Finite Group Databasebeta

← #79383

Subgroups — #79383

Order 384.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5534C211yesmaximal, characteristic, complemented
2#5521C211yesmaximal, characteristic, complemented
3C3×#433C211yesmaximal, characteristic, complemented
4#4846C211yesmaximal, characteristic, complemented
5#4844C211yesmaximal, characteristic, complemented
6#4844C211yesmaximal, characteristic, complemented
7#4842C211yesmaximal, characteristic, complemented
8#4737C211yesmaximal, characteristic, complemented
9#4732C211yesmaximal, characteristic
10#4731C211yesmaximal, characteristic, complemented
11#4723C211yesmaximal, characteristic, complemented
12#4711C211yesmaximal, characteristic, complemented
13#4710C211yesmaximal, characteristic, complemented
14C4×D24C211yesmaximal, characteristic, complemented
15C4×#204C211yesmaximal, characteristic, complemented
16#3118—31nomaximal, Sylow
17C22×D12C2211yescharacteristic
18C3×#117C2211yescharacteristic
19#930C2211yescharacteristic
20#926C2211yescharacteristic
21#924C2211yescharacteristic
22C2×D24C2211yescharacteristic
23C2×D24C2211yescharacteristic
24C2×#204C2211yescharacteristic
25C2×#204C2211yescharacteristic
26#898—21no—
27#896—21no—
28#893—21no—
29#893—21no—
30#885—21no—
31#883—21no—
32D3×C22⋊C4—21no—
33D3×C22⋊C4—21no—
34#875C2211yescharacteristic, complemented
35C4×D12C2211yescharacteristic
36C4×D12C2211yescharacteristic
37C4×D12C2211yescharacteristic
38C4×D12C2211yescharacteristic
39C4×D12C2211yescharacteristic, complemented
40#869C2211yescharacteristic, complemented
41C4×Dic6C2211yescharacteristic, complemented
42C3×C4⋊C8C2211yescharacteristic, complemented
43C3×C4⋊C8C2211yescharacteristic, complemented
44C3×C22⋊C8C2211yescharacteristic
45C3×C22⋊C8C2211yescharacteristic
46C3×#97C2211yescharacteristic, complemented
47C3×C4×C8C2211yescharacteristic, complemented
48#821C2211yescharacteristic
49#821C2211yescharacteristic
50#821C2211yescharacteristic
51#821C2211yescharacteristic
52#821C2211yescharacteristic, complemented
53#821C2211yescharacteristic, complemented
54#818C2211yescharacteristic, complemented
55#818C2211yescharacteristic, complemented
56#817C2211yescharacteristic, complemented
57#817C2211yescharacteristic, complemented
58#816C2211yescharacteristic, complemented
59#816C2211yescharacteristic, complemented
60#542—31no—
61#518—31no—
62#485—31no—
63#482—31no—
64#476—31no—
65#474—31no—
66#463—31no—
67#463—31no—
68#450—31no—
69#447—31no—
70#442—31no—
71#440—31no—
72C4×SD16—31no—
73C4×D8—31no—
74#433D311yescharacteristic, complemented
75C23×D3—21no—
76C22×C3×C4C2311yescharacteristic
77C2×#67—21no—
78C2×D12—21no—
79C2×D12—22no—
80C2×D12—22no—
81C2×D12C2311yescharacteristic
82C2×D12C2311yescharacteristic
83C2×D12C2311yescharacteristic
84C2×C4×D3—21no—
85C2×C4×D3—21no—
86C2×C4×D3—21no—
87C2×C4×D3—21no—
88C2×C4×D3—21no—
89C2×Dic6—21no—
90C2×Dic6C2311yescharacteristic
91C2×C3×C8C2311yescharacteristic
92C2×C3×C8C2311yescharacteristic
93C2×C3×C8C2311yescharacteristic
94C2×C3×C8C2311yescharacteristic
95C3×C4⋊C4D411yescharacteristic
96C3×C4⋊C4D411yescharacteristic
97C3×C22⋊C4D411yescharacteristic
98C3×C22⋊C4D411yescharacteristic
99C3×C42C2311yescharacteristic
100C3×C42C2311yescharacteristic
101#217—21no—
102#217—21no—
103(C2×D3)⋊C4—21no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4—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—
118C4×Dic3—21no—
119C4×Dic3—21no—
120D24—22no—
121D24—22no—
122#204—22no—
123#204—22no—
124C22×D4—31no—
125C2×SD16—31no—
126C2×SD16—31no—
127C2×D8—31no—
128C2×D8—31no—
129C4⋊Q8—31no—
130#126—61no—
131#124—31no—
132#124—61no—
133#123—61no—
134C22⋊Q8—31no—
135C22⋊Q8—61no—
136#121—31no—
137C4×Q8—31no—
138C4×D4—31no—
139C4×D4—31no—
140C4×D4—31no—
141C4×D4—31no—
142C4×D4—31no—
143C4×D4—61no—
144C4×D4—61no—
145#117—31no—
146#117C2×D311yescharacteristic
147C2×C22⋊C4—61no—
148C2×C22⋊C4—61no—
149#107—31no—
150#107—31no—
151#106—31no—
152#106—31no—
153C4⋊C8C2×D311yescharacteristic, complemented
154C4⋊C8C2×D311yescharacteristic, complemented
155#103—31no—
156#103—31no—
157#102—31no—
158#102—31no—
159#102—31no—
160#102—31no—
161#102—31no—
162#102—31no—
163C22⋊C8C2×D311yescharacteristic
164C22⋊C8C2×D311yescharacteristic
165#97C2×D311yescharacteristic, complemented
166C4×C8C2×D311yescharacteristic, complemented
167C23×C3C2×D411yescharacteristic
168C22×D3—21no—
169C22×D3—21no—
170C22×D3—24no—
171C22×D3—21no—
172C22×D3—81no—
173C22×D3—81no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4C2×D411yescharacteristic
177C2×C3×C4C2×D411yescharacteristic
178C2×C3×C4C2×D411yescharacteristic
179C2×C3×C4C2×D411yescharacteristic
180C2×C3×C4C2×D411yescharacteristic
181C2×C3×C4C2411yescharacteristic
182#67—81no—
183C2×Dic3—21no—
184C2×Dic3—21no—
185C2×Dic3—21no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188D12—24no—
189D12—21no—
190D12—21no—
191D12—21no—
192D12—21no—
193D12#4112yes—
194D12#4112yes—
195C4×D3—81no—
196C4×D3—81no—
197C4×D3—81no—
198C4×D3—81no—
199C4×D3—81no—
200Dic6—21no—
201Dic6—21no—
202Dic6—81no—
203C3×C8—21no—
204C3×C8—21no—
205C3×C8—21no—
206C3×C8—21no—
207C24—61no—
208C2×Q8—31no—
209C2×Q8—61no—
210C2×D4—31no—
211C2×D4—31no—
212C2×D4—31no—
213C2×D4—62no—
214C2×D4—62no—
215C2×D4—61no—
216C2×D4—61no—
217C22×C4—61no—
218C22×C4—61no—
219C22×C4—61no—
220C22×C4—61no—
221C22×C4—61no—
222C22×C4C22×D311yescharacteristic
223SD16—62no—
224SD16—62no—
225D8—62no—
226D8—62no—
227C2×C8C22×D311yescharacteristic
228C2×C8C22×D311yescharacteristic
229C2×C8C22×D311yescharacteristic
230C2×C8C22×D311yescharacteristic
231C4⋊C4—31no—
232C4⋊C4—31no—
233C4⋊C4—31no—
234C4⋊C4—31no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4D1211yescharacteristic
239C4⋊C4D1211yescharacteristic
240C22⋊C4—61no—
241C22⋊C4—61no—
242C22⋊C4—61no—
243C22⋊C4—61no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4—61no—
247C22⋊C4—61no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C22⋊C4D1211yescharacteristic
251C22⋊C4D1211yescharacteristic
252C42—61no—
253C42—61no—
254C42C22×D311yescharacteristic
255C42C22×D311yescharacteristic
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3C22×D411yescharacteristic
260C2×D3—22no—
261C2×D3—22no—
262C2×D3—41no—
263C2×D3—41no—
264C2×D3—41no—
265C2×D3—41no—
266C2×D3—41no—
267C2×D3—41no—
268C2×D3—41no—
269C2×D3—84no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4C2×#4111yescharacteristic
276C3×C4C2×#4111yescharacteristic
277Dic3—41no—
278Dic3—41no—
279Dic3—41no—
280Dic3—41no—
281Dic3—41no—
282C23—64no—
283C23—61no—
284C23—61no—
285C23—61no—
286C23—241no—
287C23—241no—
288C23C2×D1211yescharacteristic
289Q8—61no—
290Q8—61no—
291Q8—241no—
292D4—32no—
293D4—32no—
294D4—64no—
295D4—61no—
296D4—61no—
297D4—61no—
298D4—61no—
299D4—241no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—61no—
303C2×C4—61no—
304C2×C4—61no—
305C2×C4—61no—
306C2×C4—61no—
307C2×C4—241no—
308C2×C4—241no—
309C2×C4—241no—
310C2×C4—241no—
311C2×C4—241no—
312C2×C4C2×D1211yescharacteristic
313C2×C4C2×D1211yescharacteristic
314C2×C4C2×D1211yescharacteristic
315C2×C4C2×D1211yescharacteristic
316C2×C4C2×D1211yescharacteristic
317C2×C4C23×D311yescharacteristic
318C8—21no—
319C8—21no—
320C8—21no—
321C8—21no—
322C2×C3—41no—
323C2×C3#52511yescharacteristic
324C2×C3#57611yescharacteristic
325C2×C3#57711yescharacteristic
326D3—42no—
327D3—42no—
328D3—81no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—62no—
333C22—62no—
334C22—121no—
335C22—121no—
336C22—121no—
337C22—121no—
338C22—121no—
339C22—121no—
340C22—121no—
341C22—244no—
342C22C22×D1211yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—121no—
349C4—121no—
350C4—121no—
351C4—121no—
352C4—121no—
353C4D3×#4111yescharacteristic
354C4D3×#4111yescharacteristic
355C3#311811yescharacteristic, complemented, Sylow
356C2—41no—
357C2—122no—
358C2—122no—
359C2—241no—
360C2#552411yescharacteristic
361C2#575111yescharacteristic
362C2#575211yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#433C2
socleC22×C3C22×D4
prime radical#4732C2
hypercenter#433D3
hypocenterC3#3118
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #5534C2semidirect
2. #5521C2semidirect
3. C3×#433C2semidirect
4. #4846C2semidirect
5. #4844C2semidirect
6. #4844C2semidirect
7. #4842C2semidirect
8. #4737C2semidirect
10. #4731C2semidirect
11. #4723C2semidirect
12. #4711C2semidirect
13. #4710C2semidirect
14. C4×D24C2semidirect
15. C4×#204C2semidirect
34. #875C22semidirect
39. C4×D12C22semidirect
40. #869C22semidirect
41. C4×Dic6C22semidirect
42. C3×C4⋊C8C22semidirect
43. C3×C4⋊C8C22semidirect
46. C3×#97C22semidirect
47. C3×C4×C8C22semidirect
52. #821C22semidirect
53. #821C22semidirect
54. #818C22semidirect
55. #818C22semidirect
56. #817C22semidirect
57. #817C22semidirect
58. #816C22semidirect
59. #816C22semidirect
74. #433D3semidirect
153. C4⋊C8C2×D3semidirect
154. C4⋊C8C2×D3semidirect
165. #97C2×D3semidirect
166. C4×C8C2×D3semidirect
355. C3#3118semidirect

Maximal subgroups

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

subgroupindex
#55342
#55212
C3×#4332
#48462
#48442
#48422
#47372
#47322
#47312
#47232
#47112
#47102
C4×D242
C4×#2042
#31183