Finite Group Databasebeta

← #74901

Subgroups — #74901

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×C4×#67C211yesmaximal, characteristic, complemented
3C2×#883C211yesmaximal, characteristic, complemented
4C2×D3×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#386C211yesmaximal, characteristic, complemented
6#5222C211yesmaximal, characteristic, complemented
7#5213C211yesmaximal, characteristic, complemented
8#4959C211yesmaximal, characteristic, complemented
9#4955C211yesmaximal, characteristic, complemented
10#4948C211yesmaximal, characteristic, complemented
11#4944C211yesmaximal, characteristic, complemented
12#4676C211yesmaximal, characteristic, complemented
13#4670C211yesmaximal, characteristic, complemented
14#4667C211yesmaximal, characteristic, complemented
15#4664C211yesmaximal, characteristic, complemented
16#2534—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C23×C3×C4C2211yescharacteristic, complemented
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×C4×D3C2211yescharacteristic
23C22×C4×D3C2211yescharacteristic
24C2×C3×C22⋊C4C2211yescharacteristic
25C2×C3×C22⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic, complemented
27C2×#217C2211yescharacteristic
28C2×#217C2211yescharacteristic
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic, complemented
31C2×#217C2211yescharacteristic, complemented
32#937—24no—
33C4×#67—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×Dic3⋊C4C2211yescharacteristic, complemented
44C2×Dic3⋊C4C2211yescharacteristic, complemented
45C2×Dic3⋊C4C2211yescharacteristic, complemented
46C2×Dic3⋊C4C2211yescharacteristic, complemented
47C2×C4×Dic3C2211yescharacteristic, complemented
48#883—24no—
49D3×C22⋊C4—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#396—31no—
61#396—31no—
62#394—31no—
63#394—31no—
64#388—31no—
65#388—31no—
66#386—31no—
67#386D311yescharacteristic, complemented
68#381—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×D4—41no—
85C22×C3×C4—22no—
86C22×C3×C4—41no—
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×#67D414yes—
99C22×Dic3C2311yescharacteristic
100C22×Dic3C2311yescharacteristic
101C22×Dic3C2311yescharacteristic
102C22×Dic3C2311yescharacteristic
103C22×Dic3C2311yescharacteristic
104C22×Dic3C2311yescharacteristic
105C2×C4×D3—22no—
106C2×C4×D3—22no—
107C2×C4×D3—22no—
108C2×C4×D3—41no—
109C2×C4×D3—41no—
110C2×C4×D3D414yescomplemented
111C3×C22⋊C4—22no—
112C3×C22⋊C4—22no—
113C3×C22⋊C4—41no—
114#217—22no—
115#217—22no—
116#217—22no—
117#217—22no—
118#217—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—22no—
125(C2×D3)⋊C4—22no—
126(C2×D3)⋊C4—41no—
127C4⋊Dic3—22no—
128Dic3⋊C4—22no—
129Dic3⋊C4—22no—
130Dic3⋊C4—41no—
131Dic3⋊C4—41no—
132C4×Dic3—22no—
133C25—31no—
134C22×D4—31no—
135C22×D4—31no—
136C22×D4C2×D311yescharacteristic
137C23×C4—31no—
138C23×C4—31no—
139C23×C4C2×D311yescharacteristic, complemented
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
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×C3—21no—
183C23×C3—21no—
184C23×C3C2×D412yes—
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—44no—
199C22×D3—44no—
200C22×D3—44no—
201C22×D3—44no—
202C22×D3—44no—
203C22×D3—44no—
204C22×D3C2×D412yes—
205C22×D3C2×D412yes—
206C22×D3#4112yes—
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—28no—
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×Dic3C2×D412yes—
244C2×Dic3C2×D412yes—
245C4×D3—44no—
246C4×D3—44no—
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—34no—
261C2×D4—41no—
262C2×D4—62no—
263C2×D4—62no—
264C2×D4—62no—
265C2×D4—62no—
266C2×D4—121no—
267C22×C4—22no—
268C22×C4—31no—
269C22×C4—31no—
270C22×C4—34no—
271C22×C4—31no—
272C22×C4—31no—
273C22×C4—31no—
274C22×C4—31no—
275C22×C4—41no—
276C22×C4—41no—
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—41no—
295C22⋊C4—62no—
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—62no—
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—41no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—41no—
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—22no—
337C2×D3—22no—
338C2×D3—22no—
339C2×D3—416no—
340C2×D3—41no—
341C2×D3—41no—
342C2×D3—41no—
343C2×D3—41no—
344C2×D3#12114yes—
345C3×C4—22no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—41no—
350Dic3—22no—
351Dic3—22no—
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—21no—
367C23—21no—
368C23—32no—
369C23—32no—
370C23—32no—
371C23—32no—
372C23—68no—
373C23—61no—
374C23—61no—
375C23—61no—
376C23—61no—
377C23—61no—
378C23—61no—
379C23—61no—
380C23—61no—
381C23—61no—
382C23—61no—
383C23—124no—
384C23—124no—
385C23—124no—
386C23—124no—
387C23—124no—
388C23—124no—
389C23#23512yes—
390C23D3×D412yes—
391C23C23×D311yescharacteristic
392D4—44no—
393D4—68no—
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—21no—
409C2×C4—32no—
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—124no—
429C2×C4—124no—
430C2×C4D3×D412yes—
431C2×C3—42no—
432C2×C3—42no—
433C2×C3C2×#12111yescharacteristic
434C2×C3#52511yescharacteristic
435C2×C3#53411yescharacteristic
436C2×C3#54611yescharacteristic
437C2×C3#54611yescharacteristic
438C2×C3#55111yescharacteristic
439C2×C3#55111yescharacteristic
440D3—24no—
441D3—42no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—34no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—62no—
458C22—62no—
459C22—62no—
460C22—62no—
461C22—62no—
462C22—62no—
463C22—62no—
464C22—62no—
465C22—62no—
466C22—1216no—
467C22—121no—
468C22—121no—
469C22—121no—
470C22—121no—
471C22C2×#23511yescharacteristic
472C22C2×D3×D411yescharacteristic
473C22C2×D3×D411yescharacteristic
474C22#100411yescharacteristic
475C22#100411yescharacteristic
476C22D3×#4111yescharacteristic
477C22D3×#4111yescharacteristic
478C4—22no—
479C4—41no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—62no—
484C4—62no—
485C4—121no—
486C4—121no—
487C4—121no—
488C4—121no—
489C3#253411yescharacteristic, complemented, Sylow
490C2—42no—
491C2—42no—
492C2—64no—
493C2—122no—
494C2#549011yescharacteristic
495C2#554711yescharacteristic
496C2#555611yescharacteristic
497C2#558911yescharacteristic
498C2D3×#12111yescharacteristic
499C2#561011yescharacteristic
500C2#565911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#386C2
prime radicalC2×#937C2
hypercenter#386D3
hypocenterC3#2534
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×#67C2semidirect
3. C2×#883C2semidirect
4. C2×D3×C22⋊C4C2semidirect
5. C3×#386C2semidirect
6. #5222C2semidirect
7. #5213C2semidirect
8. #4959C2semidirect
9. #4955C2semidirect
10. #4948C2semidirect
11. #4944C2semidirect
12. #4676C2semidirect
13. #4670C2semidirect
14. #4667C2semidirect
15. #4664C2semidirect
19. C23×C3×C4C22semidirect
26. C2×C3×C22⋊C4C22semidirect
30. C2×#217C22semidirect
31. C2×#217C22semidirect
42. C2×C4⋊Dic3C22semidirect
43. C2×Dic3⋊C4C22semidirect
44. C2×Dic3⋊C4C22semidirect
45. C2×Dic3⋊C4C22semidirect
46. C2×Dic3⋊C4C22semidirect
47. C2×C4×Dic3C22semidirect
50. C3×#95C22semidirect
51. C3×#95C22semidirect
52. C3⋊#95C22semidirect
53. C3⋊#95C22semidirect
54. C3⋊#95C22semidirect
55. C3⋊#95C22semidirect
67. #386D3semidirect
110. C2×C4×D3D4semidirect
139. C23×C4C2×D3semidirect
164. C2×C22⋊C4C2×D3semidirect
170. #95C2×D3semidirect
171. #95C2×D3semidirect
489. C3#2534semidirect

Maximal subgroups

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

subgroupindex
C2×#9372
C2×C4×#672
C2×#8832
C2×D3×C22⋊C42
C3×#3862
#52222
#52132
#49592
#49552
#49482
#49442
#46762
#46702
#46672
#46642
#25343