Finite Group Databasebeta

← #19146642

Subgroups — #19146642

Order 5504.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583584C211yesmaximal, characteristic
2Q8×C22⋊D43C211yesmaximal, characteristic
3#14583266C211yesmaximal, characteristic, complemented
4#14583239C211yesmaximal, characteristic, complemented
5#14583229C211yesmaximal, characteristic, complemented
6#14583208C211yesmaximal, characteristic, complemented
7#14583156C211yesmaximal, characteristic, complemented
8#14583140C211yesmaximal, characteristic, complemented
9#14583108C211yesmaximal, characteristic, complemented
10#14583056C211yesmaximal, characteristic, complemented
11#14583055C211yesmaximal, characteristic, complemented
12#14583003C211yesmaximal, characteristic, complemented
13#14582970C211yesmaximal, characteristic
14#14582906C211yesmaximal, characteristic, complemented
15C2×#103×C43C211yesmaximal, characteristic, complemented
16C2×Q8×D43C2211yescharacteristic
17C2×Dic172C2211yescharacteristic
18C2×#10621885C2211yescharacteristic
19C2×#10621885C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21#13063323—21no—
22#13063323C2211yescharacteristic
23#13063320—21no—
24#13063316C2211yescharacteristic
25#13063315—21no—
26#13063308—21no—
27#13063305C2211yescharacteristic
28#13063304—21no—
29#13063304C2211yescharacteristic
30#13063304C2211yescharacteristic
31#13063301—21no—
32#13063301C2211yescharacteristic
33Q8×Dic43C2211yescharacteristic
34#13063290C2211yescharacteristic
35C4×C22⋊D43—21no—
36C4×C22⋊D43C2211yescharacteristic
37#13063284—21no—
38#13063283C2211yescharacteristic
39#13063259C2211yescharacteristic
40#13063256C2211yescharacteristic
41#13063256C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063249C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063248C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063235C2211yescharacteristic
52C22×Q8×C43C2211yescharacteristic
53C22×C8×C43C2211yescharacteristic
54C2×C4⋊C4×C43C2211yescharacteristic
55#103×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43—22no—
61C2×Q8×C43—41no—
62C2×Q8×C43C2311yescharacteristic
63C2×Q8×C43C2311yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43D411yescharacteristic
68Q8×D43—22no—
69Q8×D43—41no—
70C2×C4×D43—21no—
71C2×C4×D43C2311yescharacteristic
72C2×Dic86—21no—
73C2×Dic86C2311yescharacteristic
74C2×Dic86C2311yescharacteristic
75C2×C8×C43—41no—
76C2×C8×C43C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C4⋊C4×C43—21no—
79C4⋊C4×C43C2311yescharacteristic
80C4⋊C4×C43C2311yescharacteristic
81C22⋊Dic43—21no—
82C22⋊Dic43—21no—
83C22⋊Dic43D411yescharacteristic
84#10621885—22no—
85#10621885—41no—
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4D411yescharacteristic
90C4⋊Dic43—21no—
91C4⋊Dic43—21no—
92C4⋊Dic43—21no—
93C4⋊Dic43C2311yescharacteristic
94C4⋊Dic43C2311yescharacteristic
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4D411yescharacteristic
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109Dic172—41no—
110#10621872—41no—
111C23×C43C2×D411yescharacteristic
112C22×D43C2×D411yescharacteristic
113Q8×C43—21no—
114Q8×C43—21no—
115Q8×C43—21no—
116Q8×C43—42no—
117Q8×C43#4112yes—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2411yescharacteristic
128C22⋊D43—22no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43C2×D411yescharacteristic
134C2×Dic43C2×D411yescharacteristic
135C2×Dic43C2×D411yescharacteristic
136C4×D43—21no—
137C4×D43—21no—
138C4×D43—42no—
139Dic86—21no—
140Dic86—21no—
141Dic86—21no—
142Dic86—21no—
143Dic86—42no—
144C8×C43—21no—
145C8×C43—21no—
146C43⋊C8—21no—
147C43⋊C8—21no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43#13712yes—
151C22×C43C22×D411yescharacteristic
152C2×D43—21no—
153C2×D43—21no—
154C2×D43—21no—
155C4×C43—22no—
156C4×C43—21no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43—41no—
160C4×C43C2×#4111yescharacteristic
161C4×C43H(5,𝔽2)11yescharacteristic
162Dic43—21no—
163Dic43—21no—
164Dic43—21no—
165Dic43—41no—
166Dic43—41no—
167Dic43—41no—
168Dic43—41no—
169#3312—431nomaximal, Sylow
170C2×C43—22no—
171C2×C43#54611yescharacteristic
172C2×C43C2×#13711yescharacteristic
173C2×C43#57811yescharacteristic
174D43—41no—
175#552—431no—
176D4×Q8—431no—
177#491—431no—
178#485—431no—
179#483—431no—
180#479—431no—
181#470—431no—
182#467—431no—
183#462—431no—
184#451—431no—
185#451—431no—
186#441—431no—
187#435—431no—
188#419—431no—
189C2×#103D4311yescharacteristic, complemented
190C43#331211yescharacteristic, complemented, Sylow
191C22×Q8—431no—
192C22×Q8C2×D4311yescharacteristic
193C2×Q16—431no—
194C2×Q16—431no—
195C2×Q16—431no—
196C2×M16—431no—
197C22×C8C2×D4311yescharacteristic
198C4⋊Q8—431no—
199C4⋊Q8—861no—
200#126—861no—
201#125—431no—
202#125—861no—
203#123—861no—
204C22⋊Q8—431no—
205C22⋊Q8—431no—
206C22⋊Q8—431no—
207C22⋊Q8—431no—
208C22⋊Q8—861no—
209C22⋊Q8—861no—
210C4×Q8—431no—
211C4×Q8—431no—
212C4×D4—431no—
213C4×D4—861no—
214#117—431no—
215#117—861no—
216C2×C4⋊C4C2×D4311yescharacteristic
217#107—431no—
218#106—431no—
219#106—431no—
220C4⋊C8—431no—
221#103—431no—
222#103—431no—
223#103—431no—
224#103—431no—
225#103—431no—
226#103—431no—
227#103C2×D4311yescharacteristic
228#103C2×D4311yescharacteristic
229#103C2×D4311yescharacteristic
230#103C2×D4311yescharacteristic
231C22⋊C8—431no—
232C22⋊C8—431no—
233#97—431no—
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8—431no—
238C2×Q8—431no—
239C2×Q8—861no—
240C2×Q8—862no—
241C2×Q8—1721no—
242C2×Q8C22×D4311yescharacteristic
243C2×Q8C22×D4311yescharacteristic
244C2×D4—431no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—431no—
248C22×C4—861no—
249C22×C4C22×D4311yescharacteristic
250Q16—862no—
251Q16—1721no—
252Q16—1721no—
253M16—1721no—
254C2×C8—41no—
255C2×C8—431no—
256C2×C8—431no—
257C2×C8C22×D4311yescharacteristic
258C2×C8C22×D4311yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—431no—
261C4⋊C4—431no—
262C4⋊C4—431no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4C22×D4311yescharacteristic
274C4⋊C4C22×D4311yescharacteristic
275C22⋊C4—431no—
276C22⋊C4—431no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C42—431no—
283C42—861no—
284C42—861no—
285C42—861no—
286C23—431no—
287C23D4×D4311yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—42no—
292Q8—861no—
293Q8—861no—
294Q8—861no—
295Q8—861no—
296Q8—1722no—
297Q8#1062189812yes—
298D4—862no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—431no—
308C2×C4—431no—
309C2×C4—431no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—1722no—
317C2×C4D4×D4311yescharacteristic
318C2×C4C23×D4311yescharacteristic
319C8—21no—
320C8—21no—
321C8—861no—
322C8—861no—
323C22—21no—
324C22—21no—
325C22—861no—
326C22—861no—
327C22—861no—
328C22#1306335412yes—
329C22C2×D4×D4311yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—861no—
336C4—861no—
337C4—861no—
338C4—1721no—
339C4—1721no—
340C4—1721no—
341C4—1721no—
342C4C2×#1062189811yescharacteristic
343C4#1306337011yescharacteristic
344C2—22no—
345C2—1721no—
346C2#1458353911yescharacteristic
347C2C2×#1306335411yescharacteristic
348C2#1458371211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#103×C43C2
socleC22×C43C22×D4
hypercenterC2×#103D43
hypocenterC43#3312
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #14583266C2semidirect
4. #14583239C2semidirect
5. #14583229C2semidirect
6. #14583208C2semidirect
7. #14583156C2semidirect
8. #14583140C2semidirect
9. #14583108C2semidirect
10. #14583056C2semidirect
11. #14583055C2semidirect
12. #14583003C2semidirect
14. #14582906C2semidirect
15. C2×#103×C43C2semidirect
189. C2×#103D43semidirect
190. C43#3312semidirect