Finite Group Databasebeta

← #79440

Subgroups — #79440

Order 384.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5550C211yesmaximal, characteristic
2#5541C211yesmaximal, characteristic, complemented
3C3×C8×D4C211yesmaximal, characteristic, complemented
4#5116C211yesmaximal, characteristic, complemented
5#5114C211yesmaximal, characteristic, complemented
6#5113C211yesmaximal, characteristic, complemented
7C2×#821C211yesmaximal, characteristic, complemented
8#4847C211yesmaximal, characteristic, complemented
9#4845C211yesmaximal, characteristic, complemented
10#4737C211yesmaximal, characteristic, complemented
11#4733C211yesmaximal, characteristic, complemented
12#4731C211yesmaximal, characteristic, complemented
13#4721C211yesmaximal, characteristic, complemented
14#4697C211yesmaximal, characteristic, complemented
15C4×#204C211yesmaximal, characteristic, complemented
16#3296—31nomaximal, Sylow
17C2×#235C2211yescharacteristic
18C22×D12C2211yescharacteristic
19C22×C3×C8C2211yescharacteristic
20C22×C3×C8C2211yescharacteristic, complemented
21C3×C4×D4C2211yescharacteristic
22#937—21no—
23#935—21no—
24#930C2211yescharacteristic
25#926C2211yescharacteristic, complemented
26C2×C4⋊Dic3C2211yescharacteristic
27#924C2211yescharacteristic
28#924C2211yescharacteristic
29#924C2211yescharacteristic, complemented
30C2×Dic12C2211yescharacteristic, complemented
31C2×#204C2211yescharacteristic
32C2×#204C2211yescharacteristic
33#894—21no—
34#889—21no—
35#884—21no—
36D3×C22⋊C4—21no—
37#879—21no—
38#877—21no—
39#875C2211yescharacteristic
40C4×D12C2211yescharacteristic
41#870C2211yescharacteristic, complemented
42C4×Dic6C2211yescharacteristic, complemented
43C3×C4⋊C8C2211yescharacteristic, complemented
44C3×C22⋊C8C2211yescharacteristic
45C3×C22⋊C8C2211yescharacteristic, complemented
46C3×C4×C8C2211yescharacteristic, complemented
47#821C2211yescharacteristic
48#821C2211yescharacteristic
49#821C2211yescharacteristic
50#821C2211yescharacteristic
51#821C2211yescharacteristic
52#821C2211yescharacteristic
53#818C2211yescharacteristic, complemented
54#817C2211yescharacteristic, complemented
55#817C2211yescharacteristic, complemented
56#816C2211yescharacteristic, complemented
57#816C2211yescharacteristic, complemented
58#816C2211yescharacteristic, complemented
59#816C2211yescharacteristic, complemented
60#552—31no—
61#546—31no—
62#488—31no—
63#483—31no—
64#482—31no—
65#478—31no—
66#467—31no—
67#465—31no—
68#464—31no—
69#452—31no—
70#450—31no—
71C4×SD16—31no—
72C8×D4D311yescharacteristic, complemented
73#416—31no—
74C2×#102—31no—
75C23×D3—21no—
76C2×C3×D4D411yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C2×#67—21no—
80C2×#67—21no—
81C22×Dic3—21no—
82#235—22no—
83#235—41no—
84C2×D12—22no—
85C2×D12—21no—
86C2×D12—41no—
87C2×D12C2311yescharacteristic
88C2×D12C2311yescharacteristic
89C2×C4×D3—21no—
90C2×C4×D3—21no—
91C2×Dic6C2311yescharacteristic
92C2×Dic6C2311yescharacteristic
93C2×C3×C8—41no—
94C2×C3×C8—41no—
95C2×C3×C8C2311yescharacteristic
96C2×C3×C8C2311yescharacteristic
97C2×C3×C8C2311yescharacteristic
98C2×C3×C8C2311yescharacteristic
99C3×C4⋊C4D411yescharacteristic
100C3×C22⋊C4D411yescharacteristic
101C3×C22⋊C4D411yescharacteristic
102C3×C42C2311yescharacteristic
103#217—21no—
104#217—21no—
105#217—21no—
106#217—21no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110(C2×D3)⋊C4—21no—
111C4⋊Dic3—21no—
112C4⋊Dic3C2311yescharacteristic
113C4⋊Dic3C2311yescharacteristic
114C4⋊Dic3C2311yescharacteristic
115C4⋊Dic3C2311yescharacteristic
116Dic3⋊C4—21no—
117Dic3⋊C4—21no—
118Dic3⋊C4—21no—
119Dic3⋊C4—21no—
120Dic3⋊C4—21no—
121Dic3⋊C4—21no—
122C4×Dic3—21no—
123C4×Dic3—21no—
124Dic12—41no—
125#204—22no—
126#204—41no—
127C2×#41—31no—
128C22×D4—31no—
129C2×Q16—31no—
130C2×SD16—31no—
131C2×SD16—31no—
132C22×C8C2×D311yescharacteristic
133C22×C8C2×D311yescharacteristic, complemented
134#126—61no—
135#125—31no—
136#125—61no—
137#124—31no—
138#123—61no—
139#123—61no—
140C22⋊Q8—31no—
141C22⋊Q8—31no—
142C22⋊Q8—31no—
143#121—31no—
144#121—61no—
145#120—61no—
146C4×Q8—31no—
147C4×D4—31no—
148C4×D4C2×D311yescharacteristic
149#117—31no—
150#117—61no—
151C2×C4⋊C4—31no—
152C2×C22⋊C4—61no—
153#107—31no—
154#106—31no—
155#106—31no—
156C4⋊C8C2×D311yescharacteristic, complemented
157#103—31no—
158#103—31no—
159#103—31no—
160#103—31no—
161#102—31no—
162#102—31no—
163#102—31no—
164#102—31no—
165#102—31no—
166#102—31no—
167C22⋊C8C2×D311yescharacteristic
168C22⋊C8C2×D311yescharacteristic, complemented
169C4×C8C2×D311yescharacteristic, complemented
170C23×C3C2×D411yescharacteristic
171C23×C3C2×D411yescharacteristic
172C22×D3—21no—
173C22×D3—21no—
174C22×D3—42no—
175C22×D3—42no—
176C22×D3—81no—
177C3×D4—22no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4C2×D411yescharacteristic
183C2×C3×C4C2×D411yescharacteristic
184C2×C3×C4C2×D411yescharacteristic
185C2×C3×C4C2×D411yescharacteristic
186C2×C3×C4C2411yescharacteristic
187#67—42no—
188#67—81no—
189C2×Dic3—21no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195C2×Dic3—42no—
196D12—21no—
197D12—21no—
198D12—21no—
199D12—42no—
200D12#4112yes—
201C4×D3—42no—
202C4×D3—81no—
203Dic6—21no—
204Dic6—21no—
205Dic6—21no—
206Dic6—21no—
207C3×C8—21no—
208C3×C8—21no—
209C3×C8—21no—
210C3×C8—21no—
211C24—61no—
212#41—62no—
213#41—121no—
214C2×Q8—31no—
215C2×Q8—31no—
216C2×D4—31no—
217C2×D4—31no—
218C2×D4—62no—
219C2×D4—61no—
220C2×D4—61no—
221C2×D4—61no—
222C2×D4—121no—
223C2×D4D1211yescharacteristic
224C22×C4—61no—
225C22×C4—61no—
226C22×C4—61no—
227C22×C4C22×D311yescharacteristic
228C22×C4C22×D311yescharacteristic
229Q16—121no—
230SD16—62no—
231SD16—121no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8C22×D311yescharacteristic
235C2×C8C22×D311yescharacteristic
236C2×C8C22×D311yescharacteristic
237C2×C8C22×D311yescharacteristic
238C4⋊C4—31no—
239C4⋊C4—31no—
240C4⋊C4—31no—
241C4⋊C4—31no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4—61no—
248C4⋊C4—61no—
249C4⋊C4D1211yescharacteristic
250C22⋊C4—61no—
251C22⋊C4—61no—
252C22⋊C4—61no—
253C22⋊C4—61no—
254C22⋊C4—61no—
255C22⋊C4—61no—
256C22⋊C4—61no—
257C22⋊C4—61no—
258C22⋊C4D1211yescharacteristic
259C22⋊C4D1211yescharacteristic
260C42—61no—
261C42—61no—
262C42C22×D311yescharacteristic
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3#13512yes—
269C22×C3C22×D411yescharacteristic
270C2×D3—22no—
271C2×D3—41no—
272C2×D3—41no—
273C2×D3—41no—
274C2×D3—41no—
275C2×D3—41no—
276C2×D3—84no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4C2×#4111yescharacteristic
282C3×C4H(5,𝔽2)11yescharacteristic
283Dic3—41no—
284Dic3—41no—
285Dic3—41no—
286Dic3—41no—
287Dic3—41no—
288Dic3—41no—
289C23—61no—
290C23—61no—
291C23—122no—
292C23—122no—
293C23—241no—
294C23C2×D1211yescharacteristic
295C23C2×D1211yescharacteristic
296Q8—61no—
297Q8—61no—
298Q8—61no—
299Q8—61no—
300D4—22no—
301D4—32no—
302D4—61no—
303D4—61no—
304D4—61no—
305D4—122no—
306D4—122no—
307D4—241no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—122no—
319C2×C4—122no—
320C2×C4—241no—
321C2×C4C2×D1211yescharacteristic
322C2×C4C2×D1211yescharacteristic
323C2×C4C2×D1211yescharacteristic
324C2×C4C2×D1211yescharacteristic
325C2×C4C23×D311yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C2×C3—22no—
331C2×C3—41no—
332C2×C3#54611yescharacteristic
333C2×C3C2×#13511yescharacteristic
334C2×C3#57711yescharacteristic
335D3—42no—
336D3—81no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—62no—
343C22—121no—
344C22—121no—
345C22—121no—
346C22—121no—
347C22—121no—
348C22—244no—
349C22#90412yes—
350C22C22×D1211yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—121no—
356C4—121no—
357C4—121no—
358C4—121no—
359C4—121no—
360C4—121no—
361C4#100411yescharacteristic
362C4D3×#4111yescharacteristic
363C3#329611yescharacteristic, complemented, Sylow
364C2—22no—
365C2—41no—
366C2—122no—
367C2—241no—
368C2#555411yescharacteristic
369C2C2×#90411yescharacteristic
370C2#575111yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×C8×D4C2
socleC22×C3C22×D4
prime radical#5550C2
hypercenterC8×D4D3
hypocenterC3#3296
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #5541C2semidirect
3. C3×C8×D4C2semidirect
4. #5116C2semidirect
5. #5114C2semidirect
6. #5113C2semidirect
7. C2×#821C2semidirect
8. #4847C2semidirect
9. #4845C2semidirect
10. #4737C2semidirect
11. #4733C2semidirect
12. #4731C2semidirect
13. #4721C2semidirect
14. #4697C2semidirect
15. C4×#204C2semidirect
20. C22×C3×C8C22semidirect
25. #926C22semidirect
29. #924C22semidirect
30. C2×Dic12C22semidirect
41. #870C22semidirect
42. C4×Dic6C22semidirect
43. C3×C4⋊C8C22semidirect
45. C3×C22⋊C8C22semidirect
46. C3×C4×C8C22semidirect
53. #818C22semidirect
54. #817C22semidirect
55. #817C22semidirect
56. #816C22semidirect
57. #816C22semidirect
58. #816C22semidirect
59. #816C22semidirect
72. C8×D4D3semidirect
133. C22×C8C2×D3semidirect
156. C4⋊C8C2×D3semidirect
168. C22⋊C8C2×D3semidirect
169. C4×C8C2×D3semidirect
363. C3#3296semidirect

Maximal subgroups

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

subgroupindex
#55502
#55412
C3×C8×D42
#51162
#51142
#51132
C2×#8212
#48472
#48452
#47372
#47332
#47312
#47212
#46972
C4×#2042
#32963