Finite Group Databasebeta

← #83608

Subgroups — #83608

Order 384.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#553C211yesmaximal, characteristic, complemented
2#5555C211yesmaximal, characteristic, complemented
3#5066C211yesmaximal, characteristic, complemented
4#5064C211yesmaximal, characteristic, complemented
5#5039C211yesmaximal, characteristic, complemented
6#5038C211yesmaximal, characteristic, complemented
7#5034C211yesmaximal, characteristic, complemented
8#5033C211yesmaximal, characteristic, complemented
9#5014C211yesmaximal, characteristic, complemented
10#5011C211yesmaximal, characteristic, complemented
11#5008C211yesmaximal, characteristic, complemented
12#5003C211yesmaximal, characteristic, complemented
13#4995C211yesmaximal, characteristic, complemented
14#4968C211yesmaximal, characteristic, complemented
15C2×#808C211yesmaximal, characteristic, complemented
16#3345—31nomaximal, Sylow
17C2×#237—21no—
18C3×#126—21no—
19C3×#125C2211yescharacteristic
20C3×#123—21no—
21C3×#121—21no—
22C3×#121C2211yescharacteristic
23C3×#121C2211yescharacteristic
24C3×C4×D4—21no—
25C3×C4×D4C2211yescharacteristic
26C3×C4×D4C2211yescharacteristic
27C3×#117C2211yescharacteristic
28C2×C3×C4⋊C4C2211yescharacteristic
29C2×#213C2211yescharacteristic
30#930C2211yescharacteristic
31#930C2211yescharacteristic
32C2×C4⋊Dic3C2211yescharacteristic
33C2×C4⋊Dic3C2211yescharacteristic
34C2×#208C2211yescharacteristic
35C22×C3⋊C8C2211yescharacteristic
36#897—21no—
37#886—21no—
38#886—21no—
39C4×D12C2211yescharacteristic
40#869C2211yescharacteristic
41#832C2211yescharacteristic
42#832C2211yescharacteristic
43#832C2211yescharacteristic
44#830C2211yescharacteristic
45#830C2211yescharacteristic
46#809C2211yescharacteristic
47#809C2211yescharacteristic
48#809C2211yescharacteristic
49#808C2211yescharacteristic
50#808C2211yescharacteristic
51#808C2211yescharacteristic
52#808C2211yescharacteristic
53#808C2211yescharacteristic
54#808C2211yescharacteristic
55#807C2211yescharacteristic
56#807C2211yescharacteristic
57#807C2211yescharacteristic
58C4⋊(C3⋊C8)C2211yescharacteristic
59#803C2211yescharacteristic
60#553D311yescharacteristic, complemented
61#547—31no—
62#501—31no—
63#482—31no—
64#481—31no—
65#481—31no—
66#480—31no—
67#478—31no—
68#476—31no—
69#469—31no—
70#466—31no—
71#442—31no—
72#435—31no—
73#428—31no—
74C2×#106—31no—
75C2×C3×D4—21no—
76C2×C3×D4—21no—
77C2×C3×D4D411yescharacteristic
78C2×C3×D4C2311yescharacteristic
79C22×C3×C4—21no—
80C22×C3×C4—21no—
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C2×#67—21no—
84C2×#67—21no—
85C22×Dic3—21no—
86C22×Dic3—21no—
87#237—44no—
88C2×D12C2311yescharacteristic
89C2×C4×D3—21no—
90C2×Dic6—21no—
91C3×C4⋊C4—21no—
92C3×C4⋊C4—21no—
93C3×C4⋊C4—21no—
94C3×C4⋊C4D411yescharacteristic
95C3×C4⋊C4C2311yescharacteristic
96C3×C4⋊C4C2311yescharacteristic
97C3×C4⋊C4C2311yescharacteristic
98C3×C22⋊C4—21no—
99C3×C22⋊C4—21no—
100C3×C22⋊C4—21no—
101C3×C22⋊C4—21no—
102C3×C22⋊C4D411yescharacteristic
103C3×C22⋊C4D411yescharacteristic
104C3×C42—21no—
105C3×C42C2311yescharacteristic
106#213—22no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110C4⋊Dic3—21no—
111C4⋊Dic3—21no—
112C4⋊Dic3—21no—
113C4⋊Dic3C2311yescharacteristic
114C4⋊Dic3C2311yescharacteristic
115C4⋊Dic3C2311yescharacteristic
116#208—22no—
117C2×C3⋊C8—22no—
118C2×C3⋊C8C2311yescharacteristic
119C2×C3⋊C8C2311yescharacteristic
120C2×C3⋊C8C2311yescharacteristic
121C2×C3⋊C8C2311yescharacteristic
122C2×#41—61no—
123C2×D8—31no—
124C2×M16—31no—
125C22×C8—31no—
126C4⋊Q8—31no—
127#126—21no—
128#125C2×D311yescharacteristic
129#123—21no—
130#123—61no—
131#123—61no—
132C22⋊Q8—61no—
133#121—21no—
134#121—31no—
135#121—31no—
136#121C2×D311yescharacteristic
137#121C2×D311yescharacteristic
138C4×D4—21no—
139C4×D4—31no—
140C4×D4C2×D311yescharacteristic
141C4×D4C2×D311yescharacteristic
142#117C2×D311yescharacteristic
143C2×C4⋊C4—31no—
144C2×C4⋊C4—31no—
145C2×C4⋊C4C2×D311yescharacteristic
146#107—31no—
147#107—31no—
148#107—31no—
149#106—31no—
150#106—31no—
151#106—31no—
152#106—31no—
153#106—31no—
154#106—31no—
155C4⋊C8—31no—
156#102—31no—
157#102—31no—
158#102—31no—
159#102—31no—
160#102—31no—
161#102—31no—
162C22⋊C8—31no—
163C22⋊C8—31no—
164#97—31no—
165C23×C3—21no—
166C23×C3C2×D411yescharacteristic
167C23×C3C2×D411yescharacteristic
168C22×D3—21no—
169C3×D4—22no—
170C3×D4—21no—
171C3×D4—21no—
172C3×D4—42no—
173C3×D4—81no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—81no—
182C2×C3×C4—81no—
183C2×C3×C4C2×D411yescharacteristic
184C2×C3×C4C2×D411yescharacteristic
185C2×C3×C4C2×D411yescharacteristic
186C2×C3×C4C2×D411yescharacteristic
187C2×C3×C4C2411yescharacteristic
188#67—42no—
189#67—42no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—42no—
194C2×Dic3—42no—
195D12—21no—
196D12—21no—
197C4×D3—42no—
198Dic6—42no—
199C3⋊C8—21no—
200C3⋊C8—21no—
201C3⋊C8—21no—
202C3⋊C8#4112yescomplemented
203#41—124no—
204C2×Q8—61no—
205C2×D4—21no—
206C2×D4—21no—
207C2×D4—31no—
208C2×D4—61no—
209C2×D4—61no—
210C2×D4#6711yescharacteristic
211C2×D4C22×D311yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—61no—
215C22×C4—61no—
216C22×C4—61no—
217C22×C4C22×D311yescharacteristic
218C22×C4C22×D311yescharacteristic
219D8—62no—
220M16—62no—
221C2×C8—31no—
222C2×C8—31no—
223C2×C8—31no—
224C2×C8—31no—
225C2×C8—62no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—31no—
230C4⋊C4—31no—
231C4⋊C4—31no—
232C4⋊C4—61no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4#6711yescharacteristic
236C4⋊C4C22×D311yescharacteristic
237C4⋊C4C22×D311yescharacteristic
238C4⋊C4C22×D311yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—21no—
241C22⋊C4—21no—
242C22⋊C4—21no—
243C22⋊C4—61no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4#6711yescharacteristic
247C22⋊C4#6711yescharacteristic
248C42—21no—
249C42C22×D311yescharacteristic
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—41no—
256C22×C3—41no—
257C22×C3—41no—
258C22×C3AGL(1,ℤ/8)12yes—
259C22×C3C22×D411yescharacteristic
260C2×D3—41no—
261C2×D3—41no—
262C2×D3—41no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—41no—
268C3×C4—41no—
269C3×C4—41no—
270C3×C4C2×#4111yescharacteristic
271C3×C42−1+411yescharacteristic
272Dic3—41no—
273Dic3—41no—
274Dic3—41no—
275C23—21no—
276C23—61no—
277C23C2×#6711yescharacteristic
278C23C2×#6711yescharacteristic
279Q8—122no—
280D4—22no—
281D4—21no—
282D4—21no—
283D4—42no—
284D4—61no—
285D4—61no—
286D4—81no—
287D4—122no—
288D4—122no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—61no—
297C2×C4—61no—
298C2×C4—61no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—122no—
302C2×C4—122no—
303C2×C4—122no—
304C2×C4C2×#6711yescharacteristic
305C2×C4C2×#6711yescharacteristic
306C2×C4C2×#6711yescharacteristic
307C2×C4C2×#6711yescharacteristic
308C2×C4C23×D311yescharacteristic
309C8—32no—
310C8—61no—
311C8—61no—
312C8—61no—
313C2×C3—22no—
314C2×C3—41no—
315C2×C3—81no—
316C2×C3#54711yescharacteristic
317C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
318C2×C3#57711yescharacteristic
319D3—81no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—121no—
329C22—121no—
330C22—121no—
331C22#94912yes—
332C22C22×#6711yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—121no—
341C4—121no—
342C4—121no—
343C4D3×#4111yescharacteristic
344C4#101011yescharacteristic
345C3#334511yescharacteristic, complemented, Sylow
346C2—22no—
347C2—41no—
348C2—81no—
349C2—241no—
350C2C2×#94911yescharacteristic
351C2#582411yescharacteristic
352C2#583611yescharacteristic
subgroupG/H
centerC22C22×#67
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#553C2
socleC22×C3C22×D4
hypercenter#553D3
hypocenterC3#3345
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. C3×#553C2semidirect
2. #5555C2semidirect
3. #5066C2semidirect
4. #5064C2semidirect
5. #5039C2semidirect
6. #5038C2semidirect
7. #5034C2semidirect
8. #5033C2semidirect
9. #5014C2semidirect
10. #5011C2semidirect
11. #5008C2semidirect
12. #5003C2semidirect
13. #4995C2semidirect
14. #4968C2semidirect
15. C2×#808C2semidirect
60. #553D3semidirect
202. C3⋊C8#41semidirect
345. C3#3345semidirect

Maximal subgroups

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

subgroupindex
C3×#5532
#55552
#50662
#50642
#50392
#50382
#50342
#50332
#50142
#50112
#50082
#50032
#49952
#49682
C2×#8082
#33453