Finite Group Databasebeta

← #74890

Subgroups — #74890

Order 384.

814 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#937C211yesmaximal, characteristic
2C22×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C2×#883C211yesmaximal, characteristic, complemented
4C2×D3×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#386C211yesmaximal, characteristic, complemented
6#5220C211yesmaximal, characteristic, complemented
7#5212C211yesmaximal, characteristic, complemented
8#4961C211yesmaximal, characteristic, complemented
9#4959C211yesmaximal, characteristic, complemented
10#4956C211yesmaximal, characteristic, complemented
11#4942C211yesmaximal, characteristic, complemented
12#4675C211yesmaximal, characteristic, complemented
13#4674C211yesmaximal, characteristic, complemented
14#4668C211yesmaximal, characteristic, complemented
15#4664C211yesmaximal, characteristic, complemented
16#2412—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C23×C3×C4C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C23×Dic3C2211yescharacteristic
23C22×C4×D3C2211yescharacteristic
24C22×C4×D3C2211yescharacteristic
25C2×C3×C22⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic, complemented
27C2×C3×C22⋊C4C2211yescharacteristic, complemented
28C2×#217C2211yescharacteristic
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic, complemented
31C2×#217C2211yescharacteristic, complemented
32#937—24no—
33C2×(C2×D3)⋊C4—24no—
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
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×C4⋊Dic3C2211yescharacteristic, complemented
43C2×C4⋊Dic3C2211yescharacteristic, complemented
44C2×Dic3⋊C4C2211yescharacteristic, complemented
45C2×Dic3⋊C4C2211yescharacteristic, complemented
46#883—24no—
47D3×C22⋊C4—24no—
48C3×#95C2211yescharacteristic, complemented
49C3×#95C2211yescharacteristic, complemented
50C3⋊#95C2211yescharacteristic, complemented
51C3⋊#95C2211yescharacteristic, complemented
52C3⋊#95C2211yescharacteristic, complemented
53C3⋊#95C2211yescharacteristic, complemented
54C3⋊#95C2211yescharacteristic, complemented
55C3⋊#95C2211yescharacteristic, complemented
56C2×#123—31no—
57C2×#120—31no—
58C22×C22⋊C4—31no—
59C22×C22⋊C4—31no—
60#397—31no—
61#397—31no—
62#394—31no—
63#394—31no—
64#386—31no—
65#386—31no—
66#386D311yescharacteristic, complemented
67#385—31no—
68#381—31no—
69#380—31no—
70#380—31no—
71C24×C3C2311yescharacteristic
72C24×C3C2311yescharacteristic
73C23×D3—22no—
74C23×D3—22no—
75C23×D3—22no—
76C23×D3—22no—
77C23×D3—41no—
78C23×D3—41no—
79C23×D3D414yes—
80C23×D3C2311yescharacteristic
81C23×D3C2311yescharacteristic
82C2×C3×D4—22no—
83C2×C3×D4—22no—
84C2×C3×D4—22no—
85C22×C3×C4—22no—
86C22×C3×C4—22no—
87C22×C3×C4—41no—
88C22×C3×C4C2311yescharacteristic
89C22×C3×C4C2311yescharacteristic
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C22×C3×C4C2311yescharacteristic
93C2×#67—22no—
94C2×#67—22no—
95C2×#67—22no—
96C2×#67—22no—
97C2×#67—41no—
98C2×#67—41no—
99C22×Dic3—22no—
100C22×Dic3—22no—
101C22×Dic3—41no—
102C22×Dic3C2311yescharacteristic
103C22×Dic3C2311yescharacteristic
104C22×Dic3C2311yescharacteristic
105C22×Dic3C2311yescharacteristic
106C22×Dic3C2311yescharacteristic
107C22×Dic3C2311yescharacteristic
108C2×C4×D3—22no—
109C2×C4×D3—22no—
110C2×C4×D3—22no—
111C2×C4×D3—22no—
112C2×C4×D3—41no—
113C2×C4×D3—41no—
114C3×C22⋊C4—22no—
115C3×C22⋊C4—22no—
116C3×C22⋊C4—41no—
117#217—22no—
118#217—22no—
119#217—22no—
120#217—41no—
121(C2×D3)⋊C4—22no—
122(C2×D3)⋊C4—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)⋊C4D414yescomplemented
129C4⋊Dic3—22no—
130C4⋊Dic3—41no—
131Dic3⋊C4—22no—
132Dic3⋊C4—41no—
133C25—31no—
134C22×D4—31no—
135C22×D4—31no—
136C22×D4C2×D311yescharacteristic
137C23×C4—31no—
138C23×C4—31no—
139C23×C4—31no—
140C23×C4C2×D311yescharacteristic
141#123—64no—
142#120—64no—
143C2×C4⋊C4—31no—
144C2×C4⋊C4—31no—
145C2×C4⋊C4—31no—
146C2×C4⋊C4—31no—
147C2×C22⋊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—64no—
160C2×C22⋊C4—64no—
161C2×C22⋊C4C2×D311yescharacteristic
162C2×C22⋊C4C2×D311yescharacteristic, complemented
163C2×C22⋊C4C2×D311yescharacteristic, complemented
164#95—31no—
165#95—31no—
166#95—31no—
167#95—31no—
168#95—31no—
169#95—31no—
170#95C2×D311yescharacteristic, complemented
171#95C2×D311yescharacteristic, complemented
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—21no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3—21no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3C2×D412yes—
184C23×C3#4112yes—
185C23×C3#4112yes—
186C23×C3C2411yescharacteristic
187C22×D3—21no—
188C22×D3—21no—
189C22×D3—21no—
190C22×D3—21no—
191C22×D3—28no—
192C22×D3—21no—
193C22×D3—21no—
194C22×D3—21no—
195C22×D3—21no—
196C22×D3—21no—
197C22×D3—21no—
198C22×D3—28no—
199C22×D3—44no—
200C22×D3—44no—
201C22×D3—44no—
202C22×D3—44no—
203C22×D3—44no—
204C22×D3C2×D412yes—
205C22×D3C2×D412yes—
206C22×D3C2×D412yes—
207C22×D3#4112yes—
208C3×D4—44no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
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×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—44no—
224C2×C3×C4C2×D412yes—
225#67—44no—
226#67—44no—
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—21no—
243C2×Dic3—21no—
244C2×Dic3—44no—
245C2×Dic3C2×D412yes—
246C4×D3—44no—
247C4×D3—44no—
248C24—31no—
249C24—31no—
250C24—34no—
251C24—62no—
252C24—62no—
253C24—62no—
254C24—62no—
255C24—121no—
256C24—121no—
257C24C22×D311yescharacteristic
258C24C22×D311yescharacteristic
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—62no—
263C2×D4—62no—
264C2×D4—62no—
265C2×D4—62no—
266C2×D4—121no—
267C2×D4—121no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—31no—
271C22×C4—31no—
272C22×C4—31no—
273C22×C4—31no—
274C22×C4—31no—
275C22×C4—31no—
276C22×C4—41no—
277C22×C4—62no—
278C22×C4—62no—
279C22×C4—62no—
280C22×C4—62no—
281C22×C4—62no—
282C22×C4—62no—
283C22×C4—121no—
284C22×C4—121no—
285C22×C4—121no—
286C22×C4C22×D311yescharacteristic
287C22×C4C22×D311yescharacteristic
288C22×C4C22×D311yescharacteristic
289C22×C4C22×D311yescharacteristic
290C22×C4C22×D311yescharacteristic
291C4⋊C4—62no—
292C4⋊C4—62no—
293C4⋊C4—121no—
294C4⋊C4—121no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—34no—
298C22⋊C4—41no—
299C22⋊C4—62no—
300C22⋊C4—62no—
301C22⋊C4—62no—
302C22⋊C4—62no—
303C22⋊C4—62no—
304C22⋊C4—62no—
305C22⋊C4—62no—
306C22⋊C4—62no—
307C22⋊C4—62no—
308C22⋊C4—62no—
309C22⋊C4—121no—
310C22×C3—22no—
311C22×C3—22no—
312C22×C3—22no—
313C22×C3—22no—
314C22×C3—22no—
315C22×C3—22no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3#12314yescomplemented
324C22×C3C22×D411yescharacteristic
325C22×C3C22×D411yescharacteristic
326C22×C3C2×#4111yescharacteristic
327C22×C3C2×#4111yescharacteristic
328C22×C3C2×#4111yescharacteristic
329C22×C3H(5,𝔽2)11yescharacteristic
330C22×C3H(5,𝔽2)11yescharacteristic
331C2×D3—22no—
332C2×D3—22no—
333C2×D3—22no—
334C2×D3—22no—
335C2×D3—22no—
336C2×D3—22no—
337C2×D3—22no—
338C2×D3—22no—
339C2×D3—22no—
340C2×D3—416no—
341C2×D3—41no—
342C2×D3—41no—
343C2×D3—41no—
344C2×D3—41no—
345C2×D3#12114yes—
346C3×C4—22no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—41no—
351Dic3—22no—
352Dic3—41no—
353Dic3—41no—
354Dic3—41no—
355Dic3—41no—
356Dic3—41no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—32no—
369C23—32no—
370C23—32no—
371C23—32no—
372C23—68no—
373C23—61no—
374C23—61no—
375C23—61no—
376C23—61no—
377C23—68no—
378C23—61no—
379C23—61no—
380C23—61no—
381C23—61no—
382C23—61no—
383C23—61no—
384C23—124no—
385C23—124no—
386C23—124no—
387C23—124no—
388C23—124no—
389C23#23512yes—
390C23D3×D412yes—
391C23#23712yes—
392C23C23×D311yescharacteristic
393D4—44no—
394D4—124no—
395D4—124no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—32no—
411C2×C4—44no—
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—61no—
428C2×C4—61no—
429C2×C4—124no—
430C2×C4—124no—
431C2×C4—124no—
432C2×C4D3×D412yes—
433C2×C3—24no—
434C2×C3—81no—
435C2×C3C2×#12111yescharacteristic
436C2×C3C2×#12311yescharacteristic
437C2×C3#53411yescharacteristic
438C2×C3#54611yescharacteristic
439C2×C3#54611yescharacteristic
440C2×C3#55111yescharacteristic
441C2×C3#55111yescharacteristic
442D3—24no—
443D3—42no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—34no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—62no—
459C22—62no—
460C22—62no—
461C22—62no—
462C22—62no—
463C22—62no—
464C22—62no—
465C22—62no—
466C22—62no—
467C22—1216no—
468C22—121no—
469C22—121no—
470C22—121no—
471C22—121no—
472C22#88314yescomplemented
473C22C2×#23511yescharacteristic
474C22C2×D3×D411yescharacteristic
475C22C2×D3×D411yescharacteristic
476C22C2×#23711yescharacteristic
477C22#100411yescharacteristic
478C22D3×#4111yescharacteristic
479C22#100911yescharacteristic
480C4—22no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—62no—
486C4—121no—
487C4—121no—
488C4—121no—
489C4—121no—
490C4—121no—
491C3#241211yescharacteristic, complemented, Sylow
492C2—24no—
493C2—64no—
494C2—81no—
495C2—122no—
496C2C2×#88311yescharacteristic
497C2#555011yescharacteristic
498C2#555611yescharacteristic
499C2#559111yescharacteristic
500C2D3×#12111yescharacteristic
501C2#560511yescharacteristic
502C2#565811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#386C2
prime radicalC2×#937C2
hypercenter#386D3
hypocenterC3#2412
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×(C2×D3)⋊C4C2semidirect
3. C2×#883C2semidirect
4. C2×D3×C22⋊C4C2semidirect
5. C3×#386C2semidirect
6. #5220C2semidirect
7. #5212C2semidirect
8. #4961C2semidirect
9. #4959C2semidirect
10. #4956C2semidirect
11. #4942C2semidirect
12. #4675C2semidirect
13. #4674C2semidirect
14. #4668C2semidirect
15. #4664C2semidirect
26. C2×C3×C22⋊C4C22semidirect
27. C2×C3×C22⋊C4C22semidirect
30. C2×#217C22semidirect
31. C2×#217C22semidirect
42. C2×C4⋊Dic3C22semidirect
43. C2×C4⋊Dic3C22semidirect
44. C2×Dic3⋊C4C22semidirect
45. C2×Dic3⋊C4C22semidirect
48. C3×#95C22semidirect
49. C3×#95C22semidirect
50. C3⋊#95C22semidirect
51. C3⋊#95C22semidirect
52. C3⋊#95C22semidirect
53. C3⋊#95C22semidirect
54. C3⋊#95C22semidirect
55. C3⋊#95C22semidirect
66. #386D3semidirect
128. (C2×D3)⋊C4D4semidirect
162. C2×C22⋊C4C2×D3semidirect
163. C2×C22⋊C4C2×D3semidirect
170. #95C2×D3semidirect
171. #95C2×D3semidirect
323. C22×C3#123semidirect
472. C22#883semidirect
491. C3#2412semidirect

Maximal subgroups

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

subgroupindex
C2×#9372
C22×(C2×D3)⋊C42
C2×#8832
C2×D3×C22⋊C42
C3×#3862
#52202
#52122
#49612
#49592
#49562
#49422
#46752
#46742
#46682
#46642
#24123