Finite Group Databasebeta

← #74891

Subgroups — #74891

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×#937C211yesmaximal, characteristic
2C2×D4×Dic3C211yesmaximal, characteristic, complemented
3C22×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×#886C211yesmaximal, characteristic, complemented
5C3×#386C211yesmaximal, characteristic, complemented
6#5212C211yesmaximal, characteristic, complemented
7#4961C211yesmaximal, characteristic, complemented
8#4961C211yesmaximal, characteristic, complemented
9#4958C211yesmaximal, characteristic, complemented
10#4955C211yesmaximal, characteristic, complemented
11#4950C211yesmaximal, characteristic, complemented
12#4677C211yesmaximal, characteristic, complemented
13#4674C211yesmaximal, characteristic, complemented
14#4670C211yesmaximal, characteristic, complemented
15#4670C211yesmaximal, characteristic, complemented
16#2418—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C23×C3×C4C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C23×Dic3C2211yescharacteristic
23C23×Dic3C2211yescharacteristic, complemented
24C2×C3×C22⋊C4C2211yescharacteristic
25C2×C3×C22⋊C4C2211yescharacteristic, complemented
26C2×C3×C22⋊C4C2211yescharacteristic, complemented
27C2×#217C2211yescharacteristic
28C2×#217C2211yescharacteristic
29C2×#217C2211yescharacteristic, complemented
30#937—24no—
31D4×Dic3—24no—
32C2×(C2×D3)⋊C4—24no—
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
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×(C2×D3)⋊C4C2211yescharacteristic
43C2×C4⋊Dic3C2211yescharacteristic, complemented
44C2×C4⋊Dic3C2211yescharacteristic, complemented
45C2×C4⋊Dic3C2211yescharacteristic, complemented
46C2×C4⋊Dic3C2211yescharacteristic, complemented
47C2×C4⋊Dic3C2211yescharacteristic, complemented
48C2×C4×Dic3C2211yescharacteristic, complemented
49#886—24no—
50C3×#95C2211yescharacteristic, complemented
51C3×#95C2211yescharacteristic, complemented
52C3⋊#95C2211yescharacteristic, complemented
53C3⋊#95C2211yescharacteristic, complemented
54C3⋊#95C2211yescharacteristic, complemented
55C3⋊#95C2211yescharacteristic, complemented
56C2×#123—31no—
57C2×#120—31no—
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#386D311yescharacteristic, complemented
68#385—31no—
69#380—31no—
70#379—31no—
71C24×C3C2311yescharacteristic
72C24×C3C2311yescharacteristic
73C23×D3—22no—
74C23×D3—22no—
75C23×D3—22no—
76C23×D3—22no—
77C23×D3—22no—
78C23×D3—41no—
79C23×D3—41no—
80C23×D3C2311yescharacteristic
81C23×D3C2311yescharacteristic
82C2×C3×D4—22no—
83C2×C3×D4—22no—
84C2×C3×D4D414yes—
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—22no—
102C22×Dic3—22no—
103C22×Dic3—41no—
104C22×Dic3—41no—
105C22×Dic3C2311yescharacteristic
106C22×Dic3C2311yescharacteristic
107C22×Dic3C2311yescharacteristic
108C22×Dic3C2311yescharacteristic
109C22×Dic3C2311yescharacteristic
110C22×Dic3C2311yescharacteristic
111C3×C22⋊C4—22no—
112C3×C22⋊C4—22no—
113C3×C22⋊C4—41no—
114#217—22no—
115#217—22no—
116#217—22no—
117(C2×D3)⋊C4—22no—
118(C2×D3)⋊C4—22no—
119(C2×D3)⋊C4—22no—
120(C2×D3)⋊C4—22no—
121(C2×D3)⋊C4—22no—
122(C2×D3)⋊C4—22no—
123(C2×D3)⋊C4—22no—
124(C2×D3)⋊C4—41no—
125(C2×D3)⋊C4—41no—
126(C2×D3)⋊C4D414yescomplemented
127C4⋊Dic3—22no—
128C4⋊Dic3—22no—
129C4⋊Dic3—22no—
130C4⋊Dic3—41no—
131C4⋊Dic3—41no—
132C4×Dic3—22no—
133C25—31no—
134C22×D4—31no—
135C22×D4—31no—
136C22×D4C2×D311yescharacteristic
137C23×C4—31no—
138C23×C4—31no—
139C23×C4C2×D311yescharacteristic
140#123—64no—
141#120—64no—
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, complemented
164C2×C22⋊C4C2×D311yescharacteristic, complemented
165C2×C42—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×C3C2×D412yes—
183C23×C3C2×D412yes—
184C23×C3#4112yes—
185C23×C3#4112yes—
186C23×C3C2411yescharacteristic
187C22×D3—28no—
188C22×D3—21no—
189C22×D3—21no—
190C22×D3—21no—
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—44no—
201C22×D3—44no—
202C22×D3—44no—
203C22×D3—44no—
204C22×D3—44no—
205C22×D3—44no—
206C22×D3C2×D412yes—
207C22×D3#4112yes—
208C3×D4—28no—
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—44no—
223C2×C3×C4C2×D412yes—
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×Dic3—44no—
246C2×Dic3C2×D412yes—
247C24—31no—
248C24—31no—
249C24—62no—
250C24—62no—
251C24—62no—
252C24—62no—
253C24—62no—
254C24—121no—
255C24—121no—
256C24C22×D311yescharacteristic
257C24C22×D311yescharacteristic
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—62no—
261C2×D4—62no—
262C2×D4—62no—
263C2×D4—62no—
264C2×D4—121no—
265C2×D4—121no—
266C2×D4D1214yes—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—31no—
270C22×C4—31no—
271C22×C4—31no—
272C22×C4—31no—
273C22×C4—31no—
274C22×C4—31no—
275C22×C4—41no—
276C22×C4—62no—
277C22×C4—62no—
278C22×C4—62no—
279C22×C4—62no—
280C22×C4—121no—
281C22×C4—121no—
282C22×C4C22×D311yescharacteristic
283C22×C4C22×D311yescharacteristic
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—34no—
295C22⋊C4—41no—
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—62no—
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—41no—
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3#12314yescomplemented
323C22×C3C22×D411yescharacteristic
324C22×C3C22×D411yescharacteristic
325C22×C3C2×#4111yescharacteristic
326C22×C3C2×#4111yescharacteristic
327C22×C3C2×#4111yescharacteristic
328C22×C3H(5,𝔽2)11yescharacteristic
329C22×C3H(5,𝔽2)11yescharacteristic
330C2×D3—22no—
331C2×D3—22no—
332C2×D3—22no—
333C2×D3—22no—
334C2×D3—22no—
335C2×D3—22no—
336C2×D3—416no—
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C2×D3—41no—
341C2×D3—41no—
342C2×D3—41no—
343C2×D3—41no—
344C2×D3—41no—
345C3×C4—22no—
346C3×C4—22no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—41no—
350Dic3—22no—
351Dic3—41no—
352Dic3—41no—
353Dic3—41no—
354Dic3—41no—
355Dic3—41no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—32no—
367C23—32no—
368C23—68no—
369C23—61no—
370C23—61no—
371C23—61no—
372C23—61no—
373C23—61no—
374C23—61no—
375C23—61no—
376C23—61no—
377C23—61no—
378C23—61no—
379C23—61no—
380C23—61no—
381C23—124no—
382C23—124no—
383C23—124no—
384C23—124no—
385C23—124no—
386C23—124no—
387C23C2×D1212yes—
388C23C2×D1212yes—
389C23#23712yes—
390C23#23712yes—
391C23C23×D311yescharacteristic
392D4—28no—
393D4—124no—
394D4—124no—
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—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—32no—
409C2×C4—44no—
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×C4C2×D1212yes—
430C2×C4D3×D412yes—
431C2×C3—24no—
432C2×C3—42no—
433C2×C3C2×#12311yescharacteristic
434C2×C3#52511yescharacteristic
435C2×C3#53811yescharacteristic
436C2×C3D4211yescharacteristic
437C2×C3#54611yescharacteristic
438C2×C3#54611yescharacteristic
439C2×C3#55111yescharacteristic
440D3—42no—
441D3—42no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—62no—
456C22—62no—
457C22—62no—
458C22—62no—
459C22—62no—
460C22—62no—
461C22—1216no—
462C22—121no—
463C22—121no—
464C22—121no—
465C22—121no—
466C22—121no—
467C22—121no—
468C22—121no—
469C22—121no—
470C22#88614yescomplemented
471C22C22×D1211yescharacteristic
472C22C2×D3×D411yescharacteristic
473C22C2×#23711yescharacteristic
474C22C2×#23711yescharacteristic
475C22#100411yescharacteristic
476C22D3×#4111yescharacteristic
477C22#100911yescharacteristic
478C4—22no—
479C4—22no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—62no—
484C4—121no—
485C4—121no—
486C4—121no—
487C4—121no—
488C4—121no—
489C3#241811yescharacteristic, complemented, Sylow
490C2—24no—
491C2—42no—
492C2—122no—
493C2—122no—
494C2C2×#88611yescharacteristic
495C2D4×D1211yescharacteristic
496C2#555411yescharacteristic
497C2#559111yescharacteristic
498C2#560611yescharacteristic
499C2#561711yescharacteristic
500C2#565811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#386C2
prime radicalC2×#937C2
hypercenter#386D3
hypocenterC3#2418
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic3C2semidirect
3. C22×(C2×D3)⋊C4C2semidirect
4. C2×#886C2semidirect
5. C3×#386C2semidirect
6. #5212C2semidirect
7. #4961C2semidirect
8. #4961C2semidirect
9. #4958C2semidirect
10. #4955C2semidirect
11. #4950C2semidirect
12. #4677C2semidirect
13. #4674C2semidirect
14. #4670C2semidirect
15. #4670C2semidirect
23. C23×Dic3C22semidirect
25. C2×C3×C22⋊C4C22semidirect
26. C2×C3×C22⋊C4C22semidirect
29. C2×#217C22semidirect
43. C2×C4⋊Dic3C22semidirect
44. C2×C4⋊Dic3C22semidirect
45. C2×C4⋊Dic3C22semidirect
46. C2×C4⋊Dic3C22semidirect
47. C2×C4⋊Dic3C22semidirect
48. C2×C4×Dic3C22semidirect
50. C3×#95C22semidirect
51. C3×#95C22semidirect
52. C3⋊#95C22semidirect
53. C3⋊#95C22semidirect
54. C3⋊#95C22semidirect
55. C3⋊#95C22semidirect
67. #386D3semidirect
126. (C2×D3)⋊C4D4semidirect
163. C2×C22⋊C4C2×D3semidirect
164. C2×C22⋊C4C2×D3semidirect
170. #95C2×D3semidirect
171. #95C2×D3semidirect
322. C22×C3#123semidirect
470. C22#886semidirect
489. C3#2418semidirect

Maximal subgroups

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

subgroupindex
C2×#9372
C2×D4×Dic32
C22×(C2×D3)⋊C42
C2×#8862
C3×#3862
#52122
#49612
#49582
#49552
#49502
#46772
#46742
#46702
#24183