Finite Group Databasebeta

← #80069

Subgroups — #80069

Order 384.

434 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#41C211yesmaximal, characteristic, complemented
2#5596C211yesmaximal, characteristic, complemented
3C3×#449C211yesmaximal, characteristic, complemented
4#5238C211yesmaximal, characteristic, complemented
5#5163C211yesmaximal, characteristic, complemented
6Dic3×SD16C211yesmaximal, characteristic, complemented
7#5150C211yesmaximal, characteristic, complemented
8Dic3×D8C211yesmaximal, characteristic, complemented
9#5035C211yesmaximal, characteristic, complemented
10#4793C211yesmaximal, characteristic, complemented
11#4788C211yesmaximal, characteristic, complemented
12#4761C211yesmaximal, characteristic, complemented
13#4756C211yesmaximal, characteristic, complemented
14#4737C211yesmaximal, characteristic, complemented
15#4718C211yesmaximal, characteristic, complemented
16#3106—31nomaximal, Sylow
17C2×C3×#41C2211yescharacteristic
18C2×#237—21no—
19C2×C3×SD16C2211yescharacteristic
20C2×C3×D8C2211yescharacteristic
21C3×#121C2211yescharacteristic
22Q8×Dic3C2211yescharacteristic
23Q8×Dic3C2211yescharacteristic
24C2×#215C2211yescharacteristic
25#940C2211yescharacteristic
26#939—21no—
27D4×Dic3—21no—
28D4×Dic3—21no—
29D4×Dic3C2211yescharacteristic
30D4×Dic3C2211yescharacteristic
31D4×Dic3C2211yescharacteristic
32C2×#213C2211yescharacteristic
33#930C2211yescharacteristic
34#926—21no—
35#926C2211yescharacteristic
36C2×C4×Dic3—21no—
37C2×C4×Dic3C2211yescharacteristic
38#893C2211yescharacteristic
39#888C2211yescharacteristic
40#885—21no—
41#67⋊C4—21no—
42C3×#103C2211yescharacteristic
43C3×#102C2211yescharacteristic
44C3×C22⋊C8C2211yescharacteristic
45#835C2211yescharacteristic
46#832C2211yescharacteristic
47#832C2211yescharacteristic
48#832C2211yescharacteristic
49#830C2211yescharacteristic
50#821C2211yescharacteristic
51#821C2211yescharacteristic
52#818C2211yescharacteristic
53#817C2211yescharacteristic
54Dic3⋊C8C2211yescharacteristic
55Dic3⋊C8C2211yescharacteristic
56C8×Dic3C2211yescharacteristic
57C8×Dic3C2211yescharacteristic
58#808C2211yescharacteristic
59#807C2211yescharacteristic
60#532—31no—
61C4×#41—31no—
62#482—31no—
63#482—31no—
64#477—31no—
65#476—31no—
66#460—31no—
67#459—31no—
68#449—31no—
69#449D311yescharacteristic, complemented
70C4×SD16—31no—
71C4×SD16—31no—
72C4×D8—31no—
73C4×D8—31no—
74#431—31no—
75C3×#41—22no—
76C3×#41—22no—
77C2×C3×Q8C2311yescharacteristic
78C2×C3×D4—21no—
79C2×C3×D4—21no—
80C2×C3×D4C2311yescharacteristic
81C2×C3×D4C2311yescharacteristic
82C22×C3×C4—21no—
83C22×C3×C4C2311yescharacteristic
84C2×#67—21no—
85C2×#67—21no—
86C2×#67—21no—
87C22×Dic3—21no—
88C22×Dic3—21no—
89C22×Dic3—21no—
90C22×Dic3D411yescharacteristic
91C22×Dic3D411yescharacteristic
92#237—44no—
93C2×D12C2311yescharacteristic
94C2×C4×D3—21no—
95C2×Dic6—21no—
96C3×SD16—22no—
97C3×D8—22no—
98C2×C3×C8C2311yescharacteristic
99C2×C3×C8C2311yescharacteristic
100C3×C4⋊C4C2311yescharacteristic
101C3×C22⋊C4—21no—
102#217—21no—
103#217—21no—
104#217—21no—
105#217—21no—
106#215—22no—
107#213—22no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110C4⋊Dic3—21no—
111C4⋊Dic3—21no—
112C4⋊Dic3C2311yescharacteristic
113C4⋊Dic3C2311yescharacteristic
114C4⋊Dic3C2311yescharacteristic
115Dic3⋊C4—21no—
116C4×Dic3—21no—
117C4×Dic3—21no—
118C4×Dic3—21no—
119C4×Dic3D411yescharacteristic
120C4×Dic3D411yescharacteristic
121C4×Dic3C2311yescharacteristic
122C4×Dic3C2311yescharacteristic
123C2×C3⋊C8C2311yescharacteristic
124C2×C3⋊C8C2311yescharacteristic
125C2×#41—61no—
126C2×#41C2×D311yescharacteristic
127C2×SD16—31no—
128C2×SD16C2×D311yescharacteristic
129C2×D8—31no—
130C2×D8C2×D311yescharacteristic
131C4⋊Q8—31no—
132#127—31no—
133#124—61no—
134#121—31no—
135#121—61no—
136#121C2×D311yescharacteristic
137C4×Q8—31no—
138C4×Q8—31no—
139C4×D4—31no—
140C4×D4—31no—
141C4×D4—31no—
142C4×D4—31no—
143C4×D4—61no—
144C4×D4—61no—
145C4×D4—61no—
146#117—31no—
147#117—61no—
148C2×C42—31no—
149C2×C42—61no—
150#107—31no—
151#107—31no—
152#106—31no—
153#106—31no—
154C4⋊C8—31no—
155C4⋊C8—31no—
156#103—31no—
157#103C2×D311yescharacteristic
158#102—31no—
159#102—31no—
160#102—31no—
161#102—31no—
162#102—31no—
163#102C2×D311yescharacteristic
164C22⋊C8—31no—
165C22⋊C8C2×D311yescharacteristic
166C4×C8—31no—
167C4×C8—31no—
168C23×C3—21no—
169C23×C3—21no—
170C23×C3C2×D411yescharacteristic
171C22×D3—21no—
172C3×Q8—21no—
173C3×Q8#4112yescomplemented
174C3×D4—24no—
175C3×D4—21no—
176C3×D4—21no—
177C3×D4—21no—
178C3×D4—42no—
179C3×D4#4112yescomplemented
180C2×C3×C4—24no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4C2×D411yescharacteristic
186C2×C3×C4C2411yescharacteristic
187#67—42no—
188#67—42no—
189#67—42no—
190C2×Dic3—22no—
191C2×Dic3—22no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195C2×Dic3—42no—
196C2×Dic3—42no—
197C2×Dic3—42no—
198C2×Dic3C2×D411yescharacteristic
199C2×Dic3C2×D411yescharacteristic
200C2×Dic3C2×D411yescharacteristic
201C2×Dic3C2×D411yescharacteristic
202D12—21no—
203D12—21no—
204C4×D3—42no—
205Dic6—42no—
206C3×C8—21no—
207C3×C8—21no—
208C3⋊C8—21no—
209C3⋊C8—21no—
210#41—22no—
211#41—22no—
212#41—124no—
213C2×Q8—61no—
214C2×Q8C22×D311yescharacteristic
215C2×D4—21no—
216C2×D4—21no—
217C2×D4—31no—
218C2×D4—61no—
219C2×D4—61no—
220C2×D4—61no—
221C2×D4C22×D311yescharacteristic
222C2×D4C22×D311yescharacteristic
223C22×C4—21no—
224C22×C4—31no—
225C22×C4—31no—
226C22×C4—61no—
227C22×C4—61no—
228C22×C4—61no—
229C22×C4—61no—
230C22×C4C22×D311yescharacteristic
231SD16—22no—
232SD16—62no—
233D8—22no—
234D8—62no—
235C2×C8—31no—
236C2×C8—31no—
237C2×C8C22×D311yescharacteristic
238C2×C8C22×D311yescharacteristic
239C4⋊C4—31no—
240C4⋊C4—31no—
241C4⋊C4—31no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4C22×D311yescharacteristic
246C22⋊C4—21no—
247C22⋊C4—61no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C22⋊C4—61no—
251C22⋊C4—61no—
252C22⋊C4—61no—
253C42—31no—
254C42—31no—
255C42—31no—
256C42—31no—
257C42—61no—
258C42—61no—
259C42—61no—
260C22×C3—21no—
261C22×C3—22no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3C22×D411yescharacteristic
270C2×D3—41no—
271C2×D3—41no—
272C2×D3—41no—
273C3×C4—21no—
274C3×C4—22no—
275C3×C4—41no—
276C3×C4C2×#4111yescharacteristic
277C3×C4C2×#4111yescharacteristic
278Dic3—21no—
279Dic3—21no—
280Dic3—41no—
281Dic3—41no—
282Dic3—41no—
283Dic3#13512yes—
284Dic3AGL(1,ℤ/8)12yes—
285C23—21no—
286C23—21no—
287C23—61no—
288C23D3×D411yescharacteristic
289Q8—21no—
290Q8—122no—
291Q8#23712yescomplemented
292D4—24no—
293D4—21no—
294D4—21no—
295D4—21no—
296D4—42no—
297D4—61no—
298D4—61no—
299D4—122no—
300D4—122no—
301D4—122no—
302D4#23712yescomplemented
303C2×C4—24no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—31no—
309C2×C4—31no—
310C2×C4—31no—
311C2×C4—31no—
312C2×C4—62no—
313C2×C4—62no—
314C2×C4—61no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—122no—
318C2×C4—122no—
319C2×C4—122no—
320C2×C4—122no—
321C2×C4D3×D411yescharacteristic
322C2×C4C23×D311yescharacteristic
323C8—21no—
324C8—21no—
325C8—61no—
326C8—61no—
327C2×C3—41no—
328C2×C3—42no—
329C2×C3—81no—
330C2×C3#52511yescharacteristic
331C2×C3C2×#13511yescharacteristic
332C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
333D3—81no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—121no—
344C22—121no—
345C22—121no—
346C22C2×D3×D411yescharacteristic
347C4—21no—
348C4—22no—
349C4—32no—
350C4—32no—
351C4—41no—
352C4—61no—
353C4—61no—
354C4—121no—
355C4—121no—
356C4—121no—
357C4C2×#23711yescharacteristic
358C4C2×#23711yescharacteristic
359C3#310611yescharacteristic, complemented, Sylow
360C2—41no—
361C2—42no—
362C2—81no—
363C2—241no—
364C2#558611yescharacteristic
365C2D3×#13511yescharacteristic
366C2D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#449C2
socleC22×C3C22×D4
hypercenter#449D3
hypocenterC3#3106
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. Dic3×#41C2semidirect
2. #5596C2semidirect
3. C3×#449C2semidirect
4. #5238C2semidirect
5. #5163C2semidirect
6. Dic3×SD16C2semidirect
7. #5150C2semidirect
8. Dic3×D8C2semidirect
9. #5035C2semidirect
10. #4793C2semidirect
11. #4788C2semidirect
12. #4761C2semidirect
13. #4756C2semidirect
14. #4737C2semidirect
15. #4718C2semidirect
69. #449D3semidirect
173. C3×Q8#41semidirect
179. C3×D4#41semidirect
291. Q8#237semidirect
302. D4#237semidirect
359. C3#3106semidirect

Maximal subgroups

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

subgroupindex
Dic3×#412
#55962
C3×#4492
#52382
#51632
Dic3×SD162
#51502
Dic3×D82
#50352
#47932
#47882
#47612
#47562
#47372
#47182
#31063