Finite Group Databasebeta

← #19141495

Subgroups — #19141495

Order 5504.

434 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063320C211yesmaximal, characteristic
2C2×#13063316C211yesmaximal, characteristic, complemented
3#14582834C211yesmaximal, characteristic
4#14582834C211yesmaximal, characteristic
5#14582832C211yesmaximal, characteristic, complemented
6#14582828C211yesmaximal, characteristic
7#14582821C211yesmaximal, characteristic
8#14582796C211yesmaximal, characteristic, complemented
9#14582791C211yesmaximal, characteristic
10#14582791C211yesmaximal, characteristic
11#14582786C211yesmaximal, characteristic, complemented
12#14582784C211yesmaximal, characteristic, complemented
13#14582780C211yesmaximal, characteristic, complemented
14#14582768C211yesmaximal, characteristic, complemented
15C43×#398C211yesmaximal, characteristic, complemented
16#13063320—24no—
17#13063316—24no—
18C2×C4⋊Dic43C2211yescharacteristic
19C2×C4⋊Dic43C2211yescharacteristic
20C2×C4⋊Dic43C2211yescharacteristic
21C2×C4⋊Dic43C2211yescharacteristic
22C2×Dic43⋊C4C2211yescharacteristic
23C2×Dic43⋊C4C2211yescharacteristic
24C2×Dic43⋊C4C2211yescharacteristic
25C2×Dic43⋊C4C2211yescharacteristic
26C2×Dic43⋊C4C2211yescharacteristic
27C2×Dic43⋊C4C2211yescharacteristic
28C2×Dic43⋊C4C2211yescharacteristic
29C2×(C2×D43)⋊C4C2211yescharacteristic
30C2×(C2×D43)⋊C4C2211yescharacteristic
31C2×(C2×D43)⋊C4C2211yescharacteristic
32C2×(C2×D43)⋊C4C2211yescharacteristic
33C2×(C2×D43)⋊C4C2211yescharacteristic
34C2×(C2×D43)⋊C4C2211yescharacteristic
35C2×(C2×D43)⋊C4C2211yescharacteristic
36C2×C4×Dic43C2211yescharacteristic
37C2×C4×Dic43C2211yescharacteristic
38C2×C4×Dic43C2211yescharacteristic
39C43⋊#95C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C2×C4⋊C4×C43C2211yescharacteristic
47C2×C4⋊C4×C43C2211yescharacteristic
48C2×C4⋊C4×C43C2211yescharacteristic
49C2×C4⋊C4×C43C2211yescharacteristic
50#95×C43C2211yescharacteristic
51#95×C43C2211yescharacteristic
52#95×C43C2211yescharacteristic
53C23×D43C2311yescharacteristic
54C22×C4×C43C2311yescharacteristic
55C22×C4×C43C2311yescharacteristic
56C22×C4×C43C2311yescharacteristic
57C22×C4×C43C2311yescharacteristic
58C22×C4×C43C2311yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C22×Dic43C2311yescharacteristic
62C22×Dic43C2311yescharacteristic
63C22×Dic43C2311yescharacteristic
64C22×Dic43C2311yescharacteristic
65C22×Dic43C2311yescharacteristic
66C22×Dic43C2311yescharacteristic
67C22×Dic43C2311yescharacteristic
68C4⋊C4×C43—22no—
69C4⋊C4×C43—22no—
70C4⋊C4×C43—41no—
71C4⋊C4×C43—41no—
72(C2×D43)⋊C4—22no—
73(C2×D43)⋊C4—22no—
74(C2×D43)⋊C4—22no—
75(C2×D43)⋊C4—22no—
76(C2×D43)⋊C4—22no—
77(C2×D43)⋊C4—41no—
78(C2×D43)⋊C4—41no—
79C4⋊Dic43—22no—
80C4⋊Dic43—22no—
81C4⋊Dic43—41no—
82C4⋊Dic43D414yes—
83Dic43⋊C4—22no—
84Dic43⋊C4—22no—
85Dic43⋊C4—22no—
86Dic43⋊C4—22no—
87Dic43⋊C4—22no—
88Dic43⋊C4—22no—
89Dic43⋊C4—41no—
90C4×Dic43—22no—
91C4×Dic43—22no—
92C4×Dic43—22no—
93C23×C43C2411yescharacteristic
94C22×D43—21no—
95C22×D43—21no—
96C22×D43—21no—
97C22×D43—21no—
98C22×D43—21no—
99C22×D43—21no—
100C22×D43—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—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43C2×D412yes—
121C2×C4×C43#4112yes—
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—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43C2×D412yes—
141C2×Dic43C2×D412yes—
142C2×Dic43#4112yes—
143C22×C43C22×D411yescharacteristic
144C22×C43C2×#4111yescharacteristic
145C22×C43C2×#4111yescharacteristic
146C22×C43H(5,𝔽2)11yescharacteristic
147C22×C432−1+411yescharacteristic
148C22×C432−1+411yescharacteristic
149C22×C432−1+411yescharacteristic
150C2×D43—41no—
151C2×D43—41no—
152C2×D43—41no—
153C2×D43—41no—
154C2×D43—41no—
155C2×D43—41no—
156C2×D43—41no—
157C4×C43—22no—
158C4×C43—22no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—41no—
164Dic43—22no—
165Dic43—22no—
166Dic43—22no—
167Dic43—41no—
168Dic43—41no—
169Dic43—41no—
170Dic43—41no—
171#2721—431nomaximal, Sylow
172C2×C43#53611yescharacteristic
173C2×C43#53911yescharacteristic
174C2×C43#54111yescharacteristic
175C2×C43#54711yescharacteristic
176C2×C43#55011yescharacteristic
177C2×C43#55211yescharacteristic
178C2×C43#56311yescharacteristic
179D43—81no—
180C2×#126—431no—
181C2×#125—431no—
182#399—431no—
183#399—431no—
184#398—431no—
185#398D4311yescharacteristic, complemented
186#397—431no—
187#396—431no—
188#389—431no—
189#388—431no—
190#388—431no—
191#387—431no—
192#387—431no—
193#387—431no—
194#384—431no—
195C43#272111yescharacteristic, complemented, Sylow
196#126—864no—
197#125—864no—
198C2×C4⋊C4—431no—
199C2×C4⋊C4—431no—
200C2×C4⋊C4—431no—
201C2×C4⋊C4—431no—
202C2×C4⋊C4—431no—
203C2×C4⋊C4—431no—
204C2×C4⋊C4—431no—
205C2×C4⋊C4—431no—
206C2×C4⋊C4—431no—
207C2×C4⋊C4—431no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4C2×D4311yescharacteristic
210C2×C4⋊C4C2×D4311yescharacteristic
211C2×C4⋊C4C2×D4311yescharacteristic
212C2×C4⋊C4C2×D4311yescharacteristic
213C2×C22⋊C4—431no—
214C2×C22⋊C4—431no—
215C2×C22⋊C4—431no—
216C2×C22⋊C4—431no—
217C2×C22⋊C4—431no—
218C2×C22⋊C4—431no—
219C2×C22⋊C4—431no—
220C2×C42—431no—
221C2×C42—431no—
222C2×C42—431no—
223#95—431no—
224#95—431no—
225#95—431no—
226#95—431no—
227#95—431no—
228#95—431no—
229#95—431no—
230#95C2×D4311yescharacteristic
231#95C2×D4311yescharacteristic
232#95C2×D4311yescharacteristic
233C24—431no—
234C22×C4—431no—
235C22×C4—431no—
236C22×C4—431no—
237C22×C4—431no—
238C22×C4—431no—
239C22×C4—431no—
240C22×C4—431no—
241C22×C4C22×D4311yescharacteristic
242C22×C4C22×D4311yescharacteristic
243C22×C4C22×D4311yescharacteristic
244C22×C4C22×D4311yescharacteristic
245C22×C4C22×D4311yescharacteristic
246C22×C4C22×D4311yescharacteristic
247C22×C4C22×D4311yescharacteristic
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—434no—
253C4⋊C4—862no—
254C4⋊C4—862no—
255C4⋊C4—862no—
256C4⋊C4—862no—
257C4⋊C4—862no—
258C4⋊C4—862no—
259C4⋊C4—862no—
260C4⋊C4—862no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C22⋊C4—862no—
264C22⋊C4—862no—
265C22⋊C4—862no—
266C22⋊C4—862no—
267C22⋊C4—862no—
268C22⋊C4—1721no—
269C22⋊C4—1721no—
270C42—862no—
271C42—862no—
272C42—862no—
273C23—861no—
274C23—861no—
275C23—861no—
276C23—861no—
277C23—861no—
278C23—861no—
279C23—861no—
280C23C23×D4311yescharacteristic
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—432no—
301C2×C4—432no—
302C2×C4—432no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4D4×D4312yes—
322C2×C4#1062190212yes—
323C22—1721no—
324C22—1721no—
325C22—1721no—
326C22—1721no—
327C22—1721no—
328C22—1721no—
329C22—1721no—
330C22C2×D4×D4311yescharacteristic
331C22#41×D4311yescharacteristic
332C22C2×#1062190211yescharacteristic
333C22#1306337011yescharacteristic
334C22#1306337211yescharacteristic
335C22#1306337211yescharacteristic
336C22#1306337311yescharacteristic
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—862no—
345C4—862no—
346C4—862no—
347C4—1721no—
348C4—1721no—
349C4—1721no—
350C4—1721no—
351C2—3441no—
352C2#1458347111yescharacteristic
353C2#1458349811yescharacteristic
354C2#1458350811yescharacteristic
355C2#1458355211yescharacteristic
356C2#1458356711yescharacteristic
357C2#1458358711yescharacteristic
358C2#1458365011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#398C2
hypercenter#398D43
hypocenterC43#2721
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#13063316C2semidirect
5. #14582832C2semidirect
8. #14582796C2semidirect
11. #14582786C2semidirect
12. #14582784C2semidirect
13. #14582780C2semidirect
14. #14582768C2semidirect
15. C43×#398C2semidirect
185. #398D43semidirect
195. C43#2721semidirect