Finite Group Databasebeta

← #81407

Subgroups — #81407

Order 384.

408 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5599C211yesmaximal, characteristic, complemented
2#5532C211yesmaximal, characteristic, complemented
3C3×#482C211yesmaximal, characteristic, complemented
4#5038C211yesmaximal, characteristic, complemented
5#5002C211yesmaximal, characteristic, complemented
6#4883C211yesmaximal, characteristic, complemented
7#4875C211yesmaximal, characteristic, complemented
8#4866C211yesmaximal, characteristic, complemented
9#4852C211yesmaximal, characteristic, complemented
10#4786C211yesmaximal, characteristic, complemented
11#4781C211yesmaximal, characteristic, complemented
12#4772C211yesmaximal, characteristic, complemented
13#4760C211yesmaximal, characteristic, complemented
14#4734C211yesmaximal, characteristic, complemented
15#67⋊C8C211yesmaximal, characteristic, complemented
16#3305—31nomaximal, Sylow
17C2×#237C2211yescharacteristic
18C2×#235C2211yescharacteristic
19C3×#121C2211yescharacteristic
20C3×#117C2211yescharacteristic
21#940—21no—
22#940C2211yescharacteristic
23#939—21no—
24C2×#213C2211yescharacteristic
25#930C2211yescharacteristic
26C4×#67C2211yescharacteristic
27C22×C3⋊C8C2211yescharacteristic
28C2×D24C2211yescharacteristic
29C2×#204C2211yescharacteristic
30C2×D3×C8C2211yescharacteristic
31#895C2211yescharacteristic
32#895C2211yescharacteristic
33#893C2211yescharacteristic
34#892C2211yescharacteristic
35#888C2211yescharacteristic
36#887C2211yescharacteristic
37#885—21no—
38#884—21no—
39#884—21no—
40#67⋊C4—21no—
41#875—21no—
42#872—21no—
43C3×#107C2211yescharacteristic
44C3×#106C2211yescharacteristic
45C3×#102C2211yescharacteristic
46C3×#102C2211yescharacteristic
47C3×C22⋊C8C2211yescharacteristic
48#832C2211yescharacteristic
49#821C2211yescharacteristic
50(C2×D3)⋊C8C2211yescharacteristic
51#816C2211yescharacteristic
52Dic3⋊C8C2211yescharacteristic
53C8×Dic3C2211yescharacteristic
54#810C2211yescharacteristic
55#810C2211yescharacteristic
56#809C2211yescharacteristic
57#809C2211yescharacteristic
58#809C2211yescharacteristic
59#807C2211yescharacteristic
60#555—31no—
61#550—31no—
62#486—31no—
63#482—31no—
64#482D311yescharacteristic, complemented
65#477—31no—
66#466—31no—
67#466—31no—
68#459—31no—
69#449—31no—
70#449—31no—
71C4×SD16—31no—
72C8×D4—31no—
73#416—31no—
74#416—31no—
75C2×C3×D4—21no—
76C2×C3×D4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C2×#67—21no—
79C2×#67—21no—
80C2×#67—21no—
81C2×#67—21no—
82C2×#67—21no—
83C2×#67D411yescharacteristic
84C22×Dic3—21no—
85#237—22no—
86#237—41no—
87#235—22no—
88#235—41no—
89C2×D12—21no—
90C2×D12—21no—
91C2×D12C2311yescharacteristic
92C2×D12C2311yescharacteristic
93C2×C4×D3—21no—
94C2×C4×D3—21no—
95C2×C4×D3C2311yescharacteristic
96C2×Dic6—21no—
97C2×Dic6C2311yescharacteristic
98C2×C3×C8C2311yescharacteristic
99C2×C3×C8C2311yescharacteristic
100C3×C4⋊C4C2311yescharacteristic
101C3×C4⋊C4C2311yescharacteristic
102C3×C4⋊C4C2311yescharacteristic
103C3×C22⋊C4—21no—
104C3×C22⋊C4—21no—
105C3×C42—21no—
106#217D411yescharacteristic
107#213—41no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110(C2×D3)⋊C4—21no—
111(C2×D3)⋊C4—21no—
112(C2×D3)⋊C4—21no—
113(C2×D3)⋊C4D411yescharacteristic
114C4⋊Dic3C2311yescharacteristic
115Dic3⋊C4—21no—
116Dic3⋊C4—21no—
117Dic3⋊C4D411yescharacteristic
118C4×Dic3—21no—
119C4×Dic3—21no—
120C4×Dic3C2311yescharacteristic
121C2×C3⋊C8—41no—
122C2×C3⋊C8C2311yescharacteristic
123C2×C3⋊C8C2311yescharacteristic
124D24—41no—
125#204—22no—
126D3×C8—41no—
127C2×#41—31no—
128C2×#41—31no—
129C2×SD16—31no—
130C2×D8—31no—
131C2×D8—31no—
132C22×C8—31no—
133C22×C8—31no—
134C4⋊Q8—31no—
135#127—31no—
136#127—61no—
137#124—61no—
138#124—61no—
139#121—31no—
140#121—31no—
141#121—31no—
142#121—61no—
143#121—61no—
144#121—61no—
145#121C2×D311yescharacteristic
146C4×Q8—31no—
147C4×D4—31no—
148C4×D4—31no—
149C4×D4—61no—
150#117—31no—
151#117—61no—
152#117C2×D311yescharacteristic
153#107—31no—
154#107C2×D311yescharacteristic
155#106C2×D311yescharacteristic
156C4⋊C8—31no—
157#103—31no—
158#103—31no—
159#103—31no—
160#102—31no—
161#102—31no—
162#102—31no—
163#102—31no—
164#102—31no—
165#102C2×D311yescharacteristic
166#102C2×D311yescharacteristic
167C22⋊C8—31no—
168C22⋊C8C2×D311yescharacteristic
169C4×C8—31no—
170C23×C3—21no—
171C23×C3C2×D411yescharacteristic
172C22×D3—21no—
173C22×D3—21no—
174C22×D3C2×D411yescharacteristic
175C3×D4—21no—
176C3×D4—21no—
177C3×D4—81no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4C2×D411yescharacteristic
184C2×C3×C4C2411yescharacteristic
185#67—22no—
186#67—42no—
187#67—42no—
188#67—42no—
189#67—81no—
190#67—81no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—42no—
194C2×Dic3C2×D411yescharacteristic
195C2×Dic3C2×D411yescharacteristic
196C2×Dic3C2×D411yescharacteristic
197D12—21no—
198D12—21no—
199D12—21no—
200D12—21no—
201D12—81no—
202D12—81no—
203C4×D3—21no—
204C4×D3—21no—
205C4×D3—42no—
206C4×D3—42no—
207Dic6—21no—
208Dic6—81no—
209Dic6#4112yes—
210C3×C8—21no—
211C3×C8—21no—
212C3⋊C8—21no—
213C3⋊C8—21no—
214#41—62no—
215#41—62no—
216#41—121no—
217#41—121no—
218C2×Q8—31no—
219C2×Q8—61no—
220C2×D4—21no—
221C2×D4—31no—
222C2×D4—31no—
223C2×D4—31no—
224C2×D4—61no—
225C2×D4—61no—
226C2×D4—61no—
227C2×D4—61no—
228C2×D4—61no—
229C2×D4—61no—
230C2×D4—61no—
231C2×D4C22×D311yescharacteristic
232C22×C4—31no—
233C22×C4—61no—
234C22×C4—61no—
235C22×C4—61no—
236C22×C4C22×D311yescharacteristic
237SD16—62no—
238D8—121no—
239D8—121no—
240C2×C8—31no—
241C2×C8—31no—
242C2×C8—121no—
243C2×C8—121no—
244C2×C8C22×D311yescharacteristic
245C2×C8C22×D311yescharacteristic
246C4⋊C4—31no—
247C4⋊C4—31no—
248C4⋊C4—61no—
249C4⋊C4—61no—
250C4⋊C4C22×D311yescharacteristic
251C4⋊C4C22×D311yescharacteristic
252C4⋊C4C22×D311yescharacteristic
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—31no—
256C22⋊C4—31no—
257C22⋊C4—61no—
258C22⋊C4—61no—
259C22⋊C4—61no—
260C22⋊C4—61no—
261C22⋊C4—61no—
262C42—21no—
263C42—31no—
264C42—61no—
265C42—61no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3C22×D411yescharacteristic
273C2×D3—21no—
274C2×D3—21no—
275C2×D3—21no—
276C2×D3—41no—
277C2×D3—41no—
278C2×D3—41no—
279C2×D3—41no—
280C2×D3—41no—
281C2×D3—41no—
282C3×C4—21no—
283C3×C4—41no—
284C3×C4—41no—
285C3×C4—41no—
286C3×C4C2×#4111yescharacteristic
287C3×C4H(5,𝔽2)11yescharacteristic
288Dic3—22no—
289Dic3—21no—
290Dic3—21no—
291Dic3—41no—
292Dic3#13512yes—
293C23—21no—
294C23—31no—
295C23—61no—
296C23—61no—
297C23D3×D411yescharacteristic
298Q8—32no—
299Q8—61no—
300Q8—241no—
301D4—21no—
302D4—21no—
303D4—62no—
304D4—61no—
305D4—61no—
306D4—61no—
307D4—61no—
308D4—81no—
309D4—122no—
310D4—122no—
311D4—122no—
312D4—241no—
313D4—241no—
314D4—241no—
315D4—241no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—31no—
322C2×C4—31no—
323C2×C4—31no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—122no—
329C2×C4—122no—
330C2×C4—122no—
331C2×C4D3×D411yescharacteristic
332C2×C4C23×D311yescharacteristic
333C8—21no—
334C8—21no—
335C8—61no—
336C8—61no—
337C2×C3—41no—
338C2×C3—81no—
339C2×C3#54611yescharacteristic
340C2×C3C2×#13511yescharacteristic
341C2×C3#57611yescharacteristic
342D3—41no—
343D3—81no—
344D3—81no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—61no—
352C22—61no—
353C22—61no—
354C22—121no—
355C22—121no—
356C22—121no—
357C22—121no—
358C22—121no—
359C22—121no—
360C22C2×D3×D411yescharacteristic
361C4—21no—
362C4—32no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—61no—
367C4—62no—
368C4—61no—
369C4—121no—
370C4D3×#4111yescharacteristic
371C4#100911yescharacteristic
372C3#330511yescharacteristic, complemented, Sylow
373C2—41no—
374C2—81no—
375C2—121no—
376C2—241no—
377C2—241no—
378C2#565411yescharacteristic
379C2D3×#13511yescharacteristic
380C2#577411yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#482C2
socleC22×C3C22×D4
hypercenter#482D3
hypocenterC3#3305
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #5599C2semidirect
2. #5532C2semidirect
3. C3×#482C2semidirect
4. #5038C2semidirect
5. #5002C2semidirect
6. #4883C2semidirect
7. #4875C2semidirect
8. #4866C2semidirect
9. #4852C2semidirect
10. #4786C2semidirect
11. #4781C2semidirect
12. #4772C2semidirect
13. #4760C2semidirect
14. #4734C2semidirect
15. #67⋊C8C2semidirect
64. #482D3semidirect
372. C3#3305semidirect

Maximal subgroups

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

subgroupindex
#55992
#55322
C3×#4822
#50382
#50022
#48832
#48752
#48662
#48522
#47862
#47812
#47722
#47602
#47342
#67⋊C82
#33053