Finite Group Databasebeta

← #19147100

Subgroups — #19147100

Order 5504.

360 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#14583614C211yesmaximal, characteristic, complemented
2#14583599C211yesmaximal, characteristic, complemented
3#14583308C211yesmaximal, characteristic, complemented
4#14583222C211yesmaximal, characteristic, complemented
5#14583222C211yesmaximal, characteristic, complemented
6#14583221C211yesmaximal, characteristic, complemented
7#14583211C211yesmaximal, characteristic, complemented
8#14583199C211yesmaximal, characteristic, complemented
9#14583179C211yesmaximal, characteristic, complemented
10#14583149C211yesmaximal, characteristic, complemented
11#14583132C211yesmaximal, characteristic, complemented
12#14582972C211yesmaximal, characteristic, complemented
13#14582938C211yesmaximal, characteristic, complemented
14#14582934C211yesmaximal, characteristic, complemented
15C43×#442C211yesmaximal, characteristic, complemented
16C2×#10621872C2211yescharacteristic
17C2×C8×D43C2211yescharacteristic
18#13063325C2211yescharacteristic
19#13063318—21no—
20#13063317C2211yescharacteristic
21#13063311—21no—
22#13063311—21no—
23#13063308—21no—
24#13063299—21no—
25#13063298—21no—
26#13063296C2211yescharacteristic
27#13063296C2211yescharacteristic
28#13063296C2211yescharacteristic
29#13063296C2211yescharacteristic
30C4×D172C2211yescharacteristic
31C4×C22⋊D43—21no—
32#13063284—21no—
33#13063283C2211yescharacteristic
34#13063283C2211yescharacteristic
35#13063283C2211yescharacteristic
36C4⋊C4×D43C2211yescharacteristic
37#13063259C2211yescharacteristic
38#13063259C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063258C2211yescharacteristic
42#13063257C2211yescharacteristic
43#13063257C2211yescharacteristic
44#13063256C2211yescharacteristic
45C4⋊(C43⋊C8)C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063246C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52C2×D8×C43C2211yescharacteristic
53C4×D4×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×D4×C43C2311yescharacteristic
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×D172D411yescharacteristic
68C2×C4×D43—21no—
69C2×C4×D43C2311yescharacteristic
70C2×C4×D43C2311yescharacteristic
71C2×Dic86—21no—
72D8×C43—22no—
73C2×C8×C43C2311yescharacteristic
74C2×C8×C43C2311yescharacteristic
75C4⋊C4×C43C2311yescharacteristic
76C4⋊C4×C43C2311yescharacteristic
77C22⋊C4×C43—21no—
78C22⋊C4×C43—21no—
79C42×C43C2311yescharacteristic
80C22⋊Dic43—21no—
81C22⋊Dic43—21no—
82C22⋊Dic43—21no—
83C22⋊Dic43—21no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4D411yescharacteristic
88(C2×D43)⋊C4D411yescharacteristic
89C4⋊Dic43—21no—
90C4⋊Dic43D411yescharacteristic
91C4⋊Dic43C2311yescharacteristic
92C4⋊Dic43C2311yescharacteristic
93C4⋊Dic43C2311yescharacteristic
94C4⋊Dic43C2311yescharacteristic
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C2×C43⋊C8C2311yescharacteristic
102C2×C43⋊C8C2311yescharacteristic
103#10621872—22no—
104C8×D43—22no—
105C23×C43—21no—
106C23×C43—21no—
107C22×D43C2×D411yescharacteristic
108C22×D43C2×D411yescharacteristic
109D4×C43—21no—
110D4×C43—21no—
111D4×C43—21no—
112D4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—42no—
116C2×C4×C43—81no—
117C2×C4×C43C2×D411yescharacteristic
118C2×C4×C43C2×D411yescharacteristic
119C2×C4×C43C2411yescharacteristic
120C22⋊D43—42no—
121C22⋊D43—81no—
122C22⋊D43—81no—
123C22⋊D43—81no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43C2×D411yescharacteristic
129C2×Dic43C2×D411yescharacteristic
130D172—41no—
131C4×D43—21no—
132C4×D43—21no—
133C4×D43—21no—
134C4×D43—21no—
135C4×D43—81no—
136Dic86—81no—
137C8×C43—21no—
138C8×C43#4112yes—
139C43⋊C8—21no—
140C43⋊C8—21no—
141C22×C43—41no—
142C22×C43—41no—
143C22×C43—41no—
144C22×C43—41no—
145C22×C43—41no—
146C22×C43—41no—
147C22×C43C22×D411yescharacteristic
148C2×D43—21no—
149C2×D43—21no—
150C2×D43—21no—
151C2×D43—21no—
152C2×D43—21no—
153C2×D43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43C2×#4111yescharacteristic
159C4×C432−1+411yescharacteristic
160Dic43—21no—
161Dic43—21no—
162Dic43—41no—
163Dic43—41no—
164Dic43—41no—
165Dic43—41no—
166#3347—431nomaximal, Sylow
167C2×C43—81no—
168C2×C43—81no—
169C2×C43#54711yescharacteristic
170C2×C43#57511yescharacteristic
171C2×C43#57611yescharacteristic
172D43—41no—
173D43—41no—
174#555—431no—
175#553—431no—
176#501—431no—
177#482—431no—
178#482—431no—
179#482—431no—
180#480—431no—
181#478—431no—
182#474—431no—
183#469—431no—
184#466—431no—
185#442D4311yescharacteristic, complemented
186#435—431no—
187#428—431no—
188#427—431no—
189C43#334711yescharacteristic, complemented, Sylow
190C2×D8C2×D4311yescharacteristic
191C2×M16—431no—
192C22×C8—431no—
193C4⋊Q8—431no—
194#126—861no—
195#125—431no—
196#124—861no—
197#124—861no—
198#123—861no—
199#121—431no—
200#121—431no—
201#121—431no—
202#121—431no—
203#121—861no—
204#121—861no—
205C4×D4—431no—
206C4×D4—861no—
207C4×D4C2×D4311yescharacteristic
208C4×D4C2×D4311yescharacteristic
209#117—431no—
210#117—431no—
211#117—431no—
212#117—861no—
213C2×C4⋊C4—431no—
214#107—431no—
215#107—431no—
216#107—431no—
217#107—431no—
218#107—431no—
219#106—431no—
220#106—431no—
221#106—431no—
222#106C2×D4311yescharacteristic
223C4⋊C8—431no—
224#102—431no—
225#102—431no—
226#102—431no—
227#102—431no—
228#102C2×D4311yescharacteristic
229#102C2×D4311yescharacteristic
230C22⋊C8—431no—
231C22⋊C8—431no—
232#97C2×D4311yescharacteristic
233C2×Q8—861no—
234C2×D4—431no—
235C2×D4—861no—
236C2×D4—861no—
237C2×D4—861no—
238C2×D4—861no—
239C2×D4C22×D4311yescharacteristic
240C2×D4C22×D4311yescharacteristic
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—431no—
244C22×C4—431no—
245C22×C4—861no—
246D8—22no—
247M16—862no—
248C2×C8—431no—
249C2×C8—431no—
250C2×C8—862no—
251C2×C8C22×D4311yescharacteristic
252C2×C8C22×D4311yescharacteristic
253C4⋊C4—431no—
254C4⋊C4—431no—
255C4⋊C4—431no—
256C4⋊C4—431no—
257C4⋊C4—431no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4—861no—
262C4⋊C4C22×D4311yescharacteristic
263C4⋊C4C22×D4311yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—431no—
267C22⋊C4—431no—
268C22⋊C4—861no—
269C22⋊C4—861no—
270C22⋊C4—861no—
271C22⋊C4—861no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C42—861no—
276C42—861no—
277C42—861no—
278C42C22×D4311yescharacteristic
279C23—21no—
280C23—21no—
281C23—431no—
282C23—431no—
283Q8—3441no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—21no—
288D4—3441no—
289D4—3441no—
290D4—3441no—
291D4—1721no—
292D4—1722no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—81no—
297C2×C4—431no—
298C2×C4—431no—
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—3441no—
308C2×C4D4×D4311yescharacteristic
309C2×C4D4×D4311yescharacteristic
310C2×C4C23×D4311yescharacteristic
311C8—21no—
312C8—861no—
313C8—861no—
314C8#1062189812yes—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—861no—
322C22—861no—
323C22—861no—
324C22—861no—
325C22—861no—
326C22—861no—
327C22C2×D4×D4311yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—861no—
333C4—861no—
334C4—1721no—
335C4—1721no—
336C4—1721no—
337C4—1721no—
338C4C2×#1062189811yescharacteristic
339C4#1306337211yescharacteristic
340C2—81no—
341C2—81no—
342C2—1721no—
343C2—1721no—
344C2#1458355411yescharacteristic
345C2#1458369511yescharacteristic
346C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#442C2
socleC22×C43C22×D4
hypercenter#442D43
hypocenterC43#3347
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #14583614C2semidirect
2. #14583599C2semidirect
3. #14583308C2semidirect
4. #14583222C2semidirect
5. #14583222C2semidirect
6. #14583221C2semidirect
7. #14583211C2semidirect
8. #14583199C2semidirect
9. #14583179C2semidirect
10. #14583149C2semidirect
11. #14583132C2semidirect
12. #14582972C2semidirect
13. #14582938C2semidirect
14. #14582934C2semidirect
15. C43×#442C2semidirect
185. #442D43semidirect
189. C43#3347semidirect