Finite Group Databasebeta

← #79674

Subgroups — #79674

Order 384.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#916C211yesmaximal, characteristic, complemented
2C2×D3×SD16C211yesmaximal, characteristic, complemented
3#5576C211yesmaximal, characteristic, complemented
4#5554C211yesmaximal, characteristic, complemented
5C3×C4×SD16C211yesmaximal, characteristic, complemented
6#5028C211yesmaximal, characteristic, complemented
7#5016C211yesmaximal, characteristic, complemented
8#4864C211yesmaximal, characteristic, complemented
9#4864C211yesmaximal, characteristic, complemented
10#4810C211yesmaximal, characteristic, complemented
11#4809C211yesmaximal, characteristic, complemented
12#4783C211yesmaximal, characteristic, complemented
13#4773C211yesmaximal, characteristic, complemented
14#4696C211yesmaximal, characteristic, complemented
15C8×D12C211yesmaximal, characteristic, complemented
16#3282—31nomaximal, Sylow
17C2×#239C2211yescharacteristic, complemented
18C2×D3×Q8C2211yescharacteristic
19C2×#237C2211yescharacteristic
20C2×D3×D4C2211yescharacteristic
21C2×C3×SD16C2211yescharacteristic
22C3×C4×Q8C2211yescharacteristic, complemented
23C3×C4×D4C2211yescharacteristic
24C2×#216C2211yescharacteristic, complemented
25C2×#215C2211yescharacteristic
26C2×#214C2211yescharacteristic
27C2×#213C2211yescharacteristic
28#930—21no—
29C2×(C2×D3)⋊C4—21no—
30#916—24no—
31D3×SD16—24no—
32C2×Dic12C2211yescharacteristic, complemented
33C2×D24C2211yescharacteristic
34C2×#204C2211yescharacteristic
35C2×#204C2211yescharacteristic, complemented
36C2×D3×C8C2211yescharacteristic
37C2×D3×C8C2211yescharacteristic, complemented
38#897—21no—
39#897C2211yescharacteristic
40#897C2211yescharacteristic, complemented
41#895—21no—
42#895C2211yescharacteristic
43#895C2211yescharacteristic
44#886—21no—
45#882—21no—
46#875—21no—
47#875C2211yescharacteristic
48#875C2211yescharacteristic, complemented
49C4×D12—21no—
50C4×D12C2211yescharacteristic
51C3×#106C2211yescharacteristic, complemented
52C3×#103C2211yescharacteristic, complemented
53C3×#102C2211yescharacteristic
54C3×C4×C8C2211yescharacteristic, complemented
55(C2×D3)⋊C8C2211yescharacteristic
56(C2×D3)⋊C8C2211yescharacteristic, complemented
57#810C2211yescharacteristic, complemented
58#810C2211yescharacteristic, complemented
59#809C2211yescharacteristic
60#809C2211yescharacteristic, complemented
61C4⋊(C3⋊C8)C2211yescharacteristic, complemented
62C2×#135—31no—
63C22×SD16—31no—
64#548—31no—
65#546—31no—
66#495—31no—
67#465—31no—
68#465—31no—
69#464—31no—
70#463—31no—
71#452—31no—
72#451—31no—
73#449—31no—
74#447—31no—
75C4×SD16D311yescharacteristic, complemented
76C8×D4—31no—
77C23×D3—21no—
78C2×C3×Q8C2311yescharacteristic
79C2×C3×D4C2311yescharacteristic
80C22×C3×C4—21no—
81C2×#67—21no—
82C2×#67—21no—
83C22×Dic3—21no—
84#239—22no—
85#239—41no—
86D3×Q8—22no—
87D3×Q8—41no—
88#237—22no—
89#237—41no—
90D3×D4—22no—
91D3×D4—41no—
92C2×D12—21no—
93C2×D12—21no—
94C2×D12—21no—
95C2×D12D411yescharacteristic
96C2×D12C2311yescharacteristic
97C2×D12C2311yescharacteristic
98C2×C4×D3—21no—
99C2×C4×D3—21no—
100C2×C4×D3C2311yescharacteristic
101C2×C4×D3C2311yescharacteristic
102C2×Dic6—21no—
103C2×Dic6C2311yescharacteristic
104C2×Dic6C2311yescharacteristic
105C3×SD16D414yescomplemented
106C2×C3×C8C2311yescharacteristic
107C2×C3×C8C2311yescharacteristic
108C3×C4⋊C4—21no—
109C3×C4⋊C4C2311yescharacteristic
110C3×C4⋊C4C2311yescharacteristic
111C3×C22⋊C4—21no—
112C3×C42—21no—
113C3×C42C2311yescharacteristic
114#216—22no—
115#215—22no—
116#214—22no—
117#213—22no—
118(C2×D3)⋊C4—21no—
119(C2×D3)⋊C4—21no—
120(C2×D3)⋊C4—21no—
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)⋊C4D411yescharacteristic
127(C2×D3)⋊C4D411yescharacteristic
128C4⋊Dic3—21no—
129C4⋊Dic3—21no—
130C4⋊Dic3D411yescharacteristic
131C2×C3⋊C8C2311yescharacteristic
132C2×C3⋊C8C2311yescharacteristic
133Dic12—41no—
134D24—41no—
135#204—22no—
136#204—22no—
137D3×C8—22no—
138D3×C8—22no—
139C2×#41—31no—
140C2×#41—31no—
141C22×Q8—31no—
142C22×D4—31no—
143#135—64no—
144C2×Q16—31no—
145C2×Q16—31no—
146C2×SD16—31no—
147C2×SD16—31no—
148C2×SD16—31no—
149C2×SD16—31no—
150C2×SD16—64no—
151C2×SD16C2×D311yescharacteristic
152C2×D8—31no—
153C2×D8—31no—
154C22×C8—31no—
155C22×C8—31no—
156#124—31no—
157#124—31no—
158#124—61no—
159#123—61no—
160C22⋊Q8—31no—
161C22⋊Q8—31no—
162C22⋊Q8—61no—
163#121—31no—
164#121—31no—
165#121—61no—
166#121—61no—
167#120—61no—
168C4×Q8C2×D311yescharacteristic, complemented
169C4×D4—31no—
170C4×D4—61no—
171C4×D4C2×D311yescharacteristic
172C2×C22⋊C4—61no—
173#106C2×D311yescharacteristic, complemented
174C4⋊C8—31no—
175#103—31no—
176#103—31no—
177#103C2×D311yescharacteristic, complemented
178#102—31no—
179#102—31no—
180#102C2×D311yescharacteristic
181C22⋊C8—31no—
182C22⋊C8—31no—
183C4×C8C2×D311yescharacteristic, complemented
184C23×C3—21no—
185C22×D3—21no—
186C22×D3—21no—
187C22×D3—42no—
188C22×D3—42no—
189C22×D3—81no—
190C22×D3C2×D411yescharacteristic
191C22×D3C2×D411yescharacteristic
192C3×Q8—21no—
193C3×Q8C2×D412yes—
194C3×D4—21no—
195C3×D4C2×D412yes—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—81no—
200C2×C3×C4C2×D411yescharacteristic
201C2×C3×C4C2×D411yescharacteristic
202C2×C3×C4C2411yescharacteristic
203#67—42no—
204#67—42no—
205C2×Dic3—21no—
206C2×Dic3—21no—
207C2×Dic3—42no—
208C2×Dic3C2×D411yescharacteristic
209C2×Dic3C2×D411yescharacteristic
210D12—22no—
211D12—21no—
212D12—21no—
213D12—21no—
214D12—21no—
215D12—42no—
216D12—42no—
217D12—81no—
218C4×D3—21no—
219C4×D3—21no—
220C4×D3—21no—
221C4×D3—21no—
222C4×D3—42no—
223C4×D3—42no—
224Dic6—21no—
225Dic6—21no—
226Dic6—21no—
227Dic6—21no—
228Dic6—42no—
229C3×C8—21no—
230C3×C8C2×D412yes—
231C3⋊C8—21no—
232C3⋊C8—21no—
233C24—61no—
234#41—62no—
235#41—62no—
236#41—121no—
237#41—121no—
238C2×Q8—31no—
239C2×Q8—31no—
240C2×Q8—61no—
241C2×Q8—62no—
242C2×Q8—121no—
243C2×Q8C22×D311yescharacteristic
244C2×D4—31no—
245C2×D4—31no—
246C2×D4—31no—
247C2×D4—61no—
248C2×D4—61no—
249C2×D4—61no—
250C2×D4—61no—
251C2×D4—62no—
252C2×D4—61no—
253C2×D4—121no—
254C2×D4C22×D311yescharacteristic
255C22×C4—21no—
256C22×C4—31no—
257C22×C4—31no—
258C22×C4—61no—
259C22×C4—61no—
260C22×C4—61no—
261Q16—62no—
262Q16—121no—
263SD16—62no—
264SD16—62no—
265SD16—62no—
266SD16—62no—
267SD16D1214yescomplemented
268D8—62no—
269D8—121no—
270C2×C8—31no—
271C2×C8—31no—
272C2×C8—62no—
273C2×C8—62no—
274C2×C8C22×D311yescharacteristic
275C2×C8C22×D311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—31no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4C22×D311yescharacteristic
281C4⋊C4C22×D311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—31no—
284C22⋊C4—31no—
285C22⋊C4—61no—
286C22⋊C4—61no—
287C22⋊C4—61no—
288C22⋊C4—61no—
289C22⋊C4—61no—
290C22⋊C4—61no—
291C22⋊C4—61no—
292C22⋊C4—61no—
293C42—21no—
294C42C22×D311yescharacteristic
295C22×C3—22no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3C22×D411yescharacteristic
299C2×D3—21no—
300C2×D3—21no—
301C2×D3—21no—
302C2×D3—21no—
303C2×D3—21no—
304C2×D3—41no—
305C2×D3—41no—
306C2×D3—41no—
307C2×D3—41no—
308C2×D3—41no—
309C2×D3—41no—
310C2×D3—84no—
311C2×D3#13512yescomplemented
312C3×C4—22no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—41no—
316C3×C4—41no—
317C3×C4C22×D411yescharacteristic
318C3×C4H(5,𝔽2)11yescharacteristic
319Dic3—21no—
320Dic3—21no—
321Dic3—41no—
322Dic3—41no—
323C23—21no—
324C23—31no—
325C23—31no—
326C23—61no—
327C23—61no—
328C23—122no—
329C23—122no—
330C23—241no—
331Q8—21no—
332Q8—61no—
333Q8—61no—
334Q8—61no—
335Q8—61no—
336Q8—122no—
337Q8C2×D1212yes—
338D4—21no—
339D4—62no—
340D4—61no—
341D4—61no—
342D4—61no—
343D4—61no—
344D4—122no—
345D4—122no—
346D4—122no—
347D4—122no—
348D4—241no—
349D4C2×D1212yes—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—31no—
354C2×C4—31no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—61no—
361C2×C4—81no—
362C2×C4—122no—
363C2×C4—122no—
364C2×C4—122no—
365C2×C4D3×D411yescharacteristic
366C2×C4D3×D411yescharacteristic
367C2×C4C23×D311yescharacteristic
368C8—21no—
369C8—61no—
370C8—61no—
371C8C2×D1212yes—
372C2×C3—42no—
373C2×C3D4211yescharacteristic
374C2×C3C2×#13511yescharacteristic
375C2×C3#57711yescharacteristic
376D3—22no—
377D3—41no—
378D3—81no—
379D3—81no—
380C22—22no—
381C22—32no—
382C22—41no—
383C22—41no—
384C22—61no—
385C22—61no—
386C22—61no—
387C22—61no—
388C22—61no—
389C22—121no—
390C22—121no—
391C22—121no—
392C22—121no—
393C22—121no—
394C22—121no—
395C22—244no—
396C22C2×D3×D411yescharacteristic
397C4—21no—
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—61no—
403C4—61no—
404C4—121no—
405C4—121no—
406C4C22×D1211yescharacteristic
407C4#100911yescharacteristic
408C3#328211yescharacteristic, complemented, Sylow
409C2—42no—
410C2—62no—
411C2—121no—
412C2—241no—
413C2—241no—
414C2D4×D1211yescharacteristic
415C2#576211yescharacteristic
416C2D3×#13511yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×C4×SD16C2
socleC22×C3C22×D4
hypercenterC4×SD16D3
hypocenterC3#3282
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#916C2semidirect
2. C2×D3×SD16C2semidirect
3. #5576C2semidirect
4. #5554C2semidirect
5. C3×C4×SD16C2semidirect
6. #5028C2semidirect
7. #5016C2semidirect
8. #4864C2semidirect
9. #4864C2semidirect
10. #4810C2semidirect
11. #4809C2semidirect
12. #4783C2semidirect
13. #4773C2semidirect
14. #4696C2semidirect
15. C8×D12C2semidirect
17. C2×#239C22semidirect
22. C3×C4×Q8C22semidirect
24. C2×#216C22semidirect
32. C2×Dic12C22semidirect
35. C2×#204C22semidirect
37. C2×D3×C8C22semidirect
40. #897C22semidirect
48. #875C22semidirect
51. C3×#106C22semidirect
52. C3×#103C22semidirect
54. C3×C4×C8C22semidirect
56. (C2×D3)⋊C8C22semidirect
57. #810C22semidirect
58. #810C22semidirect
60. #809C22semidirect
61. C4⋊(C3⋊C8)C22semidirect
75. C4×SD16D3semidirect
105. C3×SD16D4semidirect
168. C4×Q8C2×D3semidirect
173. #106C2×D3semidirect
177. #103C2×D3semidirect
183. C4×C8C2×D3semidirect
267. SD16D12semidirect
311. C2×D3#135semidirect
408. C3#3282semidirect

Maximal subgroups

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

subgroupindex
C2×#9162
C2×D3×SD162
#55762
#55542
C3×C4×SD162
#50282
#50162
#48642
#48102
#48092
#47832
#47732
#46962
C8×D122
#32823