Finite Group Databasebeta

← #74879

Subgroups — #74879

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
1C2×#937C211yesmaximal, characteristic
2C2×D4×Dic3C211yesmaximal, characteristic, complemented
3C22×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×#67⋊C4C211yesmaximal, characteristic, complemented
5C2×D3×C22⋊C4C211yesmaximal, characteristic, complemented
6C3×#386C211yesmaximal, characteristic, complemented
7C4×#217C211yesmaximal, characteristic, complemented
8#4958C211yesmaximal, characteristic, complemented
9#4957C211yesmaximal, characteristic, complemented
10#4956C211yesmaximal, characteristic, complemented
11#4946C211yesmaximal, characteristic, complemented
12#4670C211yesmaximal, characteristic, complemented
13#4669C211yesmaximal, characteristic, complemented
14#4668C211yesmaximal, characteristic, complemented
15#4666C211yesmaximal, characteristic, complemented
16#2358—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C23×C3×C4C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C23×Dic3C2211yescharacteristic
23C23×Dic3C2211yescharacteristic, complemented
24C22×C4×D3C2211yescharacteristic
25C22×C4×D3C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic, complemented
28C2×C3×C22⋊C4C2211yescharacteristic, complemented
29C2×#217C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic, complemented
32#937C418yescomplemented
33D4×Dic3—24no—
34C2×(C2×D3)⋊C4—24no—
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×Dic3⋊C4C2211yescharacteristic, complemented
45C2×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C4×Dic3C2211yescharacteristic, complemented
47C2×C4×Dic3C2211yescharacteristic, complemented
48C2×C4×Dic3C2211yescharacteristic, complemented
49#67⋊C4—24no—
50D3×C22⋊C4—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#386D311yescharacteristic, complemented
68#385—31no—
69#385—31no—
70C4×C22⋊C4—31no—
71C4×C22⋊C4—31no—
72C24×C3C2311yescharacteristic
73C24×C3C2311yescharacteristic
74C23×D3—22no—
75C23×D3—22no—
76C23×D3—22no—
77C23×D3—22no—
78C23×D3—41no—
79C23×D3—41no—
80C23×D3C2×C414yescomplemented
81C23×D3C2311yescharacteristic
82C23×D3C2311yescharacteristic
83C2×C3×D4—22no—
84C2×C3×D4—22no—
85C2×C3×D4C2×C414yescomplemented
86C22×C3×C4—22no—
87C22×C3×C4—22no—
88C22×C3×C4—41no—
89C22×C3×C4C2311yescharacteristic
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C22×C3×C4C2311yescharacteristic
93C22×C3×C4C2311yescharacteristic
94C2×#67—22no—
95C2×#67—22no—
96C2×#67—41no—
97C2×#67—41no—
98C2×#67C2×C414yescomplemented
99C2×#67C2×C414yescomplemented
100C22×Dic3—22no—
101C22×Dic3—22no—
102C22×Dic3—22no—
103C22×Dic3—22no—
104C22×Dic3—41no—
105C22×Dic3—41no—
106C22×Dic3C2311yescharacteristic
107C22×Dic3C2311yescharacteristic
108C22×Dic3C2311yescharacteristic
109C22×Dic3C2311yescharacteristic
110C22×Dic3C2311yescharacteristic
111C22×Dic3C2311yescharacteristic
112C2×C4×D3—22no—
113C2×C4×D3—22no—
114C2×C4×D3—22no—
115C2×C4×D3—22no—
116C2×C4×D3—41no—
117C2×C4×D3—41no—
118C3×C22⋊C4—22no—
119C3×C22⋊C4—22no—
120C3×C22⋊C4—41no—
121#217—22no—
122#217C2×C414yescomplemented
123#217D414yescomplemented
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)⋊C4C2×C414yescomplemented
130(C2×D3)⋊C4C2×C414yescomplemented
131(C2×D3)⋊C4D414yescomplemented
132C4⋊Dic3—22no—
133Dic3⋊C4—22no—
134Dic3⋊C4—41no—
135C4×Dic3—22no—
136C4×Dic3—22no—
137C4×Dic3—41no—
138C25—31no—
139C22×D4—31no—
140C22×D4—31no—
141C22×D4C2×D311yescharacteristic
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—64no—
165C2×C22⋊C4—64no—
166C2×C22⋊C4C2×D311yescharacteristic
167C2×C22⋊C4C2×D311yescharacteristic, complemented
168C2×C22⋊C4C2×D311yescharacteristic, complemented
169C2×C42—31no—
170C2×C42—31no—
171C2×C42—31no—
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×C3—21no—
183C23×C3—21no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3C22×C412yes—
189C23×C3C22×C412yes—
190C23×C3C2×D412yes—
191C23×C3#4112yes—
192C23×C3C2411yescharacteristic
193C22×D3—21no—
194C22×D3—21no—
195C22×D3—21no—
196C22×D3—21no—
197C22×D3—28no—
198C22×D3—21no—
199C22×D3—21no—
200C22×D3—21no—
201C22×D3—21no—
202C22×D3—21no—
203C22×D3—21no—
204C22×D3—28no—
205C22×D3—44no—
206C22×D3—44no—
207C22×D3—44no—
208C22×D3—44no—
209C22×D3—44no—
210C22×D3C22×C412yes—
211C22×D3C22×C412yes—
212C22×D3C2×D412yes—
213C22×D3#4112yes—
214C3×D4—28no—
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—21no—
228C2×C3×C4—44no—
229C2×C3×C4C22×C412yes—
230C2×C3×C4C2×D412yes—
231#67—28no—
232#67—44no—
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—21no—
245C2×Dic3—21no—
246C2×Dic3—44no—
247C2×Dic3—44no—
248C2×Dic3C22×C412yes—
249C2×Dic3C22×C412yes—
250C2×Dic3C2×D412yes—
251C2×Dic3C2×D412yes—
252C2×Dic3C2×D412yes—
253C4×D3—44no—
254C4×D3—44no—
255C24—31no—
256C24—31no—
257C24—34no—
258C24—62no—
259C24—62no—
260C24—62no—
261C24—62no—
262C24—121no—
263C24—121no—
264C24C22×D311yescharacteristic
265C24C22×D311yescharacteristic
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—34no—
269C2×D4—34no—
270C2×D4—62no—
271C2×D4—62no—
272C2×D4—121no—
273C2×D4—121no—
274C2×D4C4×D314yescomplemented
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—31no—
278C22×C4—31no—
279C22×C4—31no—
280C22×C4—31no—
281C22×C4—31no—
282C22×C4—31no—
283C22×C4—41no—
284C22×C4—62no—
285C22×C4—62no—
286C22×C4—62no—
287C22×C4—62no—
288C22×C4—62no—
289C22×C4—62no—
290C22×C4—62no—
291C22×C4—62no—
292C22×C4—121no—
293C22×C4—121no—
294C22×C4—121no—
295C22×C4—121no—
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—22no—
305C22⋊C4—22no—
306C22⋊C4—34no—
307C22⋊C4—34no—
308C22⋊C4—34no—
309C22⋊C4—34no—
310C22⋊C4—34no—
311C22⋊C4—41no—
312C22⋊C4—62no—
313C22⋊C4—62no—
314C22⋊C4—62no—
315C22⋊C4—62no—
316C22⋊C4—62no—
317C22⋊C4—62no—
318C42—62no—
319C42—62no—
320C42—121no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—22no—
325C22×C3—22no—
326C22×C3—22no—
327C22×C3—22no—
328C22×C3—22no—
329C22×C3—22no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3C4×D414yescomplemented
335C22×C3C23×C411yescharacteristic
336C22×C3C22×D411yescharacteristic
337C22×C3C22×D411yescharacteristic
338C22×C3C2×#4111yescharacteristic
339C22×C3C2×#4111yescharacteristic
340C22×C3H(5,𝔽2)11yescharacteristic
341C22×C3H(5,𝔽2)11yescharacteristic
342C2×D3—22no—
343C2×D3—22no—
344C2×D3—22no—
345C2×D3—22no—
346C2×D3—22no—
347C2×D3—22no—
348C2×D3—22no—
349C2×D3—22no—
350C2×D3—22no—
351C2×D3—416no—
352C2×D3—41no—
353C2×D3—41no—
354C2×D3—41no—
355C2×D3—41no—
356C2×D3C4×D414yescomplemented
357C3×C4—22no—
358C3×C4—22no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—41no—
362Dic3—22no—
363Dic3—22no—
364Dic3—22no—
365Dic3—22no—
366Dic3—22no—
367Dic3—41no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—32no—
379C23—32no—
380C23—32no—
381C23—32no—
382C23—68no—
383C23—61no—
384C23—61no—
385C23—61no—
386C23—61no—
387C23—68no—
388C23—61no—
389C23—61no—
390C23—61no—
391C23—61no—
392C23—61no—
393C23—61no—
394C23—124no—
395C23—124no—
396C23—124no—
397C23—124no—
398C23—124no—
399C23C2×C4×D312yes—
400C23C2×C4×D312yes—
401C23D3×D412yes—
402C23#23712yes—
403C23C23×D311yescharacteristic
404D4—28no—
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—32no—
423C2×C4—32no—
424C2×C4—32no—
425C2×C4—44no—
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—61no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—124no—
440C2×C4—124no—
441C2×C4—124no—
442C2×C4—124no—
443C2×C4C2×C4×D312yes—
444C2×C4D3×D412yes—
445C2×C3—24no—
446C2×C3—42no—
447C2×C3C2×C4×D411yescharacteristic
448C2×C3C2×C4×D411yescharacteristic
449C2×C3#51811yescharacteristic
450C2×C3D4211yescharacteristic
451C2×C3#54611yescharacteristic
452C2×C3#54611yescharacteristic
453C2×C3#55111yescharacteristic
454D3—24no—
455D3—42no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—34no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—62no—
471C22—62no—
472C22—62no—
473C22—62no—
474C22—62no—
475C22—62no—
476C22—62no—
477C22—62no—
478C22—62no—
479C22—1216no—
480C22—121no—
481C22—121no—
482C22—121no—
483C22—121no—
484C22#67⋊C414yescomplemented
485C22C22×C4×D311yescharacteristic
486C22C2×D3×D411yescharacteristic
487C22C2×D3×D411yescharacteristic
488C22C2×#23711yescharacteristic
489C22#100411yescharacteristic
490C22D3×#4111yescharacteristic
491C22#100911yescharacteristic
492C4—22no—
493C4—22no—
494C4—41no—
495C4—41no—
496C4—41no—
497C4—62no—
498C4—62no—
499C4—62no—
500C4—62no—
501C4—62no—
502C4—121no—
503C3#235811yescharacteristic, complemented, Sylow
504C2—24no—
505C2—42no—
506C2—64no—
507C2—122no—
508C2C2×#67⋊C411yescharacteristic
509C2C4×D3×D411yescharacteristic
510C2#554511yescharacteristic
511C2#559111yescharacteristic
512C2#560911yescharacteristic
513C2#561011yescharacteristic
514C2#565811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×#386C2
socle, cosocleC23×C3C24
prime radicalC2×#937C2
hypercenter#386D3
hypocenterC3#2358
LCSG ▷ C22×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×#67⋊C4C2semidirect
5. C2×D3×C22⋊C4C2semidirect
6. C3×#386C2semidirect
7. C4×#217C2semidirect
8. #4958C2semidirect
9. #4957C2semidirect
10. #4956C2semidirect
11. #4946C2semidirect
12. #4670C2semidirect
13. #4669C2semidirect
14. #4668C2semidirect
15. #4666C2semidirect
23. C23×Dic3C22semidirect
27. C2×C3×C22⋊C4C22semidirect
28. C2×C3×C22⋊C4C22semidirect
31. C2×#217C22semidirect
32. #937C4semidirect
43. C2×C4⋊Dic3C22semidirect
44. C2×Dic3⋊C4C22semidirect
45. C2×Dic3⋊C4C22semidirect
46. C2×C4×Dic3C22semidirect
47. C2×C4×Dic3C22semidirect
48. C2×C4×Dic3C22semidirect
51. C3×#95C22semidirect
52. C3×#95C22semidirect
53. C3⋊#95C22semidirect
54. C3⋊#95C22semidirect
55. C3⋊#95C22semidirect
56. C3⋊#95C22semidirect
67. #386D3semidirect
80. C23×D3C2×C4semidirect
85. C2×C3×D4C2×C4semidirect
98. C2×#67C2×C4semidirect
99. C2×#67C2×C4semidirect
122. #217C2×C4semidirect
123. #217D4semidirect
129. (C2×D3)⋊C4C2×C4semidirect
130. (C2×D3)⋊C4C2×C4semidirect
131. (C2×D3)⋊C4D4semidirect
167. C2×C22⋊C4C2×D3semidirect
168. C2×C22⋊C4C2×D3semidirect
176. #95C2×D3semidirect
177. #95C2×D3semidirect
274. C2×D4C4×D3semidirect
334. C22×C3C4×D4semidirect
356. C2×D3C4×D4semidirect
484. C22#67⋊C4semidirect
503. C3#2358semidirect

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×#67⋊C42
C2×D3×C22⋊C42
C3×#3862
C4×#2172
#49582
#49572
#49562
#49462
#46702
#46692
#46682
#46662
#23583