3#478811yescharacteristic
506C2×C3#480411yescharacteristic
507C2×C3#485211yescharacteristic
508C2×C3#487211yescharacteristic
509C2×C3Dic3×C22⋊C411yescharacteristic
510C2×C3Dic3×D811yescharacteristic
511C2×C3Dic3×SD1611yescharacteristic
512D3—44no—
513C22—64no—
514C22—122no—
515C22—122no—
516C22—122no—
517C22—122no—
518C22—122no—
519C22—122no—
520C22#6379611yescharacteristic
521C22#6379711yescharacteristic
522C22#6380911yescharacteristic
523C22#6381011yescharacteristic
524C22#6389811yescharacteristic
525C22#6390211yescharacteristic
526C22#6392111yescharacteristic
527C4—94no—
528C4—122no—
529C4—122no—
530C4—122no—
531C4—182no—
532C4C4×D3×Dic311yescharacteristic
533C4#6387811yescharacteristic
534C4#6388111yescharacteristic
535C4#67⋊Dic311yescharacteristic
536C3—21no—
537C3#6878011yescharacteristic, complemented
538C3Dic3×#10211yescharacteristic, complemented
539C2—124no—
540C2#1059074011yescharacteristic
541C2#1059074211yescharacteristic
542C2#1059077511yescharacteristic
543C2#1059077711yescharacteristic
544C2#1059094011yescharacteristic
545C2#1059095611yescharacteristic
546C2#1059136811yescharacteristic
subgroupG/H
centerC23#3802
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32C4×#102
LCSG ▷ 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×C8×C3⋊Dic3C2semidirect
4. #10591274C2semidirect
6. C3×#4551C2semidirect
7. #10589163C2semidirect
21. #63898C4semidirect
23. C3×#821C4semidirect
25. #63562C4semidirect
38. #4551D3semidirect
59. C2×C32×C8C2×C4semidirect
64. C2×C3⋊(C3⋊C8)C2×C4semidirect
69. C3×C4⋊Dic3C2×C4semidirect
70. C3×C4⋊Dic3C2×C4semidirect
105. #821Dic3semidirect
142. C3×D12C42semidirect
195. C2×C3×C8C4×D3semidirect
196. C2×C3×C8C2×Dic3semidirect
209. C4⋊Dic3C4×D3semidirect
210. C4⋊Dic3C2×Dic3semidirect
247. C3⋊Dic3#102semidirect
346. D12C4×Dic3semidirect
383. C2×C8D3×Dic3semidirect
453. C32C4×#102semidirect
537. C3#68780semidirect
538. C3Dic3×#102semidirect

Maximal subgroups

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

subgroupindex
C2×#638982
C2×C8×C3⋊Dic32
C2×C3×#8212
#105912742
C2×#635622
C3×#45512
#105891632
Dic3×#1023
#687803