Finite Group Databasebeta

← #82585

Subgroups — #82585

Order 384.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#120C211yesmaximal, characteristic
2C22×#217C211yesmaximal, characteristic, complemented
3C2×#935C211yesmaximal, characteristic, complemented
4C2×D4×Dic3C211yesmaximal, characteristic, complemented
5#5247C211yesmaximal, characteristic, complemented
6#5222C211yesmaximal, characteristic, complemented
7#5222C211yesmaximal, characteristic, complemented
8#5220C211yesmaximal, characteristic, complemented
9#5220C211yesmaximal, characteristic, complemented
10#4953C211yesmaximal, characteristic, complemented
11#4949C211yesmaximal, characteristic, complemented
12#4946C211yesmaximal, characteristic, complemented
13#4944C211yesmaximal, characteristic, complemented
14#4944C211yesmaximal, characteristic, complemented
15#4942C211yesmaximal, characteristic, complemented
16#2418—31nomaximal, Sylow
17C25×C3C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C22×C3×D4C2211yescharacteristic
20C22×C3×D4C2211yescharacteristic
21C23×Dic3C2211yescharacteristic
22C23×Dic3C2211yescharacteristic
23C23×Dic3C2211yescharacteristic, complemented
24C3×#120—24no—
25C2×C3×C22⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×#217—24no—
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic
33C2×#217C2211yescharacteristic
34C2×#217C2211yescharacteristic
35C2×#217C2211yescharacteristic
36C2×#217C2211yescharacteristic
37C2×#217C2211yescharacteristic
38C2×#217C2211yescharacteristic
39C2×#217C2211yescharacteristic, complemented
40C2×#217C2211yescharacteristic, complemented
41C2×#217C2211yescharacteristic, complemented
42#935—24no—
43D4×Dic3—24no—
44C2×C4⋊Dic3C2211yescharacteristic, complemented
45C2×Dic3⋊C4C2211yescharacteristic, complemented
46C2×Dic3⋊C4C2211yescharacteristic, complemented
47C2×Dic3⋊C4C2211yescharacteristic, complemented
48C2×Dic3⋊C4C2211yescharacteristic, complemented
49C2×C4×Dic3C2211yescharacteristic, complemented
50C3⋊#95C2211yescharacteristic, complemented
51C3⋊#95C2211yescharacteristic, complemented
52C3⋊#95C2211yescharacteristic, complemented
53C3⋊#95C2211yescharacteristic, complemented
54C3⋊#95C2211yescharacteristic, complemented
55C3⋊#95C2211yescharacteristic, complemented
56C2×#123—31no—
57C2×#120D311yescharacteristic
58C2×C4×D4—31no—
59C22×C22⋊C4—31no—
60#399—31no—
61#397—31no—
62#394—31no—
63#394—31no—
64#388—31no—
65#388—31no—
66#386—31no—
67#386—31no—
68#385—31no—
69#380—31no—
70#379—31no—
71C24×C3—22no—
72C24×C3—22no—
73C24×C3—22no—
74C24×C3—22no—
75C24×C3—22no—
76C24×C3—41no—
77C24×C3—41no—
78C24×C3C2311yescharacteristic
79C24×C3C2311yescharacteristic
80C24×C3C2311yescharacteristic
81C24×C3C2311yescharacteristic
82C2×C3×D4—22no—
83C2×C3×D4—22no—
84C2×C3×D4—22no—
85C2×C3×D4—22no—
86C2×C3×D4—22no—
87C2×C3×D4—22no—
88C2×C3×D4—41no—
89C2×C3×D4—41no—
90C2×C3×D4D414yes—
91C22×C3×C4C2311yescharacteristic
92C22×C3×C4C2311yescharacteristic
93C22×C3×C4C2311yescharacteristic
94C22×Dic3—22no—
95C22×Dic3—22no—
96C22×Dic3—22no—
97C22×Dic3—22no—
98C22×Dic3—22no—
99C22×Dic3—22no—
100C22×Dic3—41no—
101C22×Dic3—41no—
102C22×Dic3—41no—
103C22×Dic3C2311yescharacteristic
104C22×Dic3C2311yescharacteristic
105C22×Dic3C2311yescharacteristic
106C22×Dic3C2311yescharacteristic
107C22×Dic3C2311yescharacteristic
108C22×Dic3C2311yescharacteristic
109C22×Dic3C2311yescharacteristic
110C22×Dic3C2311yescharacteristic
111C3×C22⋊C4—22no—
112C3×C22⋊C4—22no—
113C3×C22⋊C4—22no—
114#217—22no—
115#217—22no—
116#217—22no—
117#217—22no—
118#217—22no—
119#217—22no—
120#217—22no—
121#217—22no—
122#217—22no—
123#217—41no—
124#217—41no—
125#217—41no—
126#217D414yescomplemented
127C4⋊Dic3—22no—
128Dic3⋊C4—22no—
129Dic3⋊C4—22no—
130Dic3⋊C4—41no—
131Dic3⋊C4—41no—
132C4×Dic3—22no—
133C25C2×D311yescharacteristic
134C22×D4C2×D311yescharacteristic
135C22×D4C2×D311yescharacteristic
136C22×D4C2×D311yescharacteristic
137C23×C4—31no—
138C23×C4—31no—
139C23×C4—31no—
140#123—64no—
141#120—24no—
142C4×D4—64no—
143C2×C4⋊C4—31no—
144C2×C4⋊C4—31no—
145C2×C4⋊C4—31no—
146C2×C4⋊C4—31no—
147C2×C4⋊C4—31no—
148C2×C22⋊C4—31no—
149C2×C22⋊C4—31no—
150C2×C22⋊C4—31no—
151C2×C22⋊C4—31no—
152C2×C22⋊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—64no—
162C2×C22⋊C4C2×D311yescharacteristic
163C2×C22⋊C4C2×D311yescharacteristic
164C2×C22⋊C4C2×D311yescharacteristic
165C2×C42—31no—
166#95—31no—
167#95—31no—
168#95—31no—
169#95—31no—
170#95—31no—
171#95—31no—
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—28no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3—21no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—21no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—21no—
189C23×C3—21no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—21no—
193C23×C3—21no—
194C23×C3—21no—
195C23×C3—44no—
196C23×C3—44no—
197C23×C3—44no—
198C23×C3—44no—
199C23×C3—44no—
200C23×C3—44no—
201C23×C3C2×D412yes—
202C23×C3C2×D412yes—
203C23×C3C2×D412yes—
204C23×C3#4112yes—
205C23×C3#4112yes—
206C23×C3#4112yes—
207C23×C3C2411yescharacteristic
208C3×D4—28no—
209C3×D4—44no—
210C3×D4—44no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4C2×D412yes—
220C2×Dic3—21no—
221C2×Dic3—21no—
222C2×Dic3—21no—
223C2×Dic3—21no—
224C2×Dic3—21no—
225C2×Dic3—21no—
226C2×Dic3—21no—
227C2×Dic3—21no—
228C2×Dic3—21no—
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—21no—
233C2×Dic3—21no—
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—44no—
243C2×Dic3—44no—
244C2×Dic3—44no—
245C2×Dic3C2×D412yes—
246C2×Dic3C2×D412yes—
247C24—22no—
248C24—22no—
249C24—22no—
250C24—22no—
251C24—22no—
252C24—41no—
253C24—41no—
254C24C22×D311yescharacteristic
255C24C22×D311yescharacteristic
256C24C22×D311yescharacteristic
257C24C22×D311yescharacteristic
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—22no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4#6714yes—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—31no—
270C22×C4—31no—
271C22×C4—31no—
272C22×C4—31no—
273C22×C4—31no—
274C22×C4—31no—
275C22×C4—62no—
276C22×C4—62no—
277C22×C4—62no—
278C22×C4—62no—
279C22×C4—62no—
280C22×C4—62no—
281C22×C4—121no—
282C22×C4—121no—
283C22×C4—121no—
284C22×C4C22×D311yescharacteristic
285C22×C4C22×D311yescharacteristic
286C22×C4C22×D311yescharacteristic
287C4⋊C4—62no—
288C4⋊C4—62no—
289C4⋊C4—62no—
290C4⋊C4—121no—
291C4⋊C4—121no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—34no—
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—62no—
299C22⋊C4—62no—
300C22⋊C4—62no—
301C22⋊C4—62no—
302C22⋊C4—62no—
303C22⋊C4—62no—
304C22⋊C4—62no—
305C22⋊C4—121no—
306C22⋊C4—121no—
307C22⋊C4—121no—
308C42—62no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—22no—
312C22×C3—22no—
313C22×C3—22no—
314C22×C3—22no—
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—416no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3#12314yescomplemented
338C22×C3C22×D411yescharacteristic
339C22×C3C22×D411yescharacteristic
340C22×C3C2×#4111yescharacteristic
341C22×C3C2×#4111yescharacteristic
342C22×C3C2×#4111yescharacteristic
343C22×C3H(5,𝔽2)11yescharacteristic
344C22×C3H(5,𝔽2)11yescharacteristic
345C3×C4—22no—
346C3×C4—41no—
347C3×C4—41no—
348Dic3—22no—
349Dic3—22no—
350Dic3—41no—
351Dic3—41no—
352Dic3—41no—
353Dic3—41no—
354Dic3—41no—
355Dic3—41no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—28no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—44no—
380C23—44no—
381C23—44no—
382C23—44no—
383C23—44no—
384C23—44no—
385C23D3×D412yes—
386C23#23712yes—
387C23#23712yes—
388C23#23712yes—
389C23C2×#6712yes—
390C23C2×#6712yes—
391C23C23×D311yescharacteristic
392D4—28no—
393D4—44no—
394D4—44no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—32no—
404C2×C4—32no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—124no—
428C2×C4—124no—
429C2×C4—124no—
430C2×C4C2×#6712yes—
431C2×C3—24no—
432C2×C3—42no—
433C2×C3—42no—
434C2×C3—42no—
435C2×C3C2×#12311yescharacteristic
436C2×C3#52511yescharacteristic
437C2×C3#53811yescharacteristic
438C2×C3D4211yescharacteristic
439C2×C3#54611yescharacteristic
440C2×C3#54611yescharacteristic
441C2×C3#55111yescharacteristic
442C22—22no—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—416no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22#93514yescomplemented
471C22C2×D3×D411yescharacteristic
472C22C2×#23711yescharacteristic
473C22C2×#23711yescharacteristic
474C22C2×#23711yescharacteristic
475C22#100411yescharacteristic
476C22#100411yescharacteristic
477C22C22×#6711yescharacteristic
478C4—22no—
479C4—41no—
480C4—41no—
481C4—62no—
482C4—62no—
483C4—121no—
484C4—121no—
485C4—121no—
486C4—121no—
487C4—121no—
488C4—121no—
489C3#241811yescharacteristic, complemented, Sylow
490C2—24no—
491C2—42no—
492C2—42no—
493C2—42no—
494C2#558611yescharacteristic
495C2#558711yescharacteristic
496C2#559111yescharacteristic
497C2#559311yescharacteristic
498C2C2×#93511yescharacteristic
499C2D4×#6711yescharacteristic
500C2#580611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
Fitting, prime radicalC2×C3×#120C2
hypercenterC2×#120D3
hypocenterC3#2418
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
2. C22×#217C2semidirect
3. C2×#935C2semidirect
4. C2×D4×Dic3C2semidirect
5. #5247C2semidirect
6. #5222C2semidirect
7. #5222C2semidirect
8. #5220C2semidirect
9. #5220C2semidirect
10. #4953C2semidirect
11. #4949C2semidirect
12. #4946C2semidirect
13. #4944C2semidirect
14. #4944C2semidirect
15. #4942C2semidirect
23. C23×Dic3C22semidirect
39. C2×#217C22semidirect
40. C2×#217C22semidirect
41. C2×#217C22semidirect
44. C2×C4⋊Dic3C22semidirect
45. C2×Dic3⋊C4C22semidirect
46. C2×Dic3⋊C4C22semidirect
47. C2×Dic3⋊C4C22semidirect
48. C2×Dic3⋊C4C22semidirect
49. C2×C4×Dic3C22semidirect
50. C3⋊#95C22semidirect
51. C3⋊#95C22semidirect
52. C3⋊#95C22semidirect
53. C3⋊#95C22semidirect
54. C3⋊#95C22semidirect
55. C3⋊#95C22semidirect
126. #217D4semidirect
337. C22×C3#123semidirect
470. C22#935semidirect
489. C3#2418semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#1202
C22×#2172
C2×#9352
C2×D4×Dic32
#52472
#52222
#52202
#49532
#49492
#49462
#49442
#49422
#24183