Finite Group Databasebeta

← #19140667

Subgroups — #19140667

Order 5504.

378 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14582840C211yesmaximal, characteristic, complemented
2#14582838C211yesmaximal, characteristic, complemented
3#14582834C211yesmaximal, characteristic
4#14582833C211yesmaximal, characteristic, complemented
5#14582830C211yesmaximal, characteristic, complemented
6#14582828C211yesmaximal, characteristic
7#14582826C211yesmaximal, characteristic
8#14582821C211yesmaximal, characteristic
9#14582797C211yesmaximal, characteristic, complemented
10#14582790C211yesmaximal, characteristic
11#14582790C211yesmaximal, characteristic
12#14582790C211yesmaximal, characteristic
13#14582783C211yesmaximal, characteristic, complemented
14#14582783C211yesmaximal, characteristic, complemented
15C4×C4⋊C4×C43C211yesmaximal, characteristic, complemented
16C2×C4⋊Dic43C2211yescharacteristic
17C2×C4⋊Dic43C2211yescharacteristic
18C2×Dic43⋊C4C2211yescharacteristic
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2211yescharacteristic
22C2×Dic43⋊C4C2211yescharacteristic
23C2×Dic43⋊C4C2211yescharacteristic
24C2×Dic43⋊C4C2211yescharacteristic
25C2×(C2×D43)⋊C4C2211yescharacteristic
26C2×(C2×D43)⋊C4C2211yescharacteristic
27C2×(C2×D43)⋊C4C2211yescharacteristic
28C2×(C2×D43)⋊C4C2211yescharacteristic
29C2×(C2×D43)⋊C4C2211yescharacteristic
30C2×(C2×D43)⋊C4C2211yescharacteristic
31C2×(C2×D43)⋊C4C2211yescharacteristic
32C43⋊#95C2211yescharacteristic
33C43⋊#95C2211yescharacteristic
34C43⋊#95C2211yescharacteristic
35C43⋊#95C2211yescharacteristic
36C43⋊#95C2211yescharacteristic
37C43⋊#95C2211yescharacteristic
38C43⋊#95C2211yescharacteristic
39C43⋊#95C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C2×C4⋊C4×C43C2211yescharacteristic
45C2×C4⋊C4×C43C2211yescharacteristic
46C2×C42×C43C2211yescharacteristic
47C2×C42×C43C2211yescharacteristic
48C2×C42×C43C2211yescharacteristic
49#95×C43C2211yescharacteristic
50#95×C43C2211yescharacteristic
51C23×D43C2311yescharacteristic
52C22×C4×C43C2311yescharacteristic
53C22×C4×C43C2311yescharacteristic
54C22×C4×C43C2311yescharacteristic
55C22×C4×C43C2311yescharacteristic
56C22×C4×C43C2311yescharacteristic
57C22×C4×C43C2311yescharacteristic
58C22×C4×C43C2311yescharacteristic
59C22×Dic43C2311yescharacteristic
60C22×Dic43C2311yescharacteristic
61C22×Dic43C2311yescharacteristic
62C22×Dic43C2311yescharacteristic
63C22×Dic43C2311yescharacteristic
64C22×Dic43C2311yescharacteristic
65C22×Dic43C2311yescharacteristic
66C4⋊C4×C43—22no—
67C4⋊C4×C43—22no—
68C42×C43—22no—
69C42×C43—41no—
70C42×C43—41no—
71(C2×D43)⋊C4—22no—
72(C2×D43)⋊C4—22no—
73(C2×D43)⋊C4—22no—
74(C2×D43)⋊C4—41no—
75(C2×D43)⋊C4—41no—
76(C2×D43)⋊C4—41no—
77(C2×D43)⋊C4—41no—
78C4⋊Dic43—22no—
79C4⋊Dic43—41no—
80Dic43⋊C4—22no—
81Dic43⋊C4—22no—
82Dic43⋊C4—41no—
83Dic43⋊C4—41no—
84Dic43⋊C4—41no—
85Dic43⋊C4—41no—
86Dic43⋊C4—41no—
87C23×C43C2411yescharacteristic
88C22×D43—21no—
89C22×D43—21no—
90C22×D43—21no—
91C22×D43—21no—
92C22×D43—21no—
93C22×D43—21no—
94C22×D43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—21no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43#4112yes—
114C2×C4×C43#4112yes—
115C2×C4×C43#4112yes—
116C2×Dic43—21no—
117C2×Dic43—21no—
118C2×Dic43—21no—
119C2×Dic43—21no—
120C2×Dic43—21no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C22×C43C2×#4111yescharacteristic
138C22×C43C2×#4111yescharacteristic
139C22×C43C2×#4111yescharacteristic
140C22×C43H(5,𝔽2)11yescharacteristic
141C22×C43H(5,𝔽2)11yescharacteristic
142C22×C432−1+411yescharacteristic
143C22×C432−1+411yescharacteristic
144C2×D43—41no—
145C2×D43—41no—
146C2×D43—41no—
147C2×D43—41no—
148C2×D43—41no—
149C2×D43—41no—
150C2×D43—41no—
151C4×C43—22no—
152C4×C43—22no—
153C4×C43—22no—
154C4×C43—41no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43—41no—
158Dic43—41no—
159Dic43—41no—
160Dic43—41no—
161Dic43—41no—
162Dic43—41no—
163Dic43—41no—
164Dic43—41no—
165#2654—431nomaximal, Sylow
166C2×C43#52911yescharacteristic
167C2×C43#53911yescharacteristic
168C2×C43#53911yescharacteristic
169C2×C43#54011yescharacteristic
170C2×C43#54111yescharacteristic
171C2×C43#54211yescharacteristic
172C2×C43#54211yescharacteristic
173D43—81no—
174#400—431no—
175#400—431no—
176#399—431no—
177#398—431no—
178#398—431no—
179#397—431no—
180#397—431no—
181#396—431no—
182#389—431no—
183#388—431no—
184#388—431no—
185#388—431no—
186#387—431no—
187#387—431no—
188C4×C4⋊C4D4311yescharacteristic, complemented
189C43#265411yescharacteristic, complemented, Sylow
190C2×C4⋊C4—431no—
191C2×C4⋊C4—431no—
192C2×C4⋊C4—431no—
193C2×C4⋊C4—431no—
194C2×C4⋊C4—431no—
195C2×C4⋊C4—431no—
196C2×C4⋊C4—431no—
197C2×C4⋊C4—431no—
198C2×C4⋊C4—431no—
199C2×C4⋊C4C2×D4311yescharacteristic
200C2×C4⋊C4C2×D4311yescharacteristic
201C2×C22⋊C4—431no—
202C2×C22⋊C4—431no—
203C2×C22⋊C4—431no—
204C2×C22⋊C4—431no—
205C2×C22⋊C4—431no—
206C2×C22⋊C4—431no—
207C2×C22⋊C4—431no—
208C2×C42C2×D4311yescharacteristic
209C2×C42C2×D4311yescharacteristic
210C2×C42C2×D4311yescharacteristic
211#95—431no—
212#95—431no—
213#95—431no—
214#95—431no—
215#95—431no—
216#95—431no—
217#95—431no—
218#95—431no—
219#95—431no—
220#95—431no—
221#95—431no—
222#95—431no—
223#95C2×D4311yescharacteristic
224#95C2×D4311yescharacteristic
225C24—431no—
226C22×C4—431no—
227C22×C4—431no—
228C22×C4—431no—
229C22×C4—431no—
230C22×C4—431no—
231C22×C4—431no—
232C22×C4—431no—
233C22×C4C22×D4311yescharacteristic
234C22×C4C22×D4311yescharacteristic
235C22×C4C22×D4311yescharacteristic
236C22×C4C22×D4311yescharacteristic
237C22×C4C22×D4311yescharacteristic
238C22×C4C22×D4311yescharacteristic
239C22×C4C22×D4311yescharacteristic
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—862no—
243C4⋊C4—862no—
244C4⋊C4—862no—
245C4⋊C4—1721no—
246C4⋊C4—1721no—
247C4⋊C4—1721no—
248C4⋊C4—1721no—
249C4⋊C4—1721no—
250C4⋊C4—1721no—
251C22⋊C4—862no—
252C22⋊C4—862no—
253C22⋊C4—862no—
254C22⋊C4—1721no—
255C22⋊C4—1721no—
256C22⋊C4—1721no—
257C22⋊C4—1721no—
258C42—22no—
259C42—41no—
260C42—41no—
261C23—861no—
262C23—861no—
263C23—861no—
264C23—861no—
265C23—861no—
266C23—861no—
267C23—861no—
268C23C23×D4311yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—861no—
288C2×C4—861no—
289C2×C4—861no—
290C2×C4—861no—
291C2×C4—861no—
292C2×C4—861no—
293C2×C4—861no—
294C2×C4—861no—
295C2×C4—861no—
296C2×C4—861no—
297C2×C4—861no—
298C2×C4—861no—
299C2×C4—861no—
300C2×C4—861no—
301C2×C4—861no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4#1062189812yes—
309C2×C4#1062189812yes—
310C2×C4#1062189812yes—
311C22—1721no—
312C22—1721no—
313C22—1721no—
314C22—1721no—
315C22—1721no—
316C22—1721no—
317C22—1721no—
318C22C2×#1062189811yescharacteristic
319C22C2×#1062189811yescharacteristic
320C22C2×#1062189811yescharacteristic
321C22#1306337011yescharacteristic
322C22#1306337111yescharacteristic
323C22#1306337211yescharacteristic
324C22#1306337311yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—1721no—
333C4—1721no—
334C4—1721no—
335C4—1721no—
336C4—1721no—
337C4—1721no—
338C4—1721no—
339C2—3441no—
340C2#1458343311yescharacteristic
341C2#1458349111yescharacteristic
342C2#1458349611yescharacteristic
343C2#1458350011yescharacteristic
344C2#1458350711yescharacteristic
345C2#1458352011yescharacteristic
346C2#1458352111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC4×C4⋊C4×C43C2
hypercenterC4×C4⋊C4D43
hypocenterC43#2654
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #14582840C2semidirect
2. #14582838C2semidirect
4. #14582833C2semidirect
5. #14582830C2semidirect
9. #14582797C2semidirect
13. #14582783C2semidirect
14. #14582783C2semidirect
15. C4×C4⋊C4×C43C2semidirect
188. C4×C4⋊C4D43semidirect
189. C43#2654semidirect