Finite Group Databasebeta

← #80101

Subgroups — #80101

Order 384.

526 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5829C211yesmaximal, characteristic, complemented
2C2×#950C211yesmaximal, characteristic, complemented
3C2×D3×D8C211yesmaximal, characteristic, complemented
4#5612C211yesmaximal, characteristic, complemented
5C3×#449C211yesmaximal, characteristic, complemented
6#5169C211yesmaximal, characteristic, complemented
7#5168C211yesmaximal, characteristic, complemented
8#5153C211yesmaximal, characteristic, complemented
9#5038C211yesmaximal, characteristic, complemented
10#4819C211yesmaximal, characteristic, complemented
11#4813C211yesmaximal, characteristic, complemented
12#4776C211yesmaximal, characteristic, complemented
13#4756C211yesmaximal, characteristic, complemented
14#4734C211yesmaximal, characteristic, complemented
15#67⋊C8C211yesmaximal, characteristic, complemented
16#3280—31nomaximal, Sylow
17C2×C3×#41C2211yescharacteristic, complemented
18C2×D3×D4C2211yescharacteristic
19C2×D3×D4C2211yescharacteristic
20C2×#235C2211yescharacteristic, complemented
21C2×C3×SD16C2211yescharacteristic, complemented
22C2×C3×D8C2211yescharacteristic
23C3×#121C2211yescharacteristic, complemented
24#950—24no—
25#947C2211yescharacteristic, complemented
26#946C2211yescharacteristic
27C2×#216C2211yescharacteristic, complemented
28C2×#215C2211yescharacteristic, complemented
29#939—21no—
30#938—21no—
31#937—21no—
32#937—21no—
33#936C2211yescharacteristic, complemented
34D4×Dic3C2211yescharacteristic, complemented
35C2×#214C2211yescharacteristic, complemented
36C2×#213C2211yescharacteristic
37C2×#213C2211yescharacteristic
38#930C2211yescharacteristic, complemented
39#929—21no—
40C4×#67C2211yescharacteristic
41C2×(C2×D3)⋊C4—21no—
42C22×C3⋊C8C2211yescharacteristic, complemented
43D3×D8—24no—
44C2×D24C2211yescharacteristic
45C2×#204C2211yescharacteristic, complemented
46C2×D3×C8C2211yescharacteristic
47#897C2211yescharacteristic
48#893C2211yescharacteristic, complemented
49#883—21no—
50D3×C22⋊C4—21no—
51C3×#103C2211yescharacteristic, complemented
52C3×#102C2211yescharacteristic, complemented
53C3×C22⋊C8C2211yescharacteristic, complemented
54#832C2211yescharacteristic, complemented
55#821C2211yescharacteristic, complemented
56(C2×D3)⋊C8C2211yescharacteristic
57#816C2211yescharacteristic, complemented
58Dic3⋊C8C2211yescharacteristic, complemented
59C8×Dic3C2211yescharacteristic, complemented
60#809C2211yescharacteristic, complemented
61#807C2211yescharacteristic, complemented
62C2×#135—31no—
63C22×D8—31no—
64#546—31no—
65#546—31no—
66#495—31no—
67#467—31no—
68#466—31no—
69#463—31no—
70#463—31no—
71#450—31no—
72#450—31no—
73#449—31no—
74#449D311yescharacteristic, complemented
75C4×D8—31no—
76C8×D4—31no—
77C23×D3—21no—
78C23×D3—21no—
79C3×#41—22no—
80C3×#41—41no—
81C2×C3×Q8C2311yescharacteristic
82C2×C3×D4—21no—
83C2×C3×D4—21no—
84C2×C3×D4C2311yescharacteristic
85C2×C3×D4C2311yescharacteristic
86C22×C3×C4—21no—
87C22×C3×C4C2311yescharacteristic
88C2×#67—21no—
89C2×#67—21no—
90C2×#67—21no—
91C2×#67—21no—
92C2×#67D411yescharacteristic
93C22×Dic3—21no—
94D3×D4—22no—
95D3×D4—22no—
96D3×D4—41no—
97D3×D4—41no—
98#235—22no—
99#235—41no—
100C2×D12C2311yescharacteristic
101C2×D12C2311yescharacteristic
102C2×C4×D3—21no—
103C2×C4×D3—21no—
104C2×C4×D3C2311yescharacteristic
105C2×Dic6C2311yescharacteristic
106C3×SD16—41no—
107C3×D8—22no—
108C2×C3×C8C2311yescharacteristic
109C2×C3×C8C2311yescharacteristic
110C3×C4⋊C4C2311yescharacteristic
111C3×C22⋊C4—21no—
112#217—21no—
113#217—21no—
114#217—21no—
115#217D411yescharacteristic
116#216—22no—
117#215—22no—
118#214—22no—
119#213—22no—
120#213D414yescomplemented
121(C2×D3)⋊C4—21no—
122(C2×D3)⋊C4—21no—
123(C2×D3)⋊C4—21no—
124(C2×D3)⋊C4—21no—
125(C2×D3)⋊C4—21no—
126(C2×D3)⋊C4—21no—
127(C2×D3)⋊C4D411yescharacteristic
128C4⋊Dic3—21no—
129C4⋊Dic3C2311yescharacteristic
130Dic3⋊C4—21no—
131Dic3⋊C4D411yescharacteristic
132C4×Dic3C2311yescharacteristic
133C2×C3⋊C8—22no—
134C2×C3⋊C8C2311yescharacteristic
135C2×C3⋊C8C2311yescharacteristic
136D24—22no—
137#204—41no—
138D3×C8—22no—
139C2×#41—31no—
140C2×#41C2×D311yescharacteristic, complemented
141C22×D4—31no—
142C22×D4—31no—
143#135—64no—
144C2×Q16—31no—
145C2×SD16—31no—
146C2×SD16—31no—
147C2×SD16—31no—
148C2×SD16C2×D311yescharacteristic, complemented
149C2×D8—31no—
150C2×D8—31no—
151C2×D8—31no—
152C2×D8—64no—
153C2×D8C2×D311yescharacteristic
154C22×C8—31no—
155C22×C8—31no—
156#124—31no—
157#124—31no—
158#123—61no—
159#123—61no—
160C22⋊Q8—31no—
161C22⋊Q8—31no—
162#121—31no—
163#121—61no—
164#121—61no—
165#121C2×D311yescharacteristic, complemented
166#120—61no—
167#120—61no—
168C4×D4—31no—
169C4×D4—31no—
170C4×D4—31no—
171C2×C22⋊C4—61no—
172C2×C22⋊C4—61no—
173#107—31no—
174C4⋊C8—31no—
175#103—31no—
176#103C2×D311yescharacteristic, complemented
177#102—31no—
178#102—31no—
179#102—31no—
180#102C2×D311yescharacteristic, complemented
181C22⋊C8—31no—
182C22⋊C8C2×D311yescharacteristic, complemented
183C4×C8—31no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3C2×D411yescharacteristic
187C22×D3—21no—
188C22×D3—21no—
189C22×D3—42no—
190C22×D3—42no—
191C22×D3—42no—
192C22×D3—42no—
193C22×D3—81no—
194C22×D3—81no—
195C22×D3C2×D411yescharacteristic
196C3×Q8—21no—
197C3×Q8—21no—
198C3×D4—21no—
199C3×D4—21no—
200C3×D4—21no—
201C3×D4—42no—
202C3×D4—81no—
203C3×D4C2×D412yes—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—42no—
209C2×C3×C4C2×D411yescharacteristic
210C2×C3×C4C2411yescharacteristic
211#67—22no—
212#67—42no—
213#67—42no—
214#67—42no—
215#67—81no—
216C2×Dic3—21no—
217C2×Dic3—21no—
218C2×Dic3—81no—
219C2×Dic3C2×D411yescharacteristic
220C2×Dic3C2×D411yescharacteristic
221C2×Dic3C2×D411yescharacteristic
222D12—21no—
223D12—21no—
224D12—21no—
225D12C2×D412yes—
226C4×D3—21no—
227C4×D3—21no—
228C4×D3—42no—
229C4×D3—81no—
230Dic6—21no—
231Dic6—21no—
232C3×C8—21no—
233C3×C8—21no—
234C3⋊C8—21no—
235C3⋊C8C2×D412yes—
236C24—61no—
237C24—61no—
238#41—22no—
239#41—41no—
240#41—62no—
241#41—121no—
242C2×Q8—31no—
243C2×Q8C22×D311yescharacteristic
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—31no—
247C2×D4—31no—
248C2×D4—31no—
249C2×D4—61no—
250C2×D4—61no—
251C2×D4—62no—
252C2×D4—62no—
253C2×D4—61no—
254C2×D4—61no—
255C2×D4—121no—
256C2×D4—121no—
257C2×D4C22×D311yescharacteristic
258C2×D4C22×D311yescharacteristic
259C22×C4—21no—
260C22×C4—31no—
261C22×C4—61no—
262C22×C4—61no—
263C22×C4—61no—
264C22×C4C22×D311yescharacteristic
265Q16—62no—
266SD16—41no—
267SD16—62no—
268SD16—62no—
269SD16—121no—
270D8—22no—
271D8—34no—
272D8—62no—
273D8—62no—
274C2×C8—31no—
275C2×C8—31no—
276C2×C8—62no—
277C2×C8—62no—
278C2×C8C22×D311yescharacteristic
279C2×C8C22×D311yescharacteristic
280C4⋊C4—31no—
281C4⋊C4—31no—
282C4⋊C4—61no—
283C4⋊C4—61no—
284C4⋊C4C22×D311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—31no—
287C22⋊C4—31no—
288C22⋊C4—61no—
289C22⋊C4—61no—
290C22⋊C4—61no—
291C22⋊C4—61no—
292C22⋊C4—61no—
293C22⋊C4—61no—
294C22⋊C4—61no—
295C22⋊C4—61no—
296C22⋊C4—61no—
297C42—31no—
298C22×C3—21no—
299C22×C3—22no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3C22×D411yescharacteristic
308C2×D3—21no—
309C2×D3—21no—
310C2×D3—22no—
311C2×D3—41no—
312C2×D3—41no—
313C2×D3—41no—
314C2×D3—41no—
315C2×D3—41no—
316C2×D3—84no—
317C2×D3—84no—
318C2×D3#13512yescomplemented
319C3×C4—21no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4C22×D411yescharacteristic
323C3×C4H(5,𝔽2)11yescharacteristic
324Dic3—21no—
325Dic3—21no—
326Dic3—21no—
327Dic3—41no—
328Dic3—41no—
329C23—21no—
330C23—21no—
331C23—31no—
332C23—61no—
333C23—61no—
334C23—122no—
335C23—122no—
336C23—122no—
337C23—122no—
338C23—241no—
339C23—241no—
340C23D3×D411yescharacteristic
341Q8—21no—
342Q8—21no—
343Q8—61no—
344Q8—61no—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—32no—
349D4—42no—
350D4—62no—
351D4—61no—
352D4—61no—
353D4—61no—
354D4—81no—
355D4—122no—
356D4—122no—
357D4—122no—
358D4—241no—
359D4D3×D412yes—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—31no—
367C2×C4—42no—
368C2×C4—61no—
369C2×C4—61no—
370C2×C4—61no—
371C2×C4—61no—
372C2×C4—122no—
373C2×C4—241no—
374C2×C4—241no—
375C2×C4D3×D411yescharacteristic
376C2×C4C23×D311yescharacteristic
377C8—21no—
378C8—21no—
379C8—32no—
380C8—61no—
381C2×C3—42no—
382C2×C3—41no—
383C2×C3—81no—
384C2×C3D4211yescharacteristic
385C2×C3C2×#13511yescharacteristic
386C2×C3#57611yescharacteristic
387D3—22no—
388D3—42no—
389D3—81no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—32no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—61no—
401C22—61no—
402C22—62no—
403C22—121no—
404C22—121no—
405C22—121no—
406C22—121no—
407C22—121no—
408C22—244no—
409C22—244no—
410C22C2×D3×D411yescharacteristic
411C4—21no—
412C4—41no—
413C4—41no—
414C4—61no—
415C4—61no—
416C4—61no—
417C4—121no—
418C4—121no—
419C4C2×D3×D411yescharacteristic
420C4#100411yescharacteristic
421C3#328011yescharacteristic, complemented, Sylow
422C2—41no—
423C2—42no—
424C2—62no—
425C2—81no—
426C2—122no—
427C2—241no—
428C2#559011yescharacteristic
429C2D3×#13511yescharacteristic
430C2#577411yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#449C2
socleC22×C3C22×D4
hypercenter#449D3
hypocenterC3#3280
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #5829C2semidirect
2. C2×#950C2semidirect
3. C2×D3×D8C2semidirect
4. #5612C2semidirect
5. C3×#449C2semidirect
6. #5169C2semidirect
7. #5168C2semidirect
8. #5153C2semidirect
9. #5038C2semidirect
10. #4819C2semidirect
11. #4813C2semidirect
12. #4776C2semidirect
13. #4756C2semidirect
14. #4734C2semidirect
15. #67⋊C8C2semidirect
17. C2×C3×#41C22semidirect
20. C2×#235C22semidirect
21. C2×C3×SD16C22semidirect
23. C3×#121C22semidirect
25. #947C22semidirect
27. C2×#216C22semidirect
28. C2×#215C22semidirect
33. #936C22semidirect
34. D4×Dic3C22semidirect
35. C2×#214C22semidirect
38. #930C22semidirect
42. C22×C3⋊C8C22semidirect
45. C2×#204C22semidirect
48. #893C22semidirect
51. C3×#103C22semidirect
52. C3×#102C22semidirect
53. C3×C22⋊C8C22semidirect
54. #832C22semidirect
55. #821C22semidirect
57. #816C22semidirect
58. Dic3⋊C8C22semidirect
59. C8×Dic3C22semidirect
60. #809C22semidirect
61. #807C22semidirect
74. #449D3semidirect
120. #213D4semidirect
140. C2×#41C2×D3semidirect
148. C2×SD16C2×D3semidirect
165. #121C2×D3semidirect
176. #103C2×D3semidirect
180. #102C2×D3semidirect
182. C22⋊C8C2×D3semidirect
318. C2×D3#135semidirect
421. C3#3280semidirect

Maximal subgroups

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

subgroupindex
#58292
C2×#9502
C2×D3×D82
#56122
C3×#4492
#51692
#51682
#51532
#50382
#48192
#48132
#47762
#47562
#47342
#67⋊C82
#32803