Finite Group Databasebeta

← #80875

Subgroups — #80875

Order 384.

404 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#5618C211yesmaximal, characteristic, complemented
2#5599C211yesmaximal, characteristic, complemented
3C3×#469C211yesmaximal, characteristic, complemented
4#5158C211yesmaximal, characteristic, complemented
5#5150C211yesmaximal, characteristic, complemented
6#5133C211yesmaximal, characteristic, complemented
7#5127C211yesmaximal, characteristic, complemented
8#5037C211yesmaximal, characteristic, complemented
9#5033C211yesmaximal, characteristic, complemented
10#4866C211yesmaximal, characteristic, complemented
11#4857C211yesmaximal, characteristic, complemented
12#4775C211yesmaximal, characteristic, complemented
13#4772C211yesmaximal, characteristic, complemented
14#4764C211yesmaximal, characteristic, complemented
15#4757C211yesmaximal, characteristic, complemented
16#3309—31nomaximal, Sylow
17C2×#237C2211yescharacteristic
18C2×#235C2211yescharacteristic
19C2×C3×D8C2211yescharacteristic
20C2×C3×M16C2211yescharacteristic
21C3×#121C2211yescharacteristic
22C3×#121C2211yescharacteristic
23#940—21no—
24#940C2211yescharacteristic
25#939—21no—
26#939—21no—
27#938C2211yescharacteristic
28D4×Dic3—21no—
29D4×Dic3C2211yescharacteristic
30C2×#214C2211yescharacteristic
31C2×#213C2211yescharacteristic
32C4×#67C2211yescharacteristic
33C2×C4⋊Dic3C2211yescharacteristic
34C2×D3×C8C2211yescharacteristic
35#895C2211yescharacteristic
36#892C2211yescharacteristic
37#890C2211yescharacteristic
38#887C2211yescharacteristic
39#886—21no—
40#884—21no—
41#67⋊C4—21no—
42#879—21no—
43C3×#106C2211yescharacteristic
44C3×#102C2211yescharacteristic
45C3×#102C2211yescharacteristic
46#832C2211yescharacteristic
47#832C2211yescharacteristic
48#830C2211yescharacteristic
49#821C2211yescharacteristic
50#821C2211yescharacteristic
51(C2×D3)⋊C8C2211yescharacteristic
52#816C2211yescharacteristic
53#816C2211yescharacteristic
54#815C2211yescharacteristic
55Dic3⋊C8C2211yescharacteristic
56#810C2211yescharacteristic
57#809C2211yescharacteristic
58#807C2211yescharacteristic
59#807C2211yescharacteristic
60#553—31no—
61#550—31no—
62#490—31no—
63#482—31no—
64#480—31no—
65#479—31no—
66#469D311yescharacteristic, complemented
67#466—31no—
68#459—31no—
69#449—31no—
70#449—31no—
71#440—31no—
72#435—31no—
73#417—31no—
74#416—31no—
75C2×C3×D4—21no—
76C2×C3×D4—21no—
77C2×C3×D4C2311yescharacteristic
78C2×C3×D4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C2×#67—21no—
81C2×#67—21no—
82C2×#67—21no—
83C2×#67—21no—
84C2×#67—21no—
85C2×#67D411yescharacteristic
86C22×Dic3—21no—
87C22×Dic3—21no—
88C22×Dic3—21no—
89#237—22no—
90#237—41no—
91#235—22no—
92#235—41no—
93C2×D12—21no—
94C2×D12C2311yescharacteristic
95C2×C4×D3—21no—
96C2×C4×D3C2311yescharacteristic
97C2×Dic6C2311yescharacteristic
98C3×D8—41no—
99C3×M16—41no—
100C2×C3×C8C2311yescharacteristic
101C2×C3×C8C2311yescharacteristic
102C3×C4⋊C4C2311yescharacteristic
103C3×C4⋊C4C2311yescharacteristic
104C3×C22⋊C4—21no—
105C3×C22⋊C4—21no—
106#217—21no—
107#217—21no—
108#217D411yescharacteristic
109#214—22no—
110#213—41no—
111(C2×D3)⋊C4—21no—
112(C2×D3)⋊C4—21no—
113(C2×D3)⋊C4D411yescharacteristic
114C4⋊Dic3—21no—
115C4⋊Dic3—21no—
116C4⋊Dic3C2311yescharacteristic
117C4⋊Dic3C2311yescharacteristic
118Dic3⋊C4—21no—
119Dic3⋊C4—21no—
120Dic3⋊C4D411yescharacteristic
121C4×Dic3—21no—
122C4×Dic3—21no—
123C4×Dic3C2311yescharacteristic
124C2×C3⋊C8C2311yescharacteristic
125C2×C3⋊C8C2311yescharacteristic
126D3×C8—41no—
127C2×#41—31no—
128C2×#41—31no—
129C2×SD16—31no—
130C2×D8—31no—
131C2×D8C2×D311yescharacteristic
132C2×M16C2×D311yescharacteristic
133C22×C8—31no—
134#127—31no—
135#127—61no—
136#126—61no—
137#125—31no—
138#123—61no—
139#121—31no—
140#121—31no—
141#121—61no—
142#121—61no—
143#121—61no—
144#121C2×D311yescharacteristic
145#121C2×D311yescharacteristic
146C4×Q8—31no—
147C4×D4—31no—
148C4×D4—31no—
149C4×D4—61no—
150C4×D4—61no—
151#117—31no—
152C2×C4⋊C4—31no—
153#107—31no—
154#107—31no—
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⋊C8—31no—
169#97—31no—
170C23×C3—21no—
171C23×C3—21no—
172C23×C3C2×D411yescharacteristic
173C22×D3—21no—
174C22×D3C2×D411yescharacteristic
175C3×D4—21no—
176C3×D4—21no—
177C3×D4—21no—
178C3×D4—21no—
179C3×D4—42no—
180C3×D4—81no—
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—41no—
188#67—42no—
189#67—42no—
190#67—42no—
191#67—81no—
192#67—81no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3—42no—
197C2×Dic3—81no—
198C2×Dic3—81no—
199C2×Dic3C2×D411yescharacteristic
200C2×Dic3C2×D411yescharacteristic
201C2×Dic3C2×D411yescharacteristic
202D12—21no—
203D12—21no—
204D12—81no—
205C4×D3—21no—
206C4×D3—21no—
207C4×D3—42no—
208Dic6—21no—
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×D4—21no—
220C2×D4—21no—
221C2×D4—31no—
222C2×D4—31no—
223C2×D4—61no—
224C2×D4—61no—
225C2×D4—61no—
226C2×D4—61no—
227C2×D4—61no—
228C2×D4—61no—
229C2×D4C22×D311yescharacteristic
230C2×D4C22×D311yescharacteristic
231C22×C4—31no—
232C22×C4—61no—
233C22×C4—61no—
234C22×C4—61no—
235C22×C4—61no—
236C22×C4C22×D311yescharacteristic
237SD16—62no—
238D8—41no—
239D8—121no—
240M16—41no—
241C2×C8—31no—
242C2×C8—31no—
243C2×C8—121no—
244C2×C8C22×D311yescharacteristic
245C2×C8C22×D311yescharacteristic
246C4⋊C4—31no—
247C4⋊C4—31no—
248C4⋊C4—31no—
249C4⋊C4—61no—
250C4⋊C4—61no—
251C4⋊C4—61no—
252C4⋊C4—61no—
253C4⋊C4C22×D311yescharacteristic
254C4⋊C4C22×D311yescharacteristic
255C22⋊C4—21no—
256C22⋊C4—21no—
257C22⋊C4—31no—
258C22⋊C4—31no—
259C22⋊C4—61no—
260C22⋊C4—61no—
261C22⋊C4—61no—
262C22⋊C4—61no—
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×C3—41no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3C22×D411yescharacteristic
276C2×D3—21no—
277C2×D3—21no—
278C2×D3—21no—
279C2×D3—41no—
280C2×D3—41no—
281C2×D3—41no—
282C3×C4—21no—
283C3×C4—41no—
284C3×C4—41no—
285C3×C4C2×#4111yescharacteristic
286C3×C4H(5,𝔽2)11yescharacteristic
287Dic3—22no—
288Dic3—21no—
289Dic3—21no—
290Dic3—21no—
291Dic3—41no—
292Dic3—41no—
293C23—21no—
294C23—21no—
295C23—31no—
296C23—61no—
297C23D3×D411yescharacteristic
298Q8—32no—
299Q8—61no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—42no—
305D4—61no—
306D4—61no—
307D4—81no—
308D4—121no—
309D4—122no—
310D4—122no—
311D4—122no—
312D4—241no—
313D4—241no—
314D4—241no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—31no—
320C2×C4—31no—
321C2×C4—31no—
322C2×C4—61no—
323C2×C4—61no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—122no—
328C2×C4—122no—
329C2×C4—241no—
330C2×C4—241no—
331C2×C4D3×D411yescharacteristic
332C2×C4C23×D311yescharacteristic
333C8—21no—
334C8—21no—
335C8—61no—
336C8—61no—
337C2×C3—41no—
338C2×C3—81no—
339C2×C3—81no—
340C2×C3#54611yescharacteristic
341C2×C3#57511yescharacteristic
342C2×C3#57611yescharacteristic
343D3—41no—
344D3—81no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—61no—
355C22—61no—
356C22—61no—
357C22—121no—
358C22—121no—
359C22—121no—
360C22C2×D3×D411yescharacteristic
361C4—21no—
362C4—41no—
363C4—41no—
364C4—61no—
365C4—61no—
366C4—61no—
367C4—62no—
368C4—121no—
369C4—121no—
370C4#100411yescharacteristic
371C4D3×#4111yescharacteristic
372C3#330911yescharacteristic, complemented, Sylow
373C2—41no—
374C2—81no—
375C2—81no—
376C2—121no—
377C2—241no—
378C2#561011yescharacteristic
379C2#577311yescharacteristic
380C2#577411yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#469C2
socleC22×C3C22×D4
hypercenter#469D3
hypocenterC3#3309
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #5618C2semidirect
2. #5599C2semidirect
3. C3×#469C2semidirect
4. #5158C2semidirect
5. #5150C2semidirect
6. #5133C2semidirect
7. #5127C2semidirect
8. #5037C2semidirect
9. #5033C2semidirect
10. #4866C2semidirect
11. #4857C2semidirect
12. #4775C2semidirect
13. #4772C2semidirect
14. #4764C2semidirect
15. #4757C2semidirect
66. #469D3semidirect
372. C3#3309semidirect

Maximal subgroups

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

subgroupindex
#56182
#55992
C3×#4692
#51582
#51502
#51332
#51272
#50372
#50332
#48662
#48572
#47752
#47722
#47642
#47572
#33093