Finite Group Databasebeta

← #73577

Subgroups — #73577

Order 384.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
2C2×#882C211yesmaximal, characteristic
3C2×#67⋊C4C211yesmaximal, characteristic, complemented
4C2×D3×C22⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×D12C211yesmaximal, characteristic, complemented
6C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
7#5213C211yesmaximal, characteristic, complemented
8#4950C211yesmaximal, characteristic, complemented
9#4940C211yesmaximal, characteristic, complemented
10#4939C211yesmaximal, characteristic, complemented
11C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
12#4670C211yesmaximal, characteristic, complemented
13#4668C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4665C211yesmaximal, characteristic, complemented
16#2358—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C23×Dic3C2211yescharacteristic
21C22×D12C2211yescharacteristic
22C22×D12C2211yescharacteristic
23C22×C4×D3C2211yescharacteristic
24C22×C4×D3C2211yescharacteristic
25C22×C4×D3C2211yescharacteristic, complemented
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C42C2211yescharacteristic, complemented
29C2×C3×C42C2211yescharacteristic, complemented
30C2×#217C2211yescharacteristic
31C2×(C2×D3)⋊C4—24no—
32C2×(C2×D3)⋊C4C2211yescharacteristic
33C2×(C2×D3)⋊C4C2211yescharacteristic
34C2×(C2×D3)⋊C4C2211yescharacteristic
35C2×(C2×D3)⋊C4C2211yescharacteristic
36C2×(C2×D3)⋊C4C2211yescharacteristic
37C2×(C2×D3)⋊C4C2211yescharacteristic
38C2×(C2×D3)⋊C4C2211yescharacteristic
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C4⋊Dic3C2211yescharacteristic, complemented
44C2×C4⋊Dic3C2211yescharacteristic, complemented
45C2×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C4×Dic3C2211yescharacteristic, complemented
47#882C418yescomplemented
48#67⋊C4—24no—
49D3×C22⋊C4—24no—
50C4×D12—24no—
51C3×#95C2211yescharacteristic, complemented
52C3×#95C2211yescharacteristic, complemented
53C3⋊#95C2211yescharacteristic, complemented
54C3⋊#95C2211yescharacteristic, complemented
55C3⋊#95C2211yescharacteristic, complemented
56C3⋊#95C2211yescharacteristic, complemented
57C2×#120—31no—
58C2×C4×D4—31no—
59C2×C4×D4—31no—
60C22×C22⋊C4—31no—
61C22×C22⋊C4—31no—
62#390—31no—
63#388—31no—
64#388—31no—
65#386—31no—
66#386—31no—
67#386—31no—
68#385—31no—
69#385—31no—
70C4×C22⋊C4—31no—
71C4×C22⋊C4D311yescharacteristic, complemented
72C24×C3C2311yescharacteristic
73C23×D3—22no—
74C23×D3—22no—
75C23×D3—22no—
76C23×D3—22no—
77C23×D3—41no—
78C23×D3—41no—
79C23×D3C2×C414yescomplemented
80C23×D3C2311yescharacteristic
81C23×D3C2311yescharacteristic
82C23×D3C2311yescharacteristic
83C22×C3×C4—22no—
84C22×C3×C4—22no—
85C22×C3×C4—41no—
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
88C22×C3×C4C2311yescharacteristic
89C22×C3×C4C2311yescharacteristic
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C2×#67—22no—
93C2×#67—22no—
94C2×#67C2×C414yescomplemented
95C22×Dic3—22no—
96C22×Dic3—22no—
97C22×Dic3—41no—
98C22×Dic3C2311yescharacteristic
99C22×Dic3C2311yescharacteristic
100C22×Dic3C2311yescharacteristic
101C22×Dic3C2311yescharacteristic
102C22×Dic3C2311yescharacteristic
103C2×D12—22no—
104C2×D12—22no—
105C2×D12—41no—
106C2×D12—41no—
107C2×D12C2×C414yescomplemented
108C2×D12C2×C414yescomplemented
109C2×C4×D3—22no—
110C2×C4×D3—22no—
111C2×C4×D3—22no—
112C2×C4×D3—22no—
113C2×C4×D3—22no—
114C2×C4×D3—22no—
115C2×C4×D3—41no—
116C2×C4×D3—41no—
117C2×C4×D3—41no—
118C3×C22⋊C4C2×C414yescomplemented
119C3×C22⋊C4D414yescomplemented
120C3×C42—22no—
121C3×C42—41no—
122#217—22no—
123(C2×D3)⋊C4—22no—
124(C2×D3)⋊C4—22no—
125(C2×D3)⋊C4—22no—
126(C2×D3)⋊C4—22no—
127(C2×D3)⋊C4—22no—
128(C2×D3)⋊C4—22no—
129(C2×D3)⋊C4—22no—
130(C2×D3)⋊C4—41no—
131(C2×D3)⋊C4C2×C414yescomplemented
132(C2×D3)⋊C4C2×C414yescomplemented
133(C2×D3)⋊C4D414yescomplemented
134C4⋊Dic3—22no—
135C4⋊Dic3—41no—
136Dic3⋊C4—22no—
137C4×Dic3—22no—
138C25—31no—
139C22×D4—31no—
140C22×D4—31no—
141C22×D4—31no—
142C23×C4—31no—
143C23×C4—31no—
144C23×C4—31no—
145C23×C4—31no—
146C23×C4C2×D311yescharacteristic
147#120—38no—
148C4×D4—64no—
149C4×D4—64no—
150C2×C4⋊C4—31no—
151C2×C4⋊C4—31no—
152C2×C4⋊C4—31no—
153C2×C22⋊C4—31no—
154C2×C22⋊C4—31no—
155C2×C22⋊C4—31no—
156C2×C22⋊C4—31no—
157C2×C22⋊C4—31no—
158C2×C22⋊C4—31no—
159C2×C22⋊C4—31no—
160C2×C22⋊C4—31no—
161C2×C22⋊C4—31no—
162C2×C22⋊C4—31no—
163C2×C22⋊C4—31no—
164C2×C22⋊C4—31no—
165C2×C22⋊C4—64no—
166C2×C22⋊C4—64no—
167C2×C22⋊C4C2×D311yescharacteristic
168C2×C22⋊C4C2×D311yescharacteristic
169C2×C42—31no—
170C2×C42C2×D311yescharacteristic, complemented
171C2×C42C2×D311yescharacteristic, complemented
172#95—31no—
173#95—31no—
174#95—31no—
175#95—31no—
176#95C2×D311yescharacteristic, complemented
177#95C2×D311yescharacteristic, complemented
178C23×C3—21no—
179C23×C3—21no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3C22×C412yes—
183C23×C3C2×D412yes—
184C23×C3#4112yes—
185C23×C3C2411yescharacteristic
186C22×D3—21no—
187C22×D3—21no—
188C22×D3—21no—
189C22×D3—21no—
190C22×D3—28no—
191C22×D3—21no—
192C22×D3—21no—
193C22×D3—21no—
194C22×D3—21no—
195C22×D3—21no—
196C22×D3—21no—
197C22×D3—21no—
198C22×D3—21no—
199C22×D3—21no—
200C22×D3—21no—
201C22×D3—21no—
202C22×D3—21no—
203C22×D3—28no—
204C22×D3—44no—
205C22×D3—44no—
206C22×D3—44no—
207C22×D3—44no—
208C22×D3—44no—
209C22×D3C22×C412yes—
210C22×D3C22×C412yes—
211C22×D3C22×C412yes—
212C22×D3C2×D412yes—
213C22×D3#4112yes—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—44no—
228C2×C3×C4C22×C412yes—
229C2×C3×C4C22×C412yes—
230C2×C3×C4C2×D412yes—
231C2×C3×C4C2×D412yes—
232C2×C3×C4C2×D412yes—
233#67—28no—
234C2×Dic3—21no—
235C2×Dic3—21no—
236C2×Dic3—21no—
237C2×Dic3—21no—
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—21no—
241C2×Dic3—21no—
242C2×Dic3—21no—
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—21no—
246C2×Dic3—21no—
247C2×Dic3—44no—
248C2×Dic3C22×C412yes—
249C2×Dic3C2×D412yes—
250D12—28no—
251D12—44no—
252C4×D3—44no—
253C4×D3—44no—
254C4×D3—44no—
255C24—31no—
256C24—31no—
257C24—31no—
258C24—34no—
259C24—62no—
260C24—62no—
261C24—62no—
262C24—62no—
263C24—121no—
264C24—121no—
265C24C22×D311yescharacteristic
266C2×D4—34no—
267C2×D4—34no—
268C2×D4—34no—
269C2×D4—62no—
270C2×D4—62no—
271C2×D4—62no—
272C2×D4—62no—
273C2×D4—121no—
274C2×D4—121no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—31no—
278C22×C4—31no—
279C22×C4—31no—
280C22×C4—31no—
281C22×C4—31no—
282C22×C4—41no—
283C22×C4—62no—
284C22×C4—62no—
285C22×C4—62no—
286C22×C4—62no—
287C22×C4—62no—
288C22×C4—62no—
289C22×C4—62no—
290C22×C4—62no—
291C22×C4—121no—
292C22×C4—121no—
293C22×C4—121no—
294C22×C4—121no—
295C22×C4C22×D311yescharacteristic
296C22×C4C22×D311yescharacteristic
297C22×C4C22×D311yescharacteristic
298C22×C4C22×D311yescharacteristic
299C22×C4C22×D311yescharacteristic
300C22×C4C22×D311yescharacteristic
301C4⋊C4—62no—
302C4⋊C4—62no—
303C4⋊C4—121no—
304C22⋊C4—34no—
305C22⋊C4—34no—
306C22⋊C4—34no—
307C22⋊C4—62no—
308C22⋊C4—62no—
309C22⋊C4—62no—
310C22⋊C4—62no—
311C22⋊C4—62no—
312C22⋊C4—62no—
313C22⋊C4—62no—
314C22⋊C4—62no—
315C22⋊C4—121no—
316C22⋊C4C4×D314yescomplemented
317C22⋊C4D1214yescomplemented
318C42—22no—
319C42—41no—
320C42—62no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—22no—
325C22×C3—22no—
326C22×C3—22no—
327C22×C3C4×D414yescomplemented
328C22×C3C23×C411yescharacteristic
329C22×C3C22×D411yescharacteristic
330C22×C3C22×D411yescharacteristic
331C22×C3C2×#4111yescharacteristic
332C22×C3C2×#4111yescharacteristic
333C22×C3H(5,𝔽2)11yescharacteristic
334C22×C3H(5,𝔽2)11yescharacteristic
335C2×D3—22no—
336C2×D3—22no—
337C2×D3—22no—
338C2×D3—22no—
339C2×D3—22no—
340C2×D3—22no—
341C2×D3—22no—
342C2×D3—22no—
343C2×D3—22no—
344C2×D3—22no—
345C2×D3—22no—
346C2×D3—22no—
347C2×D3—416no—
348C2×D3—41no—
349C2×D3—41no—
350C2×D3—41no—
351C2×D3—41no—
352C2×D3—41no—
353C2×D3—41no—
354C2×D3—41no—
355C2×D3—41no—
356C2×D3C4×D414yescomplemented
357C3×C4—22no—
358C3×C4—22no—
359C3×C4—22no—
360C3×C4—22no—
361C3×C4—22no—
362C3×C4—41no—
363Dic3—22no—
364Dic3—22no—
365Dic3—41no—
366Dic3—41no—
367Dic3—41no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—32no—
373C23—32no—
374C23—32no—
375C23—32no—
376C23—32no—
377C23—68no—
378C23—61no—
379C23—61no—
380C23—61no—
381C23—61no—
382C23—68no—
383C23—61no—
384C23—61no—
385C23—61no—
386C23—61no—
387C23—61no—
388C23—61no—
389C23—61no—
390C23—61no—
391C23—61no—
392C23—61no—
393C23—61no—
394C23—61no—
395C23—124no—
396C23—124no—
397C23—124no—
398C23—124no—
399C23—124no—
400C23C2×C4×D312yes—
401C23C2×D1212yes—
402C23#23512yes—
403C23C23×D311yescharacteristic
404D4—68no—
405D4—68no—
406D4—124no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—32no—
421C2×C4—32no—
422C2×C4—44no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—61no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—61no—
436C2×C4—124no—
437C2×C4—124no—
438C2×C4—124no—
439C2×C4—124no—
440C2×C4C2×C4×D312yes—
441C2×C4C2×C4×D312yes—
442C2×C4C2×D1212yes—
443C2×C4C2×D1212yes—
444C2×C4D3×D412yes—
445C2×C3—24no—
446C2×C3C2×C4×D411yescharacteristic
447C2×C3C2×C4×D411yescharacteristic
448C2×C3#51811yescharacteristic
449C2×C3D4211yescharacteristic
450C2×C3#54611yescharacteristic
451C2×C3#54611yescharacteristic
452C2×C3#55111yescharacteristic
453D3—24no—
454D3—42no—
455D3—42no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—34no—
463C22—62no—
464C22—62no—
465C22—62no—
466C22—62no—
467C22—62no—
468C22—62no—
469C22—62no—
470C22—62no—
471C22—62no—
472C22—62no—
473C22—62no—
474C22—62no—
475C22—1216no—
476C22—121no—
477C22—121no—
478C22—121no—
479C22—121no—
480C22—121no—
481C22—121no—
482C22—121no—
483C22—121no—
484C22C4×D1214yescomplemented
485C22C22×C4×D311yescharacteristic
486C22C22×D1211yescharacteristic
487C22C2×#23511yescharacteristic
488C22C2×D3×D411yescharacteristic
489C22#100411yescharacteristic
490C22D3×#4111yescharacteristic
491C22#100911yescharacteristic
492C4—22no—
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—62no—
499C4—62no—
500C4—121no—
501C4—121no—
502C4—121no—
503C3#235811yescharacteristic, complemented, Sylow
504C2—24no—
505C2—64no—
506C2—122no—
507C2—122no—
508C2C2×C4×D1211yescharacteristic
509C2#549011yescharacteristic
510C2#552711yescharacteristic
511C2C4×D3×D411yescharacteristic
512C2#554511yescharacteristic
513C2D4×D1211yescharacteristic
514C2#555411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×C4×C22⋊C4C2
socle, cosocleC23×C3C24
prime radicalC2×#882C2
hypercenterC4×C22⋊C4D3
hypocenterC3#2358
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×(C2×D3)⋊C4C2semidirect
3. C2×#67⋊C4C2semidirect
4. C2×D3×C22⋊C4C2semidirect
5. C2×C4×D12C2semidirect
6. C3×C4×C22⋊C4C2semidirect
7. #5213C2semidirect
8. #4950C2semidirect
9. #4940C2semidirect
10. #4939C2semidirect
11. C4×(C2×D3)⋊C4C2semidirect
12. #4670C2semidirect
13. #4668C2semidirect
14. #4665C2semidirect
15. #4665C2semidirect
25. C22×C4×D3C22semidirect
28. C2×C3×C42C22semidirect
29. C2×C3×C42C22semidirect
40. C2×(C2×D3)⋊C4C22semidirect
41. C2×(C2×D3)⋊C4C22semidirect
42. C2×(C2×D3)⋊C4C22semidirect
43. C2×C4⋊Dic3C22semidirect
44. C2×C4⋊Dic3C22semidirect
45. C2×Dic3⋊C4C22semidirect
46. C2×C4×Dic3C22semidirect
47. #882C4semidirect
51. C3×#95C22semidirect
52. C3×#95C22semidirect
53. C3⋊#95C22semidirect
54. C3⋊#95C22semidirect
55. C3⋊#95C22semidirect
56. C3⋊#95C22semidirect
71. C4×C22⋊C4D3semidirect
79. C23×D3C2×C4semidirect
94. C2×#67C2×C4semidirect
107. C2×D12C2×C4semidirect
108. C2×D12C2×C4semidirect
118. C3×C22⋊C4C2×C4semidirect
119. C3×C22⋊C4D4semidirect
131. (C2×D3)⋊C4C2×C4semidirect
132. (C2×D3)⋊C4C2×C4semidirect
133. (C2×D3)⋊C4D4semidirect
170. C2×C42C2×D3semidirect
171. C2×C42C2×D3semidirect
176. #95C2×D3semidirect
177. #95C2×D3semidirect
316. C22⋊C4C4×D3semidirect
317. C22⋊C4D12semidirect
327. C22×C3C4×D4semidirect
356. C2×D3C4×D4semidirect
484. C22C4×D12semidirect
503. C3#2358semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D3)⋊C42
C2×#8822
C2×#67⋊C42
C2×D3×C22⋊C42
C2×C4×D122
C3×C4×C22⋊C42
#52132
#49502
#49402
#49392
C4×(C2×D3)⋊C42
#46702
#46682
#46652
#23583