Finite Group Databasebeta

← #19146687

Subgroups — #19146687

Order 5504.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583588C211yesmaximal, characteristic, complemented
2#14583548C211yesmaximal, characteristic
3#14583266C211yesmaximal, characteristic, complemented
4#14583240C211yesmaximal, characteristic, complemented
5#14583233C211yesmaximal, characteristic, complemented
6#14583197C211yesmaximal, characteristic, complemented
7#14583156C211yesmaximal, characteristic, complemented
8#14583140C211yesmaximal, characteristic, complemented
9#14583108C211yesmaximal, characteristic, complemented
10#14583062C211yesmaximal, characteristic, complemented
11#14583061C211yesmaximal, characteristic, complemented
12#14582996C211yesmaximal, characteristic, complemented
13#14582970C211yesmaximal, characteristic, complemented
14#14582897C211yesmaximal, characteristic, complemented
15C43×#416C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×Dic172C2211yescharacteristic
18C2×#10621885C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21#13063323C2211yescharacteristic
22#13063318—21no—
23#13063317—21no—
24#13063316C2211yescharacteristic
25#13063308—21no—
26#13063307—21no—
27#13063306—21no—
28#13063305C2211yescharacteristic
29#13063304C2211yescharacteristic
30#13063304C2211yescharacteristic
31#13063301C2211yescharacteristic
32#13063297—21no—
33#13063290C2211yescharacteristic
34D4×Dic43C2211yescharacteristic
35C4×C22⋊D43C2211yescharacteristic
36#13063282—21no—
37C2×Dic43⋊C4—21no—
38C4⋊C4×D43C2211yescharacteristic
39#13063259C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063256C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063246C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063235C2211yescharacteristic
52C2×#41×C43C2211yescharacteristic
53C22×C8×C43C2211yescharacteristic
54#117×C43C2211yescharacteristic
55#103×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59#41×C43—22no—
60#41×C43—41no—
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43C2311yescharacteristic
66C2×C22⋊D43—21no—
67C2×C22⋊D43D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70#10621900—22no—
71#10621900—41no—
72C2×C4×D43—21no—
73C2×C4×D43C2311yescharacteristic
74C2×Dic86C2311yescharacteristic
75C2×Dic86C2311yescharacteristic
76C2×C8×C43—41no—
77C2×C8×C43C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C4⋊C4×C43C2311yescharacteristic
81C22⋊C4×C43—21no—
82C42×C43—21no—
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43D411yescharacteristic
87#10621885—41no—
88#10621883—22no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4D411yescharacteristic
92C4⋊Dic43—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43C2311yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4D411yescharacteristic
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109Dic172—41no—
110#10621872—41no—
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C22×D43C2×D411yescharacteristic
114Q8×C43—21no—
115Q8×C43—21no—
116D4×C43—21no—
117D4×C43—42no—
118D4×C43#4112yes—
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×C43C2×D411yescharacteristic
126C2×C4×C43C2411yescharacteristic
127C22⋊D43—41no—
128C22⋊D43—42no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—42no—
134C2×Dic43—42no—
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138C4×D43—21no—
139C4×D43—21no—
140C4×D43—42no—
141Dic86—21no—
142Dic86—21no—
143Dic86—21no—
144Dic86—21no—
145C8×C43—21no—
146C8×C43—21no—
147C43⋊C8—21no—
148C43⋊C8—21no—
149C22×C43—22no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43C22×D411yescharacteristic
156C2×D43—21no—
157C2×D43—21no—
158C2×D43—21no—
159C4×C43—21no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43C2×#4111yescharacteristic
164C4×C43H(5,𝔽2)11yescharacteristic
165Dic43—21no—
166Dic43—21no—
167Dic43—21no—
168Dic43—41no—
169Dic43—41no—
170Dic43—41no—
171Dic43—41no—
172#3315—431nomaximal, Sylow
173C2×C43—41no—
174C2×C43—42no—
175C2×C43#54611yescharacteristic
176C2×C43#57511yescharacteristic
177C2×C43#57811yescharacteristic
178D43—41no—
179#552—431no—
180#547—431no—
181#491—431no—
182#485—431no—
183#484—431no—
184#478—431no—
185#470—431no—
186#467—431no—
187#462—431no—
188#452—431no—
189#452—431no—
190#440—431no—
191#435—431no—
192#417—431no—
193#416D4311yescharacteristic, complemented
194C43#331511yescharacteristic, complemented, Sylow
195C2×#41—431no—
196C2×#41C2×D4311yescharacteristic
197C2×Q16—431no—
198C2×Q16—431no—
199C2×SD16—431no—
200C2×M16—431no—
201C22×C8C2×D4311yescharacteristic
202C4⋊Q8—431no—
203#126—861no—
204#125—431no—
205#125—861no—
206#123—861no—
207#123—861no—
208#123—861no—
209C22⋊Q8—431no—
210C22⋊Q8—431no—
211C22⋊Q8—431no—
212C22⋊Q8—431no—
213#121—861no—
214C4×Q8—431no—
215C4×D4—431no—
216C4×D4—431no—
217#117—861no—
218#117C2×D4311yescharacteristic
219C2×C4⋊C4—431no—
220C2×C4⋊C4—861no—
221#107—431no—
222#107—431no—
223#106—431no—
224C4⋊C8—431no—
225#103—431no—
226#103—431no—
227#103—431no—
228#103—431no—
229#103—431no—
230#103C2×D4311yescharacteristic
231#103C2×D4311yescharacteristic
232#102—431no—
233#102C2×D4311yescharacteristic
234#102C2×D4311yescharacteristic
235C22⋊C8—431no—
236C22⋊C8—431no—
237#97—431no—
238#41—22no—
239#41—41no—
240#41—862no—
241#41—1721no—
242C2×Q8—431no—
243C2×Q8—431no—
244C2×Q8C22×D4311yescharacteristic
245C2×D4—21no—
246C2×D4—431no—
247C2×D4—861no—
248C2×D4C22×D4311yescharacteristic
249C22×C4—21no—
250C22×C4—431no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4C22×D4311yescharacteristic
255Q16—1721no—
256Q16—1721no—
257SD16—862no—
258M16—1721no—
259C2×C8—41no—
260C2×C8—431no—
261C2×C8—431no—
262C2×C8C22×D4311yescharacteristic
263C2×C8C22×D4311yescharacteristic
264C4⋊C4—431no—
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4C22×D4311yescharacteristic
278C4⋊C4C22×D4311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—431no—
281C22⋊C4—431no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C42—21no—
288C42—431no—
289C42—861no—
290C23—21no—
291C23—431no—
292C23D4×D4311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—861no—
296Q8—861no—
297Q8—861no—
298Q8—861no—
299D4—21no—
300D4—42no—
301D4—1721no—
302D4—1722no—
303D4#1062189812yes—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—431no—
311C2×C4—431no—
312C2×C4—431no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—1722no—
320C2×C4—1722no—
321C2×C4—1722no—
322C2×C4D4×D4311yescharacteristic
323C2×C4C23×D4311yescharacteristic
324C8—21no—
325C8—21no—
326C8—861no—
327C8—861no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—861no—
335C22—861no—
336C22—861no—
337C22C2×D4×D4311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—861no—
343C4—861no—
344C4—861no—
345C4—1721no—
346C4—1721no—
347C4—1721no—
348C4—1721no—
349C4C2×#1062189811yescharacteristic
350C4#1306337011yescharacteristic
351C2—41no—
352C2—42no—
353C2—1721no—
354C2#1458353911yescharacteristic
355C2#1458369611yescharacteristic
356C2#1458371311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#416C2
socleC22×C43C22×D4
hypercenter#416D43
hypocenterC43#3315
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #14583588C2semidirect
3. #14583266C2semidirect
4. #14583240C2semidirect
5. #14583233C2semidirect
6. #14583197C2semidirect
7. #14583156C2semidirect
8. #14583140C2semidirect
9. #14583108C2semidirect
10. #14583062C2semidirect
11. #14583061C2semidirect
12. #14582996C2semidirect
13. #14582970C2semidirect
14. #14582897C2semidirect
15. C43×#416C2semidirect
193. #416D43semidirect
194. C43#3315semidirect